Explore Math Book B Teacher's Guide SAMPLE

Teacher’s Guide

Operations and Algebraic Thinking

B

Operations and Algebraic Thinking Learning Objectives Understand and apply the concept of composition and decomposition of numbers up to 10: Chapter 1: Compose and Decompose numbers to 10

•

Students will demonstrate an ability to compose and decompose numbers up to 10 by using objects, visuals, and number sentences, reinforcing their understanding of part-part-whole relationships (aligned with CCSS.MATH.CONTENT.K.OA.A.1).

Develop addition and subtraction readiness through practical activities: •

Students will use counting and grouping strategies to solve simple addition and subtraction problems by composing and decomposing numbers, preparing them for future arithmetic skills (aligned with CCSS.MATH.CONTENT.K.OA.A.3).

Enhance problem-solving and critical thinking skills through number combinations: •

Students will engage in problem-solving exercises that challenge them to explore multiple ways to compose and decompose numbers up to 10, developing flexible thinking and strategic reasoning (aligned with CCSS.MATH.PRACTICE.MP1).

Use visual models and manipulatives to support mathematical understanding: •

Students will effectively use visual aids such as ten-frames, objects, and drawn representations to compose and decompose numbers, promoting a concrete understanding of numbers and their parts (aligned with CCSS.MATH.CONTENT.K.OA.A.5).

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 1

Lesson

1

Compose and Decompose Numbers to 10 Numbers to 10

Exercise:1 Exercise Overview: In this exercise, kindergarten students will learn to compose and decompose the numbers 4 and 5 using yellow and blue cars. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 4 and 5." Students will explore different combinations of yellow and blue cars to make 4 and 5, introducing them to the concept of composition and decomposition of numbers.

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Colored pencils or crayons in yellow and blue

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of composition and decomposition of numbers.

▪ Say, "Today we are going to learn how to make the numbers 4 and 5 using different combinations of yellow and blue cars. This will help us understand how numbers can be broken down into parts and how they can be put together." o Use visual aids (e.g., drawing on the board) to show how 4 and 5 can be made up of different combinations of two numbers.

2. Demonstrating the Exercise (5 minutes): o Open the book to the lesson titled “Compose 4 and 5.” o Show the students the two rows of cars: ▪ The first row has 1 yellow car and 3 blue cars, making a total of 4.

▪ The second row has 2 yellow cars and 3 blue cars, making a total of 5. o Explain that the yellow and blue cars represent different parts of the numbers 4 and 5.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 2

3. Guided Practice (10 minutes): Exercise a: Use the yellow and blue cars to show ways to make 4 and 5.

Instruct the students to look at the first row of cars, which shows 4 cars.

▪ Say, "In this row, we have 1 yellow car and 3 blue cars. If we add them together, we get 4 cars. So, 1 yellow car + 3 blue cars = 4." o Demonstrate this by writing on the board: "1 + 3 = 4." o Next, point to the second row of cars, which shows 5 cars.

▪ Say, "In this row, we have 2 yellow cars and 3 blue cars. If we add them together, we get 5 cars. So, 2 yellow cars + 3 blue cars = 5." o Write on the board: "2 + 3 = 5."

4. Interactive Practice (10 minutes): o

Exercise b: Encourage the students to suggest more ways to make 4 and 5.

Ask the students if they can think of any other ways to make 4 and 5 using yellow and blue cars.

▪ Say, "Now it's your turn. Can you think of different ways to make 4 using yellow and blue cars? What about 5?" o Write their suggestions on the board as they share ideas. Some examples they might come up with: ▪ For 4: "2 yellow cars + 2 blue cars" (Write: 2 + 2 = 4) ▪ For 5: "1 yellow car + 4 blue cars" (Write: 1 + 4 = 5) o Encourage different combinations for both numbers.

5. Independent Practice (5 minutes): o Allow the students to explore the cars and create more combinations on their own.

▪ Say, "Now it's your turn to come up with your own ways to make 4 and 5 using yellow and blue cars. You can color the cars in your book and write down the numbers." o Walk around the classroom to provide support and encouragement.

6. Review and Reinforcement (5 minutes): o Once the students have completed the exercise, review their work as a class. o Ask a few students to share the combinations they created for 4 and 5. o Correct any misunderstandings and praise students for their effort and creativity.

7. Conclusion and Real-World Connection (2 minutes): o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 3

o

o

Conclude by explaining that composition and decomposition of numbers are important in everyday life. For example, counting objects, understanding groups of items, and even solving problems with money.

Encourage students to practice making different combinations with other numbers at home or in class.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to break down and build up numbers.

Encouragement: Provide positive feedback and encourage students to think of as many combinations as possible.

Repetition: Reinforce the concept with other objects or numbers to ensure the understanding of composition and decomposition.

Differentiation: Offer additional help to students who may need support in understanding the concept and provide extra challenges for those who grasp it quickly.

By following these detailed steps, teachers can effectively guide their kindergarten students through the exercise in “Explore Math: Book B (Operations and Algebraic Thinking)” under the lesson “Compose 4 and 5.”

Exercise: 2-4 Exercise Overview: In this exercise, kindergarten students will explore different ways to compose the number 4 using visual combinations of fish and seals. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 4 and 5." The students will observe three different combinations of fish and seals, all of which add up to 4. The goal is to help students understand the concept of composing numbers and to guide them in writing the number combinations that make 4.

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 4

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of composing numbers and how objects can be grouped to make a total.

▪ Say, "Today we are going to learn how to make the number 4 in different ways by combining fish and seals. This will help us understand how we can put together different numbers to make a total." o Use real or visual aids (e.g., drawing on the board) to show how objects can be combined to make a specific number, such as 4.

2. Demonstrating the Exercise (5 minutes): o Open the book to the lesson titled “Compose 4 and 5.” o Show the students the three different combinations of fish and seals, each adding up to 4: ▪ One combination might show 1 fish and 3 seals.

▪ Another combination might show 2 fish and 2 seals.

▪ The third combination might show 3 fish and 1 seal. o Explain that each of these groups shows a different way to make 4.

3. Guided Practice (10 minutes): Exercise: Write ways to make 4. Write the numbers.

Instruct the students to look at each combination of fish and seals and identify how many fish and how many seals are in each group.

▪ Say, "Let’s look at the first picture. How many fish do we see? How many seals? If we count them together, how many do we get?" o Guide the students in writing the numbers for each combination.

▪ For example: "1 fish + 3 seals = 4" (Write: 1 + 3 = 4) o Repeat this for the other two combinations: ▪ "2 fish + 2 seals = 4" (Write: 2 + 2 = 4) ▪ "3 fish + 1 seal = 4" (Write: 3 + 1 = 4) 4. Interactive Practice (10 minutes): o Encourage the students to come up with their own ideas for how to make 4 using fish and seals, or other objects.

▪ Say, "Can you think of other ways to make 4 using different numbers of fish and seals? Write your own combination." o Walk around the classroom to check if students are writing the numbers correctly and understanding how to compose 4.

5. Independent Practice (5 minutes): o Allow the students to work independently to complete the exercise. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 5

Say, "Now it's your turn to write different ways to make 4 using the pictures of fish and seals. Remember to write the numbers that make 4." o Walk around and provide guidance to ensure the students understand the task.

6. Review and Reinforcement (5 minutes): o Once the students have completed the exercise, review their answers as a class. o Ask a few students to share the different combinations they wrote and explain how they made 4. o Correct any misunderstandings and provide positive reinforcement for their effort and correct answers.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that composing numbers is important in everyday life. For example, we use this concept when we count or group things together, such as toys, food, or items at home. o Encourage students to practice composing other numbers at home using different objects, such as toys, blocks, or food items.

▪

Additional Tips: • • •

•

Visual Aid: Use a large paper or whiteboard to model how to compose numbers and write the combinations.

Encouragement: Provide positive feedback to encourage creative thinking and understanding of the concept.

Repetition: Reinforce the concept with different sets of objects or numbers to ensure students grasp the idea of composition and decomposition.

Differentiation: Offer additional support to students who need more guidance and provide extra challenges for those who grasp the concept quickly.

Exercise: 5-7 Exercise Overview: In this exercise, kindergarten students will explore different ways to compose the number 5 using visual combinations of blue and yellow birds. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 4 and 5." The students will be shown three different combinations of blue and yellow birds, each totaling 5. These combinations will serve as hints for students to compose 5 on their own. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 6

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of composing numbers, specifically the number 5, using different combinations.

▪ Say, "Today we are going to learn how to make the number 5 using blue and yellow birds. There are different ways to combine these birds to make the total of 5." o Use real or visual aids (e.g., drawing on the board) to show how different numbers of objects (birds) can add up to 5.

2. Demonstrating the Exercise (5 minutes): o Open the book to the lesson titled “Compose 4 and 5.” o Show the students the three different combinations of blue and yellow birds, each combination totaling 5: ▪ One combination might show 1 blue bird and 4 yellow birds.

▪ Another combination might show 2 blue birds and 3 yellow birds.

▪ The third combination might show 3 blue birds and 2 yellow birds. o Explain that each of these groups shows a different way to make the number 5.

3. Guided Practice (10 minutes): Exercise a: Write ways to make 5. Write the numbers.

Instruct the students to look at each combination of blue and yellow birds and identify how many blue birds and how many yellow birds are in each group.

▪ Say, "Let’s look at the first picture. How many blue birds do we see? How many yellow birds? If we count them together, how many do we get?" o Guide the students in writing the numbers for each combination.

▪ For example: "1 blue bird + 4 yellow birds = 5" (Write: 1 + 4 = 5) o Repeat this for the other two combinations: ▪ "2 blue birds + 3 yellow birds = 5" (Write: 2 + 3 = 5) ▪ "3 blue birds + 2 yellow birds = 5" (Write: 3 + 2 = 5) 4. Interactive Practice (10 minutes): o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 7

Exercise b: Suggest one more way to make 5.

Ask the students if they can think of one more way to make 5 using blue and yellow birds, or any other objects.

▪ Say, "Can you think of one more way to make 5? What if we had more yellow birds and fewer blue birds?" o Guide them through coming up with another combination, such as: ▪ "4 blue birds + 1 yellow bird = 5" (Write: 4 + 1 = 5) o Encourage students to think creatively and try different combinations.

5. Independent Practice (5 minutes): o Allow the students to work independently to complete the exercise.

▪ Say, "Now it's your turn to write different ways to make 5 using the pictures of blue and yellow birds. After that, try to think of one more way to make 5." o Walk around the classroom, providing guidance and checking to make sure students understand how to compose 5.

6. Review and Reinforcement (5 minutes): o Once the students have completed the exercise, review their answers as a class. o Ask a few students to share the combinations they wrote and explain how they made 5. o Correct any misunderstandings and reinforce the idea that there are different ways to make the same number.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that composing numbers is important in everyday life. For example, we use this concept when we group or count things, such as toys, blocks, or food items. o Encourage students to practice making combinations with other numbers at home using objects they find around the house. o

Additional Tips: • • •

•

Visual Aid: Use a large paper or whiteboard to model how to compose numbers and write the combinations.

Encouragement: Provide positive feedback and encourage creative thinking.

Repetition: Reinforce the concept by composing different numbers (e.g., 6, 7) to ensure students understand composition and decomposition.

Differentiation: Offer additional help to students who need it and provide extra challenges for those who quickly grasp the concept.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 8

Exercise: 8-10 Exercise Overview: In this exercise, kindergarten students will use coloring as a visual tool to help compose and decompose the numbers 4 and 5. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 4 and 5." The students will color groups of objects in blue and yellow to show different combinations that make up 4 or 5, and then write the numbers that represent each combination.

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Crayons or colored pencils in blue and yellow Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of using coloring to understand composition and decomposition of numbers.

▪ Say, "Today we will use two colors—blue and yellow—to help us find different ways to make the numbers 4 and 5.

This will help us see how we can combine smaller groups to make a bigger number." o Explain that by using two colors, students can visually separate the groups and count each part to see how they come together to form 4 or 5.

2. Demonstrating the Exercise (5 minutes): o Open the book to the lesson titled “Compose 4 and 5.” o Show the students the uncolored groups of objects in the exercise. Point out that some groups have 4 objects, and some have 5. o Explain that the goal is to use blue and yellow to color the groups in a way that shows how to compose 4 or 5. o Say, "We will color some objects blue and others yellow. This will help us see how different groups add up to 4 or 5."

3. Guided Practice (10 minutes): Exercise: Color the objects blue and yellow to make 4 and 5. Write the numbers. o

Begin by focusing on a group of 4 objects.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 9

Say, "Let’s start with the group of 4 objects. How can we use blue and yellow to show a way to make 4?" o Suggest one possible combination, such as 2 objects in blue and 2 in yellow.

▪ Say, "If we color 2 objects blue and 2 objects yellow, we get 2 + 2 = 4." o Ask students to color a group of 4 in their books using 2 blue and 2 yellow and write the combination underneath: 2 + 2 = 4. o Now focus on the group of 5 objects.

▪ Say, "Let’s look at the group of 5 objects. How can we color them using blue and yellow to show a way to make 5?" o Suggest a combination, such as 3 objects in blue and 2 in yellow.

▪ Say, "If we color 3 objects blue and 2 objects yellow, we get 3 + 2 = 5." o Ask the students to color a group of 5 using 3 blue and 2 yellow and write the combination underneath: 3 + 2 = 5.

4. Interactive Practice (10 minutes): o Encourage the students to explore other combinations on their own.

▪ Say, "Now I want you to try coloring the remaining groups of 4 and 5 using different combinations. Try using 1 blue and 3 yellow for 4, or 4 blue and 1 yellow for 5." o Walk around the classroom to provide support and check that students are using the colors correctly and writing the corresponding numbers accurately. o Remind them to write the number combinations for each group, such as: ▪ "1 + 3 = 4" or "4 + 1 = 5".

5. Independent Practice (5 minutes): o Allow the students to complete the exercise independently.

▪ Say, "Now it's your turn to come up with your own combinations for making 4 and 5. Remember to use blue and yellow to color the objects, and write the numbers that add up to 4 or 5." o Provide assistance as needed, ensuring that students understand the task.

6. Review and Reinforcement (5 minutes): o Once the students have finished, review their answers as a class. o Ask a few students to share the combinations they created and explain why they used specific colors.

▪ For example, "I used 1 yellow and 3 blue because 1 + 3 makes 4." o Praise students for their creativity and accuracy in using colors to represent number combinations.

▪

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 10

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that using colors to see how numbers are made up of different parts is a helpful way to understand addition and grouping in everyday life. o Encourage students to practice making combinations at home using toys, blocks, or other objects, and to use different colors to show the groups.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to model how to color and create combinations for the numbers 4 and 5.

Encouragement: Provide positive feedback and praise creativity when students come up with unique combinations.

Repetition: Reinforce the concept by using different objects (e.g., crayons, counters) to show various combinations for 4 and 5.

Differentiation: Offer additional support to students who need help with coloring and composition and provide more advanced challenges for those who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 11

Lesson

2

Decompose 4 and 5

Exercise:1 Exercise Overview: In this exercise, kindergarten students will practice decomposing the numbers 4 and 5 by using rectangles to divide groups of objects. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 4 and 5." Students will use the visual tool of rectangles to break apart groups of 4 and 5 into smaller parts, helping them understand the concept of decomposition. This activity introduces students to how larger numbers can be broken down into smaller parts and prepares them for understanding subtraction and part-part-whole relationships.

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of decomposition (taking apart) of numbers.

▪ Say, "Today we are going to learn how to take apart the numbers 4 and 5. We will use rectangles to show how we can break these numbers into smaller groups." o Use visual aids (e.g., drawing on the board) to demonstrate how a group of objects (such as 4 apples) can be divided into smaller groups.

▪ For example, draw 4 apples and use rectangles to separate 2 apples in one group and 2 in another. Then show a different way by grouping 3 apples in one rectangle and 1 in another.

2. Demonstrating the Exercise (5 minutes): o Open the book to the lesson titled “Decompose 4 and 5.” o Show the students the groups of 4 and 5 objects. o Explain that they will use rectangles to divide the objects into smaller groups to see how the number can be decomposed into parts. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 12

Say, "We will use rectangles to separate the objects into smaller groups. For example, if we have 4 apples, we can draw a rectangle around 2 apples and another around the other 2 apples. That shows that 4 can be taken apart into two groups of 2."

3. Guided Practice (10 minutes): ▪

Exercise a: Use the rectangles to show ways to take apart 4 and 5.

Start by looking at the group of 4 objects (e.g., 4 apples).

