Eureka Math Squared IG- Level PK-(A print 05.23)

IMPLEMENTATION GUIDE

Welcome to Eureka Math2

I’m thrilled to find you here on the page, a tried-and-true medium for the sharing of ideas among trusted colleagues. The writing of our second generation of math curriculum was truly a labor of love. And we’ve been eagerly awaiting the chance to invite you in!

We hope you find yourself surprised and delighted by the intention and craft of Eureka Math2® and that it meets your highest expectations for teaching and learning. If you’ve been a part of our Eureka Math® community, we hope you hear your voice in Eureka Math2—that you see your suggestions coming to life in every margin note, feature, and design choice.

Here are just a few of the features I’m sure you’ll want to explore as you get to know Eureka Math2:

Readability. Words should not stand in the way of learning math— or learning anything for that matter! In Eureka Math2 we designed the written materials with active consideration for the perspective of students who need support with reading, especially those with dyslexia. We’ve reduced wordiness—eliminating unnecessary wording entirely—and we’ve been intentional in our language choices and sentence length.

Accessibility. In Eureka Math2 we’ve put into practice the latest research on supporting multilingual learners, leveraging Universal Design for Learning principles, and promoting social-emotional learning. The instructional design, instructional routines, and lesson-specific strategies support teachers as they address learner variance and support students with understanding, speaking, and writing English in mathematical contexts.

Some of the most delightful examples of our efforts in accessibility are our wordless context videos. These videos, appearing about once per topic, provide access to a mathematical context that students use for their own mathematical wonderings, generating student discourse as they craft their own word problems and answer their own questions.

Teachability. We’ve streamlined the design and content of our teacher resources to ensure that teachers have exactly what they need, right when they need it. Teachers spend their time engaged in the most valuable work possible—delivering high-quality instruction that meets the needs of their specific students. From differentiation suggestions to slide decks, from digital interactives to multiple forms of assessment, Eureka Math2 is the most teachable high-quality curriculum available.

In summary, I hope you find Eureka Math2 as genuinely revolutionary as I do. May it serve as a cherished and supportive companion as you refine your craft of teaching in the ever-vital quest to achieve the vision we know is true: Every child is capable of greatness.

Jill Diniz Chief Product Officer

Eureka Math2 is a comprehensive math program built on the foundational idea that math is best understood as an unfolding story where students learn by connecting new learning to prior knowledge. Consistent math models, content that engages students in productive struggle, and coherence across lessons, modules, and grades provide entry points for all learners to access grade-level mathematics.

Eureka Math2 is designed with access and engagement in mind. Peer discussion helps students solidify their understanding of math concepts, so every lesson includes opportunities for rich student discourse. The Eureka Math2 digital experience further supports discourse, giving all students opportunities to access learning and share their mathematical thinking while also providing teachers with windows into students’ thinking. Eureka Math2 encourages students to think like mathematicians as they tackle tough problems and answer their own questions. In Eureka Math2 classrooms, students regularly share their mathematical knowledge through discussion and reasoning.

In addition, lessons follow Universal Design for Learning principles to accommodate various learning differences and increase access for multilingual learners and emergent readers. We’ve also increased our focus on student ownership of learning and belonging in the mathematics classroom. These elements are woven into our instructional design and instructional routines, and lesson-specific strategies help teachers address learner variance.

Eureka Math2 was also designed with teachability in mind. Every classroom is unique, and we’ve designed the curriculum with that understanding. For example, we’ve intentionally built flexibility into the year-long pacing and created options for you to choose from within modules and lessons. This way you can spend your time where it’s needed most—delivering instruction that meets the needs of your specific students.

So what should you expect from this guide? Think of it as a user’s manual for the curriculum. This guide orients you to the structure and design of Eureka Math2, and to what is available in the digital experience and in print. You’ll find answers to questions both big and small:

• How does Eureka Math2 enrich my content and pedagogical knowledge?

• What is the lesson structure?

• What is included in my Teach book? What about the digital platform?

• How do students engage with the digital platform?

• What is included in the Learn book?

• What assessments are available?

We are so excited to launch this curriculum together with you. We hope this Implementation Guide is an empowering resource as you begin to teach Eureka Math2. At Great Minds® we believe that every child is capable of greatness. We are confident that, as your students notice and wonder, as you foster their interest in the mathematics, and as their minds are opened to new connections, greatness will be brought to life in your classroom each day.

Inside Teach

Each of your six Teach books includes one module. Within a module, small groups of related lessons are organized into topics.

Module-Level Components

Cover Art

Each Teach book opens with a stunning work of fine art that has a connection to the math learned within the module. The cover art is discussed or analyzed in specific lessons within the module.

Overview

Your Teach book begins with the Overview, a topic-by-topic summary that shows the development of learning throughout the module. It also provides connections to work done before and after the module, helping you understand the module’s place in the overall development of learning in and across the grade levels.

Overview

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

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.

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

Topic D

Match Written Numbers with Sets of Up to 5 Objects

Count Out a Set 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.

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

© Great Minds PBC

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

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.

Before This Module and After This Module look back and forward to reveal coherence across modules and grade levels.

The Overview describes, topic by topic, the story of learning in the module.

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.

5

Ladybug Zebra

Tiger

Fish Owl

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

The Why section gives insight into the decisions made during the writing of the module. This insight helps you understand the underlying structure of the module, flow of the content, and coherence of the different parts of the curriculum.

Lesson objectives reveal the story of each topic at a glance.

Developmental Progressions: Overview

The Developmental Progressions: Overview section is a helpful guide that describes what Developmental Progressions (DPs) are and briefly explains how to use them. The section also identifies specific DPs for the module. More guidance is provided in the Developmental Progression resource at the end of each Teach book.

