EM2_GPK_M1_Teach_23A_988434_Updated 05.23

TEACH ▸ Module 1 ▸ Sorting and Counting

What does this painting have to do with math?

The American artist Jacob Lawrence is known for his portrayals of everyday African American life. His Migration Series is painted in a modernist style, contrasting vivid colors with shades of brown and black. Lawrence’s work shows the discrimination African Americans faced and the opportunities they found, such as the educational opportunities depicted in Panel 58. What are the students writing? Why are they writing numbers?

On the cover

Panel 58 from The Migration Series, 1940–1941

Jacob Lawrence, American, 1917–2000

Casein tempera on hardboard

The Museum of Modern Art, New York, NY, USA

Jacob Lawrence (1917–2000), In the North the Negro had better educational facilities, 1940–1941. Panel 58 from The Migration Series Casein tempera on hardboard, 12 x 18 in (30.5 x 45.7 cm). Gift of Mrs. David M. Levy. The Museum of Modern Art, New York, NY, USA. © 2020 The Jacob and Gwendolyn Knight Lawrence Foundation, Seattle/Artists Rights Society (ARS), New York. Digital image © The Museum of Modern Art/Licensed by SCALA/Art Resource, NY

Great Minds® is the creator of Eureka Math® , Wit & Wisdom® , Alexandria Plan™, and PhD Science®

Published by Great Minds PBC. greatminds.org

© 2023 Great Minds PBC. All rights reserved. No part of this work may be reproduced or used in any form or by any means—graphic, electronic, or mechanical, including photocopying or information storage and retrieval systems—without written permission from the copyright holder. Where expressly indicated, teachers may copy pages solely for use by students in their classrooms.

USA

ISBN 978-1-63898-843-4

Before This Module

Overview

Children are born with an intuitive ability to organize and classify objects in their environment. During play, toddlers often naturally put things together that are similar. For example, they may put all the toy cows in a barn and all the pigs in a pen. This primes them for simple sorting activities using specific attributes in prekindergarten.

From an early age, children can think deeply about number concepts. Toddlers often attach number words to small quantities. Young children who can say “I have 2 eyes” are already developing ideas about cardinality, knowing how many are in a set. Children will often notice, for example, that a set of 2 is more than a set of 1 or that they have more or less of something than a friend has.

By the time children are three years old, they may accurately name groups of 1, 2, or 3 objects. At the park, a child might exclaim, “Look! 3 birdies!” This is the beginning of subitizing, or saying how many without counting.

Sorting and Counting

Topic A

Use Attributes to Match and Sort

Students build on their natural ability to observe their environment as they notice and compare objects and describe how they are the same and different. Students sort objects into groups based on attributes such as color, size, shape, number, and type.

Topic B

Answer How Many Questions

Through playful activities, students are introduced to core ideas about counting, collectively referred to as the number core. (See the Why section of this overview for more information.) Students integrate these elements as they explore the strategies of touch and count and move and count to help them determine how many regardless of the arrangement.

Topic C

Match Written Numbers with Sets of Up to 5 Objects

Students notice numbers everywhere! They name the written numbers 0 through 5 and match each number to the quantity it represents. Students learn that a written number can tell how many are in a group of objects even if the group is hidden or the quantity cannot be counted.

Topic D

Count Out a Set of Up to 5 Objects

Students count out a given number of objects from a larger group. When they stop counting or adding objects once they reach the target number, they strengthen their understanding of cardinality, which is knowing that the last number they said tells how many are in the set.

Topic E Sort to Decompose

Sorting objects into groups provides students with a natural context for decomposing numbers. Students think about different ways to sort and break apart numbers by using pictures and put together stories. They use number sentences, such as 5 is 3 and 2, to describe their sort.

Topic F

Match Written Numbers with Sets of Up to 10 Objects

Students apply number core concepts to sets of up to 10 objects. As the size of the group gets larger, students lean on counting strategies to keep track of the count. The mark and count strategy helps them count objects in circular or scattered configurations.

Topic G Count Out a Set of Up to 10 Objects

Students count out groups of up to 10 objects. They model add to stories and record their thinking with drawings. Students see that drawings and written numbers help them remember important information.

After This Module

8

PK Module 6

Three projects are built into the prekindergarten year. Each project is a topic in module 6. The first project, Project A, may be taught immediately after module 1 so students can apply and extend the learning of this module. However, Project A is designed for flexible use throughout the prekindergarten year.

PK Module 2

Students apply their sorting and counting skills as they analyze and compare shapes. Students sort two-dimensional shapes based on the number of straight sides. They count sides and corners as they name, compare, model, and compose shapes.

PK Module 3

Students build on their understanding of numbers by composing shapes and numbers in different ways and by describing their parts. Students use the structure of 5 to compose the numbers 6 to 10. With the concrete and visual support of the rekenrek, students notice the 5 + n pattern. Students also build an awareness of the structure of our number system as they explore the pattern of 1 more in the counting sequence.

Answer how many questions about objects in varied configurations.

Lesson 30: Let’s Count and Record! . . . . . . . . . . . . . . . . . . . . .

Organize, count, and

Match written numbers 6, 7, 8, 9, and 10 to quantities.

Why Sorting and Counting

What is the number core and how is it tied to counting?

In this module, students are introduced to four core ideas for describing the number of objects in a group. These ideas are collectively referred to as the number core.

• The number word list—Students say numbers in the appropriate count sequence (1, 2, 3, …).

• One-to-one correspondence—When counting, students pair one object with one number word, being careful not to count any objects twice or skip any objects.

• Cardinality—Students say a number to tell how many are in a group. They may know how many by subitizing, counting, or matching to a group they’ve already counted. When counting, students recognize that the last number they say represents the number of objects in the group.

• Written numbers—Students read and write the symbols used to represent numbers. They also connect the written number with the number of objects in a set.

Playful and intentional activities support students in integrating all aspects of the number core. Because number core components are not learned in isolation, most prekindergarten lessons combine three or more elements of the number core.

The number core plays a foundational role in work with number relations, operations, and place value understanding, so it is critical to start the prekindergarten year with these concepts.

Why isn’t there a lesson for each number 1 to 10?

Module 1 focuses on strategies rather than on specific numbers. As students build a toolbox of counting strategies, they apply them to different quantities arranged in different configurations (linear, array, circular, scattered).

Students use one-to-one correspondence when they say one number word for each object they touch.

Students show how many objects are in a set (cardinality) by using written numbers.

For instance, when counting in a circular configuration, students may find it challenging to identify the starting and stopping points so every object is counted once and only once. If students have learned a strategy for marking the start, they can use that strategy with any number of objects in a circular configuration. The same strategy for marking the start can also be used to count the sides and corners of shapes in module 2.

As early as possible, we want students to approach problem solving with a strategy that allows them to be accurate and efficient. When a lesson focuses on a single number, students go into the counting task anticipating the total. Counting tasks in which students do not already know the total but genuinely want to know the total open them to the process of choosing a strategy to solve a problem (MP1, MP5). For example, through counting collections, students explore organizing, counting, and representing sets of objects. With good questioning, students can begin to evaluate whether their chosen counting strategy is effective.

A focus on strategies rather than on specific numbers means that the size of a collection can be varied to meet the needs of all students. This approach creates accessibility and engagement for prekindergarten students with a range of counting experiences.

Why do you have formal math experiences in prekindergarten?

Children begin to mathematize their world from a very early age, and they come to prekindergarten with a broad range of understandings about numbers, classification and comparison, spatial relationships, and patterns. When given high-quality math experiences in a language-rich environment, young students will move along a developmental progression of critical mathematical concepts. (See the Observational Assessment in the Module Resources.)

Joy-filled lessons and theme-based projects (found in module 6) engage students in age-appropriate activities. Each project and 20- to 25-minute lesson provides teachers with meaningful questions that support each student’s mathematical development.

Students apply counting strategies when they count collections of objects.

Does this mean that play is not valued in prekindergarten? Absolutely not. We believe that children should experience math during play and throughout their day. For this reason, each topic overview includes a segment titled Math Anytime, where you can find the following information:

• Specific suggestions for infusing math throughout the day, such as during sharing or snack time or on the playground.

On the playground, count how many (swings, trees, shovels, tricycles, etc.).

• Guidance for asking purposeful questions that support the big ideas or key questions of the topic.

During sharing time, point out anything that is shared with a written number on it. Discuss what that number might mean. “What number do you see on the crayon box Sara shared? What do you think that number means?”

Ultimately, the goal is for students to see that math is all around them and that it is an integral part of their lives.

Developmental Progressions: Overview

Sorting and Counting

Developmental Progressions (DPs) are standards-aligned descriptions that detail what students should know and be able to do by the end of the year. There are 20 DPs for prekindergarten. Opportunities for students to develop the knowledge and skills associated with each DP extend across modules. For instance, PK.CC.DP1 crosses three modules. Students begin counting forward to 10 in module 1, extend their count to 20 in module 3, and count backward from 5 in module 5.

Developmental Progressions support teachers with interpreting student work on

• informal classroom observations (recording sheet provided in the Module Resources),

• data from other lesson-embedded formative assessments, and

• Module Assessments.

This module contains the eight DPs listed.

PK.CC.DP1

Count forward to 20 and backward from 5.

PK.CC.DP2

Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP4

Say one number name with each object when counting up to 10 objects.

PK.CC.DP5

Use the last number of a count to tell how many regardless, of arrangement or order counted.

PK.CC.DP3

Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP6

Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7

Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1

Sort objects into categories.

The Topic Overview identifies the DPs aligned with that topic. A chart showing the alignment of DPs by lesson is available in the Module Resources. An example of one of these DPs, along with its progression, is shown here for reference. The complete set of this module’s DPs can be found in the Developmental Progressions resource.

DPs have the following parts:

• DP Code: The code indicates the grade level and the standard domain and then lists the DPs in no particular order. For example, the first DP for prekindergarten in the Counting and Cardinality domain is coded as PK.CC.DP1.

• DP Language: The language is crafted from standards and concisely describes what will be assessed.

• Achievement Descriptor: The descriptor identifies what students know and are able to do at a particular stage of development within a developmental progression.

• Developmental Indicators: The indicators describe the precise student expectations for a particular stage of development within a developmental progression.

Developmental Progressions

Identifying a student’s current stage of development supports teachers and families in building on what students know. Each stage is aligned to research on young children’s development and provides a path to the kindergarten standards. The highlighted stage indicates the expectation for most students after they complete the prekindergarten curriculum.

PK.CC.DP1 Count forward to 20 and backward from 5.

PK Modules 1 and 3

PK Modules 3–5

K Modules 5 and 6

Count forward to 5.

• Consistently say numbers in correct sequence without skipping or repeating numbers.

• If verbal counting is not possible, use other methods, such as touching a number card, to demonstrate knowledge of number sequence.

Count forward to 10.

• Demonstrate previous indicator and extend forward count to 10.

Count forward to 20.

• Demonstrate previous indicators and extend forward count to 20.

Count backward from 5.

• Consistently say numbers in reverse sequence without skipping or repeating numbers.

Count to 100 by ones and tens.

• Demonstrate previous indicators and extend forward count to 100.

• Count by tens to 100 without skipping or repeating numbers.

Count forward from a number other than 1.

• Count forward by ones from any number 2 to 100.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

3 Years 3 to 4 Years

PK Module 1

Identify, without counting, the number of objects in a group of up to 3 objects (perceptual subitizing to 3).

• Name groups of 1, 2, and 3 objects with increasing accuracy.

For example, a student looks briefly at a picture with 3 dogs and says “three” or shows 3 fingers.

Identify, without counting, the number of objects in a group of up to 5 objects (perceptual subitizing to 5).

• Demonstrate previous indicator and extend to groups of 4 or 5 objects.

For example, a student looks briefly at a picture with 4 dogs and says

4 Years

PK Module 3

Identify, without counting, the number of objects in a group of up to 5 objects by recognizing parts (conceptual subitizing to 5).

• Identify total by composing smaller quantities.

For example, a student looks briefly at a picture with 5 dogs and says,

5 to 6 Years

K Module 1

Identify, without counting, the number of objects in a group of up to 10 objects by recognizing parts (conceptual subitizing to 10).*

• Identify total by composing smaller quantities.

For example, a student looks briefly at a picture with 8 dogs and says,

Developmental Indicators

LAUNCH

25

Use Attributes to Match and Sort

Progression of Lessons

Key Questions: What are some ways things can be the same? What are some ways they can be different? What are some ways we can sort?

Lesson 1: Make a Match

Use attributes to match objects that are exactly the same.

Lesson 2: Same and Different

Use attributes to compare objects.

20

Lesson 3: Crayon Group

Make a group that has a given attribute.

Objects can be the same size or color.

PK.MD.DP1

Things can be the same but also different. Each hand is holding up the same number of fingers, but they are different fingers.

PK.MD.DP1

All the things in this group are crayons. They are the same type of thing.

PK.CC.DP1, PK.MD.DP1

Lesson 4: Crayon and Marker Sort

Use given attributes to sort objects into two groups.

Lesson 5: Sorting Bags

Sort objects into two or more groups and explain the attributes used to sort.

We can make a marker group and a crayon group. We can sort different types of things into groups.

PK.MD.DP1

We can sort by color. We can make a yellow group, a green group, and a blue group.

PK.CC.DP1, PK.MD.DP1

Use Attributes to Match and Sort

Prekindergarten begins with students building on their natural ability to collect and organize information or data about the world. Young students must be able to organize and sort this information before they can use it to ask and answer meaningful questions such as, How do we go to school—by bus, by car, or on foot?

In topic A, students use common attributes to match two objects that are exactly the same—they have all attributes in common (e.g., the objects are the same color, size, shape, number, and type). After exploring similarities, students identify differences. For example, students may match two bears that are the same color and shape but are different sizes.

Once students can observe and compare attributes among objects, they are ready to sort. As prekindergarten students progress across a learning trajectory, they often develop in the following ways:

• Students initially sort objects into groups by using attributes given by an adult and then gradually choose a way to sort on their own.

• Students initially shift attributes during the sort. For example, they sort animals by color and then by type before gradually focusing their sort on a single attribute.

• Students initially name the group by using group characteristics (e.g., big group, little group) and then gradually name the group by using the sorting attribute (e.g., size). This provides an opportunity to revoice students’ observations while highlighting the specific attribute—for example, “Ah, you noticed that the paper clips are different sizes. We can sort by size.”

Sorting and classifying provide a natural context for counting. As the topic progresses, students participate in chorally counting the number of objects in different groups. This gentle introduction to counting prepares students for telling how many in topic B.

Terminology

This topic introduces the terms match, notice, sort, and wonder.

Fluency Anytime

Fluency activities are intended to be completed any time of the day. They are simple and require few materials. Refer to the Module Resources to choose from a more extensive list of fluency activities to support your class’s math goals.

• Counting on the Number Glove: Show fingers the math way while wearing the number glove as students watch and count out loud. Watch my number glove and count out loud. Ready?

• Counting with Movement: Say or show a number and have students move in a specific way to match the number. Look at my number. Jump this many times and count your jumps.

Math Anytime

At a block area, have students find blocks that either match exactly or are the same but a little different.

During snack time, have students sort their dry cereal and tell how they sorted.

a kitchen play area, have students sort items into groups as they put them away.

At a table of supplies (e.g., beads, erasers, buttons), have students sort the items into groups.

1 2 3 4 5

Counting on the Number Glove 3 4 5

Counting with Movement

Observational Assessment

The highlighted Developmental Progressions are addressed in this topic. Focus observations on students’ sorting and counting behaviors. Refer to the Developmental Progressions resource for specific stages of development.

Observational Assessment Recording Sheet

PK Module 1

Sorting and Counting

Developmental

PK.CC.DP1 Count forward to 20 and backward from 5.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP3 Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1 Sort objects into categories.

Student Name

Agenda

Materials

Preparation

Lesson 1 25 min

Make a Match Teacher

• A Pair of Socks by Stuart

J. Murphy

• Matching pair of socks

Students

• Sets of 2 matching objects (1 set per student pair)

• Prepare 1 set of 2 matching objects to give to each student pair during the lesson (e.g., 2 new crayons, cubes, teddy bear counters).

Lesson 2 20 min

Same and Different Teacher

• None

Students

• None

• None

Lesson 3 20 min

Crayon Group Teacher

• Empty crayon box

• Basket containing crayons (1 crayon per student) and other items (e.g., counters, craft sticks, rubber bands)

Students

• None

• Prepare a basket containing enough crayons so every student gets 1. Add other miscellaneous items (e.g., counters, craft sticks, rubber bands).

Lesson 4 20 min

Crayon and Marker Sort Teacher

• Basket containing crayons and markers

• Teddy bear counters (1 large orange bear, 1 small orange bear, 1 small green bear)

Students

• Crayon or marker

• Prepare a basket containing enough crayons and markers so every student gets 1 crayon or marker.

Lesson 5 25 min

Sorting Bags Teacher

• Sorting bag

Students

• Sorting bag (1 per student pair)

• Assemble 1 sorting bag containing 4 or 5 objects for each student. Sorting bags should contain objects that can be sorted based on 1 attribute (e.g., shape, number, size, color). See the module’s Materials resource for more information about how to prepare a differentiated set of sorting bags.

1 Make a Match

Use attributes to match objects that are exactly the same.

LAUNCH 25

Read

Hold up the book A Pair of Socks by Stuart J. Murphy. Share the title with students. Hold up a matching pair of socks.

This is a pair of socks. What do you notice?

What do you see?

They’re the same.

I have socks like that.

The socks match. They go together.

Read A Pair of Socks. Stop on page 8.

Look at the socks. I notice the socks don’t match. They are different.

What do you notice? What do you see?

One sock is dirty.

They’re both red and blue.

One sock has lots of stripes.

Continue reading. Pause on page 17.

Look at the socks. What do you notice?

The socks are different.

One sock has a dinosaur. I like dinosaurs.

They’re the same on top: red stripe, blue stripe. (Points to stripes.)

Materials

Teacher

• A Pair of Socks by Stuart J. Murphy

• Matching pair of socks

Students

• Set of 2 matching objects (1 set per student pair)

Language Support

To give students support with the word notice, consider emphasizing the word when speaking it while gesturing to your eye. Continue this support throughout the topic as needed.

Do they match? How do you know?

No. They’re different.

No. Some things are the same, but some things are different.

Continue reading. Stop when the puppy finds the matching sock and invite students to share what is the same about both socks.

Match 2 Objects That Are Exactly the Same

Distribute one object to each student. Draw students’ attention to their object’s size, color, shape, and use.

Now it’s your turn to find a match! Find a person who has something that is exactly the same as what you have.

Give students time to find a match. Circulate and ask students, “What makes your things match?” Then have students gather together again and have them sit next to the student with the matching item.

Select a pair to share their match.

Nala and Gino, what is the same about your objects?

What do you notice? What do you see?

We have blocks. They’re small.

They’re both blue.

Gino and Nala matched the 2 blocks. They are the same color and the same size. They are exactly the same. They match!

As time allows, invite other pairs to share what they notice about their matching objects. Conclude the lesson by asking students to name the different ways (e.g., patterns, size, color) their objects are the same.

What are some ways things can be the same?

Socks can have the same stripes.

Our blocks were both blue.

Things can be the same size.

UDL: Engagement

Promote engagement through movement. Invite students to move (stomp, stand, clap, or hop) if their objects are the same in one of the following ways: size, shape, or color. For example, “Clap if your object is the same size as Gino and Nala’s blocks.”

2 Same and Different

Use attributes to compare objects.

LEARN 20

Same and Different

Display the picture of the two socks that do not match.

How are these socks the same?

They both have blue.

They’re both socks.

How are the socks different?

One sock is smaller.

They look different.

One sock has stripes.

Display the image of two hands.

Repeat the routine. Invite the class to identify similarities and differences.

Display the Two Triangles interactive.

Invite students to tell what is the same about the triangles and what is different. Then prompt student thinking with the following question.

How could we make it easier to see if these triangles are exactly the same?

We could turn one of the triangles. We could turn them the same way.

Materials

Teacher

• None Students

• None

Teacher Note

Anticipate that students may not recognize that the triangles are exactly the same. Orientation is an attribute that will be further explored in module 2. Advance student thinking by asking the following questions:

• Are the triangles the same shape?

• Are they the same color?

• Are they the same size?

• What’s different? Can we move one of the triangles so they are exactly the same?