▪ Say, "Let’s start with the 4 apples. We can draw rectangles around the apples to show how we can take apart 4 into smaller groups." o Demonstrate using the following example: ▪ Example 1: Draw a rectangle around 2 apples and another rectangle around the other 2 apples. (Explain: "2 apples + 2 apples = 4.") o Write this on the board: "2 + 2 = 4." o Now move to the group of 5 objects (e.g., 5 apples).

▪ Say, "Now let’s look at the 5 apples. We can draw rectangles to show different ways to take apart 5." o Demonstrate using the following example: ▪ Example 1: Draw a rectangle around 3 apples and another around the other 2 apples. (Explain: "3 apples + 2 apples = 5.") o Write this on the board: "3 + 2 = 5."

4. Interactive Practice (10 minutes): o

Exercise b: Encourage the students to suggest more ways to take apart 4 and 5.

Ask the students to come up with more ways to decompose the numbers 4 and 5.

▪ Say, "Can you think of other ways to take apart 4 and 5?

How would you group the objects using rectangles?" o Guide them through different possibilities: ▪ For 4: "You can draw a rectangle around 3 objects and 1 object. That shows that 4 can be taken apart into 3 and 1."

(Write: 3 + 1 = 4) ▪ For 5: "You can draw a rectangle around 4 objects and 1 object. That shows that 5 can be taken apart into 4 and 1."

(Write: 4 + 1 = 5) o Allow the students to come up with their own ideas, encouraging creativity and exploration of different ways to decompose the numbers.

5. Independent Practice (5 minutes): o Let the students work independently to complete the exercise. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 13

Say, "Now it's your turn to draw rectangles to show how you can take apart the groups of 4 and 5. Try to come up with as many different ways as you can." o Walk around the classroom to provide guidance and support as needed.

6. Review and Reinforcement (5 minutes): o Once the students have completed the exercise, review their answers as a class. o Ask a few students to share how they decomposed the numbers and explain how they used the rectangles.

▪ Say, "Great job! You found many ways to take apart 4 and 5 using rectangles." o Correct any misunderstandings and provide positive reinforcement for their efforts.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that decomposing numbers is a useful skill in everyday life. For example, it helps us understand how to share or divide things into equal parts, like toys or snacks. o Encourage students to practice taking apart numbers at home using objects like toys, blocks, or snacks to create different combinations.

▪

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers using rectangles.

Encouragement: Provide positive feedback and praise creative combinations of decomposition.

Repetition: Reinforce the concept with other numbers, such as 6 or 7, to ensure students understand decomposition.

Differentiation: Offer additional help to students who need more guidance and provide extra challenges for those who quickly grasp the concept.

Exercise: 2-7 Exercise Overview: In this exercise, students will practice decomposing the numbers 4 and 5 by drawing rectangles around groups of objects to show different ways of taking apart these numbers. This activity will help students understand how numbers can be broken into smaller parts, laying a foundation for addition and subtraction concepts. The exercise is available in "Explore Math: Book B ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 14

(Operations and Algebraic Thinking)" under the lesson titled "Decompose 4 and 5."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining the concept of decomposition, or "taking apart" numbers.

▪ Say, "Today we are going to learn how to take apart the numbers 4 and 5. We will use rectangles to show how we can break these numbers into smaller parts." o Provide a visual example on the board.

▪ Draw 4 circles and explain, "We can group these circles in different ways. We can put 2 circles in one group and 2 in another, or 3 in one group and 1 in another." o Explain that students will use rectangles to group objects in different ways to show how numbers can be decomposed.

2. Demonstrating the Exercise (5 minutes): Exercise a: Draw rectangles around the objects to show one way to take apart the given number. Write the numbers. o o

o

o o

o

Open the book to the lesson titled “Decompose 4 and 5.”

Guide the students in identifying the number of objects they see (either 4 or 5).

▪ Say, "Let's look at the first group of objects. How many do we have here? We have 4 objects. We will draw rectangles around the objects to show one way to take apart 4."

Demonstrate by drawing a rectangle around 2 objects and another rectangle around the other 2 objects, showing that 4 can be broken into 2 + 2.

▪ Say, "I’m drawing a rectangle around 2 objects, and another around the other 2. Now we have 2 objects + 2 objects = 4."

Write on the board: "2 + 2 = 4."

Move to the group with 5 objects.

▪ Say, "Now let's look at the 5 objects. We can take apart 5 by drawing rectangles around different groups of objects."

Draw a rectangle around 3 objects and another around 2 objects, showing that 5 can be decomposed into 3 + 2.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 15

Say, "We can take apart 5 by grouping 3 objects in one rectangle and 2 in another. That makes 3 + 2 = 5." o Write on the board: "3 + 2 = 5."

3. Guided Practice (10 minutes): o Ask the students to practice by drawing rectangles around the objects in their books to show how they can decompose 4 and 5.

▪ Say, "Now it’s your turn. Draw rectangles around the objects to show how you would take apart 4 and 5.

Remember to write the numbers that show the groups you created." o Walk around the classroom, offering guidance and assistance as students complete the task.

▪ Encourage them to be creative and think of different ways to break apart the numbers.

4. Interactive Practice (10 minutes): ▪

Exercise b: Suggest more ways to take apart 4 and 5.

Once students have completed their first decomposition, encourage them to suggest other ways to decompose 4 and 5.

▪ Ask, "Can you think of another way to take apart the number 4? What about the number 5?" o Guide them through different possibilities: ▪ For 4: "You can group 3 objects in one rectangle and 1 in another. That shows 3 + 1 = 4."

▪ For 5: "You can group 4 objects in one rectangle and 1 in another. That shows 4 + 1 = 5." o Write these additional decompositions on the board as students share their ideas.

5. Independent Practice (5 minutes): o Allow the students to explore more combinations on their own.

▪ Say, "Now let’s see how many different ways you can find to take apart the numbers 4 and 5. Draw your rectangles and write the numbers." o Walk around to provide guidance and support.

6. Review and Reinforcement (5 minutes): o Review the different ways students have decomposed 4 and 5.

▪ Ask a few students to share their work and explain how they drew the rectangles to break apart the numbers. o Reinforce that there are multiple ways to take apart a number.

▪ Say, "Great work! You found many different ways to break apart 4 and 5. This will help us when we learn to add and subtract numbers." o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 16

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that taking apart numbers helps us understand how things can be divided or grouped in everyday life.

▪ Say, "When we understand how numbers can be broken down into smaller parts, it helps us share and divide things like toys, snacks, or other objects." o Encourage students to try decomposing other numbers at home, such as 6 or 7, using everyday objects.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate different ways to decompose numbers.

Encouragement: Provide positive feedback to encourage students to explore different combinations.

Repetition: Reinforce the concept with other numbers to deepen students' understanding of decomposition.

Differentiation: Offer extra support for students who need it and additional challenges for those who quickly grasp the concept.

Exercise: 8-9

Exercise Overview: In this exercise, students will practice decomposing the numbers 4 and 5 by drawing bananas and apples in blank boxes, showing how these numbers can be broken into smaller parts. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 4 and 5." Students will visualize and represent the process of decomposition by breaking apart groups of 4 bananas and 5 apples into smaller groups.

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 17

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining the concept of decomposition (taking apart) numbers.

▪ Say, "Today we are going to learn how to take apart the numbers 4 and 5. We will use drawings of bananas and apples to show how we can break these numbers into smaller groups." o Show a simple example on the board by drawing 4 bananas and explaining how they can be split into two smaller groups (e.g., 2 bananas + 2 bananas = 4). o Explain that students will decompose these numbers in different ways by drawing bananas and apples in blank boxes.

2. Demonstrating the Exercise (5 minutes): Exercise 8: Take apart four bananas. Draw the bananas in the blank boxes. o o o

o o

o

Open the book to the lesson titled "Decompose 4 and 5."

Show the students the section where they are asked to take apart 4 bananas.

Demonstrate by drawing 2 bananas in one blank box and 2 bananas in another, showing that 4 can be decomposed into 2 + 2.

▪ Say, "Let's take apart the number 4 by drawing 2 bananas in this box and 2 bananas in the next box. Now we have 2 + 2 = 4."

Write on the board: "2 + 2 = 4."

Next, suggest another way to decompose 4 by drawing 3 bananas in one box and 1 banana in the other.

▪ Say, "Now let's take apart 4 in a different way by drawing 3 bananas in one box and 1 banana in another. This shows that 3 + 1 = 4."

Write on the board: "3 + 1 = 4."

Exercise 9: Take apart five apples. Draw the apples in the blank boxes. o o

o o

Move to the section on taking apart 5 apples.

Demonstrate by drawing 3 apples in one box and 2 apples in the other, showing that 5 can be decomposed into 3 + 2.

▪ Say, "Now let’s take apart the number 5 by drawing 3 apples in this box and 2 apples in the other. This shows that 3 + 2 = 5."

Write on the board: "3 + 2 = 5."

Next, suggest another way to decompose 5 by drawing 4 apples in one box and 1 apple in the other.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 18

Say, "Let's try another way. We can draw 4 apples in one box and 1 apple in another. This shows that 4 + 1 = 5." o Write on the board: "4 + 1 = 5."

3. Guided Practice (10 minutes): o Allow the students to work on Exercise 8 and Exercise 9 by drawing their own bananas and apples in the blank boxes to decompose the numbers.

▪ Say, "Now it’s your turn to take apart 4 bananas and 5 apples. Draw the bananas and apples in the blank boxes to show different ways you can decompose these numbers." o Encourage the students to try different combinations. o Walk around the classroom to provide guidance and support as students complete the task.

4. Interactive Practice (10 minutes): o Encourage the students to come up with additional ways to decompose the numbers 4 and 5.

▪ Say, "Can you think of other ways to take apart 4 bananas or 5 apples? Try drawing them in different ways to show more combinations." o Guide them to think creatively and try various combinations for each number. o Ask questions like, "How many bananas could go in one box, and how many could go in the other? What about the apples?"

5. Independent Practice (5 minutes): o Allow the students to explore and draw different combinations on their own.

▪ Say, "Let’s see how many different ways you can find to take apart the numbers 4 and 5. Try different ways to decompose the bananas and apples." o Walk around and check if students are coming up with different combinations and drawing accurately.

6. Review and Reinforcement (5 minutes): o Once the students have completed the exercise, review their work as a class. o Ask a few students to share the different ways they decomposed the bananas and apples. o Reinforce that numbers can be taken apart in many ways and that this skill will help with addition and subtraction.

▪ Say, "Great work! You found many different ways to take apart the numbers 4 and 5. This will help us when we start adding and subtracting numbers."

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that decomposing numbers helps us understand how things can be divided into parts in everyday life.

▪

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 19

Say, "When we understand how numbers can be taken apart, we can use this skill to share and divide things, like toys, food, or other objects."

Encourage students to try decomposing other numbers at home using different objects, such as toys, snacks, or blocks.

▪

o

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to model how to decompose numbers and draw bananas or apples.

Encouragement: Provide positive feedback to encourage students to explore different combinations.

Repetition: Reinforce the concept with other numbers (such as 6 and 7) to strengthen understanding.

Differentiation: Offer extra support for students who need more guidance and provide additional challenges for those who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 20

Lesson

3

Compose 6 and 7

Exercise:1 Exercise Overview: In this exercise, students will practice composing the numbers 6 and 7 by using yellow and blue dots to show different ways to make these numbers.

The activity encourages students to explore various combinations of yellow and blue dots that add up to 6 or 7. The goal is to help students understand the concept of part-part-whole relationships and introduce them to the basics of addition. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 6 and 7."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Yellow and blue crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of composing numbers using visual aids, such as coloring dots to show parts of a whole.

▪ Say, "Today we are going to learn how to make the numbers 6 and 7 by using yellow and blue dots. There are different ways to combine these colors to make the numbers 6 and 7." o Provide a simple visual demonstration on the board, showing how 6 or 7 objects can be broken down into two parts. For example, draw 6 circles and show how you can color 3 yellow and 3 blue to make 6, or color 4 blue and 2 yellow to make 6 in a different way. o Explain that students will use yellow and blue dots to explore different ways to compose 6 and 7.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 21

2. Demonstrating the Exercise (5 minutes): Exercise a: Use the yellow and blue dots to show ways to make 6 and 7.

Open the book to the lesson titled “Compose 6 and 7.”

Show the students the section where they will use yellow and blue dots to make 6 and 7. o Explain that they will color the dots in different combinations to show how the numbers can be composed of two parts.

▪ Say, "Let’s start with the number 6. We can color some of the dots yellow and the rest blue. Let's see how many different ways we can make 6 using yellow and blue." o Demonstrate by coloring the dots in one of the following combinations for 6: ▪ Example 1: Color 3 yellow dots and 3 blue dots to show 3 + 3 = 6.

▪ Example 2: Color 4 yellow dots and 2 blue dots to show 4 + 2 = 6. o Write the number sentences on the board as you demonstrate.

▪ For example: "3 yellow + 3 blue = 6" or "4 yellow + 2 blue = 6." o Move to the number 7.

▪ Say, "Now let's try to make the number 7 using yellow and blue dots. We can color 5 dots yellow and 2 dots blue, or we can color 4 dots blue and 3 dots yellow." o Demonstrate different combinations for 7: ▪ Example 1: Color 5 yellow dots and 2 blue dots to show 5 + 2 = 7.

▪ Example 2: Color 4 blue dots and 3 yellow dots to show 4 + 3 = 7. o Write the number sentences on the board.

3. Guided Practice (10 minutes): o Ask the students to practice coloring their own yellow and blue dots to make 6 and 7.

▪ Say, "Now it's your turn. Use your yellow and blue crayons to color the dots and show different ways to make 6 and 7." o Encourage the students to try multiple combinations for each number. o Walk around the classroom, observing their work and offering guidance when necessary. Provide encouragement and help them understand the different combinations. o o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 22

4. Interactive Practice (10 minutes): Exercise b: Encourage the students to suggest more ways to make 6 and 7.

After students have practiced coloring dots for 6 and 7, encourage them to come up with additional combinations.

▪ Ask, "Can you think of another way to make 6? What about another way to make 7?" o Write their ideas on the board as they share different combinations.

▪ For example: "2 yellow + 4 blue = 6" or "1 yellow + 6 blue = 7." o Allow students to experiment with different possibilities.

5. Independent Practice (5 minutes): o Let students explore independently by finding more ways to compose 6 and 7 using yellow and blue dots.

▪ Say, "Now let’s see how many different ways you can find to make 6 and 7. Color the dots and write the number sentences." o Walk around to provide guidance and ensure students are experimenting with different combinations.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 6 and 7 using yellow and blue dots. o Ask a few students to share how they colored their dots and explain the combinations they created. o Reinforce the idea that numbers can be made in many different ways and that this skill helps us understand addition.

▪ Say, "Great job! You found many different ways to make 6 and 7. This will help us as we learn more about addition."

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that composing numbers helps us understand how groups of things can be put together in different ways.

▪ Say, "When we know how numbers can be made of different parts, it helps us with counting and adding in real life. We can group things like toys, food, or other objects in different ways." o Encourage students to practice making combinations of other numbers at home using toys, blocks, or other objects. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 23

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to model how to compose numbers using yellow and blue dots.

Encouragement: Provide positive feedback to encourage students to think creatively and explore different combinations.

Repetition: Reinforce the concept by practicing with other numbers (such as 8 or 9) to strengthen students' understanding of composition.

Differentiation: Offer extra support for students who need more guidance and provide additional challenges for those who grasp the concept quickly.

Exercise : 2-4 Exercise Overview: In this exercise, students will practice composing the number 6 by coloring objects yellow and red to show different combinations that add up to 6. The goal is to help students explore various ways to make the number 6 and to introduce them to the concept of part-part-whole relationships. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 6 and 7."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Yellow and red crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of composing numbers using visual tools like coloring to show how parts make up a whole.

▪ Say, "Today we are going to learn how to make the number 6 by coloring objects. We will use yellow and red to show the different ways to make 6." o Provide an example on the board using 6 circles. Color 4 circles yellow and 2 circles red, explaining that 4 + 2 = 6. Then color 3 circles yellow and 3 circles red, explaining that 3 + 3 = 6. o Explain that students will use yellow and red to explore how different parts can add up to 6. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 24

2. Demonstrating the Exercise (5 minutes): Exercise a: Color the objects yellow and red to make 6. Write the numbers.

Open the book to the lesson titled “Compose 6 and 7.”

Show the students the section where they will color objects yellow and red to make 6. o Explain that they will color some objects yellow and some red to show different combinations of 6.