Topic-Level Components

Progression of Lessons

The Progression of Lessons lists each lesson in the topic along with sample content and a student-friendly statement about each lesson’s major learning. In prekindergarten, each topic contains

• one Launch lesson to engage students and to set the purpose for learning,

• several Learn lessons in which new mathematical content is presented and explored, and

• one Land lesson to help students solidify and articulate their learning.

Use Attributes to Match and Sort

Key Questions help focus your instruction and classroom discourse. They encapsulate the key learning of the topic and may help develop coherence and connections to other concepts. Students discuss these questions to synthesize learning during the Land lesson.

Developmental Progressions (DPs) are standards-aligned descriptions that detail what students should know and be able to do based on instruction. The number of DPs addressed in each lesson varies, depending on the content.

Topic Overview

The Topic Overview is a summary of the development of learning in that topic. It typically includes information about how that topic’s learning connects to previous or upcoming content.

Terminology

Terminology is a list of mathematical terms and academic verbs introduced in the topic.

Fluency Anytime

Fluency Anytime is a list of activities intended to build students’ fluency with mathematical skills such as counting. The fluency activities are simple, require few materials, and may be completed at any time of day.

Math Anytime

Math Anytime contains suggestions for infusing math into the classroom learning environment and students’ daily routines. Ultimately, the goal is for students to see that math is all around them and that it is an integral part of their lives.

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.

At 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.

Observational Assessment

The Observational Assessment Recording Sheet indicates which Developmental Progressions you are likely to observe during that topic. When applicable, a note in the lesson’s margin indicates when there is likely to be an opportunity to observe performance related to the DPs.

Topic Preparation

At the end of the Topic Overview, you will find a page of information to help you prepare to teach the lessons within that topic.

Agenda

Lesson 1 25 min

Make a Match

Materials

Teacher

• A Pair of Socks by Stuart J. Murphy

• Matching pair of socks

Students

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

Preparation

• 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

Lesson 3 20 min

Teacher

• None Students

Crayon Group Teacher

• Empty crayon box

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

• None

Students

• None

• 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)

The Agenda shows the sequence and recommended time length of each lesson.

Materials lists the items that you and your students need for the lessons. If not otherwise indicated, each student needs one of each listed material.

• 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.

advance of the lesson.

Lesson Preparation provides guidance about materials that need to be created, assembled, or placed in

Lesson Structure

For grades K–5, each lesson is structured into four sections: Fluency, Launch, Learn, and Land. In prekindergarten, each topic uses this different structure: Each topic consists of one Launch lesson, several Learn lessons, and one Land lesson. Fluency activities can be incorporated into lessons and at other times of the day.

This structure reflects established research in child development and accommodates the unique needs of young learners, including the specific need for shorter periods of focused attention. The distribution of Launch, Learn, and Land across a topic helps keep lesson durations to 10–25 minutes. Lessons are thoughtfully crafted to incorporate physical activity, playful learning experiences, and authentic, active engagement with mathematical content. The structure provides a flexible learning experience for prekindergarten students that sparks joy, builds conceptual understanding, and fosters language development.

Launch

The Launch lesson creates an accessible entry point to the topic’s learning by introducing meaningful contexts. These lessons provide teachers with opportunities to learn students’ background knowledge and existing understanding of the mathematical concepts and language critical to the topic.

Learn

Learn lessons present new learning related to the lesson objectives. Suggested facilitation styles vary and may include direct instruction, guided instruction, partner activities, interactive videos, and digital elements. Students practice new concepts through guided play, games, and hands-on activities.

Land

The Land lesson helps students synthesize the topic’s learning. Students show their understanding by modeling math concepts and discussing the Key Questions.

Fluency

Fluency provides distributed practice with previously learned material. It is designed to prepare students for new learning by activating prior knowledge and bridging small learning gaps. Fluency activities may be incorporated into lessons. Fluency Anytime activities are also provided for each topic.

Margin Notes

There are six types of instructional guidance that appear as notes in the margins. These notes provide information about facilitation, differentiation, and coherence.

Teacher Notes communicate information that helps with implementing the lesson. Teacher Notes may enhance mathematical understanding, explain pedagogical choices, give background information, or help you identify common misconceptions.

Universal Design for Learning (UDL) suggestions offer strategies and scaffolds that address learner variance. These suggestions promote flexibility with engagement, representation, and action and expression, the three UDL principles described by CAST. These strategies and scaffolds are additional suggestions that complement the curriculum’s overall alignment with UDL Guidelines.

Language Support provides ideas for supporting students with receiving (reading and listening) and producing (speaking and writing) English in mathematical contexts. Suggestions may include ways to promote student-to-student discourse, support new and familiar content-specific terminology or academic language, or support students with multiple-meaning words.

Differentiation suggestions provide targeted ways to help meet the needs of specific learners based on your observations or other assessments. There are two types of suggestions: support and challenge. Use these to support students in the moment or to advance learning for students who are ready for a challenge.

Promoting the Standards for Mathematical Practice highlights places in the lesson where students are engaging in or building experience with the Standards for Mathematical Practice (MPs). Although most lessons offer opportunities for students to engage with more than one Standard for Mathematical Practice, this guidance identifies at least one focus MP within each topic. The notes also provide lesson-specific information, ideas, and questions that you can use to deepen students’ engagement with the focus MP.

Math Past provides guidance about how to use the module’s Math Past resource in the lesson. (See Resources in this document.)

Visual Design

In the Teach book, color coding and other types of text formatting are used to highlight facilitation recommendations and possible statements, questions, and student responses. These are always suggestions and not intended to be used as a script.