Confirm student thinking by rotating a triangle so that both are in the same position. These triangles are the same size, shape, and color. To make it easier to see that they are exactly the same, we can turn one of the triangles so they are both in the same position.

Compare Shoes

Partner students. Have partners compare what is the same and different about their shoes. Circulate and support partner discussions with questions such as the following:

• Are your shoes the same color? Do they have the same pattern? Are your shoes different colors?

• Do both of your shoes have laces?

• Which shoes would you wear for running?

After students have had sufficient time to discuss how their shoes are the same and different, gather the class in a central location. Intentionally select two students whose shoes do not match. Identify similarities and differences in the shoes.

Prompt students to think about the book A Pair of Socks by Stuart J. Murphy and their shoe comparisons.

What are some ways objects, or things, can be the same?

Things can be the same color.

They can be the same size.

They can be the same kind of shoe. They can both be boots. They can both be sandals.

What are some ways objects can be different?

They can have different things on them.

They can be different sizes.

3 Crayon Group

Make a group that has a given attribute.

LEARN 20

Make a Group

Gather students in a circle and place the empty crayon box in the middle. Show students the collection of objects in the basket.

Look at all these things! Which things go in this box?

The crayons!

Pass the basket around the circle so students can take out a crayon and add it to the empty crayon box, one crayon at a time.

We made a group. What is the same about all the things in this group?

They’re all crayons.

I wonder, or want to know, how many crayons are in the box. Let’s count and find out.

Lead the counting, making sure to touch each crayon as you say the number.

I touched each crayon to make sure I only counted it once. We said one number for each crayon.

Invite students to make a group of their own by doing the following activity.

Materials

Teacher

• Empty crayon box

• Basket containing crayons (1 crayon per student) and other items (e.g., counters, craft sticks, rubber bands)

Students

• None

Language Support

To give students support with the word wonder, consider emphasizing the word when speaking it while gesturing to your chin and modeling a questioning expression. Continue this support throughout the topic as needed.

Classroom Hunt

Now it’s your turn to make a group. Select a pair of students. Build excitement by whispering to them the kind of group they are going to make (e.g., red things, things we eat, toys they like). Instruct the pair of students to find objects in the room to make their group. Repeat with other pairs of students.

As they collect their objects, ask students to count the things in their group. Listen for students who accurately count so they can share their counting with the class.

Once all pairs have at least 2 objects, gather the class back together and invite the selected students to count their items. Then ask the student pairs what is the same about the objects in their group.

Dakota and Frankie, what is the same about all the objects, or things, in your group?

They are all toys we like.

Dakota and Frankie made a group of toys they like.

Are the objects in their group exactly the same?

No. They’re different things—stuffed animals and cars. No. They’re different colors and sizes.

The objects in Dakota and Frankie’s group are the same in one way: They are all toys. But the objects in a group don’t have to be exactly the same.

Language Support

Support language production by providing a sentence starter such as the following:

• Our objects are the same because ...

Observational Assessment

; Are students able to sort objects into given categories? (PK.MD.DP1)

; Are students saying the correct number sequence? (PK.CC.DP1)

Crayon and Marker Sort

Use given attributes to sort objects into two groups.

Which One Doesn’t Belong?

Engage students in the Which One Doesn’t Belong? routine by using the following process.

Think about which one doesn’t go with the others. Don’t say it out loud. Keep it in your head.

Give students time to formulate their own ideas, and then point to the green bear.

If you think the green bear doesn’t belong with the rest of the bears, stand up.

Gather the standing students around you and whisper to them, asking why they think the green bear does not belong. Ask everyone in the group to whisper their responses. Summarize the small group’s reasoning to the whole group.

Our friends said the green bear doesn’t belong with the other bears because it isn’t orange.

Separate the bears into two groups by color: green bears and orange bears. Repeat these steps with the large orange bear to discuss grouping by size. Separate the bears into two groups by size: big bears and little bears.

There are many different ways to make groups. We just made groups  based on size—big and little. We also made groups based on color—orange and green.

Materials

Teacher

• Basket containing crayons and markers

• Teddy bear counters (1 large orange bear, 1 small orange bear, 1 small green bear)

Students

• Crayon or marker

Teacher Note

If students need additional support identifying which object does not belong, consider pointing to the two orange bears or the two small bears and asking the following questions:

• What is the same about these two bears?

• What is different?

Consider moving objects into groups as students respond. For example, if students identify that the two bears are orange, move them to one side. This action helps students see that the remaining object, the green bear, is different and does not belong.

Crayon and Marker Sort

Show a basket with markers and crayons in it. We can call this a group of art supplies. Now it is time to clean them up.

I wonder whether I can sort the supplies to make cleanup easier. When we sort, we put things into groups. How can I sort the supplies?

Put the crayons here. (Gestures to one location.) And put the markers over there. (Gestures to a different location.)

Take out the crayons.

Let’s make two groups.

Point to a place in the room for each group to go, such as separate areas on the carpet. Give a marker or crayon to each student. Invite students to place their object in the appropriate group.

Point to the markers.

What is the same about everything in this group?

They are all markers.

We can color with them.

They all have lids.

Repeat the question for the crayon group and then ask the following question:

How did we sort to make groups?

By crayons or markers

Markers go here. (Gestures.) And crayons go there. (Gestures.)

Today, we sorted art supplies. We sorted the art supplies into two groups: crayons and markers.

Count each group. Demonstrate one-to-one correspondence while counting, making sure each object is paired with only one number word. Invite students to clap as you count and move each object into a line.

We said one number word for each marker. I moved each marker to make sure I counted it only once.

Promoting the Standards for Mathematical Practice

When students sort to make groups, they look for and make use of structure (MP7).

The structure students are recognizing is that all the objects in a group have something in common even if they are not exactly the same. This skill is essential for doing mathematics and data science at higher levels.

Differentiation: Challenge

Consider asking students to think of other ways the objects can be sorted, such as by color. Ask the following questions:

• Is there another way to sort?

• Did we have more groups when we sorted by color or when we sorted by kind of art supply?

Sorting Bags

Sort objects into two or more groups and explain the attributes used to sort. LAND

Materials

Teacher

• Sorting bag

Show a sorting bag to students and invite them to notice and wonder about its contents.

What do you notice, or see?

The shapes are different colors. I like purple.

There are big things and little things. I see shapes.

What do you wonder?

Are all the things the same shape?

How many shapes are blue?

Can I make a picture with the shapes?

How can I sort the shapes into groups?

Put the same colors together.

Put the big things here. (Points.) And put the little things there. (Points.)

As students describe ways to sort the shapes, move the shapes into groups.

We can sort objects into groups by color or by size. We can also sort in other ways. Show some of the sorting bags.

What are some other ways we can sort?

We can sort by how many, like how many legs or wheels.

We can sort by how it feels, like hard or soft.

We can sort by where you find it, like on land or in the air.

Students

• Sorting bag (1 per student pair)

Today, you will sort objects. Let’s see how many ways you can sort your objects.

Sorting Bags

Have students work in pairs and give each pair a sorting bag. Invite student pairs to sort the objects—such as those shown in the pictures—in their bags. When circulating, ask partners to name the attribute they used for the sort (e.g., color, size, shape).

Observational Assessment

; Are students able to sort objects into groups? (PK.MD.DP1)

; If students count, are they

y using a strategy to keep track of each object counted? (PK.CC.DP4)

y saying the correct number sequence? (PK.CC.DP1)

Select a student pair to share how they sorted into groups. To model one-to-one correspondence, move and count the objects in each group with the class. Continue to have student pairs share their sorts as time allows, intentionally choosing pairs that sorted by different attributes. Clearly state the attribute used in each sort.

How did we sort our objects into groups?

We put bugs together by color.

We put the dice together by the number we saw on top—fours, threes, twos, and ones.

We sorted the silverware by name—forks, spoons, and knives.

We sorted the vehicles by what kind they are.

Answer How Many Questions

Progression of Lessons

Key Questions: What do we find when we count? What are some things we can do to help us count?

Lesson 6: Matching Markers

Match to see whether there are enough.

Lesson 7: Animal Count

Move objects to track the count.

Lesson 8: Let’s Count!

Organize and count a collection of objects.

We can match or count to see whether there are enough.

PK.CC.DP1

When we move and count, we can find how many we have.

PK.CC.DP2, PK.CC.DP4, PK.CC.DP6

We can line up objects to touch and count them.

PK.CC.DP1, PK.CC.DP4, PK.CC.DP5, PK.CC.DP6

LEARN

LEARN

Lesson 9: How Many?

Answer how many questions about objects in varied configurations.

We can point to each object or move each object to help us count.

PK.CC.DP6

Answer How Many Questions

In topic A, students used attributes to sort objects into groups. The natural next step is for students to answer how many questions by counting those groups and other sets of objects.

Preschool students naturally love to count, and many enter preschool already singing or reciting the number words in order. Verbal counting is only one aspect of a preschool student’s counting development. In this topic, students are introduced to three core elements of counting—the number word list, one-to-one correspondence, and cardinality— and they practice integrating those elements in a variety of contexts.

Playful and intentional counting activities motivate students to count. For example, students can match markers with their caps to determine whether there are enough caps for all the markers, or students may count the number of caps and the number of markers to find out. Also, by counting collections of objects, students see that much of the world around them is countable. Don’t be surprised if a student is eager to tell how many rocks the student has in their pocket!

Students begin to learn strategies for counting. They may say one number word as they touch or move each object to keep track of their count. Students work toward an important milestone—understanding cardinality, or knowing that the last number they say when counting tells how many are in a set. Students begin to demonstrate an understanding of cardinality when they can count a group of objects and answer how many without recounting the set.

Finally, students explore conservation of numbers by counting the objects in a group, moving the objects, and retelling how many. For instance, as students count and arrange 5 stickers into a group, they notice and begin to trust that the number of stickers is the same regardless of their arrangement or the order in which they are counted.

Touch and Count

Conservation of Number

Terminology

This topic introduces the terms count, enough, and line.

Fluency Anytime

Fluency activities are intended to be completed any time of the day. They are simple and require few materials. Refer to the Module Resources to choose from a more extensive list of fluency activities to support your class’s math goals.

• Counting on the Number Glove: Show fingers the math way while wearing the number glove as students watch and count out loud. Watch my number glove and count out loud. Ready?

• Finger Flash: Briefly show a number the math way. Have students say the number and then show the number with their fingers in any way. Watch closely. How many fingers? Now show me the same number on your fingers.

Math Anytime

On the playground, have students count the number of objects in a group (swings, trees, shovels, tricycles, etc.). Have students touch or move the objects as they count them.

At a table of supplies (crayons, erasers, paintbrushes, etc.), have students count to see whether there are enough supplies for their group or for the class.

During snack time, have students count how many people are at each table.

During circle time, have students count the total number of students together as a class.

Observational Assessment

The highlighted Developmental Progressions are addressed in this topic. Focus observations on students’ ability to count and to answer how many questions. Refer to the Developmental Progressions resource for specific stages of development.

Observational Assessment Recording Sheet

PK Module 1

Sorting and Counting

Developmental Progressions Developmental Progressions

PK.CC.DP1 Count forward to 20 and backward from 5.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP3 Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1 Sort objects into categories.

Student Name

Agenda

Materials

Preparation

Lesson 6 20 min

Matching Markers Teacher

• None Students

• Container of 4–6 markers and caps with each set having more markers or more caps (1 set per student group)

• Prepare 1 container with 4–6 markers and caps for each student group with each set having more markers or more caps. Each group should have a slightly different number of markers and caps. The caps should be removed from the markers.

Lesson 7 20 min

Animal Count Teacher

• 6 farm animal counters in quantities of 1, 2, and 3 (e.g., 1 horse, 2 pigs, 3 sheep)

Students

• Farm Scene (in the student book)

• 6 farm animal counters in quantities of 1, 2, and 3 (e.g., 1 horse, 2 pigs, 3 sheep)

• Student book

• Tear out the Farm Scene in advance of the lesson.

• Print the Farm Scene to use for demonstration.

• Prepare 1 set of 6 farm animal counters in quantities of 1, 2, and 3 (e.g., 1 horse, 2 pigs, 3 sheep) for each student.

Lesson 8 25 min

Let’s Count! Teacher

• None Students

• Counting collection

• Work mat

• Assemble 1 counting collection bag for each student. See the module’s Materials resource for more information about how to create counting collection bags.

Lesson 9 25 min

How Many? Teacher

• Red crayons (5)

• Puppet or stuffed animal

• Index cards or small pieces of paper (3)

Students

• Index card or small piece of paper

• Small stickers (3, 4, or 5)

• Prepare 3 index cards by labeling them with the numbers 3, 4, and 5. One number should be on each card.

Matching Markers

Match to see whether there are enough. LAUNCH 20

Do We Have Enough?

Distribute a container of markers and caps to table groups. Look at your container of markers and caps. Using only your eyes, what do you notice?

The caps are not on the markers.

It is messy.

There are pink, green, and blue markers.

Model wonder statements that are mathematically relevant.

When I look in the containers, I wonder whether we have enough caps for the markers. We have enough if there is 1 cap for each marker. What do you wonder?

Expect simple statements and questions.

I wonder how many caps there are.

Why are the caps off?

With your group, find whether there are enough caps for the markers.

As table groups are having discussions, circulate and ask the following questions to assess and advance student thinking:

• How many markers are there? How many caps?

• Are there enough caps for the markers? How do you know?

Materials

Teacher

• None

Students

• Container of 4–6 markers and caps with each set having more markers or more caps (1 set per student group)

Once they are finished, gather students to a central location. Show one group’s container of markers and caps.

Do we have enough caps?

Yes. We have 1 cap left.

We don’t have enough markers.

Now let’s count the markers. As we count, let’s hold up 1 finger for each number.

1, 2, 3, 4, 5

5 markers

Let’s count the caps. As we count, let’s hold up 1 finger for each number.

1, 2, 3, 4, 5, 6

6 caps

How can knowing how many are in each group help us know whether we have enough?

If the numbers match, there are enough.

5 and 6 aren’t the same number. There are more caps.

Yes, 5 and 6 are not the same. There are enough caps for the 5 markers, and there is 1 extra cap.

To support cleaning up, invite students to work together to find their missing cap or marker. There is 1 extra cap in this container. Does anyone have an extra marker and not enough caps?

Animal Count

Move objects to track the count.

LEARN 20

Move and Count

Select 6 students to act as sheep. Invite them to move around the room. Prompt the class with the following story.

We need to get all the sheep to their home for lunch. Let’s count how many sheep we need to feed. We count to find how many there are.

Invite the class to count the sheep as they move around the room. Ask students to share their totals. Anticipate this being a challenging task.

It’s hard to count the sheep when they are moving around. What can we do to make counting easier?

We can tell them to stop moving.

We can move them home 1 at a time.

Let’s move and count each of the sheep 1 at a time. We can put them in a line, like they’re walking down the hall, to help us count.

Move each student who is acting as a sheep into a line as you count them.

How many sheep do we need to feed? 6 sheep

Show the collection of farm animal counters and the Farm Scene. Give students a chance to share what they notice about the animals.

I wonder how many sheep there are. What can we do to make counting the sheep easier?

Move the sheep

Put them in a line

Materials

Teacher

• 6 farm animal counters in quantities of 1, 2, and 3 (e.g., 1 horse, 2 pigs, 3 sheep)

Students

• Farm Scene (in the student book)

• 6 farm animal counters in quantities of 1, 2, and 3 (e.g., 1 horse, 2 pigs, 3 sheep)

• Student book

Teacher Note

The interactive, Math Stories Farm Scene, can be used to give students practice with the counting strategy move and count.

Consider allowing students to explore with the tool in small groups, or demonstrate the activity for the whole class.

Move the sheep into the field without placing them in a line as students count.

How many sheep? 3

Confirm student thinking by placing the sheep in a line and counting as you go.

The number of sheep stays the same whether we count them in a line or when they are not in a line. Repeat moving and counting the remaining animals by placing the horse in the barn and the pigs in the pen.

Practice and Play

Provide each student with a mixed set of farm animal counters and a Farm Scene. Invite students to line up the animals in their homes on the Farm Scene and then count them.

Circulate and use the following questions to assess and advance student thinking:

• How did you make groups? How many are in this group?

• What if you put all your animals together? How many would there be?

• If 1 cow goes to the barn, how many animals are left?

Once students have had sufficient time to explore, gather them and invite them to summarize their learning.

What do we find out when we count?

How many

The number of animals

How does moving things help us count?

When I move them, I know I counted them. Lining them up helps. I know which things I counted.

Differentiation: Challenge

To give students a challenge, ask comparison questions such as the following:

• Are there more horses or more pigs?

• What animal is there the most of?

Differentiation: Support

Expect students to have a wide range of counting experience. Consider providing a template to give students support in organizing their count in a line and in answering how many questions about their animals.

Observational Assessment

; Can students identify, without counting, the number of animals in a group? (PK.CC.DP2)

; Are students using a counting strategy to keep track of each object they counted? (PK.CC.DP4)

Let’s Count!

Organize and count a collection of objects.

Materials

Teacher

• None

This lesson is an opportunity to establish procedures to count collections. Counting collections provide formative assessment data on students’ understanding of number core concepts and counting strategies. Place the Observational Assessment Recording Sheet on a clipboard and circulate to observe how students count and organize.

Choose a Collection

Establish an efficient procedure for distributing the collections and mats. Teach and practice the procedure. Anticipate problems before they occur. Stop to correct and troubleshoot immediately.

Today, you are going to count the objects in a collection.

Your job is to figure out how many objects you have.

Once the procedure is established, invite students to choose a collection and to find a workspace. Give students 2 minutes to freely explore and talk about their collection with a neighbor.

Count a Collection

Invite students to begin counting.

Now it’s time to count your collection.

Students

• Counting collection

• Work mat

Teacher Note

In a counting collection lesson, students organize, count, and record all the items in a set. Each set is called a counting collection.

Each class needs a variety of counting collections made of everyday materials. For this lesson, each counting collection should have 5 to 25 objects.

Students will learn how to record their count in an upcoming lesson.

As you circulate, take note of students’ organizing strategies such as touch and count or move and count. Use the following questions to assess student thinking:

• How many do you have?

• Will you count them again so I can listen to you count?

• Will you show me how you counted?

When they finish counting their collections, encourage students to try another way to count or to switch collections with a neighbor and confirm the totals.

Look for a student who can demonstrate their counting strategy and invite them to bring their collection to a central area to share during Share, Compare, and Connect. Have the other students clean up.

Clean Up

Establish an efficient procedure for returning the collections and mats. Teach and practice the procedure.

Share, Compare, and Connect

Not every class will have enough time to complete this section of the lesson. If time allows, invite a student to demonstrate how they counted their collection.

Move and Count (Ruby’s Way)

How many beads were in Ruby’s collection? How do you know?

10. She said 10 last.

What did Ruby do to help her count?

She moved the beads.

She lined them up.

There are lots of ways we can make counting easier. Ruby used move and count and lined up her beads. She moved each bead as she counted.

Differentiation: Support

Because of the recent focus on sorting, some students may sort their collections before counting them. Consider asking the following assessing and advancing questions:

• How did you sort to make groups?

• How many are in this group? (Point to a group. Repeat for other groups.)

• Do you have more green clips or yellow clips?

• Which group has the most? How do you know?

Observational Assessment

; Are students saying the correct number sequence? (PK.CC.DP1)

; Are students saying one number name with each object they count? (PK.CC.DP4)

; Are students saying the last number in their count to tell the total? (PK.CC.DP5)

How Many?

Answer how many questions about objects in varied configurations.

Fix Puppet’s Mistake

Show students 5 real red crayons in a circular configuration and display the image of the 5 crayons in a linear configuration.

Invite students to share what they notice.

They both have red crayons.

Those are a line and those are a star.

Both have 5.

Confirm the correct number of crayons by having Puppet touch and count the crayons displayed on the slide. If no one mentions the number of crayons, have Puppet count them to find out how many.

What helped Puppet count 5 crayons?

Puppet touched each one.

Engage students in the Fix Puppet’s Mistake routine by using the following process.

Have Puppet count the real crayons in the circular configuration. As Puppet touches and counts each crayon, continue counting around the circle until students signal that Puppet’s counting is incorrect.

What mistake did Puppet make?

Puppet didn’t stop.

Puppet kept going.