▪ Say, "Let’s start with the number 6. We can color some of the objects yellow and the rest red. Let’s see how many ways we can do this." o Demonstrate by coloring the objects with the following combinations: ▪ Example 1: Color 4 objects yellow and 2 objects red. Write "4 + 2 = 6."

▪ Example 2: Color 3 objects yellow and 3 objects red. Write "3 + 3 = 6." o Write these combinations on the board as you demonstrate.

3. Guided Practice (10 minutes): o Ask the students to practice coloring their own objects yellow and red to make 6.

▪ Say, "Now it’s your turn. Use your yellow and red crayons to color the objects and show different ways to make 6." o Encourage students to try multiple combinations. o Walk around the classroom, providing guidance and ensuring students are correctly coloring and writing the number combinations.

4. Interactive Practice (10 minutes): o o

Exercise b: Suggest more ways to make 6. o

o

o

After students have completed their first combinations, encourage them to suggest additional ways to make 6.

▪ Ask, "Can you think of another way to make 6? What if we change how many objects are yellow and how many are red?"

Guide them to explore more possibilities, such as: ▪ Example 3: Color 5 objects yellow and 1 object red. Write "5 + 1 = 6."

▪ Example 4: Color 2 objects yellow and 4 objects red. Write "2 + 4 = 6."

Write these additional combinations on the board and encourage students to try them out in their books.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 25

5. Independent Practice (5 minutes): o Allow students to work independently to explore more combinations.

▪ Say, "Let’s see how many ways you can find to make 6.

Color the objects and write the number sentence for each combination." o Walk around the room, observing their work and offering assistance where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 6 using yellow and red objects. o Ask a few students to share the combinations they colored and explain how they made 6.

▪ Say, "Great job! You found many different ways to make 6.

This helps us learn how numbers are made from parts." o Correct any misunderstandings and reinforce the importance of learning different combinations for numbers.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing numbers helps us understand how groups of things can be divided into different parts.

▪ Say, "When we know how numbers can be made from different parts, it helps us in counting, adding, and even sharing things like toys, snacks, or other objects." o Encourage students to practice composing other numbers at home using toys, blocks, or other objects to create different combinations.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to model how to compose numbers using yellow and red dots or objects.

Encouragement: Provide positive feedback to encourage students to explore various combinations.

Repetition: Reinforce the concept with other numbers, such as 7, to strengthen students' understanding of composition.

Differentiation: Offer extra support for students who need more guidance and provide additional challenges for those who quickly grasp the concept.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 26

Exercises: 5-7 Exercise Overview: In this exercise, students will practice composing the number 7 by coloring vegetables red and yellow to show different combinations that add up to 7.

The activity will help students explore various ways to make the number 7 and introduce them to the concept of part-part-whole relationships. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 6 and 7."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Red and yellow crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of composing numbers by using colors to represent parts of a whole.

▪ Say, "Today we are going to learn how to make the number 7. We will color the vegetables using red and yellow to show different ways to make 7." o Show a simple example on the board. Draw 7 circles (representing vegetables) and color 4 circles red and 3 circles yellow. Explain that 4 + 3 = 7. Then, color 5 circles red and 2 circles yellow to show a different combination (5 + 2 = 7). o Explain to the students that they will color the vegetables in their books using red and yellow to show how the number 7 can be composed.

2. Demonstrating the Exercise (5 minutes): Exercise a: Color the vegetables red and yellow to make 7. Write the numbers. o o o

Open the book to the lesson titled "Compose 6 and 7."

Guide the students to the section where they will color vegetables to make 7.

Explain that they will color some vegetables red and others yellow to show different ways to make 7.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 27

Say, "Let’s start by coloring the vegetables. Some will be red, and the others will be yellow. Let’s see how we can make 7." o Demonstrate by coloring the vegetables in one of the following combinations: ▪ Example 1: Color 4 vegetables red and 3 vegetables yellow. Write "4 + 3 = 7."

▪ Example 2: Color 5 vegetables red and 2 vegetables yellow. Write "5 + 2 = 7." o Write these combinations on the board as you demonstrate.

3. Guided Practice (10 minutes): o Ask the students to practice by coloring their vegetables red and yellow to make 7.

▪ Say, "Now it’s your turn. Use your red and yellow crayons to color the vegetables and show different ways to make 7." o Encourage students to try multiple combinations and experiment with different ways to compose the number 7. o Walk around the classroom to observe their work, providing guidance and support where necessary.

4. Interactive Practice (10 minutes): ▪

Exercise b: Suggest one more way to make 7.

After students have tried a few combinations, encourage them to think of one more way to make 7 using different amounts of red and yellow.

▪ Ask, "Can you think of another way to make 7? What if you color more vegetables red and fewer yellow, or the other way around?" o Write additional combinations on the board as students suggest them, for example: ▪ Example 3: Color 6 vegetables red and 1 vegetable yellow. Write "6 + 1 = 7."

▪ Example 4: Color 3 vegetables red and 4 vegetables yellow. Write "3 + 4 = 7." o Encourage the students to try these combinations in their books.

5. Independent Practice (5 minutes): o Allow the students to explore independently by finding additional ways to compose 7.

▪ Say, "Now let’s see if you can find more ways to make 7.

Color the vegetables and write the number sentence for each combination." o Walk around and check to ensure students are experimenting with different combinations and correctly writing the number sentences. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 28

6. Review and Reinforcement (5 minutes): o Review the various ways students have found to make 7 using red and yellow vegetables. o Ask a few students to share their combinations and explain how they colored their vegetables.

▪ Say, "Great job! You found many ways to make 7 using different combinations of red and yellow vegetables. This will help us understand how numbers are made from parts." o Correct any misunderstandings and reinforce that there are many ways to make a number, and they all help us understand addition.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that composing numbers helps us learn how to divide groups of things into different parts, which is useful in everyday life.

▪ Say, "When we learn how to make numbers using different parts, it helps us in counting, sharing, and adding things like toys, food, or other objects." o Encourage students to practice making combinations of other numbers at home using toys, blocks, or other objects.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to model how to compose numbers using red and yellow dots or objects.

Encouragement: Provide positive feedback to encourage students to explore different combinations.

Repetition: Reinforce the concept with other numbers (such as 6 or 8) to strengthen students' understanding of composition.

Differentiation: Offer extra support for students who need more guidance and provide additional challenges for those who quickly grasp the concept.

Exercises 8-10

Exercise Overview: In this exercise, students will practice composing the numbers 6 and 7 by coloring objects green and red to represent different ways these numbers can be broken into parts. The activity helps students understand the part___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 29

part-whole relationship of numbers, laying a foundation for addition. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 6 and 7."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Green and red crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining that composing numbers means finding different ways to break them into parts.

▪ Say, "Today we will use green and red to show different ways to make the numbers 6 and 7. We can divide the objects into two parts—some will be green, and some will be red." o Provide a visual example on the board using 6 circles (for the number 6). Color 4 circles green and 2 circles red, explaining that 4 + 2 = 6. Then, color 3 circles green and 3 circles red, showing that 3 + 3 = 6. o Repeat for the number 7, showing combinations such as 5 + 2 and 4 + 3.

2. Demonstrating the Exercise (5 minutes): Exercise: Color the objects green and red to make 6 and 7. Write the numbers. o o o

o

o

Open the book to the lesson titled "Compose 6 and 7."

Guide students to the section where they will color the objects green and red to make the numbers 6 and 7.

Explain that they will use green and red to show different ways to create these numbers.

▪ Say, "Let’s start by coloring the objects to make 6. Some will be green, and some will be red. Let’s see how many ways we can do this."

Demonstrate by coloring the objects using the following combinations: ▪ Example 1 for 6: Color 4 objects green and 2 objects red.

Write "4 + 2 = 6."

▪ Example 2 for 6: Color 3 objects green and 3 objects red.

Write "3 + 3 = 6."

Write these combinations on the board.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 30

Move to the number 7 and demonstrate with the following combinations: ▪ Example 1 for 7: Color 5 objects green and 2 objects red.

Write "5 + 2 = 7."

▪ Example 2 for 7: Color 4 objects green and 3 objects red.

Write "4 + 3 = 7." o Write these combinations on the board as well.

3. Guided Practice (10 minutes): o Ask students to practice by coloring their own objects green and red to make 6 and 7.

▪ Say, "Now it’s your turn. Use your green and red crayons to color the objects and show different ways to make 6 and 7." o Encourage students to try several combinations for each number. o Walk around the classroom, observing their work and providing guidance as necessary.

4. Interactive Practice (10 minutes): o After students have tried a few combinations, ask them to share different ways they made 6 and 7.

▪ Ask, "Can you think of another way to make 6? What about 7? Let’s see how many different combinations we can come up with." o Write the different combinations on the board as students suggest them.

▪ For example: "2 green + 4 red = 6" or "3 green + 4 red = 7." o Encourage students to try these combinations in their books and explore new ones.

5. Independent Practice (5 minutes): o Allow students to independently explore more combinations.

▪ Say, "Now let’s see if you can find more ways to make 6 and 7. Color the objects and write the number sentence for each combination." o Walk around the room to check their work and provide assistance where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 6 and 7 using green and red. o Ask a few students to share the combinations they colored and explain how they arrived at them.

▪ Say, "Great job! You discovered many ways to make 6 and 7 using green and red. This helps us learn how numbers are made from parts." o Reinforce that numbers can be composed in many ways, which is important for understanding addition. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 31

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing numbers helps in real life when we need to group or share things.

▪ Say, "When we understand how numbers are made from parts, it helps us when we are counting, adding, or dividing things like toys, snacks, or other objects." o Encourage students to practice at home by grouping objects like toys or food to explore how different combinations can make the same number.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to model how to compose numbers using green and red objects.

Encouragement: Provide positive feedback to motivate students to explore various combinations.

Repetition: Reinforce the concept with other numbers (e.g., 8 or 9) to deepen their understanding of composition.

Differentiation: Offer extra help to students who need more guidance, and provide additional challenges for those who quickly grasp the concept.

Lesson

4

decompose 6 and 7

Exercise Overview: In this exercise, students will practice decomposing the numbers 6 and 7 by drawing rectangles around groups of objects to show different ways to take apart these numbers. This activity introduces students to the concept of breaking down numbers into smaller parts (decomposition), which builds foundational skills for subtraction and understanding number relationships.

The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 6 and 7."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers Crayons (optional)

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 32

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining the concept of decomposition, or "taking apart" numbers, and how numbers like 6 and 7 can be broken down into smaller parts.

▪ Say, "Today we are going to learn how to take apart the numbers 6 and 7 by drawing rectangles around groups of objects. We will show different ways to break these numbers into smaller parts." o Provide an example on the board by drawing 6 circles and show how they can be separated into two groups. For example, draw a rectangle around 4 circles and another around 2 circles, explaining that 4 + 2 = 6. o Then, repeat with 7 circles, drawing a rectangle around 5 circles and another around 2 circles, showing that 5 + 2 = 7. o Explain that students will use rectangles to group objects in different ways to show how numbers can be decomposed.

2. Demonstrating the Exercise (5 minutes): Exercise a: Use the rectangles to show ways to take apart 6 and 7. o o o

o o

o

Open the book to the lesson titled "Decompose 6 and 7."

Guide the students to the section where they will use rectangles to decompose the numbers 6 and 7.

Demonstrate how to draw rectangles around the objects to show different ways to take apart 6: ▪ Say, "Let’s look at the group of 6 objects. We can draw a rectangle around some of them and then draw another rectangle around the rest."

▪ Example 1: Draw a rectangle around 4 objects and another around 2 objects, showing that 4 + 2 = 6.

▪ Example 2: Draw a rectangle around 3 objects and another around 3 objects, showing that 3 + 3 = 6.

Write the number sentences on the board: "4 + 2 = 6" and "3 + 3 = 6."

Move to the number 7: ▪ Say, "Now let’s look at the 7 objects. We can take apart 7 by drawing rectangles around different groups of objects."

▪ Example 1: Draw a rectangle around 5 objects and another around 2 objects, showing that 5 + 2 = 7.

▪ Example 2: Draw a rectangle around 4 objects and another around 3 objects, showing that 4 + 3 = 7.

Write the number sentences on the board: "5 + 2 = 7" and "4 + 3 = 7."

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 33

3. Guided Practice (10 minutes): o Ask the students to practice drawing rectangles around their objects to show how to take apart 6 and 7.

▪ Say, "Now it’s your turn. Draw rectangles around the objects to show how you would take apart 6 and 7. Then write the numbers for each group." o Encourage students to try different combinations for both numbers. o Walk around the classroom to observe their work, offering guidance and support as needed.

4. Interactive Practice (10 minutes): Exercise b: Encourage the students to suggest more ways to take apart 6 and 7.

Once students have practiced decomposing 6 and 7, encourage them to suggest additional ways to decompose the numbers.

▪ Ask, "Can you think of another way to take apart 6? What about 7? How can we group the objects differently?" o Guide them to explore more possibilities: ▪ For 6: Draw 1 object in one rectangle and 5 in another, showing 1 + 5 = 6.

▪ For 7: Draw 3 objects in one rectangle and 4 in another, showing 3 + 4 = 7. o Write these additional decompositions on the board as students share their ideas.

5. Independent Practice (5 minutes): o Allow students to continue exploring independently by finding other ways to take apart 6 and 7.

▪ Say, "Now let’s see how many different ways you can find to take apart the numbers 6 and 7. Draw rectangles around the objects and write the numbers for each group." o Walk around to provide support and encourage students to try new combinations.

6. Review and Reinforcement (5 minutes): o Review the different ways students have decomposed 6 and 7. o Ask a few students to share their work with the class and explain how they drew their rectangles to take apart the numbers. o Reinforce the idea that numbers can be taken apart in many ways.

▪ Say, "Great job! You found many different ways to take apart 6 and 7. This will help us when we start learning to add and subtract." o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 34

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining that decomposing numbers is a useful skill in everyday life when we need to divide or share things.

▪ Say, "When we learn how to take apart numbers, it helps us when we need to share or divide things, like toys, food, or other objects." o Encourage students to try decomposing other numbers, such as 8 or 9, at home using everyday objects like toys or blocks.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing rectangles around objects.

Encouragement: Provide positive feedback to motivate students to explore different ways to decompose numbers.

Repetition: Reinforce the concept with other numbers to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance and provide additional challenges for those who grasp the concept quickly.

Exercises 2-7 Exercise Overview: In this exercise, students will practice decomposing the numbers 6 and 7 by drawing rectangles around objects to show different ways to break apart these numbers. This activity helps students develop their understanding of how numbers can be divided into smaller parts, laying the foundation for addition and subtraction. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 6 and 7."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers Crayons (optional)

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 35

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining the concept of decomposition, or taking apart numbers, and how numbers like 6 and 7 can be divided into smaller groups.

▪ Say, "Today we are going to learn how to take apart the numbers 6 and 7. We will do this by drawing rectangles around groups of objects to show how they can be divided into parts." o Show a simple example on the board. Draw 6 circles and explain that these 6 circles can be broken into smaller groups. Draw a rectangle around 4 circles and another rectangle around 2 circles. Explain that 4 + 2 = 6. o Repeat the process for the number 7, drawing 5 circles in one rectangle and 2 circles in another, showing that 5 + 2 = 7. o Explain that students will do something similar in their books by drawing rectangles to show how the numbers 6 and 7 can be taken apart.

2. Demonstrating the Exercise (5 minutes): Exercise: Draw rectangles around the objects to show one way to take apart the given number. Write the numbers.

Open the book to the lesson titled "Decompose 6 and 7."

Guide the students to the section where they will use rectangles to show different ways to take apart 6 and 7. o Demonstrate how to draw rectangles around the objects for the number 6: ▪ Say, "Let’s look at the 6 objects. We can draw a rectangle around some of them and then draw another rectangle around the rest to show how 6 can be split into parts."

▪ Example: Draw a rectangle around 4 objects and another around 2 objects, showing that 4 + 2 = 6.

▪ Write the number sentence: "4 + 2 = 6." o Move to the number 7: ▪ Say, "Now let’s look at the 7 objects. We can take apart 7 in different ways by drawing rectangles around smaller groups."

▪ Example: Draw a rectangle around 5 objects and another around 2 objects, showing that 5 + 2 = 7.

▪ Write the number sentence: "5 + 2 = 7."

3. Guided Practice (10 minutes): o Ask students to practice drawing rectangles around objects to show how to take apart 6 and 7. o o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 36

Say, "Now it’s your turn. Draw rectangles around the objects in your book to show how you can take apart the numbers 6 and 7. Then, write the numbers for each group." o Encourage students to try different ways to break apart the numbers. o Walk around the classroom, providing support and guidance as students work through the exercise.