• Each lesson includes a recommended time length and a materials list. LESSON

4

Crayon and Marker Sort

Use given attributes to sort objects into two groups.

Crayon and Marker Sort

LEARN 20

Show a basket with markers and crayons in it.

Which One Doesn’t Belong?

We can call this a group of art supplies. Now it is time to clean them up.

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

Materials

Teacher

Basket containing crayons and markers

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

Students

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?

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.

Crayon or marker

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

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.

Teacher Note

Take out the crayons.

Let’s make two groups.

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

Point to a place in the room for each group to go, such as separate areas on the carpet.

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:

• Dark blue text shows suggested language for questions and statements that are essential to the lesson. Light blue text shows sample student responses.

Promoting the Standards for Mathematical Practice

Give a marker or crayon to each student. Invite students to place their object in the appropriate group.

Point to the markers.

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.

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.)

• What is the same about these two bears? What is different?

Consider moving objects into groups as students respond. For example, if students

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.

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?

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.

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

; 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

Differentiation: Challenge

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

How many sheep? 3

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

Sort and Count

The number of sheep stays the same whether we count them in a line or when they are not in a line.

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

Repeat moving and counting the remaining animals by placing the horse in the barn and the pigs in the pen.

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

• How did you sort your cards?

Practice and Play

• What is this group?

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

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.

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

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

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

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

• 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.

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

• Are there more horses or more pigs?

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.

• What animal is there the most of?

UDL: Action & Expression

Differentiation: Support

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?

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.

How many feet do they have?

• Which animals would you like as a pet?

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)

• Text that resembles handwriting indicates what you might write on the board. Different colors signal that you will add to the recording at different times during the discussion.

• Bulleted lists provide suggested advancing and assessing questions to guide learning as needed.

Resources

Near the end of your Teach book, you will find resources for assessment, lesson planning, and further study.

Module Assessment

A master copy of the Module Assessment is included in the Teach book.

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)

The Standards resource lists the Standards for Mathematical Practice.

Developmental Progressions

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.

3 Years 3 to 4 Years

PK Modules 1 and 3

Count forward to 10.

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.

PK.CC.DP2

Demonstrate previous indicator and extend forward count to 10.

4 to 5 Years

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.

5 to 6 Years

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.

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 “four” or shows 4 fingers.

Years

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!”

Developmental Indicators

to 6 Years

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, “5 dogs in the top row and 3 more dogs below. 8 dogs!”

© Great Minds PBC

Developmental Progressions are standards-aligned descriptions that detail what students should know and be able to do based on instruction they receive. The number of DPs addressed in each module varies depending on the content.

Achievement Descriptors identify what students know and are able to do at a particular stage of development within a Developmental Progression, while Developmental Indicators describe precise student expectations. These resources help you identify each student’s current stage of development and prepare to support students as they progress to the next stage.

Terminology

Terminology

The following terms are critical to the work of prekindergarten module 2. This resource groups terms into categories called New, Familiar, 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 Familiar category are discipline-specific words introduced in prior modules.

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 circle

A circle is curved all the way around. It is perfectly round, like a wheel. (Lesson 5)

rectangle

A rectangle has 4 straight sides and 4 corners. (Lesson 7)

There are other shapes with 4 sides and 4 corners (e.g., trapezoids and rhombuses). Rectangles are distinguished from other four-sided shapes because they also have 4 right

angles. Prekindergarten students are not asked to use angle size to distinguish between shapes, but kindergarten students will begin to do so in kindergarten.

square rectangle

A square rectangle has 4 straight sides and 4 corners like all rectangles, but the sides are all the same. (Lesson 7) triangle

A triangle has 3 straight sides and 3 corners. (Lesson 7)

Familiar count match number sort

Academic Verbs build

Terminology is a list of new and familiar terms used in the module. New terminology includes definitions as they appear within the module.

Familiar terms were introduced or used in earlier modules.

New terminology is described in student-friendly language, and the lesson in which the terms are introduced is listed.

A small number of strategically selected academic verbs are introduced in each grade level. This verb is introduced in this module.

Observational Assessment Recording Sheet

Every module in prekindergarten has an Observational Assessment Recording Sheet. This sheet includes short checklists that summarize the module’s DPs. Use the Observational Assessment Recording Sheet to meet the needs of your classroom by recording information by date or activity and taking notes for further instruction.

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.

Standards and Developmental Progressions at a Glance

Every module in prekindergarten has two charts: a Standards for Mathematical Practice chart and a Developmental Progressions at a Glance chart. These charts identify the location and show the frequency of the Standards for Mathematical Practice and Developmental Progressions in each module. Use these charts to quickly determine where and when standards and DPs are taught within and across modules to help you target your observations. You may also use these charts in conjunction with assessment data to identify targeted ways to help meet the needs of specific learners. Use assessment data to determine which DPs to revisit with students. Use the modules’ Standards and Developmental Progressions at a Glance charts to identify lessons that contain guidance and practice problems to support student growth.

Developmental Progressions by Lesson

Prekindergarten Module 1 Standards for Mathematical Practice at a Glance

Math Past

Math Past tells the history of some big ideas that shape the mathematics in the module. It frames mathematics as a human endeavor by telling the story of the discipline through artifacts, discoveries, and other contributions from cultures around the world. Math Past provides information to inform your teaching as well as lesson-specific ideas about how to engage students in the history of mathematics.

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

Materials

The Materials resource lists items you and your students need for the module. In prekindergarten, the Materials resource also includes suggestions for self-made materials such as differentiated sorting bags, two-color beans, and a number glove.