Materials

Teacher

• Red crayons (5)

• Puppet or stuffed animal

• Index cards or small pieces of paper (3)

Students

• Index card or small piece of paper

• Small stickers (3, 4, or 5)

Promoting the Standards for Mathematical Practice

As students explain how they counted to their partner, they construct viable arguments and critique the reasoning of others (MP3).

Prompt students to engage with MP3 by asking questions such as the following:

• How would you count your partner’s stickers?

• Are some cards easier to count than others?

• Did you both count the same way or different ways? How do you know?

How can we help fix Puppet’s mistake?

Put the crayons in a line

Move them and count (Points to the crayons.)

Select a counting strategy to use and have Puppet count the crayons by using that strategy. Then ask students how many crayons are in the group. Emphasize that both groups have 5 crayons.

Sticker Count

Pass out a strip of 3, 4, or 5 stickers and an index card or a small piece of paper to each student. Invite students to count their stickers and then stick them onto the index card in any configuration.

Have students trade their index card with a partner. Invite each partner to count the stickers and to explain how they counted. Once students have shared their counting strategy, have them trade cards with a different partner and count those stickers.

Let’s sort our cards by number.

Place three index cards labeled 3, 4, and 5 where students can put their cards according to the number of stickers they have. Invite a student to hold up their card, count the stickers on it, tell how many, and then place the card in the correct group. End the discussion by asking the following question:

What did we do to keep track of our count?

We pointed to each sticker as we counted.

We moved the stickers when we counted them.

Observational Assessment

; Are students using a counting strategy to keep track of each sticker they count? (PK.CC.DP4)

; Are students saying the last number in their count to tell the total? (PK.CC.DP5)

; Are some configurations harder for students to count? (PK.CC.DP6)

Teacher Note

Collect the sticker cards at the end of the lesson and laminate them for future use. Place them in a central location so students can practice counting in different configurations and sorting the cards by number.

Match Written Numbers with Sets of Up to 5 Objects

Progression of Lessons

Key Questions: Where do we see numbers? What do numbers tell us about a group of things?

Lesson 10: Written Numbers

Match written numbers 1, 2, 3, 4, and 5 to quantities.

Match written numbers 0, 1, 2, 3, 4, and 5 to quantities. Understand the meaning of 0.

Numbers are everywhere in our world. Sometimes numbers tell us how many things there are.

PK.CC.DP1, PK.CC.DP3

The number 2 tells us how many rabbits.

PK.CC.DP2, PK.CC.DP3

number 3 tells us how many fingers to show.

The

Lesson 11: Match Game

LEARN

20

Lesson 13: Rosetta Stone

Explore written numbers and symbols.

LEARN

25

Lesson 14: Rice Scoops

Use numbers to tell how many.

LAND

Lesson 15: Let’s Count!

Organize and count a collection of objects.

People have used numbers for a long time. We can see the different ways numbers look. We can learn how people used numbers a long time ago.

PK.CC.DP3

When we can’t count, the numbers tell us how many scoops are in each cup.

PK.CC.DP3, PK.CC.DP5

We can put our objects in a line to count them. The last number we say tells how many in our collection.

PK.CC.DP1, PK.CC.DP4, PK.CC.DP5, PK.CC.DP6

Match Written Numbers with Sets of Up to 5 Objects

In topic B, students combined three aspects of the number core to count groups of objects: the number word list, one-to-one correspondence, and cardinality. A fourth aspect of the number core, written numbers1, is the focus of topic C. Written numbers can be found many places in a prekindergarten student’s world—on buses, sports jerseys, clocks—and many young children come to school able to name some numbers. This topic begins by inviting all students to name written numbers 0 through 5.

Naming is only the first step in working with written numbers. Students also need to match each number to the quantity it represents. This means that students know, for example, that the written number 4 tells how many are in a group of 4 objects. With experience, they see that 4 can be used to show the number of objects in a group regardless of the unit or what the object is, as in 4 seahorses, 4 fingers, or 4 cats.

As students match numbers with the quantity they represent, they begin to trust that the number 4 represents 4 of something even when the quantity is hidden or cannot be counted. For example, students know that a cup of rice that is labeled with a 4 represents 4 scoops of rice even though students cannot see each scoop.

This topic focuses on written numbers 0–5. Students will work with written numbers 6–10 in topic F.

1 The technical term for a symbol that stands for a number is numeral. However, since students use the word number to refer to a written symbol, we will say written number. This provides consistency and ease of language.

Terminology

This topic introduces the term number.

Fluency Anytime

Fluency activities are intended to be completed any time of the day. They are simple and require few materials. Refer to the Module Resources to choose from a more extensive list of fluency activities to support your class’s math goals.

• Counting with Movement: Show a number card from 1 to 5 and have students move in a specific way to match the number. Look at my number. Clap this many times and count your claps.

• Number Flash: Show a number card between 1 and 5. Students say the number, and then show the number with their fingers. Look at my number. Show me this number on your fingers.

Math Anytime

At a table, set out 5 containers with 1 to 5 objects and number cards 1–5. Have students match each container with the number card that shows how many objects are in the container.

During sharing time, point out something that has a number on it. Discuss what that number might mean. For example, ask, “What number do you see on the crayon box? What do you think that number means?”

On the playground, provide students with a number card. Say, “Let’s go on a number scavenger hunt. Can you find this many?”

As students line up, show a number card for students to match. Say, “Show me the number on your fingers.”

Observational Assessment

The highlighted Developmental Progressions are addressed in this topic. Focus observations on students’ ability to match written numbers 0–5 with sets of up to 5 objects. Refer to the Developmental Progressions resource for specific stages of development.

Observational Assessment Recording Sheet

PK Module 1

Sorting and Counting

Developmental

PK.CC.DP1 Count forward to 20 and backward from 5.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP3 Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1 Sort objects into categories.

Student Name

Agenda

Materials

Preparation

Lesson 10 20 min

Written Numbers Teacher

• Numbers by Henry Pluckrose

• “I Can Count” song lyrics (in the teacher edition)

Students

• None

• None

Lesson 11 25 min

Match Game Teacher

• Match cards 0–5 Students

• Match cards 0–5 (1 set per student group)

• The Match cards have a set of pictures on one side and a number on the other. Only use cards with numbers and configurations of 0–5. Save these sets of cards for use in later lessons.

Lesson 12 15 min

Count the Math Way Teacher

• Right-hand number glove Students

• Match cards 0–5 (1 set per student pair)

• Create number gloves. Start with the right-hand glove. Write numbers on the fingertips, beginning with 1 on the pinkie finger and ending with 5 on the thumb. Continue with the left-hand glove, beginning with the 6 on the thumb and ending with 10 on the pinkie finger. Save the gloves for use in later lessons.

Lesson 13 20 min

Rosetta Stone Teacher

• Large rock Students

• None

• Project the Rosetta Stone picture or use the picture provided in the teacher edition.

Agenda

Lesson 14 25 min

Rice Scoops

Teacher

• Small, clear cups (5)

• Sticky notes (5)

Materials

Students

• None

Lesson 15 25 min

Let’s Count!

• Container of uncooked rice

• Spoon

Teacher

• Unifix® Cubes (8)

• White paper

Students

• Counting collection (1 per student)

• Work mat

Preparation

• Write a number 1–5 on each sticky note. Place a sticky note on each cup and line them up in numerical order.

• Assemble 1 counting collection bag for each student. See the module’s Materials resource for more information about how to create counting collection bags.

LAUNCH 20

Written Numbers

Match written numbers 1, 2, 3, 4, and 5 to quantities.

Read About Numbers

Show students the book Numbers by Henry Pluckrose and read the title to them.Have students tell a partner about the numbers they recognize.

Read Numbers. Pause for students to make personal connections.

Where did you see numbers in this book? What did the numbers show us?

I saw 10 on the bus. My bus is number 4. Numbers are on the license plates.

Where do you see numbers at school or at home?

They are on the clock. The calendar has numbers.

Sing About Numbers

Display the I Can Count interactive.

Let’s learn a song about numbers.

Sing the first two stanzas of the song “I Can Count” by using the interactive. Reveal each set of pictures as you sing, but do not reveal the number below them yet.

Materials

Teacher

• Numbers by Henry Pluckrose

• “I Can Count” song lyrics (in the teacher edition)

Students

• None

Teacher Note

This type of open-ended group discussion is an opportunity to teach prekindergarten students what is mathematically relevant and what is not. Gently rein in their responses, especially personal stories, when they do not fit the math discussion.

1 bluebird in a tree.

2 bees buzz over me.

Continue singing and counting to 5 using the number stairs. Sing the song again, from beginning to end.

Notice and Wonder

What do you notice about the pictures from our song?

The pictures make stairs that go up. There are blue boxes at the bottom.

When a student wonders about the blue boxes or the stairs “going up,” seize the opportunity to focus the class on counting and the relationship between quantities and written numbers.

We can use numbers to tell us how many things there are. What number would show how many blue birds are here? (Point to the blue bird.) 1

Sing the song again, starting from the beginning. This time, after singing about each picture, reveal the written number. Consider pausing before revealing the 3 and asking students to guess what number will show up.

What do the numbers tell us about in our picture?

They tell us how many things are in the line.

The numbers tell us which line of pictures is the tallest. The ducks are the tallest.

We are going to learn about different ways we can use numbers.

Teacher Note

The I Can Count interactive can be introduced as an interactive anchor chart. It can be made by using I Can Count Cutouts 1–5, chart paper, magnetic numbers or Numeral Dot cards, and double-sided tape. Save the chart for use throughout module 1. Numbers 6–10 will be added in topic F, or when students are ready.

I Can Count

Sing to the tune of “Once I Caught a Fish Alive”

1 bluebird in a tree.

2 bees buzz over me.

3 flowers growing free.

I can count! 1, 2, 3

4 cats sleep in the sun.

5 ducks are having fun.

Each one splashes as it dives.

I count 1, 2, 3, 4, 5.

6 squirrels each gather seeds.

7 birds have chicks to feed.

Each chick eats just what it’s given.

1, 2, 3, 4, 5, 6, 7

8 beans grow on a vine.

9 snails creep in a line.

1, 2, 3, 4—watch that slime!

5, 6, 7, 8, and 9

10 cars go for a drive.

Count them: 1, 2, 3, 4, 5,

6, 7, 8, 9, 10.

Let’s go count them all again.

Match Game

Match written numbers 0, 1, 2, 3, 4, and 5 to quantities. Understand the meaning of 0.

Materials

LEARN 25

Set aside the orange Match cards 0–5. Hold up the 2 card showing the image side.

Look at this card. How many leaves are on this card? 2

Turn over the card to show the written number 2.

The number 2 tells us how many leaves.

Hold up the empty 0 card.

How many leaves are on this card?

There aren’t any leaves on that card!

Turn over the card to show the written number 0.

You’re right. There aren’t any leaves. 0 is a number that means none.

Continue with another orange card until you have counted all the images and shown all the written numbers on the cards 0–5. Then return those cards to the deck and shuffle all the cards.

Display six cards in two rows of three, making sure that some show objects and some show written numbers. At least one pair of cards should represent the same number. Ask a student to select a card.

Teacher

• Match cards 0–5

Students

• Match cards 0–5 (1 set per student group)

Language Support

Support students in understanding 0 by comparing the card with some leaves to a card with no leaves. Students will use a variety of words to describe 0, such as no, none, aren’t any, and zero. Look for opportunities to use the word zero during the school day to help students build meaning.

Observational Assessment

; Watch as students match cards. Are they able to accurately match a written number to a group? (PK.CC.DP3)

; Can students identify, without counting, the number of objects shown on the card? (PK.CC.DP2)

How many rabbits? 2

Can you find another card that shows the same number?

Select another student to find a card that matches.

How can we be sure these cards match?

We counted 2 rabbits. This is 2.

There are numbers on the back. We can see if the numbers match.

So, what does the number 2 tell us about the rabbits?

There are 2 rabbits.

Can we use the number 2 to tell us about other things?

Yes, my brother is 2.

I have 2 sisters.

Do you see any other matches?

No.

Fill in the empty spaces with cards from the deck. Play until all matches are found.

Divide the class into small groups, distribute Match cards, and invite groups to play the match game independently. As students play, take the opportunity to provide feedback and assess student understanding. Encourage students to use the written numbers on the back of the cards to confirm that the cards match.

Promoting the Standards for Mathematical Practice

Using written numbers to represent groups of objects is an early and essential step toward students modeling with mathematics (MP4)

Throughout their mathematical career, students will move from concrete representations to abstract representations. Here, they move from the concrete pictures, which can be counted, to the more abstract written numbers. Modeling with written numbers in this way preserves the necessary information (how many) while de-emphasizing unnecessary information (the specific objects).

Language Support

Consider using strategic, flexible pairings throughout the module based on students’ mathematical and English language proficiency.

• Pair students who have different levels of mathematical proficiency.

• Pair students who have different levels of English language proficiency.

As applicable, complement any of these options by pairing students who speak the same native language.

Count the Math Way

Count the math way with written numbers.

Materials

Teacher

• Right-hand number glove

Put the number glove on your right hand and hold up number 1.

Let’s count the math way.

What number do you see? 1

Continue counting the math way with the number glove as students identify each number to 5. Show a closed fist for 0. Invite students to hold up their own fingers as they count to 5.

Pair students and give each pair a set of Match cards 0–5. Position pairs next to each other with enough space to spread out the Match cards.

• Partner A spreads out the Match cards with the written number side up.

• Partner B puts their left hand on the table (support students in finding their left hand).

• Call out a number from 0 to 5 and display the number the math way on the number glove.

• Partner A selects the called number from the Match cards and holds it up.

• Partner B shows the called number on their fingers the math way. Call several numbers before having partners switch roles.

Students

• Match cards 0–5 (1 set per student pair)

Teacher Note

Counting the math way is a fluency activity that will be used throughout the year. Modeling counting the math way with the number glove as students count exposes them to a potentially new way to show a count on their fingers. Eventually, students will count the math way on their fingers.

What did numbers tell us about today?

How many fingers to show

The number was the same as our fingers.

3 tells us how many fingers.

Rosetta Stone

Explore written numbers and symbols.

Materials

LEARN 20

Display the pictures of the archaeologist and the Rosetta Stone. An archaeologist is someone who travels around the world looking for objects from long ago. The things they find tell us how people lived in the past. Archaeologists use what they find to learn new things. One of the things they have found are rocks with carvings in them.

Pass around the large rock. Explain that people in the past carved into rocks because paper had not been invented yet! Display the picture of the student and the rock with symbols on it.

This archaeologist discovered a rock with symbols carved into it and needs our help to understand what the symbols mean.

What do you notice about the rock?

I see numbers! 1, 2, 3, 4, 5

I see a sun and a moon!

You can count the dots in the middle: 1, 2, 3, 4, 5.

I don’t know what the writing on the bottom is.

Teacher

• Large rock Students

• None

Display the artifact with the bottom row of symbols highlighted.

The archaeologist thinks people from long ago wrote their numbers by using these symbols. How can you help the archaeologist figure out what they mean?

I think they mean 1, 2, 3, 4, 5. Just like the other pictures. The first picture looks like a 1.

That picture has 3 lines going up and down. I think it means 3.

As students share ideas about how to help the archaeologist figure out what the unknown symbols mean, consider asking the class to revoice or extend their classmates’ thinking. Point to the symbol under the 5.

How can we use the number 5 to figure out this symbol?

It’s 5 because there are 5 dots on top of it. The number 5 is there too.

How did we use the written numbers to figure out what we didn’t know?

The numbers are in a line. There’s 1, 1 dot, and 1 line. The numbers are in order.

Numbers have been used by people for a long time. We can see different ways numbers looked a long time ago and learn how people used them.

Math Past

The stone in this activity is based on a real artifact known as the Rosetta Stone. The Rosetta Stone was carved in ancient Egypt in 196 BCE, but it was not rediscovered until 1799 CE!

The Rosetta Stone shows the same text written in three different languages: two ancient Egyptian forms of writing and ancient Greek. At the time of the stone’s rediscovery, no one knew how to read the two ancient Egyptian scripts. However, some scholars could read ancient Greek and were able to use this knowledge to translate the other two languages. This allowed other ancient Egyptian texts to be translated and taught us much more about the ancient Egyptians than we previously knew.

Use the Math Past resource to share more information about the Rosetta Stone with students.

Differentiation: Challenge

Consider covering some of the boxes in the bottom row to provide a challenge. Alternatively, ask students to use the code to reason about the next numbers in the sequence or have them develop their own code.

LEARN 25

Rice Scoops

Use numbers to tell how many.

How Many Are Hidden?

Display the I Can Count interactive with the 4 cats covered. Point to the number 4.

Look at our I Can Count chart. Some of the pictures are covered up so we can’t see them. (Point to the covered column.) Can this number tell us how many cats are hidden?

Yes! There are 4 cats.

Reveal the cats and count to check. Continue using the interactive with pictures covered to have students guess how many pictures are hidden. Then repeat the activity by covering the number.

Now the number is hidden. Can the pictures tell us which number is hidden?

Yes! 3 is hidden.

Use the interactive to repeat the series of questions for as many groups of pictures and numbers as time allows.

Scoop Count

Display the container of rice and five small, clear cups, all in a row. Label each cup with a number from 1 to 5. Invite students to watch and count as you put scoops of rice into the cups.

Materials

Teacher

• Small, clear cups (5)

• Sticky notes (5)

• Container of uncooked rice

• Spoon

Students

• None

Promoting the Standards for Mathematical Practice

Throughout topic C, students repeatedly express their reasoning skills (MP8) as they match written numbers to different groups of objects. It takes time for students to trust that the same written number can be used to represent the number of objects in different groups (e.g., 2 can represent the number of bees on the number stairs, the number of leaves on a Match card, and the number of banana chips in the snack mix).

Scoop Count requires students to trust that the written number represents the number of scoops in the cup even though the scoops can no longer be counted.

Use the number on the cup to tell me when to stop adding scoops.

Slowly add scoops of rice while counting out loud. Pause after each scoop to allow students to think about when you should stop adding scoops.

How did we use the numbers on the cups?

The numbers told us how many scoops of rice to put into a cup.

Pick up the number 4 cup and turn the number away from students.

How can we figure out how many scoops of rice are in this cup?

We can count, 1, 2, 3, and we know 4 comes next.

Turn the cup around to see the 4 on the cup!

Can we count each scoop of rice, one by one, in the cup?

No, the scoops are all mixed together.

No, but there are numbers on the cups. We don’t need to count the scoops again.

Turn the cup around to reveal that the cup is labeled with the number 4.

The number on this cup tells us how many scoops of rice are in it. When we see the number 4, does it always tell us about 4 scoops of rice?

It can tell us about other things too.

4 was the number of cats in our song.

How did numbers help us today?

They helped us remember what we counted.

They told us how many.

We use numbers to tell us about a lot of different things. When we count, we use numbers to tell us how many. We also use numbers to help us remember how many there are when we can’t count them again.

LAND 25

Let’s Count!

Organize and count a collection of objects.

Choose a Collection

Briefly review the procedure for choosing and counting a collection. Today, you are going to count the objects in a collection. Your job is to figure out how many objects you have. Invite students to choose a collection and find a workspace.

Count a Collection

As students count, circulate and take note of organizing strategies such as touch and count or move and count. Use the following questions to assess student thinking:

• How many do you have?

• Can you count again so I can listen to you count?

• Can you show me how you counted?

As students finish counting their collections, encourage them to try another way to count or to switch collections with a neighbor and confirm the total.

Look for two students who can demonstrate their counting strategy and invite them to bring their collection to a central area.

Materials

Teacher

• Unifix® Cubes (8)

• White paper

Students

• Counting collection (1 per student)

• Work mat

Observational Assessment

; Are students saying the correct number sequence? (PK.CC.DP1)

; Are students saying one number name with each object they count? (PK.CC.DP4)

; Are students saying the last number in their count to tell the total? (PK.CC.DP5)

Share, Compare, and Connect

Invite the selected students to demonstrate how they counted their collection. Use the example below to guide your discussion.

Line Up, Touch and Count (Yasmin's Way)

Yasmin, how did you count your collection?

I put the cubes in a line. I counted them like this. (Touches and counts each cube.) 1, 2, 3, 4, 5, 6, 7, 8

How many cubes do you have? 8 cubes

Class, let’s pretend Yasmin wants to share her collection with a grown-up at home. How can she draw the collection so she can bring it home to share?

She can trace the blocks.

She can line them up and draw them.