4. Interactive Practice (10 minutes): o Once students have practiced drawing rectangles to take apart the numbers 6 and 7, encourage them to share their work with the class.

▪ Ask, "Who can show us how they took apart 6 or 7? Can you explain how you used the rectangles to break the number into parts?" o Allow students to share their combinations, such as: ▪ For 6: "3 + 3 = 6" or "1 + 5 = 6."

▪ For 7: "4 + 3 = 7" or "2 + 5 = 7." o Write the different decompositions on the board as students explain their work.

5. Independent Practice (5 minutes): o Allow students time to independently explore more ways to take apart the numbers 6 and 7.

▪ Say, "Let’s see if you can find more ways to take apart 6 and 7. Draw rectangles around the objects and write the numbers for each group." o Walk around the room to check if students are coming up with different combinations and provide help where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students decomposed the numbers 6 and 7. o Ask a few students to share their work with the class and explain how they grouped the objects using rectangles.

▪ Say, "Great job! You found many different ways to take apart the numbers 6 and 7. This will help you with addition and subtraction in the future." o Reinforce that there are many ways to take apart a number, and these skills will help them understand math better.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how taking apart numbers helps us divide or share things in real life.

▪ Say, "When we learn how to take apart numbers, it helps us understand how to divide or share things like toys, food, or other objects." o Encourage students to practice decomposing other numbers at home using objects like toys or snacks.

▪

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 37

Additional Tips: • • •

•

Visual Aid: Use a large paper or whiteboard to model how to take apart numbers by drawing rectangles around objects.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different ways to decompose numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 8 or 9) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support for students who need more guidance, and provide additional challenges for those who quickly grasp the concept.

Exercises 8-9 Exercise Overview: In this exercise, students will practice decomposing the numbers 6 and 7 by drawing balloons and balls in blank boxes to represent different ways to break these numbers into smaller parts. This activity reinforces the concept of decomposition, which is essential for developing addition and subtraction skills. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 6 and 7."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers Crayons (optional for coloring the balloons and balls)

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by reviewing the concept of decomposition, explaining that it means breaking numbers into smaller parts.

▪ Say, "Today we are going to practice taking apart the numbers 6 and 7 by drawing balloons and balls. We will learn how these numbers can be split into different groups." ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 38

On the board, draw 6 circles (representing balloons) and show how they can be divided into two groups by drawing two boxes: one containing 4 balloons and another containing 2. Explain that 4 + 2 = 6. o Repeat for the number 7 by drawing 7 circles (representing balls) and dividing them into a group of 5 and a group of 2. Explain that 5 + 2 = 7.

2. Demonstrating the Exercise (5 minutes): o

Exercise 8: Take apart six balloons. Draw the balloons in the blank boxes. o o o

o o o o

Open the book to the lesson titled "Decompose 6 and 7."

Guide the students to the section where they will draw balloons in blank boxes to take apart the number 6.

Say, "Let’s start with the number 6. You can draw some balloons in one box and the rest in the other box to show how to take apart 6."

Demonstrate by drawing 4 balloons in one box and 2 balloons in the other, explaining that 4 + 2 = 6.

Write the number sentence "4 + 2 = 6" on the board.

Then, suggest another way: draw 3 balloons in one box and 3 in the other, explaining that 3 + 3 = 6.

Write the number sentence "3 + 3 = 6."

Exercise 9: Take apart seven balls. Draw the balls in the blank boxes.

Move on to the number 7.

Say, "Now let’s try the number 7. You can draw some balls in one box and the rest in the other to show how to take apart 7." o Demonstrate by drawing 5 balls in one box and 2 balls in the other, explaining that 5 + 2 = 7. o Write the number sentence "5 + 2 = 7" on the board. o Suggest another way: draw 4 balls in one box and 3 balls in the other, explaining that 4 + 3 = 7. o Write the number sentence "4 + 3 = 7."

3. Guided Practice (10 minutes): o Ask the students to practice drawing their own balloons and balls in the blank boxes to show how to take apart 6 and 7.

▪ Say, "Now it’s your turn. Draw the balloons in the blank boxes to take apart 6, and then draw the balls in the blank boxes to take apart 7. You can decide how many to put in each box." o Encourage students to experiment with different ways to break down the numbers. o Walk around the classroom, observing their work and providing guidance and support as needed. o o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 39

4. Interactive Practice (10 minutes): o After students have completed the exercises, encourage them to share their work with the class.

▪ Ask, "Who can show us how they took apart the number 6 using the balloons? And who would like to share how they took apart the number 7 using the balls?" o Allow students to share the different ways they decomposed the numbers, for example: ▪ For 6: "3 + 3 = 6" or "2 + 4 = 6."

▪ For 7: "5 + 2 = 7" or "4 + 3 = 7." o Write their number sentences on the board as they explain their work.

5. Independent Practice (5 minutes): o Allow students time to independently explore more ways to take apart 6 and 7 by drawing balloons and balls.

▪ Say, "Let’s see if you can find even more ways to take apart 6 and 7. Draw the balloons and balls in the blank boxes and write the numbers for each group." o Walk around the room to ensure students are trying different combinations and provide assistance if needed.

6. Review and Reinforcement (5 minutes): o Review the various ways students found to decompose 6 and 7. o Ask a few students to share how they drew their balloons and balls, and explain their number sentences.

▪ Say, "Great job! You found many different ways to take apart 6 and 7. This will help you understand how numbers can be broken into parts, which is important for math." o Reinforce that there are many ways to take apart a number, and this skill helps with addition and subtraction.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how taking apart numbers helps in real life when we need to divide or share things.

▪ Say, "When we learn how to take apart numbers, it helps us when we need to divide things like toys, food, or other objects into different groups." o Encourage students to practice taking apart other numbers, such as 8 or 9, using objects at home like toys or snacks.

Additional Tips: • •

Visual Aid: Use a large paper or whiteboard to model how to decompose numbers by drawing balloons or balls in blank boxes.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different ways to take apart numbers.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 40

• •

Repetition: Reinforce the concept by practicing with other numbers to deepen students' understanding of decomposition.

Differentiation: Offer extra support for students who need more guidance, and provide additional challenges for those who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 41

Lesson

5

Compose 8 and 9

Exercises 1 Exercise Overview: In this exercise, students will practice composing the numbers 8 and 9 by using yellow and blue dots to show different ways these numbers can be broken into parts. This activity introduces students to the concept of composing numbers (part-part-whole relationships), which is foundational for addition. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 8 and 9."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Yellow and blue crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining that composing numbers means finding different ways to make a whole number using smaller parts.

▪ Say, "Today we are going to learn how to make the numbers 8 and 9 by using yellow and blue dots. We can divide these numbers into different parts, some yellow and some blue." o On the board, demonstrate how the number 8 can be made using two parts. Draw 8 circles (representing dots) and color 5 of them yellow and 3 of them blue. Explain that 5 + 3 = 8. Then show another combination by coloring 4 yellow and 4 blue, explaining that 4 + 4 = 8. o Repeat the process for the number 9. Draw 9 circles and color 6 yellow and 3 blue, showing that 6 + 3 = 9. Then show another combination: 5 yellow and 4 blue, explaining that 5 + 4 = 9.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 42

2. Demonstrating the Exercise (5 minutes): Exercise a: Use the yellow and blue dots to show ways to make 8 and 9.

Open the book to the lesson titled "Compose 8 and 9."

Guide the students to the section where they will use yellow and blue dots to show ways to make 8 and 9. o Say, "Let’s start by using the yellow and blue dots to show different ways to make 8. We will color some dots yellow and the rest blue." o Demonstrate the first example for the number 8 by coloring 5 dots yellow and 3 dots blue. Write "5 + 3 = 8" on the board. o Then show another example: color 4 dots yellow and 4 dots blue.

Write "4 + 4 = 8." o Now move to the number 9: ▪ Say, "Now let’s make 9. You can color some dots yellow and the rest blue to show how to make 9."

▪ Demonstrate by coloring 6 dots yellow and 3 dots blue, writing "6 + 3 = 9."

▪ Then show another combination by coloring 5 dots yellow and 4 dots blue. Write "5 + 4 = 9."

3. Guided Practice (10 minutes): o Ask the students to practice using the yellow and blue dots to make 8 and 9.

▪ Say, "Now it’s your turn! Use your yellow and blue crayons to color the dots and show different ways to make 8 and 9.

Write the numbers for each combination." o Encourage students to try multiple combinations for each number. o Walk around the classroom, observing their work and providing guidance as needed.

4. Interactive Practice (10 minutes): o o

Exercise b: Encourage the students to suggest more ways to make 8 and 9. o

o

o

After the students have completed the first set of combinations, encourage them to think of other ways to make 8 and 9.

▪ Ask, "Can you think of more ways to make 8? How about 9? What if you color more dots yellow and fewer dots blue, or the other way around?"

Allow students to share their ideas with the class. Write the combinations on the board as they suggest them, such as: ▪ For 8: 6 yellow + 2 blue = 8, or 3 yellow + 5 blue = 8.

▪ For 9: 7 yellow + 2 blue = 9, or 2 yellow + 7 blue = 9.

Encourage students to try these new combinations in their books.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 43

5. Independent Practice (5 minutes): o Give students time to independently explore more ways to make 8 and 9 using the yellow and blue dots.

▪ Say, "Let’s see how many different ways you can find to make 8 and 9. Color the dots and write the number sentence for each combination." o Walk around the room to check their work and provide support as needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 8 and 9 using yellow and blue dots. o Ask a few students to share their combinations and explain how they colored their dots.

▪ Say, "Great job! You discovered many ways to make 8 and 9 using yellow and blue. This helps us learn how numbers are made from parts." o Reinforce that there are many ways to compose a number, and this understanding is important for learning addition.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing numbers helps in everyday life when we group or add objects.

▪ Say, "When we know how to make numbers using different parts, it helps us in counting, adding, and grouping things, like toys, food, or other objects." o Encourage students to practice making combinations of other numbers at home using objects like toys or snacks.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to model how to compose numbers using yellow and blue dots.

Encouragement: Provide positive feedback to motivate students to explore different combinations.

Repetition: Reinforce the concept with other numbers (such as 10) to strengthen students' understanding of composition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for those who quickly grasp the concept.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 44

Exercises 2-4 Exercise Overview: In this exercise, students will practice composing the number 8 by coloring objects yellow and red, showing different ways that 8 can be made by combining two parts. This exercise is designed to introduce students to the concept of composing numbers, which builds foundational skills for understanding addition. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 8 and 9."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Yellow and red crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Start by introducing the concept of composing numbers, explaining that it means breaking a whole number into two parts.

▪ Say, "Today we are going to use yellow and red to show different ways to make the number 8. You will color some objects yellow and some red, then write the numbers that represent each part." o On the board, demonstrate how to break the number 8 into parts by drawing 8 circles. Color 5 of them yellow and 3 of them red. Explain that 5 + 3 = 8. o Show another combination by coloring 4 yellow and 4 red, explaining that 4 + 4 = 8. o Write these number sentences on the board: "5 + 3 = 8" and "4 + 4 = 8."

2. Demonstrating the Exercise (5 minutes): Exercise a: Color the objects yellow and red to make 8. Write the numbers. o o o

Open the book to the lesson titled "Compose 8 and 9."

Guide the students to the section where they will color the objects yellow and red to show ways to make 8.

Say, "Let’s start by coloring the objects to show one way to make 8. We will color some objects yellow and the rest red."

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 45

Demonstrate the first example by coloring 5 objects yellow and 3 objects red, explaining that 5 + 3 = 8. o Write "5 + 3 = 8" on the board. o Now show another way to make 8 by coloring 4 objects yellow and 4 objects red, explaining that 4 + 4 = 8. o Write "4 + 4 = 8" on the board.

3. Guided Practice (10 minutes): o Ask students to practice by coloring their own objects yellow and red to show different ways to make 8.

▪ Say, "Now it’s your turn! Use your yellow and red crayons to color the objects and show different ways to make 8. Then write the numbers for each part." o Encourage students to try at least two different combinations to make 8. o Walk around the classroom, observing their work and providing support and guidance as needed.

4. Interactive Practice (10 minutes): o

Exercise b: Suggest more ways to make 8.

After students have practiced making 8 with their yellow and red objects, encourage them to come up with more ways to compose 8.

▪ Ask, "Can you think of more ways to make 8 using yellow and red? Let’s see how many combinations we can come up with!" o Allow students to share their suggestions with the class. Write their ideas on the board, such as: ▪ "6 yellow + 2 red = 8" ▪ "3 yellow + 5 red = 8" o Encourage the students to try these new combinations in their books.

5. Independent Practice (5 minutes): o Give students time to independently explore additional ways to make 8 using yellow and red crayons.

▪ Say, "Now, see if you can find even more ways to make 8.

Color the objects and write the number sentences for each combination." o Walk around the room to ensure students are trying different combinations and provide help where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 8 using yellow and red objects. o Ask a few students to share their combinations with the class and explain how they chose to color their objects.

▪ Say, "Great job! You all found many ways to make 8 using yellow and red. This helps us understand how numbers are ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 46 o

made from parts, which will be important when we learn addition." o Reinforce the idea that numbers can be made in different ways, which helps build a strong understanding of number composition.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing numbers is helpful in real-life situations when grouping or counting objects.

▪ Say, "Knowing how to make numbers in different ways helps us when we need to count or group things, like toys, snacks, or other objects." o Encourage students to practice composing other numbers at home, using objects like toys or blocks.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to compose numbers by coloring objects yellow and red.

Encouragement: Provide positive feedback to motivate students to explore different combinations.

Repetition: Reinforce the concept with other numbers (such as 9 or 10) to strengthen students' understanding of composition.

Differentiation: Offer extra support to students who need more guidance and provide additional challenges for students who quickly grasp the concept.

Exercises 5-7 Exercise Overview: In this exercise, students will practice composing the number 9 by coloring objects yellow and blue, showing different ways that 9 can be made by combining two parts. This exercise helps students understand how numbers can be broken down into smaller parts, which is essential for understanding addition. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 8 and 9."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Yellow and blue crayons or colored pencils Pencils Erasers

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 47

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Introduce the idea of composing numbers, explaining that it means combining two smaller parts to make a whole number.

▪ Say, "Today we are going to learn how to make the number 9 by using yellow and blue colors to show two parts. You will color some objects yellow and some blue, and then write the numbers that represent each part." o On the board, draw 9 circles to represent the objects. Color 6 circles yellow and 3 circles blue. Explain that 6 + 3 = 9. o Show another combination by coloring 5 yellow and 4 blue.

Explain that 5 + 4 = 9. o Write these number sentences on the board: "6 + 3 = 9" and "5 + 4 = 9."

2. Demonstrating the Exercise (5 minutes): Exercise a: Color the objects yellow and blue to make 9. Write the numbers.

Open the book to the lesson titled "Compose 8 and 9."

Guide the students to the section where they will color the objects yellow and blue to show different ways to make 9. o Say, "Let’s start by coloring the objects to show one way to make 9. You can color some objects yellow and the rest blue." o Demonstrate the first example by coloring 6 objects yellow and 3 objects blue, explaining that 6 + 3 = 9. o Write "6 + 3 = 9" on the board. o Now show another way to make 9 by coloring 5 objects yellow and 4 objects blue, explaining that 5 + 4 = 9. o Write "5 + 4 = 9" on the board.

3. Guided Practice (10 minutes): o Ask the students to practice coloring their own objects yellow and blue to show different ways to make 9.

▪ Say, "Now it’s your turn! Use your yellow and blue crayons to color the objects and show different ways to make 9.

Then write the numbers for each part." o Encourage students to try at least two different combinations to make 9. o Walk around the classroom, observing their work and providing support and guidance as needed.

4. Interactive Practice (10 minutes): o o

Exercise b: Suggest more ways to make 9. o

After students have completed the first set of combinations, encourage them to think of more ways to compose 9.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 48

Ask, "Can you think of more ways to make 9 using yellow and blue? Let’s see how many combinations we can find!" o Allow students to share their suggestions with the class. Write their ideas on the board, such as: ▪ "7 yellow + 2 blue = 9" ▪ "4 yellow + 5 blue = 9" ▪ "8 yellow + 1 blue = 9" o Encourage students to try these new combinations in their books.

5. Independent Practice (5 minutes): o Give students time to independently explore additional ways to make 9 using yellow and blue crayons.