Fluency Anytime

Fluency Anytime contains a list of all the fluency activities presented within the module as well as instructions for implementing them. Incorporating these activities consistently and frequently will support students in attaining math goals. Refer to this resource throughout the module and look for opportunities in your daily schedule to repeat the selected activities.

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

Number Rhymes

Number Rhymes are included as an optional resource in select modules. The rhymes contain suggested language to help students remember how to write each number. As students are ready, refer to this resource to support their number-writing practice.

Works Cited

A robust knowledge base underpins the structure and content framework of Eureka Math2. A listing of the key research appears in the Works Cited for each module.

Inside Learn

Learn is students’ companion text to the instruction in Teach. It contains all the pages your students need as you implement each lesson.

Cover Art

Each Learn book includes the same work of fine art included on the cover of the Teach book. The art has a connection to the math learned within the grade.

Components

The components that go with each lesson are indicated by icons in the student book.

The magnifying glass icon indicates a lesson page that students use during the guided or directed portion of the lesson.

The gears icon indicates the Problem Set. This is a carefully crafted set of problems or activities meant for independent practice during the lesson.

1 2 3 4 5 6 7 8 9 10 0

Family Math

Family Math is a letter to families that describes the major concepts in the current topic. Each letter uses words and phrases that should be familiar to the student from the lessons in the topic. Family Math also includes simple and practical at-home activities and literature connections to extend the learning and help students see mathematics in their world.

An orange bar on the side of a page indicates a removable, a student page that should be removed from the Learn book. A removable may be used inside a personal whiteboard so students can practice skills several times in different ways, or it may be cut, assembled, or rearranged for an activity during a lesson or across multiple lessons.

Inside the Digital Platform

The Great Minds Digital Platform is organized into five key curriculum spaces: Teach, Assign, Assess, Analyze, and Manage. On the digital platform, lessons include the same features as in the Teach book, as well as a few more elements that are unique to the digital space. For example, on the digital platform, the side navigation panel previews digital presentation tools, such as slides, that accompany lessons.

Each space within the digital platform supports you to maximize the features that Eureka Math2 offers.

Teach

Teach contains all the information in the print version, as well as digital curriculum components such as assessments, digital interactives, and slides to project for students. Use this space to access the curriculum components you need for daily instruction.

Manage

The Manage space allows administrators and teachers to view rostering data for their schools or classes. It is also where you can set or reset a student’s password.

This section discusses Teach in detail. Visit the Help Center to read more about Teach and Manage.

teach

On the digital platform, use Teach to navigate to the curriculum, level, and module landing pages for easy access to different components.

The curriculum landing page, or the bookshelf, gives easy access to the entire curriculum.

The grade-level landing pages provide a brief description of the year-long learning. Use the drop-down arrows in the top navigation panel to view different grade levels.

The module-level landing page houses all the module-, topic-, and lesson-level resources needed to teach each module.

The Module Overview includes resources from the Teach book, including Why, Terminology, Math Past, Module Assessment, and additional module-level resources.

The Topic Overview includes the Progression of Lessons and topic-level resources.

Access the Developmental Progressions for the topic.

Lessons are visible at a glance.

Access the Developmental Progressions for the entire module.

Slides

Each Eureka Math2 lesson provides projectable slides that have media and content required to facilitate the lesson, including the following:

• Fluency activities

• Digital experiences such as videos, teacher-led interactives, and demonstrations

• Images and text from Teach or Learn cued for display by prompts such as display, show, present, or draw students’ attention to

• Pages from Learn including Classwork, removables, and Problem Sets

Some slides contain interactive components such as buttons or demonstrations.

Pacing

Year at a Glance

In prekindergarten, there are 119 lessons and three optional projects. Small groups of related lessons are organized into topics. Topics are organized into modules. The following table shows the modules by title and gives the total number of lessons and assessment days per year.

1 Sorting and Counting Counting and Cardinality Counting, Comparison, and Addition

2

5 Math Stories Addition and Subtraction

Place Value Concepts to Compare, Add, and Subtract

6 Math in Play Place Value Foundations Attributes of Shapes • Advancing Place Value, Addition, and Subtraction

Place Value Concepts Through Metric Measurement and Data • Place Value, Counting, and Comparing Within 1,000

Money, Data, and Customary Measurement

Instructional Days

Plan to teach one lesson per day of instruction. Each prekindergarten lesson is designed for an instructional period that lasts 10–30 minutes. All Eureka Math2 grade levels have fewer lessons than the typical number of instructional days in a school year to provide some flexibility in the schedule for assessment and responsive teaching and to allow for unexpected circumstances.

Module

3: Units of Any Number

1 Multiplication and Division with Units of 2, 3, 4, 5, and 10

4: Fractional Units

Place Value Concepts for Addition and Subtraction

5: Fractions Are Numbers

Place Value Concepts for Multiplication and Division with Whole Numbers

2 Place Value Concepts Through Metric Measurement

3 Multiplication and Division with Units of 0, 1, 6, 7, 8, and 9

Place Value Concepts for Multiplication and Division

Multiplication and Division of Multi-Digit Numbers

4 Multiplication and Area Foundations for Fraction Operations

5 Fractions as Numbers Place Value Concepts for Decimal Fractions

6 Geometry, Measurement, and Data

Angle Measurements and Plane Figures

Addition and Subtraction with Fractions

Multiplication and Division with Fractions

Place Value Concepts for Decimal Operations

Addition and Multiplication with Area and Volume

Foundations to Geometry in the Coordinate Plane

Total

145 lessons

142 lessons

137 lessons

Optional Lessons

Some lessons in each grade level are optional. Optional lessons are clearly designated in the instructional sequence, and they are included in the total number of lessons per grade level. Assessments do not include new learning from optional lessons.