These are great ideas! Let’s trace the cubes to make a drawing of Yasmin’s collection.

Model How to Record a Collection

Model tracing the collection of Unifix Cubes. Guide students in counting the squares during the recording. After the recording, count the cubes again and emphasize that the drawing shows the 8 cubes.

Let’s try another way to draw Yasmin’s collection. First, I will line up the cubes. I will draw a circle for the first cube on my paper. Then, I will put that cube on the circle. I’ll do that with each cube until I’ve counted all my cubes.

Model drawing a circle and then placing a cube in the circle. Continue the process until all the cubes have been counted. Count the circles, and then count the cubes again.

My drawing shows the 8 cubes I counted. What number can I write to show how many cubes I counted? 8

Write 8 under the circles.

What do numbers tell us about our collections?

The numbers tell how many.

Count Out a Set of Up to 5 Objects

Progression of Lessons

Key Questions: How do we use numbers? How do we know when to stop counting?

Count out a group of objects to match a written number, part 1.

Lesson 17: Bean Bag Toss

Count out a group of objects to match a written number, part 2.

25

Play a game to develop counting and cardinality concepts with numbers to 5.

The number 4 tells us how many bean bags to toss into the hoop. We stop counting when the number of bean bags matches the number 4.

PK.CC.DP3, PK.CC.DP7

The number on the die tells us how many spaces to move the bear. We know to stop counting when we say the number we rolled.

PK.CC.DP4, PK.CC.DP7

The numbers tell us how many of each snack to put in the snack mix.

PK.CC.DP3, PK.CC.DP7

Lesson 18: Forest Path Game

Forest Pa th

Lesson 16: Number Recipe

LEARN

Count Out a Set of Up to 5 Objects

In topics B and C, students counted an existing group of objects to answer how many questions. In this topic, they count out a given number of objects from a larger group. This has relevance to students’ lives, whether they are getting 3 crayons from a box or grabbing 3 lemons from the store. This difference requires multitasking since students must keep the target number in their head, say the number words in order, and attend to one-to-one correspondence all at the same time.

Simple roll-and-count board games also support students in their counting development. How?

• Students see that numbers can tell them how many spaces to move on the board.

• Students learn to stop counting when they reach a target number. For example, if a student rolls a 4, they must hop forward 4 spaces (without counting the space they are starting on) and know to stop when they reach the target number of hops.

• Students are counting a set that is invisible once it has been counted. Rather than being easily seen, the quantity is embedded within the board game path. So, if a bear is on the eighth space, the student may have first rolled a 3 and then a 5. This lays the foundation for work on the number path in later modules.

• Students build on their intuitive understanding of comparison. Students realize that they would rather roll a 4 than a 2 because they will hop more times, move farther on the path, and ultimately be the first to reach the finish line!

At the end of the topic, students count out a group of objects to model what is happening in a math story. This primes students to decompose sets in topic E.

Terminology

No new terms are introduced in this topic.

Fluency Anytime

Fluency activities are intended to be completed any time of the day. They are simple and require few materials. Refer to the Module Resources to choose from a more extensive list of fluency activities to support your class’s math goals.

• Sunrise Counting: Have students gradually rise from a crouching position to standing on tiptoes as they count from 0 to 10. Let’s count to 10 as we make the sun rise. Ready?

• Dot Card Flash: Briefly show students a 5-group card 1–5 (digital download). Have students say how many dots are on the card and then air write the number of dots. Watch closely. How many dots do you see? (Flash the card.) Write the number in the air with your finger.

Math Anytime

During snack time, label tables with numbers 2–5. Look at the numbers on the tables. Find a seat so there are exactly that many people sitting at that table.

At a kitchen play area, set out number cards 1–5. Have students order food by giving a number card to a student server. The server counts out that number of ordered items.

At a table, write a different number on pieces of paper or index cards. Use the stickers to match the number on your paper.

During snack time, have students pass out a certain number of items to each student or table.

Sunrise Counting

Two!

Observational Assessment

The highlighted Developmental Progressions are addressed in this topic. Focus observations on students’ ability to count out a set of up to 5 objects. Refer to the Developmental Progressions resource for specific stages of development.

Observational Assessment Recording Sheet

PK Module 1

Sorting and Counting

Developmental Progressions Developmental Progressions

PK.CC.DP1 Count forward to 20 and backward from 5.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP3 Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1 Sort objects into categories.

Student Name

Agenda

Materials

Preparation

Lesson 16 25 min

Number Recipe Teacher

• 5 to 6 bowls of healthy snacks (per student group)

• Plastic gloves

Students

• Number Recipe (in the student book)

• Crayons

• Small bowl

• Plastic gloves

• Student book

• Prepare 5 or 6 bowls of different healthy snacks (e.g., dried fruit, baby carrots, sesame sticks, etc.). Put one type of snack in each bowl. Make enough bowls so each student group gets all 5 or 6 snacks.

• Tear out Number Recipe before beginning the lesson.

Lesson 17 20 min

Bean Bag Toss Teacher

• Exercise hoops or chalk circles (6)

• Numeral Dot cards 0–5

• Bean bags (15)

Students

• None

• If exercise hoops are not available, use chalk to draw 6 large circles in a row.

• Take out Numeral Dot cards 0–5 from the set. If the cards are too small for students to see, write numbers 0 to 5 on paper.

Lesson 18 25 min

Forest Path Game Teacher

• Game Board, Forest Path side

• Number dice

• Teddy bear counter

• Puppet or stuffed animal

Students

• Game Board, Forest Path side (1 per student pair)

• Number dice (1 per student pair)

• Teddy bear counter

• None

Lesson 19 20 min

Math Stories Teacher

• Fish crackers or counters (15–20)

• Paper cup or small bowl

Students

• Shipwreck Scene (in the student book)

• Fish crackers or counters (15–20)

• Paper cup or small bowl

• Student book

• Tear out Shipwreck Scene before beginning the lesson.

• Place 15–20 fish crackers or counters in a bowl for each student before the lesson begins.

• Print the Shipwreck Scene to use for demonstration.

Number Recipe

Count out a group of objects to match a written number, part 1.

Materials

LAUNCH 25

Place six bowls of healthy snacks at each table. Each bowl should contain one kind of healthy snack. Pass out the Number Recipe removable and a small empty bowl to each student.

We are going to make a healthy snack mix. Hold up 1 finger the math way.

Put your finger on the 1 on your recipe.

Pick a snack and put 1 piece of it next to the number 1.

Give students time to choose a snack and put it in the box next to number 1 on the page.

Put your snack in your bowl and say 1.

Use a crayon to draw the snack in the box beside the number 1.

Continue choosing and recording snacks one number at a time. Have students count as they move the snacks to their recipe page and bowl. Select a student to share about their snack mix by displaying their recipe and bowl. Share as many student recipes as time allows.

Omar, how many snap peas did you put in your snack mix? 3

Teacher

• 5 to 6 bowls of healthy snacks (per student group)

• Plastic gloves

Students

• Number Recipe (in the student book)

• Crayons

• Small bowl

• Plastic gloves

• Student book

Promoting the Standards for Mathematical Practice

This accessible and relevant context allows students to begin constructing viable arguments (MP3). Encourage students to share why they picked a particular snack for a given number.

A student who explains that they chose 5 banana chips because those are their favorite not only understands how to count out a group of 5 but also that 5 represents the largest quantity.

Class, how can we be sure there are 3 snap peas?

I can count them in his bowl. Look on the paper. Omar drew them by the number 3.

How many sesame sticks did you put in your snack mix, Omar? None! 0. They’re yucky.

Could you make the same snack mix again tomorrow? How would you know how many of each snack to add to the bowl?

We could look at our paper. It tells us. The numbers tell us how many of each thing to put in.

Teacher Note

Use students’ food preferences to help them think about quantity. Respond to a student who says they do not like one of the choices with, “It sounds like you don’t want any sesame sticks. What number means none?”

Students may be tempted to choose their favorite snack first. Help them reason about quantity by asking, “Would you rather have 1 banana chip or 5 banana chips?”

UDL: Representation

Students may have a wide range of fine motor skills. Consider having students record their recipe in a variety of ways including the following:

• Leaving the snack on the page.

• Coloring the box with a color that matches the snack.

• Drawing the snack.

LEARN 20

Bean Bag Toss

Count out a group of objects to match a written number, part 2.

Materials

Teacher

• Exercise hoops or chalk circles (6)

• Numeral Dot cards 0–5

Set up six exercise hoops labeled with cards 0–5. Gather students around the exercise hoops at a distance where they can see the written numbers and are challenged to toss a bean bag inside the hoops.

Stand next to 0 and use your foot to point to the number. Move and use your foot to point to the next number as the class counts.

Engage students in a movement activity that incorporates counting to 5 and associates counting forward with getting bigger.

Let’s count to 5. Crouch down as small as you can to show 0.

Get bigger slowly as we count to 5. 0, 1, 2, 3, 4, 5

Repeat one or two times beginning at 0 each time.

Pass out a bean bag to each student.

We are going to play bean bag toss. Let’s toss bean bags into each hoop to match the number. The number tells how many bean bags go in each hoop.

• Bean bags (15)

Students

• None

Teacher Note

Modify the activity to fit the number of students in the class. If there are fewer than 15 students, begin the game with a few bags already in the hoops. If there are more than 15 students, strategically remove bags from a few hoops once all the hoops are filled and let the remaining students throw.

These suggestions allow more students to throw later in the game when they must be more intentional about their toss.

Facilitate students tossing their bean bags into a hoop. Each student will toss 1 bean bag into a hoop until the hoops have the number of bags that match the written number. Pause strategically during the game to have students share about the written numbers and quantities in each hoop.

Whisper to your neighbor: Which hoops need more bean bags?

Whisper to your neighbor: Which hoops already have enough bags?

I heard someone say hoop 5 needs more bags. Let’s check. Count the bags in the hoop labeled with 5 and confirm that the hoop needs more bags.

Continue playing the game until everyone has thrown their bean bag. If time allows, play again. Begin tossing from the opposite end of the student line so all students practice strategizing about where to throw their bag.

What did the numbers in our game tell us?

How many bean bags go in the hoops

If I took all the bean bags out of this hoop, would you still know how many we threw in that hoop? (Remove the bean bags in hoop 2.)

Yes, the number tells us.

The 2 tells me.

How did you know when to stop throwing bean bags into a hoop?

We stopped when the bean bags matched the number.

When we had enough

Observational Assessment

Invite students to say which hoop they are aiming for before they toss.

; Are they able to tell which hoops need more bags and which ones have enough? (PK.CC.DP3)

Forest Path Game

Play a game to develop counting and cardinality concepts with numbers to 5.

Materials

Teacher

• Game Board, Forest Path side

• Number dice

Have students gather around to play a game with Puppet. The goal of the game is to get both bears to their honey jars.

Place the bears next to the path. Roll the die.

How many spaces can I move? 4

Show me the number with your fingers the math way.

Move your bear while counting aloud, emphasizing one-to-one correspondence. Stop dramatically after 4 moves.

Roll the die for Puppet.

How many spaces can Puppet move? Show me with your fingers the math way. Have Puppet make a mistake by not stopping when it reaches the rolled number.

What’s wrong with Puppet’s move?

Puppet didn’t stop after 3.

Puppet doesn’t know how to count.

Let’s help Puppet count. Let’s whisper count until we get to the number Puppet should stop at and then let’s shout the last number.

One, two, three!

• Teddy bear counter

• Puppet or stuffed animal

Students

• Game Board, Forest Path side (1 per student pair)

• Number dice (1 per student pair)

• Teddy bear counter

UDL: Engagement

The goal of the Forest Path Game is to get both bears to the honey. However, some students may treat it like a race. Consider practicing positive behaviors such as these before starting the game:

• Good sportsmanship: “Good game! Thanks for playing with me.”

• Self-talk: “Maybe I’ll be first next time.”

• Cooperation: “Let’s clean up together.”

• Correcting mistakes: “I think you should be on a different space. Let’s count again together.”

Take a few more turns until students understand how to play the game. Consider having Puppet make errors in one-to-one correspondence or count the starting space.

Distribute game boards, teddy bear counters, and dice to student pairs. Consider having both dot and number dice available to provide students with a choice.

Give students time to play the game. When time is up, collect the materials, gather students, and discuss the following questions:

Which numbers did you want to roll? Why?

Big numbers so I can get to the honey fast.

3 is my favorite number.

Which numbers did you not want to roll? Why?

1; it would take a long time to get to the honey.

Observational Assessment

As students play, take note of their ability to count.

; Are students saying the correct number sequence? (PK.CC.DP1)

; Are students pairing one move with one number word? (PK.CC.DP4)

; Do students recognize the number rolled? (PK.CC.DP3)

LAND 20

Math Stories

Count out a group of objects to model math stories.

Model Math Stories

Distribute the Shipwreck Scene and a cup of fish crackers or other counters to each student.

There are 5 fish swimming together in the ocean.

Count out 5 fish and put them in the ocean.

Tell the math story, pausing after each sentence to let the students move their fish.

3 fish swim to the ship. Show that with your fish.

2 fish swim to the treasure chest. Show that with your fish.

Observe students as they move their fish. Remind them to use the 5 fish they counted out of their cups. Repeat the story as needed.

How many fish are at the ship? 3

Tell me about the 2 fish.

They are at the treasure chest.

Are there still 5 fish altogether? Yes.

Consider giving students an opportunity to retell the story. Then invite them to eat the 5 fish crackers on their paper, if applicable. As time permits, continue telling math stories by using the suggested problems in the following chart. Guide students to count out a new set of fish for each story.

Materials

Teacher

• Fish crackers or counters (15–20)

• Paper cup or small bowl

Students

• Shipwreck Scene (in the student book)

• Fish crackers or counters (15–20)

• Paper cup or small bowl

• Student book

Teacher Note

The interactive, Math Stories Shipwreck Scene, can be used to practice acting out math stories.

Consider allowing students to explore with the tool in small groups, or demonstrate the activity for the whole class.

Language Support

Support comprehension for all learners by pointing to the parts of the story shown in the image such as the shipwreck and the treasure chest. Use gestures to show the meaning of phrases such as swim to the ship.

Story Problems

4 fish are swimming in the ocean. 2 fish swim to the ship. 2 fish swim to the treasure chest.

Complexities

The parts are the same. This requires students to provide a more descriptive explanation of the fish as they identify the parts.

Observational Assessment

; As students model the story, can they count out a given number from a larger group? (PK.CC.DP7)

5 fish are swimming in the ocean. 4 fish swim to the ship. 1 fish swims to the treasure chest.

5 fish are at the pirate ship. 2 fish swim away. Are there still 5 fish at the pirate ship?

The total is 5. This requires students to count to 5 and decompose the total into 2 parts of 4 and 1.

The total is decomposed into 2 parts. This requires students to consider whether the total stays the same when a part is taken away.

How did you know how many fish to put on your paper? I counted.

The story told me how many fish to get out of my cup. I counted to move the fish to the ship or the treasure chest.

Sort to Decompose

Progression of Lessons

Key Question: How can we sort the same group in different ways?

Sort the same characters in more than one way.

Decompose the same number in more than one way.

Represent a sort with written numbers.

We can group the 5 characters in different ways, for example, 3 short and 2 tall or 4 grown-ups and 1 child.

PK.MD.DP1

5 can be 2 and 3. If we group the students in a different way, 5 can be 2 and 2 and 1.

PK.CC.DP3, PK.MD.DP1

There are 10 animals. 5 animals have stripes and 5 animals have spots.

PK.CC.DP3, PK.MD.DP1

Lesson 22: Animal Sort

Lesson 20: Character Sort

Lesson 21: How Many Ways?

Button Group

Zipper Group

LEARN

20

Lesson 23: Story Cards

Sort objects shown in a picture in more than one way.

LAND

Lesson 24: Mystery Eggs

Model story problems to decompose a number.

There are 5 flowers in the picture. 3 flowers are white and 2 flowers are purple.

PK.MD.DP1

We can draw a math story about 5 eggs. 3 of the eggs are blue and 2 of the eggs are brown.

25 EUREKA MATH2 PK ▸ M1 ▸ TE © Great Minds PBC 85

Sort to Decompose

In topic E, sorting is a natural context for understanding decomposition, or breaking something—a group, a number, a shape—into parts. When students sort objects into groups, they are decomposing. Children intuitively do this during play when, for example, they are sharing toys: “I want the 3 yellow cars. You can have the 3 red ones.” They learn to navigate what to do when the sets are not equal too!

While preschool students naturally focus on self, they also see that differences exist in our world. Contexts in the first two lessons support the development of a healthy identity as students notice similarities and differences, grouping themselves without assigning value to the attributes they noticed. In lesson 21, careful consideration is given to using the term group, and students form groups based on the presence, rather than the absence, of something.

Sorting activities in topic E differ from those in topic A in the following ways:

• Students sort the same group of objects in more than one way by using different attributes each time. First, I sorted the fish by size. Then I sorted them by color.

• Students may begin to sort objects by categories that are not visually obvious. These animals come out during the day. Those animals come out at night.

• Students study a picture and sort the objects without being able to physically move them. There are 5 flowers: 3 are big and 2 are little.

• Students count all the objects before sorting. They also tell how many are in each group after sorting. There are 5 characters. 2 are tall and 3 are short.

Sorting activities support students in the shift from decomposing a group of objects to decomposing a number in more than one way. For example, 10 is 5 and 5, and 10 is 3 and 7. Teacher drawings support students in making connections between the number in the whole group and the numbers in the parts before students begin to use part–total language in module 3.

Terminology

This topic introduces the term number sentence.

Fluency Anytime

Fluency activities are intended to be completed any time of the day. They are simple and require few materials. Refer to the Module Resources to choose from a more extensive list of fluency activities to support your class’s math goals.

• Show Me Another Way: Have students show a number from 1 to 5 the math way. Then have them show the same number another way. Show me 3 the math way. Show me 3 another way.

• Counting with Movement: Show a number card from 6 to 10 and have students move in a specific way to match the number. Look at my number. Jump this many times and count your jumps.

Math Anytime

At a block area, ask students to build a structure with 5 blocks. Then ask them to use the same 5 blocks to make a different structure.

As students line up to go out to the playground, send them in pairs to line up. Another time, send students to line up one at a time or in groups of 3.

During art, have students put 10 beads on a chenille stem or string. Practice sorting the beads into different groups. How many different ways can we make 10?

During circle time, work together to sort lost-and-found items.

Show Me Another Way 3 4 5

Counting with Movement

Observational Assessment

The highlighted Developmental Progressions are addressed in this topic. Focus observations on students’ ability to sort to decompose in more than one way. Understanding these concepts will help students answer the key questions. Refer to the Developmental Progressions resource for specific stages of development.

Observational Assessment Recording Sheet

PK Module 1

Sorting and Counting

Student Name

Developmental Progressions Developmental Progressions Dates and Details of Observations

PK.CC.DP1 Count forward to 20 and backward from 5.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP3 Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1 Sort objects into categories.

Agenda

Materials

Preparation

Lesson 20 25 min

Character Sort Teacher

• Five Creatures by Emily Jenkins

• Character Cards (in the teacher edition)

• Exercise hoops (2)

Students

• None

• Tear out the Character Cards (in the teacher edition) in the Resources section. Consider cutting out the characters and gluing craft sticks to the backs of the cards so students can easily hold each card.

Lesson 21 25 min

How Many Ways? Teacher

• Number Path cards 0–5

• Exercise hoops (2–5)

Students

• None

• Take out cards 0–5 from the Number Path card set.

• Have white paper and a marker ready to make additional Number Path cards as needed.

Lesson 22 25 min

Animal Sort Teacher

• Animal cards, set A

• Numeral Dot cards (2 sets)

Students

• Animal cards (1 set per student pair or group)

• Numeral Dot cards (2 sets per student pair)

• None

Lesson 23 20 min

Story Cards Teacher

• Dry-erase marker

Students

• Story card

• Dry-erase marker

• If the slide cannot be displayed, take out the flower story card from the set.

Lesson 24 25 min

Mystery Eggs Teacher

• Personal whiteboard

• Puppet or stuffed animal

Students

• Mystery Eggs removable (in the student book)

• Crayons (black, blue, and brown)

• Student book

• Print the Mystery Eggs removable to use for demonstration and insert into a personal whiteboard.

Character Sort

Sort the same characters in more than one way.