▪ Say, "Now, see if you can find more ways to make 9. Color the objects and write the number sentences for each combination." o Walk around the room to check their work and provide support where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 9 using yellow and blue objects. o Ask a few students to share their combinations with the class and explain how they colored their objects.

▪ Say, "Great job! You found many different ways to make 9 using yellow and blue. This helps us understand how numbers are made from parts, which is very important when learning addition." o Reinforce the idea that numbers can be made in different ways, and this understanding will help in future math learning.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing numbers is useful in everyday life when grouping or counting objects.

▪ Say, "When we know how to make numbers in different ways, it helps us when we need to group or count things like toys, snacks, or other objects." o Encourage students to practice composing other numbers at home using objects like toys or snacks.

▪

Additional Tips: Visual Aid: Use a large paper or whiteboard to demonstrate how to compose numbers by coloring objects yellow and blue.

• Encouragement: Provide positive feedback to motivate students to explore different combinations.

• Repetition: Reinforce the concept with other numbers (such as 8 or 10) to strengthen students' understanding of composition.

• Differentiation: Offer extra support to students who need more guidance and provide additional challenges for students who quickly grasp the concept. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 49 •

Exercises 8-10 Exercise Overview: In this exercise, students will practice composing the numbers 8 and 9 by coloring objects orange and green to show different ways to make these numbers. They will also write the numbers that correspond to the parts they have created. This exercise is designed to help students understand how numbers are composed of smaller parts, a foundational concept for addition. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 8 and 9."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Orange and green crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the idea of composing numbers, explaining that it means using two smaller parts to make a whole number.

▪ Say, "Today, we are going to learn how to make the numbers 8 and 9 using orange and green colors. You will color some objects orange and some green, and then write the numbers that show how you divided the number." o On the board, demonstrate how to break the number 8 into parts by drawing 8 circles to represent the objects. Color 5 of them orange and 3 of them green, then explain that 5 + 3 = 8. o Show another example by coloring 4 orange and 4 green.

Explain that 4 + 4 = 8. o Do the same for the number 9, coloring 6 circles orange and 3 circles green, and then showing another combination by coloring 5 orange and 4 green. o Write these number sentences on the board: ▪ "5 + 3 = 8" ▪ "4 + 4 = 8" ▪ "6 + 3 = 9" ▪ "5 + 4 = 9"

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 50

2. Demonstrating the Exercise (5 minutes): Exercise: Color the objects orange and green to make 8 and 9. Write the numbers.

Open the book to the lesson titled "Compose 8 and 9."

Guide the students to the section where they will color the objects orange and green to show different ways to make 8 and 9. o Say, "Let’s start with the number 8. You can color some objects orange and the rest green to show different ways to make 8." o Demonstrate the first example by coloring 5 objects orange and 3 objects green, explaining that 5 + 3 = 8. o Write "5 + 3 = 8" on the board. o Show another way to make 8 by coloring 4 objects orange and 4 objects green, explaining that 4 + 4 = 8. o Write "4 + 4 = 8" on the board. o Now, move to the number 9: ▪ Say, "Next, let’s try the number 9. You can color some objects orange and the rest green to show how to make 9."

▪ Demonstrate by coloring 6 objects orange and 3 objects green, writing "6 + 3 = 9" on the board.

▪ Show another example by coloring 5 objects orange and 4 objects green, writing "5 + 4 = 9."

3. Guided Practice (10 minutes): o Ask the students to practice coloring their own objects orange and green to show different ways to make 8 and 9.

▪ Say, "Now it’s your turn! Use your orange and green crayons to color the objects and show different ways to make 8 and 9. Then write the numbers that show how you made each part." o Encourage students to try at least two different combinations for each number (8 and 9). o Walk around the classroom, observing their work and providing guidance as needed.

4. Interactive Practice (10 minutes): o After students have completed coloring the objects and writing the numbers, encourage them to share their combinations with the class.

▪ Ask, "Who would like to share how they made 8 using orange and green? What combination did you come up with?" o Allow students to share their ideas, and write their combinations on the board, such as: ▪ For 8: "6 orange + 2 green = 8" or "3 orange + 5 green = 8."

▪ For 9: "7 orange + 2 green = 9" or "4 orange + 5 green = 9." ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 51 o o

o Encourage students to try different combinations in their books.

5. Independent Practice (5 minutes): o Allow students time to explore more ways to make 8 and 9 independently.

▪ Say, "Now, see if you can find even more ways to make 8 and 9. Color the objects and write the numbers for each combination." o Walk around the room to check their progress and provide support where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 8 and 9 using orange and green objects. o Ask a few students to share their combinations and explain how they colored the objects.

▪ Say, "Great job! You found many ways to make 8 and 9 using orange and green. This helps us understand how numbers can be made from smaller parts, which will help us with addition." o Reinforce that numbers can be composed in different ways, and this understanding will help with future math concepts.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how knowing how to compose numbers helps us when grouping or adding objects in real life.

▪ Say, "When we know how to make numbers using different parts, it helps us when we need to count, group, or add things, like toys or snacks." o Encourage students to practice composing other numbers at home using toys or other objects.

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to model how to compose numbers by coloring objects orange and green.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different combinations.

Repetition: Reinforce the concept with other numbers to strengthen students' understanding of composition.

Differentiation: Offer extra support to students who need more guidance and provide additional challenges for students who quickly grasp the concept.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 52

Lesson

6

Decompose 8 and 9

Exercises 1 Exercise Overview: In this exercise, students will practice decomposing the numbers 8 and 9 by using rectangles to break them into smaller parts. This helps students understand how numbers can be taken apart into different groups, which is essential for learning subtraction and reinforcing part-part-whole relationships. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 8 and 9."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers Rectangles (either printed on the page or drawn by students)

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Introduce the concept of decomposing numbers, explaining that it means taking a number apart into two or more smaller groups.

▪ Say, "Today, we are going to practice taking apart the numbers 8 and 9. You will use rectangles to show how we can divide these numbers into smaller parts." o On the board, demonstrate decomposing 8 by drawing 8 circles (representing objects). Draw two rectangles around 5 circles in one group and 3 circles in another, explaining that 5 + 3 = 8. o Show another example by drawing rectangles around 4 circles in one group and 4 in another, explaining that 4 + 4 = 8. o Repeat for the number 9. Draw 9 circles and divide them into two groups, such as 6 and 3, and explain that 6 + 3 = 9. Then show another example: 5 and 4, explaining that 5 + 4 = 9.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 53

2. Demonstrating the Exercise (5 minutes): Exercise a: Use the rectangles to show ways to take apart 8 and 9.

Open the book to the lesson titled "Decompose 8 and 9."

Guide the students to the section where they will use rectangles to take apart the numbers 8 and 9. o Say, "Let’s start by using rectangles to show one way to take apart 8. Draw rectangles around some of the objects, and then around the rest." o Demonstrate the first example by drawing a rectangle around 5 objects and another around 3 objects. Write "5 + 3 = 8" on the board. o Now show another way to take apart 8 by drawing rectangles around 4 objects and 4 objects, and write "4 + 4 = 8" on the board. o Move on to the number 9: ▪ Say, "Now, let’s take apart the number 9 using rectangles."

▪ Demonstrate by drawing a rectangle around 6 objects and another around 3 objects. Write "6 + 3 = 9" on the board.

▪ Show another example by drawing rectangles around 5 objects and 4 objects. Write "5 + 4 = 9" on the board.

3. Guided Practice (10 minutes): o Ask the students to practice using rectangles to decompose the numbers 8 and 9.

▪ Say, "Now it’s your turn! Draw rectangles to take apart the number 8 in different ways, and then do the same for 9.

Write the numbers that show how you took each number apart." o Encourage students to try at least two different ways to decompose 8 and two ways to decompose 9. o Walk around the classroom, observing their work and providing support and guidance as needed.

4. Interactive Practice (10 minutes): o o

Exercise b: Encourage the students to suggest more ways to take apart 8 and 9. o

o

After students have completed their decompositions, encourage them to think of other ways to take apart 8 and 9.

▪ Ask, "Can you think of more ways to take apart 8? How about 9? What if you drew rectangles around a larger group in one rectangle and a smaller group in the other?"

Allow students to share their ideas with the class. Write their ideas on the board, such as: ▪ For 8: "6 + 2 = 8" or "7 + 1 = 8."

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 54

▪ For 9: "7 + 2 = 9" or "8 + 1 = 9."

Encourage students to try these new combinations in their books.

5. Independent Practice (5 minutes): o Give students time to independently explore more ways to take apart 8 and 9 using rectangles.

▪ Say, "Let’s see how many different ways you can find to take apart 8 and 9. Draw rectangles around the objects and write the number sentences for each way you take the number apart." o Walk around the room to check their progress and provide assistance if needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to take apart 8 and 9. o Ask a few students to share their decompositions and explain how they divided the objects into smaller groups.

▪ Say, "Great job! You found many different ways to take apart 8 and 9. This helps us understand how numbers can be broken into smaller parts, which is important when we learn subtraction." o Reinforce that numbers can be taken apart in many ways, which will help with future math skills.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers helps in real-life situations when we need to divide or share objects.

▪ Say, "Knowing how to take apart numbers helps us when we need to divide things, like sharing snacks or toys." o Encourage students to practice decomposing other numbers at home using objects like toys or snacks. o

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing rectangles around objects.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different decompositions.

Repetition: Reinforce the concept with other numbers (such as 10) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for those who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 55

Exercises 2-7 Exercise Overview: In this exercise, students will practice decomposing the numbers 8 and 9 by drawing rectangles around objects to break the whole number into smaller parts. They will then write the corresponding numbers to show how the number was decomposed. This exercise reinforces the concept of part-partwhole relationships, which is important for developing an understanding of subtraction. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 8 and 9."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining the concept of decomposing numbers, which involves breaking a whole number into smaller parts.

▪ Say, "Today, we are going to take apart the numbers 8 and 9. This means breaking the number into two smaller groups, and we’ll use rectangles to show how we do this." o On the board, demonstrate decomposing 8 by drawing 8 circles (representing objects). Draw a rectangle around 5 of the circles and another rectangle around the remaining 3 circles, explaining that 5 + 3 = 8. o Show another example by drawing rectangles around 4 circles in one group and 4 circles in another group, explaining that 4 + 4 = 8. o Repeat for the number 9. Draw 9 circles and divide them into two groups: draw a rectangle around 6 circles and another around 3, explaining that 6 + 3 = 9. Then show another example: draw rectangles around 5 circles and 4 circles, explaining that 5 + 4 = 9.

2. Demonstrating the Exercise (5 minutes): Exercise: Draw rectangles around the objects to show one way to take apart the given number. Write the numbers. o

Open the book to the lesson titled "Decompose 8 and 9."

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 56

Guide the students to the section where they will use rectangles to take apart the numbers 8 and 9. o Say, "Let’s start with the number 8. Look at the objects in the picture and draw rectangles around some of them to show one way to take apart 8." o Demonstrate the first example by drawing a rectangle around 5 objects and another rectangle around 3 objects, explaining that this shows 5 + 3 = 8. o Write "5 + 3 = 8" on the board. o Now move to the number 9: ▪ Say, "Now let’s try the number 9. Draw rectangles to take apart 9."

▪ Demonstrate by drawing a rectangle around 6 objects and another around 3 objects, and write "6 + 3 = 9" on the board.

3. Guided Practice (10 minutes): o Ask the students to practice drawing rectangles around the objects to decompose the numbers 8 and 9.

▪ Say, "Now it’s your turn! Draw rectangles to show how you would take apart the numbers 8 and 9. Then write the numbers that show how you took the number apart." o Encourage students to try at least two different ways to decompose 8 and two ways to decompose 9. o Walk around the classroom, observing their work and providing support and guidance as needed.

4. Interactive Practice (10 minutes): o After students have completed their decompositions, encourage them to think of additional ways to take apart 8 and 9.

▪ Ask, "Can you think of more ways to take apart 8? How about 9? What if you drew rectangles around bigger or smaller groups of objects?" o Allow students to share their ideas with the class. Write their suggestions on the board, such as: ▪ For 8: "7 + 1 = 8" or "6 + 2 = 8."

▪ For 9: "7 + 2 = 9" or "8 + 1 = 9." o Encourage students to try these new combinations in their books.

5. Independent Practice (5 minutes): o Give students time to independently explore more ways to take apart 8 and 9 using rectangles.

▪ Say, "Let’s see how many different ways you can find to take apart 8 and 9. Draw rectangles around the objects and write the number sentences for each way you take the number apart." o Walk around the room to check their progress and provide support where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to take apart 8 and 9. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 57 o

Ask a few students to share their decompositions and explain how they divided the objects into smaller groups.

▪ Say, "Great work! You found many ways to take apart 8 and 9. This helps us understand how numbers are made of smaller parts, which is important when we learn subtraction." o Reinforce the idea that numbers can be taken apart in multiple ways, which will help with future math learning.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers is useful when we need to divide objects in real-life situations.

▪ Say, "Knowing how to take apart numbers helps us when we need to divide things, like sharing toys or snacks." o Encourage students to practice decomposing other numbers at home using objects like toys or snacks. o

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing rectangles around objects.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different decompositions.

Repetition: Reinforce the concept with other numbers to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance and provide additional challenges for those who grasp the concept quickly.

Exercises 8-9 Exercise Overview: In this exercise, students will practice decomposing the numbers 8 and 9 by drawing the appropriate number of pens and rulers and then breaking them into smaller groups. This reinforces the part-part-whole relationship that is fundamental for understanding subtraction and number composition. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 8 and 9."

Materials Needed: • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 58

•

Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining the concept of decomposition, which involves taking apart a whole number into smaller groups.

▪ Say, "Today, we are going to practice taking apart the numbers 8 and 9. This means breaking these numbers into smaller groups using pens and rulers." o On the board, draw 8 pens and show how you can take apart the 8 pens by dividing them into two groups, for example, 5 pens in one group and 3 pens in another. o Then, do the same with 9 rulers. Draw 9 rulers and divide them into two groups, for example, 6 rulers in one group and 3 rulers in another. Explain that this is how we can decompose numbers.

2. Demonstrating the Exercise (5 minutes): Exercise 8: Take apart eight pens. Draw the pens in the blank boxes. o o o o

o o

Open the book to the section of the lesson titled "Decompose 8 and 9."

Guide the students to the exercise that involves taking apart 8 pens.

Say, "Let’s start by drawing 8 pens in the blank boxes. Once you’ve drawn them, we’ll take them apart into two groups."

Demonstrate by drawing 8 pens on the board. Then, draw a line between the pens to divide them into two groups, for example, 4 pens in one group and 4 pens in the other.

Write the number sentence on the board: "4 + 4 = 8."

Encourage the students to think of another way to divide the pens, for example, 5 pens and 3 pens, and write "5 + 3 = 8."

Exercise 9: Take apart nine rulers. Draw the rulers in the blank boxes. o o o

o o

Move on to the next exercise where students will take apart 9 rulers.

Say, "Now let’s do the same thing with 9 rulers. Draw 9 rulers in the blank boxes, and then we’ll divide them into smaller groups."

On the board, draw 9 rulers and show how to decompose them into two groups, for example, 6 rulers in one group and 3 rulers in another.

Write the number sentence: "6 + 3 = 9."

Ask students to suggest another way to take apart 9 rulers, for example, 7 rulers and 2 rulers, and write "7 + 2 = 9."

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 59

3. Guided Practice (10 minutes): o Ask students to complete both exercises by drawing 8 pens and 9 rulers in their books and then decomposing them into two groups.

▪ Say, "Now it’s your turn! Draw 8 pens in the boxes and take them apart by dividing them into two groups. Then do the same with 9 rulers." o Encourage students to think of at least two different ways to decompose the numbers 8 and 9. o Walk around the classroom, observing their work and providing guidance as needed.

4. Interactive Practice (10 minutes): o After students have completed the exercises, encourage them to share their decompositions with the class.

▪ Ask, "Can anyone share how they took apart 8 pens? What about 9 rulers? How did you divide them?" o Write students' ideas on the board, such as: ▪ For 8 pens: "5 + 3 = 8" or "6 + 2 = 8."

▪ For 9 rulers: "7 + 2 = 9" or "4 + 5 = 9." o Encourage students to try these different combinations in their books.

5. Independent Practice (5 minutes): o Give students time to explore more ways to decompose the numbers 8 and 9 independently.

▪ Say, "Let’s see how many different ways you can find to take apart 8 and 9. Draw your pens and rulers, and then divide them into two groups in different ways." o Walk around the room to check their progress and offer support where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to decompose 8 and 9. o Ask a few students to share their decompositions and explain how they divided the objects.