Lessons may be optional for the following reasons:

• The lesson is primarily for enrichment.

• The lesson offers more practice with skills, concepts, or applications.

• The lesson bridges gaps between standards.

• The lesson can be used more than once or anywhere in the instructional sequence.

Module 6 Projects

Module 6 is composed of three projects that are designed for prekindergarten students to engage playfully with math content through meaningful contexts. Through these open and exploratory projects, students apply some of the big ideas of prekindergarten mathematics such as counting, comparison, patterns, and operations. These projects are meant to be student driven and used flexibly when students could benefit from a pause in instructional structure and routine to synthesize and joyfully apply their learning.

The projects are specifically designed to draw on students’ learning in previous modules. These projects may also expose students to concepts that will be taught later in the year. Each project follows a similar structure.

• Launch: An idea or problem is presented for students to research and explore.

• Learn: Students work together as doers of mathematics, exploring mathematical ideas through play. In Learn, students may investigate an idea or solve a problem.

• Land: Students share and reflect on their learning. Once projects are complete, students may continue to add to and work on them by using new materials, scenarios, and ideas.

Pacing Your instruction

The total lesson count at each grade level and many of the elements in the lesson structure provide flexibility. As needed, use that flexibility to adjust pacing so that it meets the needs of your students or your school’s schedule.

Focus on the major work of the grade.

In 2009, the National Research Council recommended two areas of focus for early childhood math instruction: (1) number, including whole number, operations, and relations, and (2) geometry, spatial thinking, and measurement.1 The prekindergarten curriculum prioritizes Developmental Progressions in these focal areas. They are considered the major work of the grade and more time is devoted to these DPs overall. These DPs also appear early and are revisited over the course of the year, so students have ample opportunity to work with them. Whenever possible, the major work of the grade is naturally embedded in lessons, even when the lesson objective targets other areas of mathematics.

Use observational assessment data to make decisions.

Use student performance during lessons, including data from the observational assessment prompts and from written work, to make strategic decisions. The Observational Assessment Recording Sheet can help you keep track of student performance that demonstrates knowledge and skills. Look at upcoming content and, based on your observations, choose the pathway that best advances student understanding and allows students to demonstrate what they know. For example, lessons may provide access to a concept by teaching the concept in more than one way, but students may not need to achieve proficiency with every strategy or method taught.

1National Research Council. Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Washington, DC: The National Academies Press, 2009, page 337.

Think flexibly about how and when to use components.

Dedicated time for math in the prekindergarten schedule is critical. However, there is flexibility in when and where math instruction occurs. Lessons may suggest a location, such as at tables, on the carpet, or outdoors, but most activities are as portable as the materials required. Consider using the following components flexibly throughout the day.

• Fluency Anytime—Fluency activities can be incorporated into morning meetings and transitions. As students become more familiar with fluency activities and games, consider using them at stations where students can work independently, in pairs, or with a trusted adult.

• Math Anytime—Use the suggestions provided in each Topic Overview to incorporate math into other parts of the day, such as during art, music, outdoor play, stations, and mealtimes.

• Assessment—One-on-one interview assessments can take place anytime during the school day. Observational assessments may also be noted during conversations, independent work, and free play. Use the Observational Assessment Recording Sheet or your own organizational system to track student progress.

Expect students to develop proficiency over time.

Students achieve proficiency with the developmental progressions over time. Keep moving through lessons even when your students demonstrate only partial proficiency in the moment. Modules and lessons build student knowledge steadily so that students meet grade-level expectations by the end of the school year, and the curriculum’s assessments are designed accordingly.

Distributed practice of each concept and skill is built into the curriculum to help students achieve and maintain proficiency. Set a goal to have 80% of students demonstrate proficient performance on ongoing assessments. Use small group work or short exercises to support students who need more time or different instruction to understand the concepts.

Lesson Facilitation

Eureka Math2 lessons are designed to let students drive the learning through sharing their thinking and work. Varied activities and suggested styles of facilitation blend guided discovery with direct instruction. The result allows teachers to systematically develop concepts, skills, models, and discipline-specific language while maximizing student engagement.

Effective Delivery

No matter what style of facilitation lessons suggest, effective delivery prioritizes student engagement; promotes student-to-student discussion; fosters students’ ownership of and sense of belonging in the mathematics community; and helps students make connections within mathematics and across disciplines. The following are some of the ways that the curriculum supports these elements of your instruction.

Lessons prioritize student engagement by

• maximizing the number of students actively participating at any given time,

• creating space for students to share, discuss, and self-reflect,

• inviting students’ curiosity by posing questions or scenarios that spur them to notice and wonder, and

• presenting intriguing artifacts or questions that create a need for new knowledge.

Lessons promote student-to-student discussion by

• providing language models that allow students to share their thinking,

• employing routines that encourage student-to-student dialogue, and

• using open-ended questions and scenarios to generate opportunities for authentic class discussion.

Lessons foster student ownership and belonging by

• including guided discovery so that students generate, test, share, critique, and refine their ideas,

• incorporating the Standards for Mathematical Practice by design so that opportunities to engage with them arise naturally,

• adjusting for age-appropriateness and reading proficiency in student materials to maximize students’ independence, and

• providing tools to support students with their processing and verbal expression.