Materials

LAUNCH 25

Read

Show the book Five Creatures by Emily Jenkins. Explain that a creature is a living person or an animal. Tell students that there are 5 creatures in this story: a mom, a dad, a girl, and 2 cats.

In this story, the girl sorts, or groups, 5 creatures in different ways. The creatures are the characters in this book.

Invite students to predict how the girl might sort the characters and then read the book aloud. Pause after page 2.

How did the girl sort the creatures, or characters, in this book?

There are people and animals. She sorted by people and by cats.

Continue reading. Pause periodically to ask how the girl sorted.

After a few pages in the book, the narrator gives only one attribute for sorting, saying, “Three who sleep in my bed.” Students may infer that 2 characters sleep somewhere else. Consider asking students what they could call the group that sleeps somewhere else.

Teacher

• Five Creatures by Emily Jenkins

• Character Cards (in the teacher edition)

• Exercise hoops (2)

Students

• None

Teacher Note

As early as infancy, children notice differences and begin to categorize the world around them. This is natural and supports students in developing a healthy identity. When adults support students in processing differences, we affirm that it is safe to observe and inquire about the world.

Act It Out

Intentionally choose 5 students to act as 5 characters. Give each of the students a character card to hold up.

Some of the characters are short and some are tall. Sort, or group, the characters. Have students sort the characters into two groups and place each group of character cards into the corresponding exercise hoop. Ask the rest of the class questions such as the following:

What groups do you see?

A tall group

A short group

How many are in the short group? 3

How many are in the tall group? 2

How many characters are there if we put the groups back together? 5

Select 5 new students to act as characters. This time, invite these students to choose the attribute they will use to form the groups. Provide support as needed.

Ask the rest of the class questions such as the following:

• What groups do you see?

• How many are in the group?

• How many characters are there if we put the groups back together?

Invite the whole class to compare the sorts.

Did we sort the characters in the same way or a different way?

We sorted them in a different way.

Sometimes the mom and dad were with the cats.

The second time the girl was by herself.

We can sort, or group, the 5 characters in different ways.

Language Support

The terms sort and group are often used interchangeably. Support students by regularly pairing these words. Because sorting can feel uncomfortable when referring to people, use the term group in these instances.

To support using the term group as a noun and a verb, consider the following language and actions:

• When the term group is used as a noun, point and say, for example, “You made a tall group!”

• When the term group is used as a verb, gesture as if waving a magician’s hand over the exercise hoops and say, for example, “Group the characters.”

How Many Ways?

Decompose the same number in more than one way.

Clothing Sort

Intentionally choose 5 students who can be grouped in two different ways according to attributes of their clothing such as zippers, buttons, and shirt colors. Have the remaining students play the role of the audience.

When I look closely, I notice different things about our clothing. Some have zippers, and some have buttons.

Invite the selected students to make two groups: a button group and a zipper group. Have each group stand together in an exercise hoop. If any students have both zippers and buttons, invite them to create a new group.

How many students are in the button group? 2

How many students are in the zipper group? 3

How many students are there if we put the groups back together? 5

Show the Number Path cards 0–5. Invite two students to come forward to match each group with the correct number.

We grouped students by their clothing. There are 5 students. There are 2 students in the button group and 3 students in the zipper group. We can say that in a number sentence: 5 is 2 and 3.

Materials

Teacher

• Number Path cards 0–5

• Exercise hoops (2–5)

Students

• None

Teacher Note

Consider this lesson’s discussion as an opportunity to build community and to ensure that each student’s apparel is discussed with care, warmth, and validation. It is important not to assign value or judgment to attributes such as, “Look at those cool zippers on Shay’s sneakers!” Instead, consider saying, “We all wear different clothes. Some have buttons, some have zippers, some have ties, and some have other things.”

UDL: Engagement

Choose clothing attributes that are meaningful to the class. Instead of zippers and buttons, the class can be grouped by sandals and sneakers or another clothing feature.

Button Group

Zipper Group

Find Another Way

I wonder if we can use clothing to group the same students in a different way. What else do you notice?

Some people have pants, and some have dresses. Pari and Xander have blue shirts.

This time let’s group the same students by shirt or dress color.

Invite the selected students to group themselves based on shirt or dress color or another chosen attribute. Add additional exercise hoops if there are more than two groups.

How many students are in the blue shirt group? 2

How many students are in the yellow shirt group? 2

How many students are in the red dress group? 1

How many students are there if we put them back together? 5 students

Show the Number Path cards 0–5. Invite two students to come forward to match each group with the correct number.

Listen to my number sentence: 5 is 2 and 2 and 1. There are 5 students. 2 students have blue shirts, 2 students have yellow shirts, and 1 student has a red dress.

As time permits, choose 5 different students who can be grouped in two different ways according to attributes of their clothing.

Let’s think about the ways we sorted. What happened when we grouped 5 students in different ways today?

People changed groups.

We had different numbers in the groups.

We put different number cards with the groups.

We saw that 5 can be 2 and 3. We also saw that 5 can be 2 and 2 and 1. Our number sentence changed when we grouped the students in a different way.

UDL: Engagement

Allowing students to choose attributes that they find interesting puts students at the center of their learning and promotes relevance.

Use the following general guidelines to support students with the activity:

• If a student does not self-identify with a specific group, invite them to create a new group.

• If a student self-identifies with more than one group, allow them to do so and encourage them to tell or show why.

• If a student creates a new group and is the only student with that attribute, affirm that being unique, or different, is a positive quality.

It is not important that students pick a specific group but rather that they see that differences exist in our world.

Observational Assessment

; Can students identify the number of people in a group without counting? (PK.CC.DP2)

1

2 2

blue shirt group

yellow shirt group

red dress group

Animal Sort

Represent a sort with written numbers.

Materials

LEARN 25

Guess My Rule

Engage students in the Guess My Rule routine by using the following process. This routine engages students in thinking about how objects are sorted.

I am going to sort my 10 animal cards into groups. Try to guess how I am sorting the animals. Think about what is the same about the animals in the groups.

Establish a silent signal for students to show when they think they know the sorting rule. Then sort 4 or 5 of the cards one at a time into two groups: animals with fur and animals with feathers. Invite several students to share their ideas.

How am I sorting? What is my rule?

You’re sorting by animals! Those are all birds. Both of these have hair. (Points to the fox and lion.)

These have wings. (Points to the birds.) These have ears. (Points to the fox and lion.)

Those are great ideas! Let’s add another card. (Place the eagle card.) What do you think my rule is now?

These animals have a black nose.

These fly, and those don’t fly.

Show students the next card and ask them where they think the card belongs. Once all the cards have been sorted, invite students to guess the rule and to explain their thinking.

You found the rule. This group has feathers. This group has fur.

I wonder how many animals are in each group. Let’s count them!

Teacher

• Animal cards, set A

• Numeral Dot cards (2 sets)

Students

• Animal cards

(1 set per student pair or group)

• Numeral Dot cards

(2 sets per student pair)

Promoting the Standards for Mathematical Practice

The Guess My Rule routine gives students an opportunity to look for and express regularity in repeated reasoning (MP8). Students look for a pattern in how the animals are sorted and revise their rule as more animals are added to the sort.

This mathematical practice will be important throughout students’ academic careers. Students will often be asked to look for patterns and to test new cases to see if the pattern still holds.

Swan Duck Eagle Fox Lion

Slowly touch each animal card in the feathers group as students count, and then repeat with the fur group. Label each group with a Numeral Dot card. Count the total and say the label.

There are 5 animals with feathers. There are 5 animals with fur. There are 10 animals altogether.

I can make a drawing to show my sort.

Draw 5 circles, write the number 5 above them, and draw a picture below them to represent a feather. Draw another set of 5 circles, write the number 5 above them, and draw a picture below them to represent fur. Circle the two groups of 5 and write the number 10 above the large circle.

5 animals with feathers and 5 animals with fur make 10 animals in all.

Sort and Count

Now it’s your turn to sort animal cards! Before you sort, count your cards to see how many animals you have altogether.

As students sort, circulate and ask questions that emphasize the numbers of animals, such as the following:

• How did you sort your cards?

• What is this group?

• How many animals are in this group? How many are in the other group? How many animals are there altogether?

• Can you sort in a different way? How many animals are in each group now? How many animals do you have altogether?

Encourage students to label the groups with their Numeral Dot cards after they sort.

; Are students able to sort the animal cards into groups? (PK.MD.DP1)

; Are students able to accurately match a written number to a group? (PK.CC.DP3)

Teacher Note

The Numeral Dot cards may become disorganized as students work, but the cards will still be functional. As students select numerals to label each group, be sure to ask which number matches the group.

UDL: Action & Expression

Support students in planning their sorts by using ideas shared during Guess My Rule or by asking the following questions:

• How do the animals look?

• How do they move?

• How many feet do they have?

• Which animals would you like as a pet?

LEARN 20

Story Cards

Sort objects shown in a picture in more than one way.

Tell a Math Story

Display the flower story card. Give students time to share what they notice about the flowers.

How many flowers are there? 5

Write the number 5 at the top of the picture.

How could we sort the flowers?

We can sort by color. Those are white, and those are purple. (Points to each color of flower.)

There could be a big group and a little group.

We can sort by color or size. Let’s sort by color first.

Invite a student to circle one group of flowers. Ask the class to tell how many flowers are in that group. Count to confirm, and write the number below the circled group. Repeat for the second group.

Tell a simple story about the flowers.

There are 5 flowers. 3 are white and 2 are purple. Erase the card.

Materials

Teacher

• Dry-erase marker

Students

• Story card

• Dry-erase marker

Differentiation: Challenge

Students are not expected to write numbers as they circle groups, but some may want to try. Consider providing a visual example for students to replicate or writing the number and having them trace it. The Number Rhymes resource located in the Module Resources provides suggested language to help students remember number formation.

This time let’s look at the size of the flowers.

Whisper to your neighbor how many big flowers you see.

Invite a student to circle the big flowers. Count to confirm, and write the number below the circled group. Repeat for the second group. This models how students will practice independently.

Invite a student to tell a simple story about the big and small flowers.

There are 2 big flowers and 3 little flowers.

How many flowers, big and little, are there altogether? Can you add that to your story?

There are 2 big flowers and 3 little flowers. There are 5 flowers.

Pass out a story card and a dry-erase marker to each student. Ask students to circle groups they see on the card. If students select a group that is difficult to circle, invite them to point out the objects in the group.

Look at your story cards. Think about how to sort them. Circle the groups you see. Tell a story about your groups to your neighbor.

Have students switch story cards with a neighbor and repeat as time allows.

Observational Assessment

; Are students able to sort the images into groups? (PK.MD.DP1)

; Can students answer how many questions with different configurations? (PK.CC.DP6)

Mystery Eggs

Model story problems to decompose a number.

Draw a Math Story

Show students the Mystery Eggs removable.

What do you notice? What do you wonder?

I see a bird’s nest. Where are the birds?

There is a nest. Whose is it?

Many different creatures can live in nests. Puppet found this nest. Listen to Puppet’s story about the nest.

There are 5 eggs in the nest.

Invite students to use their black crayon to draw the eggs in the nest to match Puppet’s story. Then tell more of Puppet’s story.

3 of the eggs are blue and 2 of the eggs are brown. Color the eggs to match Puppet’s story.

As students color, encourage them to retell Puppet’s story.

Circulate and ask questions such as the following:

• How many eggs are there?

• How can you sort the eggs in the nest?

• Which number tells how many blue eggs there are? Which number tells how many brown eggs there are?

As students finish coloring, invite them to retell Puppet’s story again. Then revoice the story as a number sentence.

Materials

Teacher

• Personal whiteboard

• Puppet or stuffed animal

Students

• Mystery Eggs removable (in the student book)

• Crayons (black, blue, and brown)

• Student book

Puppet found a nest with 5 eggs in it. There are 3 blue eggs and 2 brown eggs. We can say that in a number sentence: 5 is 3 and 2.

What creatures might hatch, or come out of, the eggs?

Dinosaurs

Turtles

Birds

Invite students to draw in the empty space on their removable what they think will hatch from the eggs.

Share, Compare, and Connect

Gather students with their drawings. Invite a few students who made different groupings to share their drawings and to tell a simple math story about the creatures that may hatch. Restate the total with a number sentence.

Ruby, how many eggs are in the nest? 5

Can you tell us a story about what hatched from your eggs?

3 chickens and 2 dinosaurs

Oh my! You will have 5 creatures: 3 chickens and 2 dinosaurs! We can say a number sentence to match your story: 5 is 3 and 2.

Xander, how many eggs are in your nest? 5

Share your story about the eggs.

4 snakes and 1 turtle came out of 5 eggs.

You have 5 creatures, too: 4 snakes and 1 turtle. The number sentence for your story is 5 is 4 and 1.

Show the Mystery Eggs removable so all students can see it. Draw 5 eggs in the nest and write 5 above the eggs. As students answer the following question, circle the different ways to make 5.

What are some ways we showed 5?

5 is 4 and 1.

5 is 3 and 2.

Observational Assessment

; Are students able to count and answer how many questions? (PK.CC.DP6)

Match Written Numbers with Sets of Up to 10 Objects

Progression of Lessons

Key Question: What are some things we can do to help us count?

Lesson 25: More Written Numbers

Match written numbers 6, 7, 8, 9, and 10 to quantities.

Lesson 26: Count on the Rekenrek

Count to 10 on the rekenrek.

20

Lesson 27: 5-Groups

Count objects in a 5-group configuration.

1 2 3 4 5

The numbers tell us how many are in each set. The number 6 matches 6 squirrels.

PK.CC.DP1, PK.CC.DP3

We can count 10 beads on the top row. 5 are red and 5 are white. We can show 10 on our fingers too. 5 and 5 on our fingers make 10.

PK.CC.DP1

5-groups help us count. 6 is 5 on the top and 1 on the bottom.

PK.CC.DP1

LEARN

LEARN

LEARN

20

Lesson 28: Counting with Puppet

Answer how many questions about objects in varied configurations.

LEARN

25

Lesson 29: Match Game

Match written numbers 6, 7, 8, 9, and 10 to quantities.

LAND

Lesson 30: Let’s Count and Record!

Organize, count, and record a collection of objects.

We can mark and count to tell how many leaves. The number 8 tells us there are 8 leaves in the group.

We can put a mark on each thing to help us keep track of the count.

PK.CC.DP6

PK.CC.DP2, PK.CC.DP3, PK.CC.DP6

We can line up our objects to count. We can trace them to record how many are in our collection.

PK.CC.DP1, PK.CC.DP4, PK.CC.DP5, PK.CC.DP6

Match Written Numbers with Sets of Up to 10 Objects

Topic F expands on the ideas in topics B and C as students extend number core concepts and counting strategies to sets of 6–10 objects in various configurations. As the size of the group gets larger, students keep track of the count using three key strategies:

• Touch and count (one number word said as each object is touched)

• Move and count (one number word said as each object is moved)

• Mark and count (one number word said as each object is marked)

Students progress from counting objects in linear configurations to counting in circular and scattered configurations. Because circular and scattered arrangements lack a clear starting and stopping point, young students often lose track of the count. For this reason, students learn an alternate strategy, called mark and count, to ensure that each object is counted exactly once. As students help Puppet fix counting mistakes, they playfully critique their world. This is the beginning of mathematical agency.

5 is a special number in the life of a preschooler, and students may already come to school eager to give a “high five.” Students are introduced to the rekenrek, a tool with 5 red beads and 5 white beads on each row. The rekenrek helps students “just see,” or subitize, small quantities while building toward composing and decomposing numbers 6–10. Through the structure of 5-groups, students also learn to subitize 5 as a unit, which serves as an anchor as students visualize quantities 6–10. 5-groups become a familiar model that will be used through grade 5.

Terminology

No new terms are introduced in this topic.

Fluency Anytime

Fluency activities are intended to be completed any time of the day. They are simple and require few materials. Refer to the Module Resources to choose from a more extensive list of fluency activities to support your class’s math goals.

• Show Me Another Way: Have students show a number from 1 to 5 the math way. Then have them show the same number another way. Show me 3 the math way. Show me 3 another way.

• Counting on the Rekenrek to 10: Slide the beads, one at a time, from behind the panel as students count. First, count to 10 by using only the beads in the top row. Then count to 10 with 5 beads in the top row and 5 beads in the bottom row. Say how many beads there are as I slide them over.

Math Anytime

At a table, set out drawing materials, a set of number cards 1–10, and a collection of up to 10 objects. Ask students to count the collection and record their count.

During music and movement, play the I Can Count video and sing along with students. Invite students to act out the song.

During art, have students create a simple number book. Glue the picture that matches the number on the page.

During movement time, give students either a dot card or a numeral card. Find your match.

Counting on the Rekenrek to 10

Show Me Another Way

Observational Assessment

The highlighted Developmental Progressions are addressed in this topic. Focus observations on students’ counting behaviors and ability to answer how many questions. Refer to the Developmental Progressions resource for specific stages of development.

Observational Assessment Recording Sheet

PK Module 1

Sorting and Counting

Developmental Progressions Developmental Progressions

PK.CC.DP1 Count forward to 20 and backward from 5.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP3 Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1 Sort objects into categories.

Student Name

Agenda

Materials

Preparation

Lesson 25 25 min

More Written Numbers Teacher

• “I Can Count” song lyrics (in the teacher edition)

• Number Path cards

Students

• None

• None

Lesson 26 10 min

Count on the Rekenrek Teacher

• 20-bead rekenrek Students

• None

• None

Lesson 27 20 min

5-Groups Teacher

• Number Path cards

• 20-bead rekenrek

Students

• None

• None

Lesson 28 20 min

Counting with Puppet Teacher

• Puppet or stuffed animal

Students

• Story cards

• Dry-erase marker

• Project the Students pictures or use the pictures provided in the teacher edition.

Lesson 29 25 min

Match Game Teacher

• Match cards 6–10 Students

• Match cards 6–10 (1 set per student pair or per student group)

• Take out Match cards with numerals and configurations of 6–10.

Lesson 30 30 min

Let’s Count and Record! Teacher

• Puppet or stuffed animal

• Counting collection

Students

• Counting collection (1 per student, up to 10 items)

• Work mat

• White paper

• Assemble 1 counting collection bag for each student. See the module’s Materials resource for more information about how to create counting collection bags. Save students’ recordings of their collections for use at the end of the year.

More Written Numbers

Match written numbers 6, 7, 8, 9, and 10 to quantities.

About Numbers

Display the I Can Count interactive.

Let’s sing our song about numbers. Sing the first two stanzas of the song “I Can Count” (through 5) by using the interactive.

Continue singing and using the number stairs to 10. Reveal each set of pictures as you sing, but do not reveal the numbers below 6–10.

Notice and Wonder

What do you notice about the stairs as we sing our song?

The stairs start small and get bigger. They go up.

Why do you think the stairs get taller?

There are more things as the stairs go up. 5 is more than 1.

As students make connections to big ideas (e.g., the relationship between quantity and number, each number is one more than the number before it), allow time for them to explore these ideas.

Materials

Teacher

• “I Can Count” song lyrics (in the teacher edition)

• Number Path cards

Students

• None

UDL: Representation

Consider rereading the book Numbers by Henry Pluckrose to activate prior knowledge about numbers. Ask the following questions to make connections to today’s learning:

• Where do you see numbers in the book?

• What can numbers show us?

• Where do you see numbers in your world?

What do you wonder?

What comes after the cars?

Does the song keep going? To 20?

What is hiding under the blue boxes?

Sing the song together as a class while pointing to each picture.

Whisper to a neighbor what you think is in the blue boxes.

Which number tells how many squirrels there are? How do you know?

6. 6 comes after 5 when I count.

6. I can count the squirrels. 1, 2, 3, 4, 5, 6

Continue the process for numbers 7 and 8. For numbers 9–10, hide the snails and cars by using the interactive.

Can this number tell us how many snails are hidden? (Point to the 9.)

Yes. That number tells me there are 9.

Yes. That’s 9. 9 snails matches the song.

Reveal the 9 snails and continue the process for the number 10.

What do the numbers tell us?

How many things are in each group

Number Path

Pass out Number Path cards to ten students. Then ask those students to line up in order. Invite the other students to check that the numbers are in order by using the I Can Count chart for support, as needed.

Then have the students who are holding the cards pass them to ten new students and repeat the process until all students have had a turn.