▪ Say, "Great work! You all found many different ways to take apart 8 pens and 9 rulers. This helps us understand how numbers are made up of smaller parts." o Reinforce the idea that numbers can be decomposed in multiple ways, which is important for understanding subtraction and other math concepts.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers can be useful in real-life situations.

▪ Say, "When we know how to take apart numbers, it helps us when we need to share or group things, like dividing toys or snacks." o Encourage students to practice decomposing other numbers at home using everyday objects like toys or blocks. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 60

Additional Tips: •

• •

•

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing objects and dividing them into smaller groups.

Encouragement: Provide positive feedback to motivate students to explore different ways of decomposing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 10 or 11) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 61

Lesson

7

Compose 10

Exercise 1 Exercise Overview: In this exercise, students will use yellow and blue dots to explore different ways to compose the number 10. This activity introduces students to the idea of composing numbers by combining smaller groups, an essential skill for developing addition concepts. Students will use visual aids (dots) to create combinations that add up to 10 and suggest their own combinations. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 10."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Yellow and blue crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of composing numbers.

Explain that composing a number means combining smaller groups to make a bigger number.

▪ Say, "Today, we’re going to learn how to make the number 10 by using yellow and blue dots. You will color some dots yellow and some dots blue to create different combinations that add up to 10." o On the board, draw 10 circles to represent the dots and show an example of composing 10. Color 6 circles yellow and 4 circles blue. Explain that 6 yellow + 4 blue = 10. o Show another example by coloring 7 yellow and 3 blue dots, and explain that 7 yellow + 3 blue = 10. o Write these number sentences on the board: ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 62

"6 + 4 = 10" "7 + 3 = 10" 2. Demonstrating the Exercise (5 minutes): ▪ ▪

Exercise a: Use the yellow and blue dots to show ways to make 10.

Open the book to the lesson titled "Compose 10."

Guide the students to the section where they will color the yellow and blue dots to show different ways to make 10. o Say, "Let’s start by coloring some dots yellow and the rest blue.

We want to find different ways to make 10." o Demonstrate the first example by coloring 5 dots yellow and 5 dots blue, explaining that 5 + 5 = 10. o Write "5 + 5 = 10" on the board. o Show another way to make 10 by coloring 8 dots yellow and 2 dots blue, explaining that 8 + 2 = 10. o Write "8 + 2 = 10" on the board.

3. Guided Practice (10 minutes): o Ask the students to practice coloring their own dots yellow and blue to show different ways to make 10.

▪ Say, "Now it’s your turn! Use your yellow and blue crayons to color the dots and show different ways to make 10. Then write the numbers that show how you made each part." o Encourage students to try at least two different combinations for making 10. o Walk around the classroom, observing their work and providing support and guidance as needed.

4. Interactive Practice (10 minutes): o o

Exercise b: Encourage the students to suggest more ways to make 10.

After students have completed coloring the dots and writing the numbers, encourage them to think of more ways to compose 10.

▪ Ask, "Can you think of more ways to make 10? Let’s see how many different combinations we can find using yellow and blue dots!" o Allow students to share their ideas with the class. Write their ideas on the board, such as: ▪ "9 yellow + 1 blue = 10" ▪ "4 yellow + 6 blue = 10" ▪ "3 yellow + 7 blue = 10" o Encourage students to try these new combinations in their books.

5. Independent Practice (5 minutes): o Give students time to independently explore more ways to make 10 using the yellow and blue dots. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 63

Say, "Now, see if you can find even more ways to make 10.

Color the dots and write the number sentences for each combination." o Walk around the room to check their progress and provide support where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 10 using yellow and blue dots. o Ask a few students to share their combinations and explain how they colored their dots.

▪ Say, "Great job! You found many different ways to make 10 using yellow and blue dots. This helps us understand how numbers can be made from smaller parts, which will help when we learn addition." o Reinforce the idea that numbers can be composed in many different ways, which is a key concept in math learning.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing numbers helps in reallife situations when grouping or adding objects.

▪ Say, "Knowing how to make numbers from smaller parts helps us when we need to add things or group objects together, like toys or snacks." o Encourage students to practice composing other numbers at home using objects like toys or snacks.

▪

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to compose numbers by coloring dots yellow and blue.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different combinations.

Repetition: Reinforce the concept by practicing with other numbers (such as 9 or 11) to strengthen students' understanding of composition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 64

Exercises 2-10 Exercise Overview: In this exercise, students will use blue and red colors to show different ways to compose the number 10 using balloons. This activity reinforces the concept of number composition, where students learn that a whole number (10) can be made by combining smaller groups. After coloring the balloons, students will write the numbers that represent how they made 10. They will then suggest other ways to compose 10. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Compose 10."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Blue and red crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by introducing the concept of composing numbers.

Explain that composing a number means combining smaller groups to make a larger number.

▪ Say, "Today, we are going to learn how to make the number 10 by coloring balloons in two different colors— blue and red. You will color some balloons blue and some red to show different ways to make 10." o On the board, draw 10 circles to represent balloons. Color 6 balloons blue and 4 balloons red. Explain that 6 blue + 4 red = 10. o Show another example by coloring 7 balloons blue and 3 balloons red, and explain that 7 blue + 3 red = 10. o Write these number sentences on the board: ▪ "6 + 4 = 10" ▪ "7 + 3 = 10" 2. Demonstrating the Exercise (5 minutes): Exercise a: Color the balloons blue and red to make 10. Write the numbers. o o

Open the book to the lesson titled "Compose 10."

Guide the students to the exercise where they will color the balloons blue and red to show different ways to make 10.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 65

Say, "Let’s start by coloring some balloons blue and the rest red.

We want to find different ways to make 10." o Demonstrate the first example by coloring 5 balloons blue and 5 balloons red, explaining that 5 + 5 = 10. o Write "5 + 5 = 10" on the board. o Show another way to make 10 by coloring 8 balloons blue and 2 balloons red, explaining that 8 + 2 = 10. o Write "8 + 2 = 10" on the board.

3. Guided Practice (10 minutes): o Ask the students to practice coloring their own balloons blue and red to show different ways to make 10.

▪ Say, "Now it’s your turn! Use your blue and red crayons to color the balloons and show different ways to make 10.

Then write the numbers that show how you made each part." o Encourage students to try at least two different combinations for making 10. o Walk around the classroom, observing their work and providing support and guidance as needed.

4. Interactive Practice (10 minutes): o

Exercise b: Suggest more ways to make 10.

After students have completed coloring the balloons and writing the numbers, encourage them to think of more ways to compose 10.

▪ Ask, "Can you think of more ways to make 10? Let’s see how many different combinations we can find using blue and red balloons!" o Allow students to share their ideas with the class. Write their suggestions on the board, such as: ▪ "9 blue + 1 red = 10" ▪ "4 blue + 6 red = 10" ▪ "3 blue + 7 red = 10" o Encourage students to try these new combinations in their books.

5. Independent Practice (5 minutes): o Give students time to independently explore more ways to make 10 using the blue and red balloons.

▪ Say, "Let’s see if you can find even more ways to make 10.

Color the balloons and write the number sentences for each combination." o Walk around the room to check their progress and offer support where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to make 10 using blue and red balloons. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 66

Ask a few students to share their combinations and explain how they colored their balloons.

▪ Say, "Great work! You found many different ways to make 10 using blue and red balloons. This helps us understand how numbers can be made from smaller parts, which is important when we learn addition." o Reinforce the idea that numbers can be composed in many different ways, which is a key concept in math learning.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing numbers helps in reallife situations when grouping or adding objects.

▪ Say, "Knowing how to make numbers from smaller parts helps us when we need to add things or group objects together, like toys or snacks." o Encourage students to practice composing other numbers at home using objects like toys or snacks. o

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to compose numbers by coloring balloons blue and red.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different combinations.

Repetition: Reinforce the concept by practicing with other numbers (such as 9 or 11) to strengthen students' understanding of composition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 67

Lesson

8

Decompose 10

Exercise 1

Exercise Overview: In this exercise, students will practice decomposing the number 10 by drawing rectangles to break it into smaller parts. This activity introduces students to the concept of "taking apart" numbers, which is foundational for understanding subtraction. After using rectangles to decompose 10, students will trace the number 10 and suggest additional ways to take apart the number. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 10."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining the concept of decomposing numbers.

Emphasize that decomposing a number means breaking it into two or more smaller groups.

▪ Say, "Today, we are going to practice taking apart the number 10. This means finding different ways to break 10 into smaller groups, and we’ll use rectangles to show how we can do that." o On the board, draw 10 circles to represent 10 objects. Show one example of decomposing 10 by drawing a rectangle around 6 circles and another around 4 circles. Explain that 6 + 4 = 10. o Show another example by drawing rectangles around 5 circles in one group and 5 circles in another group, explaining that 5 + 5 = 10. o Write these number sentences on the board: ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 68

"6 + 4 = 10" "5 + 5 = 10" 2. Demonstrating the Exercise (5 minutes): ▪ ▪

Exercise a: Use the rectangles to show ways to take apart 10. Trace the number.

Open the book to the lesson titled "Decompose 10."

Guide the students to the exercise where they will use rectangles to take apart the number 10. o Say, "Let’s start by using rectangles to show one way to take apart 10." o Demonstrate the first example by drawing a rectangle around 7 objects and another rectangle around the remaining 3 objects, explaining that 7 + 3 = 10. o Write "7 + 3 = 10" on the board. o Next, trace the number 10 in the book and encourage students to do the same. o Now, ask students to use their books to show another way to take apart 10 using rectangles.

3. Guided Practice (10 minutes): o Ask the students to practice using rectangles to take apart the number 10.

▪ Say, "Now it’s your turn! Use your pencil to draw rectangles around the objects to show different ways to take apart the number 10. Then trace the number 10 in the space provided." o Encourage students to think of at least two different ways to decompose 10. o Walk around the classroom, observing their work and providing guidance and support where needed.

4. Interactive Practice (10 minutes): o o

Exercise b: Encourage the students to suggest more ways to take apart 10. o

o

After students have completed their rectangles and tracing, encourage them to think of additional ways to take apart 10.

▪ Ask, "Can you think of more ways to take apart 10? Let’s see how many different ways we can find to break the number 10 into smaller groups!"

Allow students to share their ideas with the class. Write their suggestions on the board, such as: ▪ "9 + 1 = 10" ▪ "8 + 2 = 10" ▪ "6 + 4 = 10" ▪ "5 + 5 = 10"

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 69

Encourage students to try these new combinations in their books, using rectangles to break apart the objects.

5. Independent Practice (5 minutes): o Give students time to explore more ways to decompose the number 10 independently.

▪ Say, "Now let’s see how many different ways you can take apart 10. Use your pencil to draw rectangles and write the number sentences for each way you take apart 10." o Walk around the room to check their progress and offer support where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to take apart 10. o Ask a few students to share their decompositions and explain how they divided the objects into smaller groups.

▪ Say, "Great job! You found many different ways to take apart the number 10. This helps us understand how numbers can be made up of smaller parts, which will help us when we learn subtraction." o Reinforce the idea that numbers can be decomposed in many ways, which is an important skill in math.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers helps in real-life situations when dividing or grouping objects.

▪ Say, "Knowing how to take apart numbers helps us when we need to share or divide things, like toys or snacks." o Encourage students to practice decomposing other numbers at home using everyday objects, like blocks or toys. o

Additional Tips: •

• •

•

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing objects and dividing them into smaller groups using rectangles.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different ways of decomposing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 9 or 11) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 70

Exercises 2-7 Exercise Overview: In this exercise, students will practice decomposing the number 10 by drawing rectangles around flowers to break the total number into smaller parts. They will then write the numbers that represent how the number 10 was taken apart. This activity reinforces number decomposition, which is a key skill for understanding subtraction and part-part-whole relationships. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 10."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Start by explaining the concept of decomposing numbers.

Highlight that decomposing means breaking down a number into two or more smaller parts.

▪ Say, "Today, we are going to practice taking apart the number 10 by drawing rectangles around groups of flowers. This will help us see how 10 can be split into smaller numbers." o On the board, draw 10 flowers and show an example of decomposing the number by drawing a rectangle around 6 flowers and another rectangle around 4 flowers.

▪ Explain that 6 + 4 = 10. o Show another example by drawing a rectangle around 5 flowers in one group and 5 flowers in another group, explaining that 5 + 5 = 10. o Write these number sentences on the board: ▪ "6 + 4 = 10" ▪ "5 + 5 = 10"

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 71

2. Demonstrating the Exercise (5 minutes): Exercise: Draw rectangles around the flowers to show one way to take apart the given number. Write the numbers.

Open the book to the lesson titled "Decompose 10."

Guide the students to the section where they will decompose 10 by drawing rectangles around groups of flowers. o Say, "Let’s begin by drawing a rectangle around some flowers to show one way to take apart the number 10. Then, write the numbers that show how many flowers are in each group." o Demonstrate by drawing a rectangle around 7 flowers and another rectangle around the remaining 3 flowers. Explain that this shows 7 + 3 = 10. o Write "7 + 3 = 10" on the board.

3. Guided Practice (10 minutes): o Ask students to practice drawing rectangles around the flowers in their books to show different ways to decompose 10.

▪ Say, "Now it’s your turn! Use your pencil to draw rectangles around the flowers to show one way to take apart the number 10. Then, write the numbers that show how you took apart the flowers." o Encourage students to think of at least two different ways to decompose 10 by drawing rectangles around various groupings of flowers. o Walk around the classroom, observing their work and providing guidance and support as needed.

4. Interactive Practice (10 minutes): o After students have completed their decompositions, encourage them to think of additional ways to decompose the number 10.

▪ Ask, "Can you think of more ways to take apart the number 10 using rectangles around the flowers? Let’s see how many combinations we can come up with!" o Allow students to share their ideas with the class. Write their suggestions on the board, such as: ▪ "9 + 1 = 10" ▪ "8 + 2 = 10" ▪ "4 + 6 = 10" ▪ "5 + 5 = 10" o Encourage students to try these new combinations in their books.

5. Independent Practice (5 minutes): o Give students time to independently explore more ways to decompose 10 by drawing rectangles around the flowers.

▪ Say, "Let’s see how many different ways you can find to take apart 10. Draw rectangles around the flowers and write the number sentences for each way you take apart the number 10." ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 72 o o

Walk around the room to check their progress and offer support where needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to take apart 10. o Ask a few students to share their decompositions and explain how they grouped the flowers.

▪ Say, "You found many different ways to take apart the number 10 using rectangles around the flowers. This helps us understand how numbers can be broken into smaller parts, which is useful for addition and subtraction." o Reinforce the idea that numbers can be decomposed in many ways, which is an important foundational math skill.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers is useful in everyday life when dividing or grouping objects.

▪ Say, "Knowing how to take apart numbers helps us when we need to divide things like flowers, toys, or even snacks into smaller groups." o Encourage students to practice decomposing other numbers at home using real-life objects like toys or snacks. o

Additional Tips: •

• •

•

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing objects and dividing them into smaller groups using rectangles.

Encouragement: Provide positive feedback and encouragement to motivate students to explore different decompositions.

Repetition: Reinforce the concept by practicing with other numbers (such as 9 or 11) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

Exercises 8-9 Exercise Overview: In this exercise, students will practice decomposing the number 10 by drawing flowers in blank boxes. The exercise encourages students to understand how to take apart a group of 10 into smaller groups, reinforcing their understanding of number decomposition. This exercise is available in ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 73

"Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Decompose 10."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by explaining the concept of decomposing numbers.

Emphasize that decomposing a number means breaking it into smaller groups.

▪ Say, "Today, we are going to take apart the number 10 by drawing flowers in the blank boxes. This will help us understand how to break the number 10 into smaller groups." o On the board, draw 10 flowers and show how they can be grouped in different ways. For example, draw a line between 6 flowers and 4 flowers and explain that 6 + 4 = 10. o Show another example by drawing 5 flowers in one group and 5 flowers in another, explaining that 5 + 5 = 10. o Write the number sentences on the board: ▪ "6 + 4 = 10" ▪ "5 + 5 = 10" 2. Demonstrating the Exercise (5 minutes): Exercise: Take apart ten flowers. Draw the flowers in the blank boxes.

Open the book to the lesson titled "Decompose 10."

Guide the students to the exercise where they will draw the flowers to show how they can decompose the number 10. o Say, "Let’s start by drawing 10 flowers in the blank boxes. Once you’ve drawn them, we’ll take them apart into two groups." o Demonstrate on the board by drawing 10 flowers in two separate groups. For example, draw 7 flowers in one group and 3 in the other, explaining that this shows 7 + 3 = 10. o Write "7 + 3 = 10" on the board.