Lessons help students make connections by

• building content and language sequentially so that it’s easier to relate new learning with prior knowledge,

• incorporating Math Past, a component that contextualizes current learning within the history of mathematics, and

• using artwork to convey broad artistic and mathematical principles.

sample Dialogue

Lessons include sample dialogue that represents how the teacher and students in a classroom might explore concepts and problems. Sample dialogue gives a sense of how instruction might look and feel. It is not a script and should not be used that way. Instead, use the sample dialogue as if you are observing a class taught by a trusted colleague. For example, the sample dialogue can help you

• identify lines of questioning that advance students toward the objective,

• determine when and how to use precise terminology, or

• navigate content that might be new to you or challenging to teach or learn.

Sample dialogue often includes possible student responses or reasoning. However, sometimes the lesson advances without relying on a certain kind of response, or sometimes responses are expected to vary so much that possible student responses are not provided. For example, sample student responses are not usually included with a question that’s meant to be used as a simple turn and talk. When they are present, the provided responses serve as examples of the kind of thinking you might expect to hear. As you listen to your own students, consider using the sample responses to help you identify teachable moments.

classroom culture

Consider the following ideas to help set norms that support a collaborative culture:

• We value and respect each other’s contributions. Everyone has knowledge that is worth listening to and building on.

• We are all expected to explain and discuss our thinking.

• We will solve problems in many different ways.

• We embrace a growth mindset. Making mistakes is part of learning. We will analyze and learn from the mistakes we make.

As the culture of your mathematics classroom becomes established, you may feel the need to shift your instruction. For example, students will begin to share, compare, and critique with confidence. Respond by challenging yourself to maximize student action and conversation over teacher action and speech. Leverage the structures and questions within lessons to increase guided discovery and connection-making so that students generate ideas. Your primary roles then evolve to navigating and developing their emerging mathematical thinking.

instructional Routines

Eureka Math2 uses instructional routines, or predictable patterns of classroom interaction, to allow students and teachers to focus on mathematical content. Routines intentionally support engagement, discussion, and building content knowledge. Directions for a routine are included in a lesson every time the routine is used. That way, the specific facilitation guidance is immediately available to you as you work through the lesson. Many of the same routines appear across grade levels from prekindergarten to Algebra I, using age-appropriate variations.

Launch, Learn, Land

Lessons intentionally include routines that

• promote student engagement in the Standards for Mathematical Practice;

• promote student-to-student dialogue and integrate reading, writing, and listening;

• align to Social Emotional Learning (SEL) core competencies; and

• align to Stanford Language Design Principles.

Although many routines are embedded in lessons, the following routines consistently appear by name within prekindergarten lessons. This prevalence helps students recognize the routines and develop ownership over them.

Same and Different Provides structure for comparing attributes of objects, which builds mathematical reasoning and language

Which One Doesn’t Belong? Promotes metacognition and mathematical discourse as students use precise language to compare different examples

Fix Puppet’s Mistake Promotes effective communication techniques for critiquing others’ work, correcting errors, and clarifying meaning

Guess My Rule Promotes reasoning and language development as students analyze groups of objects to determine common attributes

Universal Design for Learning

Universal Design for Learning (UDL) is a framework based on current research from cognitive neuroscience that recognizes learner variance as the norm rather than the exception. The guiding principles of the UDL framework are based on the three primary networks of the brain. Although the concept of UDL has roots in special education, UDL is for all students. When instruction is designed to meet the needs of the widest range of learners, all students benefit. Eureka Math2 lessons are designed with these principles in mind. Lessons throughout the curriculum provide additional suggestions for Engagement, Representation, and Action & Expression. Learn more about UDL in Eureka Math2 here.

Multilingual Learner support

Multilingual learners, or learners who speak a language other than English at home, require specific learning supports for gaining proficiency with the English needed to access the mathematics. Research suggests that best practices for these learners include opportunities and supports for student discourse and for using precise terminology. In addition to precise domain-specific terminology, high-impact academic terminology that supports learners across learning domains is explicitly introduced and used repeatedly in various contexts to build familiarity and fluency across the grade levels. Eureka Math2 is designed to promote student discourse through classroom discussions, partner or group talk, and rich questions in every lesson. Learn more about supporting multilingual learners in Eureka Math2 here.

Readability

A student’s relationship with reading should not affect their relationship with math. All students should see themselves as mathematicians and have opportunities to independently engage with math text. Readability and accessibility tools empower students to embrace the mathematics in every problem. Lessons are designed to remove reading barriers for students while maintaining content rigor. Some ways that Eureka Math2 clears these barriers are by including wordless context videos, providing picture support for specific words, and limiting the use of new, non-content-related vocabulary, multisyllabic words, and unfamiliar phonetic patterns. Learn more about how Eureka Math2 supports readability here.

The assessment system in prekindergarten helps you understand student learning by generating data from many perspectives. The system includes

• a recording sheet to guide your observations during lessons and

• Module Assessments.

All Eureka Math2 assessments are considered formative because they are intended to inform instruction. The assessments may also be considered summative when you choose to use the data to produce a grade or report that becomes part of a student, school, or district record.

On its own, a single assessment does not show a complete picture of student progress. For example, a short assessment might use a single question to assess student understanding of part of a standard, thus producing a limited perspective. Use a combination of observational and scored assessments to understand and report on overall student performance.

Components

Observational Assessment Recording Sheet

In prekindergarten, an Observational Assessment Recording Sheet accompanies every module. This sheet lists the module’s Developmental Progressions. Record your observations often so you can use your observational assessments to inform your understanding of student performance. You may also use the recording sheet to record evidence of students’ engagement with the Standards for Mathematical Practice.

Each Topic Overview shows a picture of the module recording sheet. Highlighting on the picture indicates which of the module’s DPs are the focus of the topic.

Within the lesson itself, a note in a margin box indicates when the opportunity to observe performance related to the Developmental Progressions is likely to arise. However, you should use the recording sheet to make notes about student performance during any part of the lesson or throughout your day.