UDL: Representation

If you introduced the I Can Count interactive as an interactive anchor chart in topic C, add the I Can Count Cutouts 6–10. Invite students to interact with the chart. After singing the song and revealing the pictures, strategically remove some numbers or groups of pictures. Ask students to identify the locations for the missing items and to explain their thinking.

Count on the Rekenrek

Count to 10 on the rekenrek.

LEARN 10

Count on the Rekenrek

Show students the rekenrek with the side panel attached. Start with all the beads behind the panel.

This math tool is called a rekenrek.

Show 1 the math way with your right pinkie finger. Then show 1 on the rekenrek by sliding 1 red bead in the top row from behind the panel.

I am showing 1 on my fingers and 1 on the rekenrek. Show me 1 on your fingers.

(Holds up 1 finger.)

Students are not expected to hold up their fingers the math way. Have students show numbers 2–10 on their fingers while you show each number on the top row of the rekenrek. Slide the beads back behind the panel after counting to 10.

Now let’s count by using the rekenrek. Say how many beads there are as I slide them over. Ready?

Slide the beads in the top row from behind the panel, one at a time, as students count to 10.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10

How many beads are there? (Gesture to the 10 beads.) 10

What do you notice about the 10 beads on the rekenrek?

They are red and white.

5 are red and 5 are white.

Materials

Teacher

• 20-bead rekenrek

Students

• None

UDL: Action & Expression

Since fine motor demands may prevent students from holding up their fingers the math way, allow them to show their fingers another way. However, consider providing time for students to practice counting the math way.

It is important to model counting the math way because it is like the progression of numbers from left to right on the rekenrek.

Student View

Student View

Show me 10 on your fingers.

Slide the beads back behind the panel. Have students count to 10 on the rekenrek again, this time showing 10 as 5 beads on the top row and 5 beads on the bottom row.

How many beads are in the top row? 5

How many beads are in the bottom row? 5

How many beads are there altogether? 10

Show me 10 on your fingers. Let’s move our hands to match the rekenrek. (Demonstrate showing 5 fingers on each hand, holding one hand above the other.)

Continue counting on the rekenrek to 10 as time and student engagement allow. Periodically ask students during the count to say how many beads you have counted so far. Have students show that same number with their fingers.

Teacher Note

Hold the rekenrek on your lap or place it on a shelf next to you. The panel should be to the right side of the rekenrek when viewed from the front. Move the beads from behind the panel to the left side of the rekenrek. When counting on the rekenrek, students see the progression of numbers from left to right, like counting the math way. Students see the quantity increase as they count.

5-Groups

Count objects in a 5-group configuration.

Materials

LEARN 20

5-Group Hands

Show students the Number Path cards. Have students count as you point to each card.

Teacher

• Number Path cards

• 20-bead rekenrek

Students

• None

UDL: Action & Expression

Point to or hold up the Number Path card that shows 6.

How many squirrels are on the top? (Point.) 5

How many squirrels are on the bottom? (Point.) 1

This card shows 6 as 5 and 1 more. We call that a 5-group.

Demonstrate holding out one hand showing 5 fingers above your other hand showing 1 finger.

We can show this 5-group on our hands. Hold up 5 fingers on top and 1 finger on the bottom, like this.

Your turn! Show me the 5-group on your hands.

Continue to 10, having students show the 5-groups with their hands.

5-Groups on the Rekenrek

Play part 1 of the video 5-Groups at the Game, which shows 10 people entering a stadium to sit

Since many students are still developing the ability to subitize, provide an opportunity for students to count the objects on each card.

Teacher Note

When quantities of 6–10 objects (e.g., teddy bear counters, dots) are arranged in a 5-group formation, the objects are in two rows. The top row has 5 objects, and the bottom row has 1, 2, 3, 4, or 5 objects.

down in 5-group formation for a game. Pause the video to show the 10 people lined up at the ticket booth.

What do you notice? What do you see?

There are kids in a line.

I see chairs.

What do you wonder?

How many are in line?

Are there enough chairs?

Play part 2 of the video.

How many people are watching the game? How do you know?

I counted 10, see? (Touches and counts the people in the video.)

There are 5 in that row and 5 in that row. (Gestures to the top row and then the bottom row.) That’s 10.

Show students the rekenrek with the side panel attached. Start with all the beads behind the panel.

The two rows of people remind me of our math tool with the two rows of beads, the rekenrek!

How can we make 10 on the rekenrek, just like the 10 people at the game?

5 on the top and 5 on the bottom

Slide the red beads in the top row and then in the bottom row from behind the panel, one at a time, as students count to 10.

Show me 10 with your 5-group hands.

What does 10 look like on the rekenrek and on your hands?

5 and 5

5 on top and 5 on bottom

The structure of 5-groups helps students visualize quantities of 6–10 as 5 and some more. The consistent grouping of 5 on the top row encourages subitizing so students do not have to count all the objects each time. Just like they trust there are 5 fingers on one hand, they begin to trust that there are 5 objects on the top row without counting.

UDL: Engagement

If you are unable to show the video or would like to provide a movement break, invite students to act out 5-Groups at the Game. Set up two rows of 5 chairs. Choose 10 students to line up next to the chairs. After they “buy a ticket to the game,” ask students to sit down, one at a time. Have them fill up the back row first from left to right and then fill up the front row from left to right. Encourage the class to count out loud as each student sits in a chair.

Student View

LEARN 20

Counting with Puppet

Answer how many questions about objects in varied configurations.

Fix Puppet’s Mistake

Invite students to find a place to stand anywhere in the room while Puppet counts to 10. Then have Puppet exclaim, “Freeze!”

Puppet is going to count how many friends are here today. Have Puppet count students in a haphazard way, intentionally counting some students twice and not counting other students. Keep counting incorrectly until students stop Puppet. Engage students in the Fix Puppet’s Mistake routine by using the following process.

What mistake did Puppet make?

Puppet forgot to count me!

Puppet counted me lots of times. You should only count people once!

How can we help fix Puppet’s mistake?

We could line up.

We could sit down when we are counted.

Invite all students to stand in a line. Have Puppet correctly count all of the students as they stand in line. Begin counting from either end of the line. Have the class tell how many students are in line.

Why is it easier for Puppet to count you when you are standing in a line?

Puppet can see who has been counted.

When we are counting things, we can move them into a line to make it easier to count!

Materials

Teacher

• Puppet or stuffed animal

Students

• Story cards

• Dry-erase marker

Mark and Count

Display the picture of students scattered throughout a cafeteria.

How can we help Puppet count the students in this picture since we can’t move them into a line?

Cover each one up after Puppet counts them.

Cross out each one as Puppet counts.

Have Puppet cross out each student while counting them.

How many students? 8

Display the picture of students sitting in a circle. Have Puppet start counting around the circle and stop counting before getting all the way around. In Puppet’s voice, incorrectly announce how many students there are.

What mistake did Puppet make?

Puppet stopped counting.

Puppet needs to go all the way around.

How can we mark the students in this picture to help Puppet count correctly?

Cross them out again.

Put a mark on the yellow shirt. Then Puppet will know where to start and stop.

Have Puppet count both ways to validate each strategy.

If we can’t move things, we can mark them to help us count.

Pass out story cards with totals of 7 to 10 objects and dry-erase markers. Invite students to practice marking and counting objects in different configurations.

Promoting the Standards for Mathematical Practice

As students begin to count larger groups of objects, it is increasingly important to attend to precision (MP6). Students learn strategies such as move and count or mark and count to help them attend to precision.

As students use the story cards to count, promote MP6 by asking, “What can we do to help us count carefully?” or “How do you know you have counted correctly?” Listen for students to mention counting each object only once and not skipping any objects.

Observational Assessment

; Do students notice that some configurations make counting more difficult than others? (PK.CC.DP6)

; Are students using a counting strategy, keeping track of each object they counted? (PK.CC.DP4)

LEARN 25

Match Game

Match written numbers 6, 7, 8, 9, and 10 to quantities.

Find a Match

Shuffle the Match cards. Show six cards in two rows of three, making sure that some cards show objects, some cards show written numbers, and at least two cards represent the same number.

Point to the card with 8 leaves. Ask a student to model how to touch and count each object.

How many leaves? 8

Turn to the entire class.

Let’s find a card that matches.

Select another student to find a card that matches.

How can we be sure these cards match?

We counted 8 leaves. This is the number 8.

8 7 6

Materials

Teacher

• Match cards 6–10

Students

• Match cards 6–10 (1 set per student pair or per student group)

We can look on the back of the cards to see if the numbers are the same.

Turn over the cards to show the numbers. Ask students to confirm that the numbers are exactly the same.

What does the number 8 tell us?

There are 8 leaves.

Do you see other cards that match? How do you know they match?

Yes. Number 6 and 6 dogs match.

8 8

UDL: Representation

As students play the match game with the cards for numbers 6–10, the amount of visual information increases. Consider the following suggestions to reduce the amount of visual information:

• Show the number side of three or more cards.

• Replace a greater number with a number between 0 and 5.

• Show only four cards at a time.

As you find matches, put them aside. Fill in the empty spaces with cards from the deck. If there are no matches, add another card from the deck. Continue playing until students have found all the matches.

Invite students to play. Pair or group students and give each pair or group a set of cards. Support groups as they lay out the cards in two rows of three. As students play, take note of their ability to count by using all of the number core components.

Observational Assessment

; Watch as students match cards. Are they able to accurately match a written number to a group? (PK.CC.DP3)

; Can students answer how many questions as they count items in different configurations? (PK.CC.DP6)

Promoting the Standards for Mathematical Practice

Using written numbers to represent groups of objects is an early and essential step in students modeling with mathematics (MP4).

Throughout their mathematical career, students will move from concrete representations to abstract representations. Here, they move from the concrete pictures, which can be counted, to the more abstract written numbers. Modeling with written numbers in this way preserves the necessary information (how many) while de-emphasizing unnecessary information (the specific objects).

LAND 30

Let’s Count and Record!

Organize, count, and record a collection of objects.

Model Recording a Collection

Bring students together in a place where they can see Puppet and a collection of objects. Have Puppet count the objects correctly.

Puppet counted this collection and wants to show it on paper, like we did with Yasmin’s collection last time. But Puppet isn’t sure how to do it. What do you think Puppet could do?

Draw a picture or dots.

Trace the rocks.

Write numbers.

Model recording by using students’ suggestions.

Choose a Collection

Introduce the recording sheet and establish a procedure for choosing and counting a collection.

Today, you are going to count the objects, or things, in a collection and show your work on paper.

Once the procedure is established, invite students to choose a collection and find a workspace.

Materials

Teacher

• Puppet or stuffed animal

• Counting collection

Students

• Counting collection

(1 per student, up to 10 items)

• Work mat

• White paper

Count and Record a Collection

Circulate and notice how students organize, count, and record.

• Organizing strategies may include touch and count or move and count for different configurations (linear, array, or scattered).

• Recordings may include drawings, stamps, or numbers. Use the following questions to assess and advance student thinking:

• How many? Can you count your collection again so I can listen to you count?

• How will you show the things you counted on paper? What will you draw or write?

• Does your drawing match your collection? How do you know?

As students finish counting their collections, encourage them to record their count.

Select student examples that demonstrate different ways to record, including drawings and numbers. Take photographs to project if possible. If not, set aside selected work for sharing. Have students clean up the rest of the work. Collect written representations to review as formative assessments after the lesson. Keep students’ first recordings for use at the end of the year.

Share, Compare, and Connect

Not every class will have enough time to complete this section of the lesson. If time allows, invite the students whose samples were selected previously to demonstrate how they recorded their collection.

Trace and Count (Emiko’s Way)

Emiko, how did you show your work on paper?

I traced the keys.

Does your drawing match your collection? How do you know?

Yes. I counted 8 keys and my drawing shows 8 keys.

What does 8 tell us about?

How many keys

Teacher Note

To maintain a focus on recording, limit the size of each collection to 10 items.

Students may choose a variety of ways to record. Students’ drawings will vary significantly. Some drawings will clearly show individual objects in a collection while others may be hard to distinguish. With time and experience, students develop their fine motor skills as well as their understanding of numbers and what it means to represent a set.

Observational Assessment

; Are students saying the correct number sequence? (PK.CC.DP1)

; Are students saying one number name with each object they count? (PK.CC.DP4)

; Are students saying the last number in their count to tell the total? (PK.CC.DP5)

Count Out a Set of Up to 10 Objects

Progression of Lessons

Key Questions: How do we know when to stop counting? What can we do to help us remember how many?

Lesson 31: Match or No Match?

Count out a group to match a written number.

Lesson 32: Make It Match

Count out a group of objects to match a written number and record.

20

Lesson 33: Dinosaur World

Count out groups to model add to with result unknown math stories.

We can count out a group of 7 objects to match the number 7.

PK.CC.DP3, PK.CC.DP7

We can make a math drawing to help us remember how many friends are in each group. Our drawing matches the number 7.

PK.CC.DP3, PK.CC.DP7

We can use cubes to show our math story. 3 dinosaurs and 1 dinosaur make 4 dinosaurs.

PK.CC.DP7

Lesson 34: Culminating Activity

Sort objects into groups and label them with written numbers.

After This Module

Module 6 Project A

Module 6 is composed of three projects. The goal of the first project, Project A, is for students to apply the learning of this module. The project can be completed any time after module 1. All projects are optional, student-driven, and exploratory.

We can sort our objects into groups. We can count how many in each group and find a number card that matches.

PK.CC.DP3, PK.CC.DP6, PK.MD.DP1

You can find the details of and materials for each project in the module 6 teacher edition.

Count Out a Set of Up to 10 Objects

Topic G revisits concepts from topic D, during which students counted out a group of objects to match a written number from 1 to 5. Counting out a set from a larger group requires multitasking. Students must remember the target number while saying the number words in order and attending to one-to-one correspondence.

In previous topics, students began to record their math thinking. For example, students represented their counting collections on paper by tracing, stamping, drawing, or writing numbers. Students also began to model story problems with a drawing. Contexts were intentionally easy to draw (e.g., eggs in a nest) to support students with this more sophisticated level of abstraction.

In this topic, students encounter an age-appropriate challenge when they are asked to represent dinosaurs stomping through the forest. While most young students find it far more exciting to draw a dinosaur than a circle, and rightfully so, they experience the need to make a mathematical drawing rather than a detailed artistic drawing. Remember, it takes time and practice for preschoolers to see the value in efficient math drawings. Trust that students will arrive at this level of abstraction in their own time.

Drawings can be used to see how students make sense of a problem. Consider looking for the following:

• Do students draw 1 item or symbol for each object?

• Do students match a quantity to a written number?

• Do students use their drawing to retell the situation or story?

As they work with addition and subtraction story problems, students continue to show their thinking with mathematical drawings and models such as number bonds, which are used consistently throughout the PK–5 experience.

Terminology

No new terms are introduced in this topic.

Fluency Anytime

Fluency activities are intended to be completed any time of the day. They are simple and require few materials. Refer to the Module Resources to choose from a more extensive list of fluency activities to support your class’s math goals.

• Show Me Another Way: Have students show a number from 1 to 5 the math way. Then have them show the same number another way. Show me 5 the math way. Show me 5 another way.

• Counting on the Rekenrek to 10: Slide the beads, one at a time, from behind the panel as students count. First, count to 10 by using only the beads in the top row. Then count to 10 with 5 beads in the top row and 5 beads in the bottom row. Say how many beads there are as I slide them over.

Math Anytime

At a block area, set out number cards 1–10. Have students choose a card and build a structure with that number of blocks.

At a kitchen play area, set out number cards 1–10. Have students order a food item and give a number card to a student server. The server counts out that number of ordered items.

At a table, set out small bowls with a number written inside each bowl. Put objects into the bowls to match the number written inside.

During art, show students a number card. Make a picture of a group that matches the number on the card.

Counting on the Rekenrek to 10

Show Me Another Way

Observational Assessment

The highlighted Developmental Progressions are addressed in this topic. Focus observations on students’ sorting and counting behaviors. Refer to the Developmental Progressions resource for specific stages of development.

Observational Assessment Recording Sheet

PK Module 1

Sorting and Counting

Student Name

Developmental Progressions Developmental Progressions Dates and Details

PK.CC.DP1 Count forward to 20 and backward from 5.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP3 Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1 Sort objects into categories.

Agenda

Materials

Preparation

Lesson 31 20 min

Match or No Match? Teacher

• 20-bead rekenrek

• Set of 10 objects in a bag

• Match cards 5–10

Students

• Match cards 5–10 (1 set per student or per student pair)

• Set of 10 objects in a bag (1 set per student or per student pair)

• Take out Match cards with numerals and configurations of 5–10.

• Prepare bags with 10 objects for each student (e.g., teddy bear counters, cubes, pom-poms).

Lesson 32 25 min

Make It Match Teacher

• Numeral Dot cards

• Chalk or exercise hoops

Students

• White paper

• Numeral Dot cards

• None

Lesson 33 20 min

Dinosaur World Teacher

• None Students

• Prehistoric Scene (in the student book)

• Unifix® Cubes (10–15)

• None

Lesson 34 25 min

Culminating Activity Teacher

• Numeral Dot cards Students

• Natural item

• Sorting bag (1 per student pair)

• Numeral Dot cards (2 sets per student pair)

• Before the lesson, invite students to bring a leaf, a shell, or some other natural item to class.

LAUNCH 20

Match or No Match?

Count out a group to match a written number.

Match or No Match?

Display the picture of the card with 3 dots and the 3 card.

Do these cards match? How do you know?

Yes! I see 3 dots and the number 3.

Yes. They go together. They’re both 3.

Display the picture of the card with 3 dots and the 4 card.

Do these cards match? How do you know?

No, they aren’t the same.

They don’t! I see 3 dots, but the number is 4.

Continue the process with the following pictures.

Materials

Teacher

• 20-bead rekenrek

• Set of 10 objects in a bag

• Match cards 5–10

Students

• Match cards 5–10

(1 set per student or per student pair)

• Set of 10 objects in a bag

(1 set per student or per student pair)

Hold up a set of 10 objects in a bag and the 8 card.

How can we make a group of objects that matches this number?

Make a group with 8 things

Count out 8 things and then it will match the number 8

Count out 8 objects. Demonstrate placing the objects in a 5-group formation. Although it is not expected that students organize their objects in 5-groups, using this configuration encourages students to look for 5 to help them count.

Count Out a Group to Match

Distribute a set of 10 objects in a bag and Match cards 5–10 to each student or student pair. Invite students to stack their Match cards number side up. Have students pull a card and count out a group of objects to match the number on the card. When finished, students can verify their count with a partner and then place the objects back into the bag and choose a new card.

Circulate as students count. Ask the following questions to assess and advance student thinking:

• Does the number of objects in the group match the number on the card? How do you know?

• How did you know when to stop counting?

• Let’s put your objects in a 5-group. Does the number of objects still match the number on the card?

Observational Assessment

; Can students count out a given number from a larger group? (PK.CC.DP7)

Differentiation: Support

If students need support with counting out a group of objects to match a written number, provide a number path to 10. Students can place 1 object in each box to verify they have counted out a group of objects that matches the number.

Differentiation: Challenge

For students who can already count out a group of 10 objects, consider providing bags of up to 12 objects. Write numbers 11 and 12 on index cards and invite students to count out a group of objects to match each number. When students are able to count out a group of up to 12 objects, increase the count to 15 objects and then to 20 objects.

2 3 4 5

Make It Match

Count out a group of objects to match a written number and record.

Making Groups of Friends

Use chalk of different colors to draw circles, or lay out several exercise hoops. Label the circles by placing a Numeral Dot card, number side up, in each circle. Gather students around the circles so that they can see the numbers.

The number on the card tells how many friends should stand in each circle. Each circle of friends is a group.

As students work together to form groups, consider using the following questions to help students solve how to make groups that match each number:

• What number is on the card?

• Count how many friends are in the group. Are there enough? Are there too many?

• How can we make the group and the number match? Do we need more friends or less friends?

Pause before all groups are established. Select a group that needs more students.

Does the number on the card match the number of friends in this group? How do you know?

No, the number is 4. I only see 2 friends.

Materials

Teacher

• Numeral Dot cards

• Chalk or exercise hoops

Students

• White paper

• Numeral Dot cards

Language Support

Consider providing students with the following language to support their problem solving while they are forming groups:

• We have enough friends. Please join another group.

• We need more friends. Please join our group.

They don’t match. We need more friends.

How can we make the group of friends match the number on the card?