3. Guided Practice (10 minutes): o Ask the students to draw their own 10 flowers in the blank boxes and think of ways to take apart the number 10.

▪ Say, "Now it’s your turn! Draw 10 flowers in the blank boxes and think about how you can take them apart into smaller groups. After you draw the flowers, write the numbers that show how many flowers are in each group." o o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 74

Encourage students to think of different combinations. For example: ▪ "9 + 1 = 10" ▪ "8 + 2 = 10" o Walk around the classroom, observing their work and providing guidance where needed.

4. Interactive Practice (10 minutes): o After students have drawn and taken apart their 10 flowers, encourage them to suggest more ways to decompose the number 10.

▪ Ask, "Can you think of more ways to take apart 10 flowers?

Let’s see how many different ways we can find!" o Allow students to share their ideas with the class. Write their suggestions on the board, such as: ▪ "6 + 4 = 10" ▪ "5 + 5 = 10" ▪ "3 + 7 = 10" o Encourage students to try these new combinations by drawing more flowers in the blank boxes.

5. Independent Practice (5 minutes): o Give students time to explore more ways to take apart 10 by drawing flowers and dividing them into different groups.

▪ Say, "Let’s see how many different ways you can find to take apart 10 flowers. Draw the flowers and write the number sentences for each way you take apart the number 10." o Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to take apart 10. o Ask a few students to share how they decomposed the 10 flowers.

▪ Say, "You found many different ways to take apart 10 flowers. This helps us understand how numbers can be broken down into smaller parts, which will help when we learn subtraction." o Reinforce the concept that numbers can be decomposed in many different ways.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers can help in everyday situations.

▪ Say, "Knowing how to take apart numbers helps us when we need to share or divide things, like flowers, toys, or snacks." o Encourage students to practice decomposing other numbers at home by drawing objects like toys or snacks. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 75

Additional Tips: •

• •

•

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing objects and dividing them into smaller groups.

Encouragement: Provide positive feedback to motivate students to explore different ways of decomposing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 9 or 11) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 76

Exercises 1-7 Exercise Overview: In this exercise, students will use blue and red colors to show different ways to compose the given numbers by coloring objects. They will also write the number sentences that correspond to their color choices. This activity reinforces students' understanding of composing and decomposing numbers, focusing on how smaller numbers can combine to make a total up to 10. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Revision: Compose and Decompose Up to 10."

Materials Needed: • • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Blue and red crayons or colored pencils Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Start by reviewing the concept of composing and decomposing numbers. Explain that composing numbers means combining smaller parts to make a larger number, while decomposing means breaking a number into smaller groups.

▪ Say, "Today, we are going to practice making numbers by coloring objects blue and red. You will color some objects blue and some red to show how different parts add up to the given number." o On the board, draw 8 circles (to represent objects) and show an example of decomposing 8 by coloring 5 circles blue and 3 circles red. Explain that 5 + 3 = 8. o Show another example by coloring 6 circles blue and 2 circles red, explaining that 6 + 2 = 8. o Write these number sentences on the board: ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 77

"5 + 3 = 8" "6 + 2 = 8" 2. Demonstrating the Exercise (5 minutes): ▪ ▪

Exercise: Color the objects blue and red to make the given numbers.

Write the numbers.

Open the book to the lesson titled "Revision: Compose and Decompose Up to 10." o Guide the students to the exercise where they will color objects blue and red to make the given numbers. o Say, "Let’s begin by looking at the first number. Your job is to color some of the objects blue and some red to make that number.

After you finish coloring, write the numbers that show how you took apart the number." o Demonstrate by coloring 4 objects blue and 2 objects red to make 6. Explain that 4 + 2 = 6. o Write "4 + 2 = 6" on the board.

3. Guided Practice (10 minutes): o Ask the students to color their own objects blue and red to match the given numbers.

▪ Say, "Now it’s your turn! Use your blue and red crayons to color the objects and show how to make the given numbers. After coloring, write the numbers that show how you took apart the total." o Encourage students to think of different combinations. For example, if the number is 7: ▪ Color 3 objects blue and 4 objects red for "3 + 4 = 7" ▪ Or color 5 objects blue and 2 objects red for "5 + 2 = 7" o Walk around the classroom, observing their work and providing support where needed.

4. Interactive Practice (10 minutes): o After students have colored their objects and written the number sentences, encourage them to think of other ways to compose the numbers.

▪ Ask, "Can you think of other ways to make the same number? Let’s see how many different ways we can find to make these numbers!" o Allow students to share their ideas with the class. Write their suggestions on the board, such as: ▪ "For 8: 7 + 1 = 8, 6 + 2 = 8, 4 + 4 = 8" o Encourage students to try these new combinations by coloring the objects and writing the corresponding numbers in their books.

5. Independent Practice (5 minutes): o Give students time to explore more ways to compose the given numbers by coloring objects and writing number sentences. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 78 o

Say, "Let’s see how many different ways you can find to take apart the given numbers. Color the objects and write the number sentences for each way you compose the number." o Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to compose the numbers. o Ask a few students to share how they colored their objects and wrote their number sentences.

▪ Say, "You found many different ways to compose the numbers by coloring the objects blue and red. This helps us understand how numbers can be made up of smaller parts, which will help us when we learn addition and subtraction." o Reinforce the concept that numbers can be composed in many different ways.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing and decomposing numbers can help in everyday situations.

▪ Say, "Knowing how to compose and decompose numbers helps us when we need to add things together or break them into smaller groups, like toys or snacks." o Encourage students to practice composing other numbers at home by grouping real-life objects like toys, snacks, or crayons.

▪

Additional Tips: •

• • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to compose numbers by coloring objects and dividing them into smaller groups.

Encouragement: Provide positive feedback to motivate students to explore different ways of composing and decomposing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 9 or 10) to strengthen students' understanding of composition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 79

Exercises 8-11 Exercise Overview: In this exercise, students will practice writing ways to compose each of the given numbers by filling in two numbers that add up to the given total. The words “and” and two blank branches below each number encourage students to think of different ways to break the number into two parts. This activity reinforces their understanding of composing numbers up to 10 by identifying pairs that sum up to a given number. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Revision: Compose and Decompose Up to 10."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by reviewing the concept of composing numbers. Explain that composing numbers means putting together two smaller numbers to make a larger number.

▪ Say, "Today, we are going to practice finding pairs of numbers that add up to the given number. You will fill in the branches with two numbers that make up the total." o On the board, write the number 10 and draw two branches under it with the word "and" between them. Write "6" on one branch and "4" on the other, explaining that 6 + 4 = 10. o Show another example by writing "7" and "3" on the branches, explaining that 7 + 3 = 10. o Write these number sentences on the board: ▪ "6 and 4 = 10" ▪ "7 and 3 = 10" 2. Demonstrating the Exercise (5 minutes): Exercise: Work it out. Write a way to compose each of the given numbers. Write the numbers. o o

Open the book to the lesson titled "Revision: Compose and Decompose Up to 10."

Guide the students to the section where they will compose the numbers using the branches provided.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 80

Say, "Let’s begin by looking at the number at the top. Your job is to write two numbers on the branches that add up to the number. These two numbers will show one way to make the number." o Demonstrate by writing "3" and "7" on the branches below the number 10. Explain that this shows 3 + 7 = 10. o Say, "You can compose 10 by using 3 and 7."

3. Guided Practice (10 minutes): o Ask the students to look at the given numbers in their books and fill in the branches with two numbers that add up to each number.

▪ Say, "Now it’s your turn! Look at the number at the top and think of two numbers that add up to make it. Write those numbers on the branches." o Encourage students to try different combinations. For example: ▪ If the number is 9, they can write: ▪ "5 and 4 = 9" ▪ "6 and 3 = 9" o Walk around the classroom, observing their work and providing guidance where needed.

4. Interactive Practice (10 minutes): o After students have written their number pairs, encourage them to think of other ways to compose the numbers.

▪ Ask, "Can you think of other pairs of numbers that add up to the same total? Let’s see how many different ways we can make these numbers!" o Allow students to share their ideas with the class. Write their suggestions on the board, such as: ▪ For 8: "5 and 3 = 8", "6 and 2 = 8", "7 and 1 = 8" o Encourage students to try these new combinations in their books.

5. Independent Practice (5 minutes): o Give students time to explore more ways to compose the given numbers independently.

▪ Say, "Let’s see how many different ways you can find to compose each of the given numbers. Write two numbers on the branches for each number." o Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to compose the numbers. o Ask a few students to share their number pairs and explain how they wrote the numbers.

▪ Say, "You found many different ways to compose the numbers. This helps us understand how numbers can be made up of smaller parts, which will help us when we learn addition and subtraction." ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 81 o

Reinforce the concept that numbers can be composed in many different ways.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing numbers helps in realworld situations when combining objects.

▪ Say, "Knowing how to compose numbers helps us when we need to add things together, like toys or snacks. We can combine small groups to make a total number." o Encourage students to practice composing other numbers at home by grouping objects like toys, snacks, or crayons. o

Additional Tips: • • • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to compose numbers by writing pairs of numbers on branches.

Encouragement: Provide positive feedback to motivate students to explore different ways of composing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 5 or 6) to strengthen students' understanding of composition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

Exercises 1-6 Exercise Overview: In this exercise, students will practice decomposing numbers up to 10 by drawing rectangles around groups of balls to show how the total number can be split into smaller groups. After drawing the rectangles, students will write the numbers that correspond to the groups they created. This activity reinforces the concept of number decomposition and helps students understand how a total number can be broken into parts. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Revision: Compose and Decompose Up to 10."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 82

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by reviewing the concept of decomposing numbers.

Explain that decomposing a number means breaking it into smaller groups, which can help with understanding subtraction and part-part-whole relationships.

▪ Say, "Today, we are going to practice taking apart numbers by drawing rectangles around groups of balls.

After that, you will write the numbers that show how you split the total into smaller parts." o On the board, draw 6 balls. Show an example by drawing a rectangle around 4 balls and another rectangle around the remaining 2 balls. Explain that this shows 4 + 2 = 6. o Show another example by drawing a rectangle around 3 balls and another around 3 balls, explaining that 3 + 3 = 6. o Write these number sentences on the board: ▪ "4 + 2 = 6" ▪ "3 + 3 = 6" 2. Demonstrating the Exercise (5 minutes): Exercise: Draw rectangles around the balls to show one way to take apart the given numbers. Write the numbers.

Open the book to the lesson titled "Revision: Compose and Decompose Up to 10." o Guide the students to the section where they will decompose the given numbers by drawing rectangles around groups of balls. o Say, "Let’s start by drawing rectangles around the balls to show one way to take apart the total number of balls. After you draw the rectangles, write the numbers that show how many balls are in each group." o Demonstrate by drawing 8 balls on the board. Draw a rectangle around 5 balls and another rectangle around the remaining 3 balls. Explain that this shows 5 + 3 = 8. o Write "5 + 3 = 8" on the board.

3. Guided Practice (10 minutes): o Ask the students to draw their own rectangles around the balls in their books to show how they can take apart the given numbers.

▪ Say, "Now it’s your turn! Draw rectangles around the balls to show how you would take apart the total number of balls. After you’ve drawn the rectangles, write the numbers that show how many balls are in each group." o Encourage students to try different combinations. For example: ▪ If the total is 7, they can draw: ▪ A rectangle around 4 balls and another around 3 balls for "4 + 3 = 7" o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 83

Or a rectangle around 5 balls and another around 2 balls for "5 + 2 = 7" o Walk around the classroom, observing their work and providing guidance where needed.

4. Interactive Practice (10 minutes): o After students have drawn their rectangles and written the number sentences, encourage them to think of other ways to take apart the numbers.

▪ Ask, "Can you think of other ways to take apart the same number? Let’s see how many different ways we can find to take apart these numbers!" o Allow students to share their ideas with the class. Write their suggestions on the board, such as: ▪ For 8: "6 + 2 = 8", "7 + 1 = 8", "5 + 3 = 8" o Encourage students to try these new combinations in their books by drawing rectangles around the balls and writing the corresponding numbers.

5. Independent Practice (5 minutes): o Give students time to independently explore more ways to decompose the given numbers by drawing rectangles around the balls and writing the numbers.

▪ Say, "Let’s see how many different ways you can find to take apart the numbers. Draw rectangles around the balls and write the number sentences for each way you decompose the total." o Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to decompose the numbers. o Ask a few students to share their decompositions and explain how they grouped the balls.

▪ Say, "You found many different ways to take apart the numbers. This helps us understand how numbers can be broken down into smaller parts, which is useful for addition and subtraction." o Reinforce the concept that numbers can be decomposed in many ways.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers helps in real-world situations, such as dividing or grouping objects.

▪ Say, "Knowing how to take apart numbers helps us when we need to divide or share things, like toys or snacks." o Encourage students to practice decomposing other numbers at home by grouping real-life objects like toys or snacks.

▪

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 84

Additional Tips: •

• •

•

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing objects (balls or other items) and dividing them into smaller groups using rectangles.

Encouragement: Provide positive feedback to motivate students to explore different ways of decomposing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 9 or 5) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

Exercises 7-12 Exercise Overview: In this exercise, students will practice decomposing numbers 7 and 9 by drawing rectangles around groups of flowers and insects to show three different ways to break the total into smaller parts. After drawing the rectangles, students will write the numbers that correspond to each group they created. This exercise reinforces the concept of number decomposition and encourages students to explore multiple ways to break apart numbers up to 10. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Revision: Compose and Decompose Up to 10."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by reviewing the concept of decomposing numbers.

Explain that decomposing a number means breaking it into smaller groups, and there are often multiple ways to decompose the same number. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 85

Say, "Today, we are going to take apart the numbers 7 and 9 in three different ways by drawing rectangles around groups of flowers and insects. After drawing the rectangles, we will write the numbers to show how we broke them apart." o On the board, draw 7 flowers. Show an example by drawing a rectangle around 4 flowers and another around the remaining 3 flowers. Explain that this shows 4 + 3 = 7. o Show another example by drawing a rectangle around 5 flowers and another around 2 flowers, explaining that 5 + 2 = 7. o Write these number sentences on the board: ▪ "4 + 3 = 7" ▪ "5 + 2 = 7" 2. Demonstrating the Exercise (5 minutes): ▪

Exercise 1: Draw rectangles around the flowers to show three ways to take apart 7. Write the numbers.

Open the book to the lesson titled "Revision: Compose and Decompose Up to 10." o Guide the students to the first section of the exercise where they will draw rectangles around the flowers to show three different ways to take apart 7. o Say, "Let’s begin by looking at the 7 flowers. Your job is to draw rectangles around the flowers in three different ways to show how we can break apart the number 7. After you’ve drawn the rectangles, write the numbers that show how many flowers are in each group." o Demonstrate one example on the board by drawing 7 flowers, then drawing a rectangle around 6 flowers and another around the remaining 1 flower. Write the number sentence: "6 + 1 = 7." o Say, "That’s one way to take apart 7. Now let’s find more ways!"

3. Guided Practice for Decomposing 7 (10 minutes): o Ask the students to draw three different rectangles around the flowers in their books to show three ways to take apart 7.

▪ Say, "Now it’s your turn! Draw rectangles around the flowers in three different ways. After you’ve drawn the rectangles, write the numbers that show how many flowers are in each group." o Encourage students to try different combinations, such as: ▪ "5 and 2 = 7" ▪ "3 and 4 = 7" o Walk around the classroom, observing their work and providing support where needed. o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 86

4. Interactive Practice for Decomposing 9 (10 minutes): Exercise 2: Draw rectangles around the insects to show three ways to take apart 9. Write the numbers.

Next, move on to the second section of the exercise where students will decompose 9. o Say, "Now let’s take apart 9 by drawing rectangles around the insects. Just like we did with the flowers, we will find three different ways to break apart 9. After you’ve drawn the rectangles, write the numbers that show how many insects are in each group." o Demonstrate one example on the board by drawing 9 insects, then drawing a rectangle around 7 insects and another around 2 insects. Write the number sentence: "7 + 2 = 9." o Encourage students to think of other combinations for 9, such as: ▪ "6 and 3 = 9" ▪ "5 and 4 = 9" o Ask the students to try different combinations on their own and write the numbers.

5. Independent Practice (10 minutes): o Give students time to complete both exercises independently by drawing rectangles around the flowers and insects and writing the corresponding numbers.