Module Assessments

Typical Module Assessments consist of three to five interview-style items that assess proficiency with the major concepts, skills, and applications taught in the module. Module Assessments include the most important content, but they may not assess all the strategies and standards taught in the module. Many items allow students to show evidence of understanding one or more of the Standards for Mathematical Practice (MPs). You may use the Standards for Mathematical Practice chart and Developmental Progressions at a Glance chart to find which MPs you may be more likely to see from your students on a given assessment item in relation to the content that is assessed. Give these assessments when a student shows inconsistent proficiency over the course of a module based on notes you make on the Observational Assessment Recording Sheet.

Module Assessments provide suggested language for the interview-style items. As needed, and if possible, consider assessing students in their home language. When students are unable to answer or they respond incorrectly to the first few questions, end the assessment, and retry after more instruction.

Developmental Progressions

Developmental Progressions, or DPs, are standards-aligned descriptions that detail what students should know and be able to do by the end of prekindergarten. There are 20 DPs for prekindergarten, encompassing the areas of counting and cardinality, measurement and data, geometry, and operations and algebraic thinking. The DP language is crafted from standards and concisely describes what will be assessed. The Developmental Progressions are grounded in research and reflect the trajectory of learning that takes place across various stages of development throughout the prekindergarten years. Opportunities for students to develop the knowledge and skills associated with each DP extend across modules. For example, PK.CC.DP1 is reflected in three modules: Students begin counting 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.

The DPs also serve as a tool to help teachers predict and prepare for the next stage of student learning.

Achievement Descriptors and Developmental Indicators

Each DP has its own set of Achievement Descriptors and Developmental Indicators, which are organized by age-based developmental stages. Each stage is aligned to research on young children’s development and provides a clear path to the kindergarten standards. The Achievement Descriptors and Developmental Indicators provide specific descriptions of anticipated student knowledge and performance within each developmental stage. Achievement Descriptors identify what students know and are able to do at a particular stage of development within a Developmental Progression, while Developmental Indicators describe precise student expectations. Achievement Descriptors and Developmental Indicators are more detailed than DPs and help you analyze and evaluate what you see or hear in the classroom as well as what you see in students’ written work.

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 Descriptors and Developmental Indicators use language that offers insights about which MPs may be observed as students engage with assessment items. For example, Achievement Descriptors and Developmental Indicators that begin with create or represent likely invite students to show evidence of MP2: Reason abstractly and quantitatively.

• 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

The following is an example of a prekindergarten DP. The highlighted stage indicates the expectation for most students after they complete the prekindergarten curriculum.

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

Count forward to 5.

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

If verbal counting

Achievement Descriptor

Developmental Indicators

Respond to student Assessment Performance

After administering an assessment, use the assessment data and the Observational Assessment Recording Sheets to analyze student performance by each DP. Use the student age and module information in the Developmental Progression to evaluate students’ progress.

Students who meet the Developmental Indicators for their age are progressing as expected, even if additional concepts were presented in the module. For example, a 3-year-old student who can identify a circle and a square rectangle on the Module 2 Assessment is meeting expectations even if they are not able to consistently identify all triangles.

Developmental

PK.G.DP2 Name and identify shapes (circles, square rectangles, triangles, and rectangles), regardless of their orientation or overall size.

4 to 5 Years

3 Years 4 Years

PK Module 2

Name and identify circles and squares.

Name and identify typical circles and squares.

Begin to recognize typical triangles.

Name and identify circles, squares, and triangles.

Demonstrate previous indicator and extend to naming and identifying all triangles.

Begin to recognize typical rectangles.

Name and identify circles, square rectangles, triangles, and rectangles, regardless of their orientation or overall size.

• Demonstrate previous indicators and extend to naming and identifying all rectangles.

• Begin to recognize a square as a special type of rectangle.

Informally name three-dimensional shapes by using words such as ball can, and box

5 to 6 Years

K Module 2

Name and identify shapes, regardless of their orientation or overall size.

Demonstrate previous indicators and extend to naming and identifying hexagons. Begin to name three-dimensional shapes such as sphere, cube, cylinder, and cone.

PK.G.DP3 Compare two- and three-dimensional shapes of different sizes and orientations by using informal language to describe how their attributes are similar and different (e.g., number of sides and corners).

4 Years

3 Years 3 to 4 Years

PK Module 2

Sort typical shapes.

When shown typical shapes in various sizes, sort by the type of shape.

Rotate a shape to match a typical shape.

Sort two- and three-dimensional shapes. Sort all shapes by type when the shapes are shown in the same orientation and size.

If data indicate that a student is not yet meeting the Developmental Indicator(s) for their age, examine the indicators in the previous stage of development within the same DP, and use the lower-complexity task to build toward full understanding. Look for natural ways to incorporate the previous indicator(s) into the daily schedule. Fluency Anytime and Math

Begin to sort shapes by type when the shapes are shown in different orientations and sizes.

Compare two- and threedimensional shapes of different sizes and orientations by using informal language to describe how their attributes are similar and different.

• Identify most attributes such as the number of straight sides and corners when comparing twodimensional shapes.

May have difficulty recognizing differences in side

5 to 6 Years

K Module 2

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

4 Years

PK Modules 1, 3, and 5

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.

2 to 3 Years

PK Module 1

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.

PK Module 1

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.

5 to 6 Years

K Module 6

Count out a given number of 10–20 objects from a larger group.

• Demonstrate previous indicators and extend count beyond 10 objects.

4 Years

PK Modules 1–4

K Module 1

Sort objects into categories. Consistently sort objects into given groups, such as grouping socks by color. May sort objects into self-selected categories.