We can ask more friends to join the group. Frankie and Mateo need a group!

Consider repeating the process to check a group that has too many students. Allow time for students to finish making groups. Count the number of students in each group to confirm that the number of students matches the number on the card.

Drawing Groups of Friends

Provide each student with the Numeral Dot card that matches the number of students in their group. Then gather students in a central location.

We are going to draw a picture to help us remember how many friends were in each group. What can you draw to show how many friends were in your group?

I can draw people.

I can make dots or circles.

Demonstrate recording a group by using students’ suggestions.

Distribute paper and invite each student to record how many friends were in their group.

Circulate while students record to ensure the number of friends in the group matches the number on their card. Invite a student to share their drawing.

Let’s count how many friends were in Niko’s group.

After students count, have the student reveal the number on their Numeral Dot card.

Does the drawing match the number? How do you know?

Yes, we counted 6 friends. I see the number 6 on the card.

Repeat as time allows.

Collect students’ drawings to review as a formative assessment after the lesson.

Dinosaur World

Count out groups to model add to with result unknown math stories.

LEARN 20

Build excitement by asking students to whisper something they know about dinosaurs. Use the Prehistoric Scene interactive to model the following story.

1 dinosaur was splashing in a pond. 2 more dinosaurs came to splash in the pond. Retell the story, one sentence at a time, and ask students to help model the story with the interactive. Then distribute the Prehistoric Scene removable and Unifix Cubes to each student. Retell the math story, pausing after each sentence to let students count out and move their cubes.

Let’s pretend our cubes are dinosaurs and show what happened.

1 dinosaur was splashing in a pond. Show that with your cubes.

2 more dinosaurs came to splash. Show that with your cubes.

How many dinosaurs are splashing in the pond? 3

That’s right. 1 dinosaur and 2 dinosaurs make 3 dinosaurs. 1 and 2 make 3. Incorporate movement before going on to the next section. Encourage students to pretend to be dinosaurs by directing them to do the following:

• Stomp your big dinosaur feet 8 times.

• Stretch your neck to reach the leaves at the tops of trees. Make yourself a tall dinosaur!

• Chomp your sharp dinosaur teeth 6 times.

Materials

Teacher

• None Students

• Prehistoric Scene (in the student book)

• Unifix® Cubes (10–15)

Promoting the Standards for Mathematical Practice

As students use cubes to show the dinosaur story problems, they reason abstractly and quantitatively (MP2).

At the heart of this mathematical practice is the act of contextualizing and decontextualizing. Students contextualize by looking at their cubes and explaining what they represent in the story. Students decontextualize by using objects, drawings, or symbols to represent the dinosaurs in the story and by using the representation to solve the problem.

Model Addition Stories

Invite students to listen to another story.

3 dinosaurs were stomping through the forest. 1 more dinosaur came to stomp.

What happened first? Show that with your cubes.

Observe as students count out their cubes. Repeat the story as needed.

What happened next? Show what happened with your cubes.

How many dinosaurs were there altogether? 4

Restate the total with a number sentence.

3 dinosaurs and 1 dinosaur make 4 dinosaurs. 3 and 1 make 4.

Invite students to share their recording with a neighbor. Then model the problem with a drawing.

How many dinosaurs were stomping through the forest at first? 3

I can draw 3 circles to show the 3 dinosaurs.

Draw 3 circles and label them with the number 3.

Then how many dinosaurs came to stomp? 1

Draw 1 circle and label it with the number 1.

How many dinosaurs were stomping altogether? 4

Circle the two groups and label the circle with the number 4.

3 dinosaurs and 1 dinosaur make 4 dinosaurs. 3 and 1 make 4.

What happens to a group when some more join?

There are more dinosaurs. The group gets bigger.

Observational Assessment

; Are students able to count out a given number to model the story? (PK.CC.DP7)

Teacher Note

The interactive, Math Stories Prehistoric Scene, can be used to give students practice acting out math stories.

Consider allowing students to explore with the tool in small groups, or demonstrate the activity for the whole class.

Culminating Activity

Sort objects into groups and label them with written numbers. LAND

Materials

Teacher

• Numeral Dot cards

Before the lesson, invite students to bring a leaf, a shell, or some other natural item to class. Consider items that students engage with on a regular basis.

Notice and Wonder

Gather students and place the items students brought in a central location.

What do you notice about our collection?

Some of the leaves are brown.

Those look like plates. (Gestures to the round leaves.)

How can we sort these, or make groups?

We can make a group that has brown and a group that doesn’t have brown. The plate ones can be a group.

Encourage students to test ideas by creating different groups. If an idea or a grouping does not work, foster productive struggle by asking, “What else can we try?”

I wonder how many are in each group. How can we find out?

(Starts.) 1, 2, 3, 4, … Count!

Move the items into a line as you count. Ask students to say how many at the end of each count. Restate the total and gesture to the entire group.

Students

• Natural item

• Sorting bag (1 per student pair)

• Numeral Dot cards (2 sets per student pair)

Teacher Note

If needed, invite students to create extra Numeral Dot cards by using small sheets of paper. Creating cards provides an opportunity for interested students to practice writing numbers. The Number Rhymes resource provides suggested language to help students remember how to form numbers.

This group has 2 leaves that look like plates. (Gesture to the group of 2 leaves.)

Invite a student to label the group with a Numeral Dot card. Continue with the remaining groups.

Sort and Count

Distribute sorting bags and Numeral Dot cards to student pairs. Give students time to consider differences among the objects and to choose a way to sort. Ask them to label each group with a number.

Circulate and ask partners to answer the following questions about their groups:

What is the same about everything in this group?

Which number matches this group?

How many are in that group? How do you know?

I counted 1, 2, 3, 4, 5.

I can just see.

Ask student pairs to stand when they are finished. Student pairs who finish early can represent their sort on paper or think of another way to sort their objects.

Observational Assessment

; Are students able to sort objects into self-selected categories? (PK.MD.DP1)

; Are they able to accurately count and match a written number to a group? (PK.CC.DP3), (PK.CC.DP6)

Promoting the Standards for Mathematical Practice

When students sort the objects they brought for the lesson, they make sense of problems and persevere in solving them (MP1)

Because the collection of objects is student-made, it might be more difficult to find categories that can be used to sort. Support students in persevering through this challenge by testing ideas, and encourage them to try something else if one idea does not work.

Observational Assessment Recording Sheet

PK Module 1

Sorting and Counting

Developmental Progressions Developmental Progressions

PK.CC.DP1 Count forward to 20 and backward from 5.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

PK.CC.DP3 Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

PK.MD.DP1 Sort objects into categories.

Notes

Student Name

Dates and Details of Observations

PP Partially Proficient P Proficient HP Highly Proficient

Developmental Progressions by Lesson

Module Assessment

PK Module 1

Sorting and Counting

Use the suggested language or support students in their native language to assess students’ understanding of math content. If a student is unable to answer the first few questions, end the assessment and retry after more instruction.

Materials

• Bag of 20 teddy bear counters (various colors and sizes)

• Pennies picture (provided removable)

• Frog picture (provided removable)

• Eureka Math2 Numeral Dot cards (0–10)

Assessment Questions

1. Show the picture of the pennies.

Count the pennies. (PK.CC.DP1, PK.CC.DP4)

How many pennies are there? (PK.CC.DP5, PK.CC.DP6)

2. Show the picture of the frogs.

Count the frogs. (PK.CC.DP1, PK.CC.DP4)

How many frogs are there? (PK.CC.DP5, PK.CC.DP6)

3. Place 4 teddy bear counters in your hand. Open and close the hand quickly.

How many bears are there? (PK.CC.DP2)

Teacher note: If the student is unable to answer without counting, try again with fewer bears.

4. Place the bag of teddy bear counters and the 6 card in front of the student. Point to the number 6.

What number is this?

Teacher note: If the student does not recognize the number, say, “This is 6.”

Count out 6 bears. (PK.CC.DP7)

How many bears are there? (PK.CC.DP5)

5. Place the teddy bear counters in a pile in front of the student.

How can we sort these bears? (PK.MD.DP1)

Teacher note: If needed, prompt the student to sort by color.

Sort these bears.

Point to a group the student made.

How many bears are in this group? (PK.CC.DP1, PK.CC.DP4, PK.CC.DP5, PK.CC.DP6)

Lay out the number cards in order from 0 to 10. Point to the group again.

Which number shows how many bears are in this group? (PK.CC.DP3)

Standards

Standards for Mathematical Practice

MP1 Make sense of problems and persevere in solving them.

MP2 Reason abstractly and quantitatively.

MP3 Construct viable arguments and critique the reasoning of others.

MP4 Model with mathematics.

MP5 Use appropriate tools strategically.

MP6 Attend to precision.

MP7 Look for and make use of structure.

MP8 Look for and express regularity in repeated reasoning.

Developmental Progressions

Identifying a student’s current stage of development supports teachers and families in building on what students know. Each stage is aligned to research on young children’s development and provides a path to the kindergarten standards. The highlighted stage indicates the expectation for most students after they complete the prekindergarten curriculum.

PK.CC.DP1 Count forward to 20 and backward from 5.

3 Years

Count forward to 5.

3 to 4 Years

4 to 5 Years

5 to 6 Years

PK Modules 1 and 3

• Consistently say numbers in correct sequence without skipping or repeating numbers.

• If verbal counting is not possible, use other methods, such as touching a number card, to demonstrate knowledge of number sequence.

Count forward to 10.

• Demonstrate previous indicator and extend forward count to 10.

PK Modules 3–5

Count forward to 20.

• Demonstrate previous indicators and extend forward count to 20.

Count backward from 5.

• Consistently say numbers in reverse sequence without skipping or repeating numbers.

K Modules 5 and 6

Count to 100 by ones and tens.

• Demonstrate previous indicators and extend forward count to 100.

• Count by tens to 100 without skipping or repeating numbers.

Count forward from a number other than 1.

• Count forward by ones from any number 2 to 100.

PK.CC.DP2 Identify, without counting, the number of objects in a group of up to 5 objects (i.e., subitize).

3 Years

3 to 4 Years

4 Years 5 to 6 Years

PK Module 1

Identify, without counting, the number of objects in a group of up to 3 objects (perceptual subitizing to 3).

• Name groups of 1, 2, and 3 objects with increasing accuracy.

For example, a student looks briefly at a picture with 3 dogs and says “three” or shows 3 fingers.

Identify, without counting, the number of objects in a group of up to 5 objects (perceptual subitizing to 5).

• Demonstrate previous indicator and extend to groups of 4 or 5 objects.

For example, a student looks briefly at a picture with 4 dogs and says “four” or shows 4 fingers.

PK Module 3

Identify, without counting, the number of objects in a group of up to 5 objects by recognizing parts (conceptual subitizing to 5).

• Identify total by composing smaller quantities.

For example, a student looks briefly at a picture with 5 dogs and says, “3 brown dogs and 2 white dogs. 5 dogs!”

Identify, without counting, the number of objects in a group of up to 10 objects by recognizing parts (conceptual subitizing to 10).*

• Identify total by composing smaller quantities.

For example, a student looks briefly at a picture with 8 dogs and says, “5 dogs in the top row and 3 more dogs below. 8 dogs!”

* This Achievement Descriptor is not assessed in the Eureka Math2  TM Kindergarten Curriculum.

PK.CC.DP3

3 to 4 Years 4 Years 5 to 6 Years

Recognize and name some written numbers.

• Name numbers when presented with a written number from 0 to 10.

Represent a group of objects with a written number 0–5.

• Match written numbers 0–5 to their corresponding sets of objects.

• Write numbers 0–5 with variability in size, control, spacing, and orientation.

Represent a group of objects with a written number 6–10.

• Demonstrate previous indicators and extend group size to 10 objects.

• Demonstrate previous indicators and extend number writing to represent a group of 10 objects.

PK.CC.DP4 Say one number name with each object when counting up to 10 objects.

Say one number name with each object when counting up to 5 objects.

• Count each object exactly once without skipping any object or assigning 2 objects the same number.

• Begin to use strategies to track the count such as touching, moving, or marking objects.

Say one number name with each object when counting up to 10 objects.

• Demonstrate previous indicator and extend group size to 10 objects.

Say one number name with each object when counting more than 10 objects.

• Demonstrate previous indicators and extend group size beyond 10 objects.

Represent a group of objects with a written number 0–20.

• Demonstrate previous indicators and extend group size to 20 objects.

Write numbers 0–20.

• Write numbers 0–20 with greater consistency in size, control, spacing, and orientation.

Organize objects to count more efficiently.

• Demonstrate previous indicators and begin to use organizing strategies when counting a larger collection.

• May create groups of 2, 5, or 10 objects and skip-count.

Represent a group of objects with a written number 0–10 (with 0 representing a group with no objects).

PK.CC.DP5 Use the last number of a count to tell how many, regardless of arrangement or order counted.

3 Years

PK Module 1

Inconsistently use the last number of a count to tell how many.

• Inconsistently repeat final number when asked a how many question.

• Recount if the order or arrangement changes.

4 Years

PK Modules 1–5

K Module 1

Use the last number of a count to tell how many regardless of arrangement or order counted.

• Consistently repeat final number when asked a how many question.

• Verbally refer to or gesture to the entire group of objects and not to the last item counted when asked to identify objects in a previous count. For example, “Where are the 5 objects?”

5 to 6 Years

K Modules 1–6

Say how many without recounting when objects are rearranged.

• Consistently use the final number of a previous count to tell how many when objects are rearranged.

PK.CC.DP6 Count to answer how many questions about as many as 10 objects arranged in a line, a rectangular array, a circle, or a scattered configuration.

4 Years 5 to 6 Years

PK Modules 1 and 3

K Module 1

Count to answer how many questions about as many as 5 objects arranged in a line.

• When shown a picture of 5 flowers in a line, count and answer 5 when asked a how many question.

Count to answer how many questions about as many as 10 objects arranged in a line or a rectangular array.

• Demonstrate previous indicator and extend count to 10 objects in a line or a rectangular array.

Count to answer how many questions about as many as 10 objects arranged in a circle or a scattered configuration.

• Demonstrate previous indicators and extend count to 10 objects in a circle or a scattered configuration.

K Module 6

Count to answer how many questions about as many as 20 objects arranged in a line, a rectangular array, or a circle configuration.

• Demonstrate previous indicators and extend count to 20 objects in organized configurations.

PK.CC.DP7 Count out a given number of 1–10 objects from a larger group.

4 Years

5 to 6 Years

PK Modules 1, 3, and 5 K Module 6

Count out a given number of 1–5 objects from a larger group.

• Accurately count out a given number of objects.

Count out a given number of 6–10 objects from a larger group.

• Demonstrate previous indicator and extend count to 10 objects.

PK.MD.DP1 Sort objects into categories.

Identify attributes of an object, such as color or shape.

• Point to the corresponding objects when given an attribute, such as pointing to the blue sock.

Identify whether objects are the same or different.

• Match objects that have a common attribute.

Sort objects into given categories.

• Begin to sort objects into given groups but then change the attribute during the sort.

For example, a student begins to sort bears by size and then changes to sort by color.

Count out a given number of 10–20 objects from a larger group.

• Demonstrate previous indicators and extend count beyond 10 objects.

Sort objects into categories.

• Consistently sort objects into given groups, such as grouping socks by color.

• May sort objects into self-selected categories.

Count the number of objects in each category of a sort and order the groups by count.

• Demonstrate previous indicators and order the groups based on the number of objects in each group.

• May compare groups based on the number of objects in each group.

Terminology

The following terms are critical to the work of prekindergarten module 1. This resource groups terms into categories called New and Academic Verbs. The lessons in this module incorporate terminology with the expectation that students work toward applying it during discussions.

Items in the New category are discipline-specific words that are introduced to students in this module. These items include the definition, description, or illustration as it is presented to students. At times, this resource also includes italicized language for teachers that expands on the wording used with students.

Items in the Academic Verbs category are high-utility terms that are used across disciplines. These terms come from a list of academic verbs that the curriculum strategically introduces at this grade level.

New count

When we want to find out how many of something there are, we count. (Lesson 7)

enough

When there is enough of something, we don’t need any more. For example, if there is 1 cap for every marker, there are enough caps. (Lesson 6)

line

Objects organized straight across (or up and down) are in a line. (Lesson 7)

match

Things match when they go together. (Lesson 1)

number

We use numbers to show or say how many things there are. (Lesson 10)

number sentence

We can use a number sentence to tell how we put together a number, such as 5 is 3 and 2.

The term number sentence is also used to describe an equation that uses symbols, such as + and =. An example is 5 = 3 + 2. (Lesson 21)

sort

When we sort, we put things into groups. We can sort by color, size, or something else. (Lesson 4)

Academic Verbs notice wonder

Math Past

Decoding the Mathematics of Ancient Egypt

What is the Rosetta Stone?

How did ancient Egyptians write numbers?

What kind of mathematics did ancient Egyptians study?

Show students a picture of the Rosetta Stone, which served as the basis for the “artifact” students helped our archaeologist interpret in this module. Tell students that archaeologists were able to use the Rosetta Stone to learn how to read a language they weren’t familiar with. This is also a good time to celebrate any knowledge students have of different languages, including languages they speak at home with their families. Consider asking students whose families read and write in different languages to bring to class a sample of writing in a language other than English.

The Rosetta Stone dates to 196 BCE and was rediscovered accidentally by a French military officer in 1799 CE during Napoleon’s invasion of Egypt. As you can see in the picture, the stone is covered in text divided into three sections. The top two sections depict different systems of writing used by ancient Egyptians called hieroglyphic script and demotic script. The bottom section is written in ancient Greek.

At the time of the rediscovery of the Rosetta Stone, no one was able to read ancient Egyptian scripts. However, many people were

still able to read ancient Greek, and that section of the stone explicitly states that all three sections contain the same passage written in different scripts. Scholars used the section written in ancient Greek to translate the other two sections and decode the ancient Egyptian scripts.

In class, students studied an “artifact” modeled after the Rosetta Stone that shows the numbers 1 through 5 written in different ways. The top row shows written numbers, which students have been learning to use in class. The middle row shows the numbers represented by dots in the familiar arrangements found on dice. The bottom row needs to be decoded. It shows the numbers 1 through 5 written in an ancient Egyptian script known as hieratic. The picture below shows the hieratic numerals 1 to 9. Consider showing students this extended sequence so students can help decode more ancient numerals.

Egyptian Hieratic Numeral System

The hieratic script developed as a cursive form of the Egyptian hieroglyphic script, allowing ancient Egyptians to more easily use ink to write on papyrus (a paperlike substance) or other materials. Demotic script, which is found on the Rosetta Stone, evolved from hieratic. Because most administrative and accounting needs were documented with ink rather than carved into stone, hieratic and demotic numerals are commonly seen in ancient Egyptian mathematics.

Since the rediscovery of the Rosetta Stone, many different ancient Egyptian artifacts that detail the Egyptians’ understanding

of mathematics have been studied. These artifacts are usually written on papyrus or leather and show that ancient Egyptians had a deep understanding of concepts in algebra, fractions, and geometry. Evidence of their understanding of geometry is clear in the construction of the pyramids. Consider burying paper showing the segments of the stone used in class or other Egyptian glyphs in the sandbox or other play spaces for students to find.

One of the most famous examples of this kind of artifact is the Ahmes, or Rhind, papyrus. Ahmes is the scribe who copied the mathematical information from an older document onto the papyrus in 1650 BCE. Rhind is the Scottish collector who purchased the papyrus in 1858 CE. The Ahmes papyrus contains more than 80 problems, each presented with a solution. The recovered parts of the Ahmes papyrus create a continuous roll measuring 3.5 feet in width and 17 feet in length! Consider having students unroll three paper towel rolls until each has a strip that is 17 feet long.

Putting these together will approximate the size of the Ahmes papyrus. That’s a huge sheet of paper!

The writing on the Ahmes papyrus is in hieratic script, which was translated thanks to its relationship to hieroglyphic script, which was in turn decoded by using the Rosetta Stone.

Many artifacts show that mathematics was an important part of life in the ancient world. Although we know of even older artifacts showing humans’ understanding of mathematics, the papyruses of ancient Egypt are the earliest known examples of humans describing their mathematical understanding in a systematic, formal way. This allowed scholars to understand what the Egyptians were thinking with little guesswork required. Luckily for us, the Egyptians wrote the Rosetta Stone in many different languages so more people would be able to read it. Otherwise, we would not be aware of ancient Egyptians’ deep understanding of mathematics.