▪ Say, "Now let’s see how many different ways you can find to take apart 7 and 9. Draw the rectangles and write the number sentences for each way you decompose the numbers." o Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to decompose 7 and 9. o Ask a few students to share how they grouped the flowers and insects and what numbers they wrote.

▪ Say, "You found many different ways to take apart the numbers 7 and 9. This helps us understand how numbers can be broken down into smaller parts, which is important when we start learning about addition and subtraction." o Reinforce the idea that there are multiple ways to decompose a number, and each way is correct.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers can help in everyday situations, such as dividing or sharing objects.

▪ Say, "Knowing how to take apart numbers helps us when we need to divide things, like toys or snacks, into smaller groups." o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 87

o

Encourage students to practice decomposing other numbers at home by using real-life objects like toys, snacks, or crayons.

Additional Tips: •

• •

•

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing objects (flowers, insects, or other items) and dividing them into smaller groups using rectangles.

Encouragement: Provide positive feedback to motivate students to explore different ways of decomposing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 8 or 10) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 88

Exercise 1 Exercise Overview: In this exercise, students will count the total number of books, write the number in a yellow box, and then write three different ways to compose that number. The purpose of the activity is to help students develop problemsolving skills by practicing the composition and decomposition of numbers up to 10. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Problem Solving: Compose and Decompose Up to 10."

Materials Needed: •

“Explore Math: Book B (Operations and Algebraic Thinking)”

•

Pencils

•

Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o

Begin by reviewing the concept of composing and decomposing numbers. Explain that composing a number means putting together smaller numbers to make a total, and decomposing means breaking the number into smaller groups.

▪

Say, "Today, we will practice counting the total number of books and then finding different ways to make that number using smaller parts. We are going to write the total number in the yellow box and then show three ways to compose it."

o

On the board, draw 8 books and ask the students to count them out loud with you.

o

After counting, say, "We counted 8 books. Now we will write the number 8 in the yellow box."

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 89

2. Demonstrating the Exercise (5 minutes): Exercise: Count the books. Write the number in the yellow box. Write three ways to make that number. o

Open the book to the lesson titled "Problem Solving: Compose and Decompose Up to 10."

o

Guide the students to the exercise where they will count the books and write the number in the yellow box.

o

Say, "Let’s count the books together. How many books are there?"

o

After counting, say, "We have 8 books. Now, write the number 8 in the yellow box."

o

Show students how to write the number 8 in the yellow box.

3. Guided Practice for Writing Three Ways to Compose 8 (10 minutes): o

Explain that after writing the total number of books, students will think of three different ways to make the number 8 by using smaller numbers.

▪

o

Say, "Now that we know there are 8 books, we will find three different ways to make 8 by using two smaller numbers."

Write examples on the board, such as: ▪

"5 + 3 = 8"

▪

"6 + 2 = 8"

▪

"4 + 4 = 8"

o

Say, "These are three ways to make the number 8. Let’s see if you can find your own ways to make 8."

o

Ask the students to fill in three different ways to compose the number 8 in their books. Encourage them to think of different combinations.

▪

Walk around the room, observing their work and providing guidance as needed.

4. Interactive Practice (10 minutes): o

After students have written their number combinations, encourage them to share their ideas with the class.

▪

Ask, "Can anyone share one way you found to make the number 8?"

Write their ideas on the board, such as: ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 90 o

o

▪

"7 + 1 = 8"

▪

"3 + 5 = 8"

▪

"2 + 6 = 8"

Encourage students to think of other ways they could make 8 and allow them to share their suggestions.

5. Independent Practice (5 minutes): o

Give students time to independently complete the exercise by writing three ways to make 8 in their books.

▪

o

Say, "Let’s see how many different ways you can find to make 8. Write your ideas in your books and remember, the numbers should add up to 8."

Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o

Review the different combinations students found to compose the number 8.

o

Ask a few students to share their number sentences and explain how they composed the number 8.

▪

o

Say, "You found many different ways to make the number 8. This helps us understand that numbers can be broken down into smaller parts, and it’s important to know how to put them together and take them apart."

Reinforce the concept of composing and decomposing numbers by reminding students that every number can be made in several different ways.

7. Conclusion and Real-World Connection (2 minutes): o

Conclude by explaining how composing and decomposing numbers helps in real-world situations when adding or dividing objects.

▪

o

Say, "Knowing how to compose and decompose numbers helps us when we need to add things together, like toys or books, or when we need to share things equally with friends."

Encourage students to practice composing and decomposing other numbers at home using real-life objects like toys or snacks.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 91

Additional Tips: •

Visual Aid: Use a large paper or whiteboard to demonstrate how to compose numbers by drawing objects (such as books) and writing different number combinations.

•

Encouragement: Provide positive feedback to motivate students to explore different ways of composing numbers.

•

Repetition: Reinforce the concept by practicing with other numbers (such as 7 or 9) to strengthen students' understanding of composition.

•

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

Exercise 2 Exercise Overview: In this exercise, students will count the total number of sheep in the first row, write the number in a yellow box, and then draw rectangles around groups of sheep in three rows to show three different ways to decompose that number. After drawing the rectangles, students will write the numbers that correspond to each group they created. This activity helps students practice decomposing numbers up to 10 and reinforces part-part-whole relationships.

The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Problem Solving: Compose and Decompose Up to 10."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by reviewing the concept of composing and decomposing numbers. Explain that decomposing a number means breaking it into smaller groups, which helps us understand addition and subtraction.

▪ Say, "Today, we are going to count the sheep in the first row and write that number in the yellow box. Then, we will ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 92

draw rectangles around the sheep in three rows to show three ways to take apart the number." o On the board, draw 4 sheep and ask the students to count them out loud with you. o After counting, say, "There are 4 sheep. Now we will write the number 4 in the yellow box."

2. Demonstrating the Exercise (5 minutes): Exercise: Count the sheep in the first row. Write the number in the yellow box. Draw rectangles around the sheep in the three rows to show three ways to make that number. Write the numbers.

Open the book to the lesson titled "Problem Solving: Compose and Decompose Up to 10." o Guide the students to the exercise where they will count the sheep and write the number in the yellow box. o Say, "Let’s start by counting the sheep in the first row. How many sheep are there?" o After counting, say, "There are 4 sheep in the first row. Now, write the number 4 in the yellow box." o Demonstrate how to write the number 4 in the yellow box.

3. Guided Practice for Drawing Rectangles (10 minutes): o Explain that after writing the number 4, students will draw rectangles around groups of sheep in the three rows to show different ways to take apart the number 4.

▪ Say, "Now that we know there are 4 sheep, we will draw rectangles around the sheep in three different ways to show how we can break apart the number 4 into smaller groups." o Write examples on the board, such as: ▪ Draw a rectangle around 3 sheep and another around 1 sheep for "3 + 1 = 4" ▪ Draw a rectangle around 2 sheep and another around 2 sheep for "2 + 2 = 4" o Say, "These are two ways to take apart the number 4. Now let’s find one more way to take apart 4." o Ask the students to draw rectangles around the sheep in their books to show three different ways to decompose the number 4.

Encourage them to think of different combinations.

▪ Walk around the room, observing their work and providing guidance where needed.

4. Interactive Practice (10 minutes): o After students have drawn their rectangles, encourage them to write the number sentences for each way they decomposed 4.

▪ Say, "Now that you’ve drawn your rectangles, let’s write the numbers that show how you took apart the number 4." o Ask the students to fill in the number sentences in their books. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 93 o

▪ Example: "2 + 2 = 4", "3 + 1 = 4", "4 + 0 = 4" Encourage students to share their number combinations with the class.

5. Independent Practice (5 minutes): o Give students time to independently complete the exercise by drawing rectangles around the sheep in different ways and writing the corresponding number sentences.

▪ Say, "Let’s see how many different ways you can find to take apart the number 4. Draw your rectangles around the sheep and write the numbers in your books." o Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to decompose the number 4. o Ask a few students to share how they grouped the sheep and what numbers they wrote.

▪ Say, "You found many different ways to take apart the number 4. This helps us understand how numbers can be broken down into smaller parts, which is important for addition and subtraction." o Reinforce the idea that there are multiple ways to decompose a number, and each way is correct.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers helps in everyday situations when dividing or grouping objects.

▪ Say, "Knowing how to take apart numbers helps us when we need to divide things, like toys or snacks, into smaller groups." o Encourage students to practice decomposing other numbers at home by using real-life objects like toys, snacks, or crayons. o

Additional Tips: •

• •

•

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing objects (such as sheep) and dividing them into smaller groups using rectangles.

Encouragement: Provide positive feedback to motivate students to explore different ways of decomposing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 6 or 7) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 94

Exercise 3 Exercise Overview: In this exercise, students will count the total number of team members, write the number in a yellow box, and then write three different ways to compose that number. This activity helps students practice composing and decomposing numbers up to 10 and strengthens their understanding of partpart-whole relationships. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Problem Solving: Compose and Decompose Up to 10."

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by reviewing the concept of composing and decomposing numbers. Explain that composing a number means putting together smaller numbers to make a total, and decomposing means breaking the number into smaller parts.

▪ Say, "Today, we are going to count the total number of team members and write that number in the yellow box.

After that, we will think of three different ways to compose that number by using smaller numbers." o On the board, draw 6 team members and ask the students to count them out loud with you. o After counting, say, "There are 6 team members. Now we will write the number 6 in the yellow box."

2. Demonstrating the Exercise (5 minutes): Exercise: Count the team members. Write the number in the yellow box.

Write three ways to make that number. o o o

Open the book to the lesson titled "Problem Solving: Compose and Decompose Up to 10."

Guide the students to the exercise where they will count the team members and write the number in the yellow box.

Say, "Let’s start by counting the team members. How many are there?"

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 95

After counting, say, "There are 6 team members. Now, write the number 6 in the yellow box." o Show students how to write the number 6 in the yellow box.

3. Guided Practice for Writing Three Ways to Compose 6 (10 minutes): o Explain that after writing the total number of team members, students will think of three different ways to make the number 6 by using smaller numbers.

▪ Say, "Now that we know there are 6 team members, we will write three ways to make the number 6 by using two smaller numbers." o Write examples on the board, such as: ▪ "4 + 2 = 6" ▪ "3 + 3 = 6" ▪ "5 + 1 = 6" o Say, "These are three ways to make the number 6. Let’s see if you can find your own ways to make 6." o Ask the students to fill in three different ways to compose the number 6 in their books. Encourage them to think of different combinations.

▪ Walk around the room, observing their work and providing guidance where needed.

4. Interactive Practice (10 minutes): o After students have written their number combinations, encourage them to share their ideas with the class.

▪ Ask, "Can anyone share one way you found to make the number 6?" o Write their ideas on the board, such as: ▪ "2 + 4 = 6" ▪ "1 + 5 = 6" ▪ "3 + 3 = 6" o Encourage students to think of other ways they could make 6 and allow them to share their suggestions.

5. Independent Practice (5 minutes): o Give students time to independently complete the exercise by writing three ways to make 6 in their books.

▪ Say, "Let’s see how many different ways you can find to make 6. Write your ideas in your books and remember, the numbers should add up to 6." o Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o Review the different combinations students found to compose the number 6. o Ask a few students to share their number sentences and explain how they composed the number 6.

▪ Say, "You found many different ways to make the number 6. This helps us understand that numbers can be broken ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 96 o

down into smaller parts, and it’s important to know how to put them together and take them apart." o Reinforce the concept of composing and decomposing numbers by reminding students that every number can be made in several different ways.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how composing and decomposing numbers helps in real-world situations when adding or dividing objects.

▪ Say, "Knowing how to compose and decompose numbers helps us when we need to add things together, like toys or snacks, or when we need to share things equally with friends." o Encourage students to practice composing and decomposing other numbers at home using real-life objects like toys or snacks.

Additional Tips: •

• • •

Visual Aid: Use a large paper or whiteboard to demonstrate how to compose numbers by drawing objects (such as team members) and writing different number combinations.

Encouragement: Provide positive feedback to motivate students to explore different ways of composing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 5 or 7) to strengthen students' understanding of composition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

Exercise 4 Exercise Overview: In this exercise, students will count the total number of snacks in the first row, write that number in the yellow box, and then draw rectangles around the snacks in three different rows to show three ways to decompose that number.

After drawing the rectangles, students will write the numbers that correspond to each grouping. The activity helps students practice composing and decomposing numbers up to 10, building their understanding of part-partwhole relationships. The exercise is available in "Explore Math: Book B (Operations and Algebraic Thinking)" under the lesson titled "Problem Solving: Compose and Decompose Up to 10." ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 97

Materials Needed: • • •

“Explore Math: Book B (Operations and Algebraic Thinking)” Pencils Erasers

Steps to Conduct the Exercise: 1. Introduction to the Concept (5 minutes): o Begin by reviewing the concept of composing and decomposing numbers. Explain that composing a number means putting together smaller parts to make a total, and decomposing means breaking it into smaller groups.

▪ Say, "Today, we will count the number of snacks in the first row and write that number in the yellow box. Then, we will draw rectangles around the snacks in three rows to show three different ways to decompose that number." o On the board, draw 6 snacks and ask the students to count them out loud with you. o After counting, say, "There are 6 snacks in the first row. Now, we will write the number 6 in the yellow box."

2. Demonstrating the Exercise (5 minutes): Exercise: Count the snacks in the first row. Write the number in the yellow box. Draw rectangles around the snacks in the three rows to show three ways to make that number. Write the numbers.

Open the book to the lesson titled "Problem Solving: Compose and Decompose Up to 10." o Guide the students to the exercise where they will count the snacks and write the number in the yellow box. o Say, "Let’s count the snacks in the first row together. How many snacks are there?" o After counting, say, "There are 6 snacks. Now, write the number 6 in the yellow box." o Show students how to write the number 6 in the yellow box.

3. Guided Practice for Drawing Rectangles (10 minutes): o Explain that after writing the number 6, students will draw rectangles around groups of snacks in the three rows to show different ways to take apart the number 6.

▪ Say, "Now that we know there are 6 snacks, we will draw rectangles around the snacks in three different ways to show how we can break apart the number 6 into smaller groups." o Write examples on the board, such as: ▪ Draw a rectangle around 4 snacks and another around 2 snacks for "4 + 2 = 6" o

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 98

Draw a rectangle around 3 snacks and another around 3 snacks for "3 + 3 = 6" o Say, "These are two ways to take apart the number 6. Now let’s find more ways." o Ask the students to draw rectangles around the snacks in their books to show three different ways to decompose the number 6.

Encourage them to think of different combinations.

▪ Walk around the room, observing their work and providing guidance where needed.

4. Interactive Practice (10 minutes): o After students have drawn their rectangles, encourage them to write the number sentences for each way they decomposed the number 6.

▪ Say, "Now that you’ve drawn your rectangles, let’s write the numbers that show how you took apart the number 6." o Ask the students to fill in the number sentences in their books.

▪ Example: "4 + 2 = 6", "3 + 3 = 6", "5 + 1 = 6" o Encourage students to share their number combinations with the class.

5. Independent Practice (5 minutes): o Give students time to independently complete the exercise by drawing rectangles around the snacks in different ways and writing the corresponding number sentences.

▪ Say, "Let’s see how many different ways you can find to take apart the number 6. Draw your rectangles around the snacks and write the numbers in your books." o Walk around the room to check their progress and offer support as needed.

6. Review and Reinforcement (5 minutes): o Review the different ways students found to decompose the number 6. o Ask a few students to share how they grouped the snacks and what numbers they wrote.

▪ Say, "You found many different ways to take apart the number 6. This helps us understand how numbers can be broken down into smaller parts, which is important for addition and subtraction." o Reinforce the idea that there are multiple ways to decompose a number, and each way is correct.

7. Conclusion and Real-World Connection (2 minutes): o Conclude by explaining how decomposing numbers helps in everyday situations, such as dividing or grouping objects.

▪ Say, "Knowing how to take apart numbers helps us when we need to divide things, like toys or snacks, into smaller groups." o Encourage students to practice decomposing other numbers at home by using real-life objects like toys, snacks, or crayons. ___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 99 ▪

Additional Tips: •

• •

•

Visual Aid: Use a large paper or whiteboard to demonstrate how to decompose numbers by drawing objects (such as snacks) and dividing them into smaller groups using rectangles.

Encouragement: Provide positive feedback to motivate students to explore different ways of decomposing numbers.

Repetition: Reinforce the concept by practicing with other numbers (such as 7 or 8) to strengthen students' understanding of decomposition.

Differentiation: Offer extra support to students who need more guidance, and provide additional challenges for students who grasp the concept quickly.

___________________________________________________________________________ Explore Math – Book B: Operations and Algebraic Thinking Page | 100