5 to 6 Years

K Module 3

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.

Some DPs are the focus of several modules. Use assessment data to support students at their current stage of development as concepts resurface in later modules. Additional opportunities for practice are built into lessons, Fluency Anytime, and Module 6 projects.

Plan to Teach

Study a Module

Begin your planning process by familiarizing yourself with the module’s story. Use the following guide to help you review the module as a whole.

Preview the Learning

Module Resource

Read the Overview to preview the learning and understand the coherence among modules.

• Overview

• Before This Module and After This Module

Guiding Questions

• What big ideas does the module teach?

• What concepts, skills, and language can I expect my students to bring to new learning?

• How does the work of this module support learning in future modules?

Investigate the Development of Learning

Module Resource

Review the Table of Contents to understand the module’s structure and consider how it aligns with the school calendar.

Read the Why section for insight into the module’s instructional design and pedagogical choices.

Guiding Questions

• What do the topic titles tell me about the development of learning across the module?

• How many lessons are in the module and in each topic?

• What does the Why section tell me about the module’s design?

• In what ways does this information change my thinking about the content, sequence, models, strategies, and language in this module?

Preview the additional module resources:

• Terminology

• Math Past

• Materials

• How will introducing the module terminology support students’ language development and understanding of the module’s big ideas?

• How does Math Past provide human or historical context for the learning in this module?

• What materials do I need for the lessons in this module? What do I need to gather or prepare in advance?

Explore the Assessment

Module Resource

Read the Developmental Progressions Resource to understand the expectations for students in this module and in future modules.

Guiding Questions

• What are the Developmental Progressions for this module and how do they relate to my state’s content standards?

• What is expected of students of different ages in this module?

• How do the Developmental Indicators add to my understanding of the mathematics this module develops?

Preview the Module Assessment to see a way that students may be assessed on their learning.

• How does the Module Assessment assess the big ideas of the module?

• How do the models, strategies, and language of the module appear in this assessment?

• In what ways might students show their understanding?

Review the Observational Assessment Recording Sheet.

• How are the big ideas of the module reflected in the Observational Assessment Recording Sheet?

• How will I record and assess the learning in this module?

Study a topic

Within a module, small groups of related lessons are organized into topics. Plan to teach by topic to ensure that each lesson’s instruction supports students in connecting prior knowledge to new learning. Use the following guide to help you study each topic.

Preview the Learning

Topic Resource

Review the Progression of Lessons to get a sense of how the learning develops.

Read the Topic Overview narrative to understand the scope of the topic.

Guiding Questions

• What do the Key Questions tell you about the focus of this topic?

• What do the italicized “We can” statements tell you about the focus of each lesson?

• What big ideas does the topic teach?

• In what ways does this information change my thinking about the content, sequence, models, strategies, and language in this topic?

Investigate the Development of Learning

Lesson Resource

Read the lessons to understand the flow and coherence of the topic.

Guiding Questions

• How do mathematical concepts and language develop across the topic?

• What is the purpose of each lesson within the topic?

• What activities or routines are suggested? How might those activities and routines inform my pacing, location, and group structure?

• How do I anticipate my students will engage with the contexts and concepts presented in the lessons?

Read the additional topic resources:

• Terminology

• Fluency Anytime

• Math Anytime

• Family Math

• What skills are targeted by the suggested fluency activities? When might I use fluency activities throughout a topic to provide opportunities for practice?

• How can I provide opportunities for students to see the math they are learning as a meaningful part of their world?

• Where will the content of this topic naturally fit into our daily schedule?

• How can families support their children’s learning?

• How can families help me and their children recognize how this math shows up in our communities and cultures?

Explore the Assessment

Topic Resource

Review the Observational Assessment Recording Sheet and the Developmental Progressions.

Prepare for Instruction

Guiding Questions

• Which Developmental Progressions are addressed in this topic?

• When will I have an opportunity to observe and assess students’ understanding of the topic’s Developmental Progressions?

Effective instruction requires both knowledge of the content being taught and awareness of the support students need to access grade-level content. Difficulty with pacing at the lesson level tends to occur when teachers feel pressured to ask every question and engage with every problem presented in every lesson. Using the curriculum with fidelity means honoring the integrity of its structure and the intent of the guidance within lessons. The following recommendations will help you make strategic decisions as you prepare to teach with both the content and your students in mind.

Task Guiding Questions

Complete the suggested activities yourself to experience the math from students’ point of view.

• How do the activities develop students’ understanding of the lesson objective and Key Questions?

• What tools or materials will I need to teach this lesson?

• What tools or materials might my students need? How can I organize materials to maximize engagement and learning?

• What prior knowledge, language, and fine motor skills are required for success with this lesson?

Anticipate, prioritize, and customize.

• Considering both my allotted instructional time and the needs of my students, do I need to customize the lesson?

• How will I differentiate the activities to support my students? How can the suggestions provided in the margin boxes help with differentiation?

• What questions, phrasing, or terminology will I use from the sample dialogue to support development of mathematical content and language?

• What grouping structures will support students as they learn?

• Are there contexts or materials I need to change to meet the unique needs of my class?

• How will I use the module and topic resources (Fluency Anytime, Math Anytime, Family Math, and Math Past) to help students see the math they are learning in the world around them?

Prepare the environment.

• What tools or materials do I need to prepare in advance? How can I organize the materials to fit my chosen grouping structure?

• Do I need to make any adjustments to the arrangement of my room either to capitalize on space in the room or to maximize student collaboration?

Read the Observational Assessment box.

• What indicates student understanding?

• How will I structure the schedule or classroom environment so I can listen to students and collect this data?