Materials

The following materials are needed to implement this module. The suggested quantities are based on a class of 20 students and 1 teacher. See Preparation in each Topic Overview for more information about specific materials used in each lesson.

1 20-bead demonstration rekenrek

1 A Pair of Socks by Stuart J. Murphy

2 Bags of rice

5 Baskets or containers

15 Bean bags

30 Bowls of healthy snacks

21 Counting collections

21 Crayon sets

5 Cups, clear

2 Dot dice, set of 8

21 Dry-erase markers

1 Eureka Math2TM Animal cards

1 Eureka Math2TM Forest Path Game boards, set of 12

1 Eureka Math2TM Match cards, set of 12

1 Eureka Math2TM Number Path cards

2 Eureka Math2TM Numeral Dot cards, set of 10

21 Eureka Math2TM PK Story cards

6 Exercise hoops

1 Farm animal counters, set of 504

1 Five Creatures by Emily Jenkins

2 Foam number dice, set of 6

23 Index cards

30 Markers

1 Numbers by Henry Pluckrose

1 Package of bowls

1 Package of fish crackers

1 Pair of number gloves, left and right

21 Pairs of plastic gloves

21 Personal whiteboards

21 Personal whiteboard erasers

1 Puppet or stuffed animal

1 Rock, large

1 Socks, 1 matching pair

21 Sorting bags

1 Spoon

100 Stickers, small

5 Sticky notes

2 Teddy bear counters, set of 96

1 Unifix® Cubes, set of 1,000

Visit http://eurmath.link/materials to learn more.

1 White paper, ream

21 Work mats

Self-Created Materials

To create number gloves, you will need a new pair of cleaning gloves and a permanent marker. Lay out the gloves with the palms facing up. Start with the right-hand glove and write numbers on the fingertips beginning with 1 on the pinkie finger. Continue across the fingers, ending with 5 on the thumb. Continue with the left-hand glove, beginning with 6 on the thumb and ending with 10 on the pinkie finger.

Sorting Bags

In module 1, students sort objects in a variety of ways and explore attributes such as number, size, shape, and color. They use sorting bags, or bags of strategically selected objects that can be classified by attribute. Use sorting bags to provide extra practice in stations, in small group instruction, or at other times throughout module 1.

Use the chart to create sorting bags that vary by attribute and complexity. Create one or more sorting bags for each attribute.

You do not need to create a class set for every bag type because students choose from the assortment of bags each day.

Students are not limited to one way of sorting items in a bag, even if the bag is designed with a specific attribute in mind. For example, students may sort a bag of buttons by color, shape, or size. They also may sort into unique categories based on their personal experience. Giving students the autonomy to sort as they choose allows them to explore categories and attributes independently.

Attributes

Difficulty Color Size Name or Type Shape Location Use or Activity

Complex Different objects with the same pattern

Different objects with contrasting dimensions (e.g., long, thin items; short, wide items; long, wide items; short, thin items)

Similar objects with different attributes (e.g., insects and spiders)

Different objects, two-dimensional and threedimensional shapes

Similar objects, 3 types of transportation (e.g., students who ride the bus, walk, or bike to school)

Objects with multiple uses, 3 uses (e.g., use to play, use to write, use to build)

Moderate Different objects, 3 colors

Easy Same objects, 2 colors

Different objects, 3 sizes (small, medium, and large)

Same objects, 2 sizes

Different objects, 3 types (e.g., fly, cat, and fish)

Different objects, 2 obvious types (e.g., fly and cat)

Different objects, 3 shapes

Different objects, 3 locations

Different objects, 3 uses

Same objects, 2 shapes (e.g., round button and square button)

Different objects, 2 obvious locations (e.g., apple in lunch box, car in toy box)

Different objects, 2 obvious uses (e.g., use to eat, use to write)

Easy • Large yellow bears, small yellow bears, large blue bears, small blue bears (size, color)

• Yellow banana, yellow school bus, yellow lemon, yellow marker, red apple, red fire truck, red marker, green lettuce, green car (color, type, use)

• Green apple, peas, watermelon, banana, yellow squash, corn, red apple, raspberry, cherry (color, shape, type, size)

Moderate • Small white rocks, small black rocks, medium black rocks, large gray rocks (size, color, shape)

• Small round brown buttons, large round brown buttons, medium round pink buttons, small heart-shaped pink buttons, large square blue buttons, small round green buttons (color, size, shape)

• Bird, insect, airplane, boat, duck, pool float (transportation, air or water; type, alive or not; use, fly or float)

Complex • Polka-dot shirt, polka-dot pants, polka-dot plate, striped jacket, striped cup, plaid socks, plaid napkin (color, use)

• Fish, fox, dolphin, dog, donkey, clam, cow, coyote, camel (name, first sound; location, water or land)

• Scissors, pencil, crayon, marker, eraser, toothbrush, comb, flip-flops, umbrella, bathing suit (use, location)

Counting Collections

Throughout the prekindergarten year, students will organize, count, and record collections of objects. Each class needs a variety of counting collections made of everyday materials. At the beginning of the year, collections of 4–20 objects are appropriate for most students. By the end of the year, prekindergarten students may be ready to count collections of 40 objects.

Does this sound like a lot of materials management? Establishing routines and an organization system for counting collections makes the process much more manageable, and the student learning will be worth it.

Creating and Organizing Collections

Counting collections can be assembled by using materials easily found in classrooms or homes. Buttons, beans, bottle caps, pompoms, erasers, craft sticks, crayons … almost anything can be part of a counting collection. Put each collection in a resealable bag or container.

objects are in each bag to help gauge student counting accuracy, especially with larger collections. Consider having a designated container for items that were missed during cleanup.

Routine Materials

Develop a set of materials that each pair of students will use routinely for counting collection lessons. Each student pair needs one counting collection and two sheets of paper, but providing a work mat and two clipboards will help prekindergarten students stay organized. A piece of 11" × 17" paper makes a good work mat. Counting collection lessons are a great opportunity for formative assessment, so consider having an observational checklist available.

Choice Materials and Organizing Tools

Students may choose to use organizing tools as they count and record. Cups, bowls, and number paths can support collection organization, counting, and recording. Teacher notes provide specific ideas for using organizing tools to support or challenge students. These types of materials should be displayed and made available for students to use as they wish.

Counting Collection Bins

4–10 objects

11–25 objects

26–40 objects

We suggest sorting and storing collections in color-coded bins based on the number of objects in the collection. Place a corresponding-colored sticker on each collection so students can easily return it to the proper bin. Begin the year with a written inventory of how many

Fluency Anytime

This resource compiles the fluency activities students learn throughout the module. Young children need frequent and consistent fluency experiences throughout the day. Create opportunities to repeat selected fluency activities during class transitions, such as when lining up or moving from the rug to tables.

5-Group Hands

Show students a Number Path card. Have students show the 5-group with their hands. How many squirrels?

Show me the 5-group on your hands.

Counting on the Rekenrek to 10

Slide the beads, one at a time, from behind the panel as students count. First, count to 10 by using only the beads in the top row. Count to 10 with 5 beads in the top row and 5 beads in the bottom row.

Say how many beads there are as I slide them over.

Counting the Math Way

Show fingers the math way as students watch and count out loud. Begin with counting to 3, then to 5, and finally to 10.

Watch my fingers and count out loud. Ready?

Counting on the Number Glove

Show fingers the math way while wearing the number glove as students watch and count out loud. Begin with counting to 3, then to 5, and finally to 10.

Watch my number glove and count out loud. Ready?

Counting on the Rekenrek to 10

Counting the Math Way

Counting on the Number Glove

5-Group Hands

Counting with Movement

Say or show a number and have students move in a specific way to match the number. Begin with numbers within 5 and build to numbers within 10.

Look at my number. Jump this many times and count your jumps.

Dot Card Flash

Briefly show students a 5-group card 1–5 (digital download). Have students say how many dots are on the card and then air write the number of dots.

Watch closely. How many dots do you see? (Flash the card.) Write the number in the air with your finger.

Finger Flash

Briefly show a number the math way. Have students say the number and then show the number with their fingers in any way.

Watch closely. How many fingers? Now show me the same number on your fingers.

“I Can Count” Song

Play the I Can Count video and sing along with students. Start with numbers 1 to 5 and build to numbers 1 to 10.

1 bluebird in a tree. 2 bees buzz over me. 3 flowers growing free. I can count! 1, 2, 3.

Counting with Movement

Two!

Dot Card Flash

Finger Flash

Seven!

Number Flash

Show students a number card. Have students say the number and then show the number with their fingers. Begin with numbers 1 to 5 and build to numbers to 10.

Look at my number. Show me this number on your fingers.

Show Me Another Way

Have students show a number from 1 to 5 the math way. Then have them show the same number another way.

Show me 3 the math way. Show me 3 another way.

Sunrise Counting

Have students rise gradually from a crouching position to standing on tiptoes as they count from 0 to 10.

Let’s count to 10 as we make the sun rise. Ready?

Number Flash

Show Me Another Way

Sunrise Counting

Number Rhymes

The following rhymes can help students remember how to write each number. Encourage students to place their pencils or crayons on the starting dot before saying the rhyme.

I start at the top, and around I go.

I come back up to make 0.

Top to bottom, and then I am done. I just wrote the number 1.

Half a moon, there’s more to do. Slide to the right. I wrote a 2.

To the right and around the tree.

Around again to make a 3.

A little line down, to the right some more.

Now a big line down to make a 4.

2 1

Down the side, around a hive.

Give it a hat.

I wrote a 5.

Down the side, and then a curl.

The 6 makes a little swirl.

Across the sky, then drop a line.

I make a 7 every time.

Make an S and do not stop.

I see an 8 when I close the top.

Draw a loop and drop a line.

That is the way I make a 9.

Works Cited

Carpenter, Thomas P., Megan L. Franke, and Linda Levi. Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School. Portsmouth, NH: Heinemann, 2003.

Carpenter, Thomas P., Megan L. Franke, Nicholas C. Johnson, Angela C. Turrou, and Anita A. Wager. Young Children’s Mathematics: Cognitively Guided Instruction in Early Childhood Education. Portsmouth, NH: Heinemann, 2017.

CAST. Universal Design for Learning Guidelines version 2.2. Retrieved from http://udlguidelines.cast.org, 2018.

Clements, Douglas H., and Julie Sarama. Learning and Teaching Early Math: The Learning Trajectories Approach. 2nd ed. New York: Routledge, 2014.

Common Core Standards Writing Team. Progressions for the Common Core State Standards in Mathematics. Tucson, AZ: Institute for Mathematics and Education, University of Arizona, 2011–2015. https://www.math.arizona .edu/~ime/progressions/.

Cooke, Roger. The History of Mathematics: A Brief Course. Hoboken, NJ: John Wiley & Sons, 2011.

Danielson, Christopher. How Many?: A Counting Book: Teacher’s Guide. Portland, ME: Stenhouse, 2018.

Danielson, Christopher. Which One Doesn’t Belong?: A Teacher’s Guide. Portland, ME: Stenhouse, 2016.

Erikson Institute. Early Math Collaborative—Transforming Mathematics in Early Childhood Education. Retrieved from https://www.erikson.edu/professional-development/early -math-collaborative, 2021.

Flynn, Mike. Beyond Answers: Exploring Mathematical Practices with Young Children. Portland, ME: Stenhouse, 2017.

Fosnot, Catherine Twomey, and Maarten Dolk. Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction. Portsmouth, NH: Heinemann, 2001.

Franke, Megan L., Elham Kazemi, and Angela Chan Turrou (Ed.). Choral Counting and Counting Collections: Transforming the PreK–5 Math Classroom. Portsmouth, NH: Stenhouse, 2018.

Fuson, Karen. Focus in Kindergarten: Teaching with Curriculum Focal Points. Reston, VA: National Council of Teachers of Mathematics, 2010.

Hattie, John, Douglas Fisher, and Nancy Frey. Visible Learning for Mathematics, Grades K–12: What Works Best to Optimize Student Learning. Thousand Oaks, CA: Corwin Mathematics, 2017.

Huinker, DeAnn, and Victoria Bill. Taking Action: Implementing Effective Mathematics Teaching Practices. Kindergarten–Grade 5, edited by Margaret Smith. Reston, VA: National Council of Teachers of Mathematics, 2017.

Kelemanik, Grace, Amy Lucenta, Susan Janssen Creighton, and Magdalene Lampert. Routines for Reasoning: Fostering the Mathematical Practices in All Students. Portsmouth, NH: Heinemann, 2016.

Ma, Liping. Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. New York: Routledge, 2010.

National Association for the Education of Young Children and National Council of Teachers of Mathematics. Early Childhood Mathematics: Promoting Good Beginnings. Washington, DC: National Association for the Education of Young Children, 2002.

National Council of Teachers of Mathematics. Catalyzing Change in Early Childhood and Elementary Mathematics: Initiating Critical Conversations. Reston, VA: National Council of Teachers of Mathematics, 2020.

National Governors Association Center for Best Practices, Council of Chief State School Officers (NGA Center and CCSSO). Common Core State Standards for Mathematics.

Washington, DC: National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010.

National Research Council. Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press, 2001.

National Research Council. Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Washington, DC: The National Academies Press, 2009.

Otto, Albert Dean, and National Council of Teachers of Mathematics. Developing an Essential Understanding of Multiplication and Division for Teaching Mathematics in Grades 3–5. Reston, VA: National Council of Teachers of Mathematics, 2011.

Parker, Thomas, and Scott Baldridge. Elementary Mathematics for Teachers. Okemos, MI: Sefton-Ash, 2004.

Smith, Margaret S., and Mary K. Stein. 5 Practices for Orchestrating Productive Mathematics Discussions, 2nd ed. Reston, VA: National Council of Teachers of Mathematics, 2018.

Smith, Margaret S., Victoria Bill, and Miriam Gamoran Sherin. The 5 Practices in Practice: Successfully Orchestrating Mathematics Discussions in Your Elementary Classroom. Thousand Oaks, CA: Corwin Mathematics; Reston, VA: National Council of Teachers of Mathematics, 2020.

Stanford University. Development and Research in Early Math Education. Retrieved from https://dreme.stanford .edu, 2021.

Suzuki, Jeff. Mathematics in Historical Context. Washington, DC: Mathematical Association of America, 2009.

Van de Walle, John A. Elementary and Middle School Mathematics: Teaching Developmentally. New York: Pearson, 2004.

Zwiers, Jeff, Jack Dieckmann, Sara Rutherford-Quach, Vinci Daro, Renae Skarin, Steven Weiss, and James Malamut. Principles for the Design of Mathematics Curricula: Promoting Language and Content Development. Retrieved from Stanford University, UL/SCALE website: https:// ul.stanford.edu/resource/principles-design-mathematicscurricula, 2017.

Credits

Great Minds® has made every effort to obtain permission for the reprinting of all copyrighted material. If any owner of copyrighted material is not acknowledged herein, please contact Great Minds for proper acknowledgment in all future editions and reprints of this module.

Common Core State Standards for Mathematics © Copyright 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

All United States currency images Courtesy the United States Mint and the National Numismatic Collection, National Museum of American History.

For a complete list of credits, visit http://eurmath.link/media-credits.

Page 7, LightField Studios/Shutterstock.com; page 8, Denis Kuvaev/Shutterstock.com; page 18, cover of A Pair of Socks by Stuart J. Murphy, courtesy; HarperCollins; page 18, aslysun/

ShutterStock.com; page 22, Asier Romero/ShutterStock.com; pages 46, 54, cover of Numbers by Henry Pluckrose. Copyright © 2018 by Watts Publishing Group. Used by permission of Children’s Press, an imprint of Scholastic Inc.; pages 62, 64, Bratislav Stefanovic/Alamy Stock Photo; pages 62, 64, Peter Horree/Alamy Stock Photo; pages 84, 90, cover of Five Creatures by Emily Jenkins, courtesy of Square Fish; page 91, Pensee Sauvage/Shutterstock.com; pages 94, 95, ShutterStock.com; pages 98, 99, Lubava/Shutterstock.com; page 152, Peter Horree/ Alamy Stock Photo; page 152, Sidhe/ShutterStock.com; page 153, WitR/Shutterstock.com; page 153, Rhind Mathematical Papyrus: detail (recto, left part of the first section) Thebes, End of the Second Intermediate Period (c.1550 BC). Courtesy British Museum Department of Ancient Egypt and Sudan. Photo credit: The Picture Art Collection / Alamy Stock Photo.

All other images are the property of Great Minds.

Acknowledgments

Beth Barnes, Melissa Benner, Lauren Brown, Dawn Burns, Mary Christensen-Cooper, Dr. Hazel Coltharp, Katie Cummings, Cheri DeBusk, Stephanie DeGiulio, Jill Diniz, Melissa Elias, Lacy Endo-Peery, Kimberly Hager, Brittney Hawkins, Kelly Kagamas Tomkies, Kate McGill Austin, Shelley Petre, John Reynolds, Lori Sponenburgh, Janel Verrilli, Philippa Walker, Lisa Watts Lawton, MaryJo Wieland

Ana Alvarez, Lynne Askin-Roush, Trevor Barnes, Brianna Bemel, Carolyn Buck, Lisa Buckley, Adam Cardais, Christina Cooper, Kim Cotter, Lisa Crowe, Jessica Dahl, Brandon Dawley, Cherry dela Victoria, Delsena Draper, Sandy Engelman, Tamara Estrada, Ubaldo Feliciano-Hernández, Soudea Forbes,

Jen Forbus, Liz Gabbard, Diana Ghazzawi, Lisa Giddens-White, Laurie Gonsoulin, Adam Green, Dennis Hamel, Cassie Hart, Sagal Hassan, Kristen Hayes, Marcela Hernandez, Abbi Hoerst, Libby Howard, Elizabeth Jacobsen, Ashley Kelley, Lisa King, Sarah Kopec, Drew Krepp, Cindy Medici, Ivonne Mercado, Sandra Mercado, Brian Methe, Patricia Mickelberry, Mary-Lise Nazaire, Corinne Newbegin, Tara O’Hare, Max Oosterbaan, Tamara Otto, Christine Palmtag, Laura Parker, Katie Prince, Gilbert Rodriguez, Todd Rogers, Karen Rollhauser, Neela Roy, Gina Schenck, Amy Schoon, Aaron Shields, Leigh Sterten, Mary Sudul, Lisa Sweeney, Tracy Vigliotti, Dave White, Charmaine Whitman, Glenda Wisenburn-Burke, Howard Yaffe

Exponentially Better

Knowledge2 In our tradition of supporting teachers with everything they need to build student knowledge of mathematics deeply and coherently, Eureka Math2 provides tailored collections of videos and recommendations to serve new and experienced teachers alike.

Digital2 With a seamlessly integrated digital experience, Eureka Math2 includes hundreds of clever illustrations, compelling videos, and digital interactives to spark discourse and wonder in your classroom.

Accessible2 Created with all readers in mind, Eureka Math2 has been carefully designed to ensure struggling readers can access lessons, word problems, and more.

Joy2 Together with your students, you will fall in love with math all over again—or for the first time—with Eureka Math2.

What does this painting have to do with math?

The American artist Jacob Lawrence is known for his portrayals of everyday African American life. His Migration Series is painted in a modernist style, contrasting vivid colors with shades of brown and black. Lawrence’s work shows the discrimination African Americans faced and the opportunities they found, such as the educational opportunities depicted in panel 58. What are the students writing? Why are they writing numbers?

On the cover

Panel 58 from The Migration Series, 1940–1941

Jacob Lawrence, American, 1917–2000

Casein tempera on hardboard

The Museum of Modern Art, New York, NY, USA

Module 1

Sorting and Counting

Module 2

Shapes

Module 3

Parts and Patterns

Module 4

Ways to Compare

Module 5

Math Stories

Module 6

Math in Play

ISBN 978-1-63898-843-4

Jacob Lawrence (1917–2000), In the North the Negro had better educational facilities, 1940–1941. Panel 58 from The Migration Series. Casein tempera on hardboard, 12 x 18 in (30.5 x 45.7 cm). Gift of Mrs. David M. Levy. The Museum of Modern Art, New York, NY, USA. © 2020 The Jacob and Gwendolyn Knight Lawrence Foundation, Seattle/Artists Rights Society (ARS), New York. Digital image © The Museum of Modern Art/Licensed by SCALA/Art Resource, NY