# Lesson 4

Decompose Even and Odd Numbers

## Warm-up: Number Talk: Equal Addends (10 minutes)

### Narrative

The purpose of this Number Talk is to elicit strategies and understandings students have for finding sums when both addends are the same and sums when one addend is one less or one more than the other. These understandings help students develop fluency and will be helpful later in this lesson when students will need to be able to decompose numbers into two equal addends or two addends that are as close as possible as they reason about even and odd numbers.

### Launch

• Display one expression.
• “Give me a signal when you have an answer and can explain how you got it.”
• 1 minute: quiet think time

### Activity

• Keep expressions and work displayed.
• Repeat with each expression.

### Student Facing

Find the value of each expression mentally.

• $$6 + 6$$
• $$7 + 7$$
• $$7 + 8$$
• $$8 + 9$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “How are the expressions the same? How are they different?”

## Activity 1: Share in Different Ways (20 minutes)

### Narrative

The purpose of this activity is for students to recognize that even numbers can be represented as the sum of two equal addends. The activity is designed to elicit student curiosity about which types of decompositions are possible and which are not. Students may notice many patterns in the ways even and odd numbers can be decomposed which will be useful in future lessons. However, the synthesis should be focused on representing even numbers as sums of equal addends.

MLR5 Co-Craft Questions. Keep books or devices closed. Display only the problem stem sentences, without revealing the questions, and ask students to write down possible mathematical questions that could be asked about the situation. Invite students to compare their questions before revealing the task. Ask, “What do these questions have in common? How are they different?” Reveal the intended questions for this task and invite additional connections.
Representation: Internalize Comprehension. Provide students with a graphic organizer, such as a sorting mat that has images of gift bags or simply two large circles, to physically share the “cookies” (images of cookies cut out or counters, chips, etc.). Use this to give a concrete example that supports the context of the problems.
Supports accessibility for: Organization, Visual-Spatial Processing, Conceptual Processing

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Figure out different ways the students could share their cookies.”
• “Show your thinking for each way. Use equations to show the groups.”
• “Some ways may not be possible. Be ready to show and explain why.”
• 5 minutes: independent work time
• “Share your thinking with your partner. How are your equations the same? How are they different?”
• 10 minute: partner discussion

### Student Facing

1. Kiran baked 12 cookies. He wants to put them in two gift bags. Show a few different ways he can share the cookies.

1. Can both bags have the same amount of cookies?

$$12 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

2. Can both bags have an even number of cookies?

$$12 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

3. Can both bags have an odd number of cookies?

$$12 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

4. Can one bag have an even number of cookies and the other have an odd number of cookies?

$$12 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

2. Lin baked 14 cookies. She wants to put them in two gift bags. Show a few different ways she can share the cookies.

1. Can both bags have the same amount of cookies?

$$14 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

2. Can both bags have an even number of cookies?

$$14 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

3. Can both bags have an odd number of cookies?

$$14 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

4. Can one bag have an even number of cookies and the other have an odd number of cookies?

$$14 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

3. Noah baked 15 cookies. He wants to put them in two gift bags. Show a few different ways he can share the cookies.

1. Can both bags have the same amount of cookies?

$$15 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

2. Can both bags have an even number of cookies?

$$15 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

3. Can both bags have an odd number of cookies?

$$15 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

4. Can one bag have an even number of cookies and the other have an odd number of cookies?

$$15 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}$$

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “What did you notice about the possible ways the students could share their cookies?” (Kiran and Lin could share their cookies in the most ways. Noah could only share with one bag of even and one bag of odd.)
• Display:
• $$12 = 6 + 6$$
• $$14 = 7 + 7$$
• $$15 = 7 + 8$$
• “How do these equations represent the student’s cookies?”
• “Which students baked an even number of cookies? Use the equations to explain how you know.” (Kiran and Lin because the equations show you can split their cookies into two equal groups.)

## Activity 2: Represent Numbers with Two Addends (15 minutes)

### Narrative

The purpose of this activity is for students to represent even numbers as a sum of two equal addends. They sort all numbers between 0 and 20 into even and odd and notice that all even numbers can be represented as sums of two equal addends while odd numbers cannot (MP8). Students may also use the sorting activity to understand and explain why 0 is an even number.

### Required Materials

Materials to Gather

• Groups of 2

### Activity

• “Let’s try to decompose more numbers into two equal addends.”
• “Take turns picking a number between 0 and 20. Decide together whether the number is even or odd and record it in the table.”
• “Then try to decompose the number into two equal addends. If you can, record it on the table.”
• “If you cannot find a way to decompose the number into two equal addends, find two addends that are as close together as possible that make your number.”
• Demonstrate with Kiran (12) and Noah’s (15) cookies as needed.
• “Keep going until you have sorted all the numbers from 0 to 20.”
• 10 minutes: partner work time

### Student Facing

1. Pick a number between 0 and 20.
2. Decide with your partner whether the number is even or odd.
3. Complete the equation to show your number as the sum of two equal addends. If you cannot use two equal addends, use two addends that are as close as possible.

even

odd

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

$$\underline{\hspace{0.9 cm}} = \underline{\hspace{0.9 cm}} + \underline{\hspace{0.9 cm}}$$

### Student Response

For access, consult one of our IM Certified Partners.

If students place an odd number in the even group or an even number in the odd group,  consider asking:

• “How could you use counters or a drawing to show if this number is odd or even?”

### Activity Synthesis

• Display the completed table.
• “What do you notice about even and odd numbers?” (All the even numbers have the same addends. All the even numbers are “doubles.” The odd numbers have one addend that is one more than the other.)
• “Explain why even numbers can be decomposed into two equal addends.”

## Lesson Synthesis

### Lesson Synthesis

Draw or display:

“Is there an even or odd number of dots? Explain.” (Even. I see two equal groups of 4. I see 4 pairs and no dots left over.)

“What is an equation that would show that the number of dots is even?” ($$4 + 4 = 8$$, $$8 = 4 + 4$$)

## Cool-down: Two Equal Addends (5 minutes)

### Cool-Down

For access, consult one of our IM Certified Partners.

## Student Section Summary

### Student Facing

In this section, we learned that groups of objects have either an even or odd number of members. We learned that an even number of objects can be split into 2 equal groups or into groups of 2 with no objects left over. We learned that an odd number of objects always has one object left over when you make 2 equal groups or groups of 2. We also learned that even numbers can be represented as an equation with 2 equal addends.

Odd

$$3 + 3 + 1 = 7$$

Even

$$4 + 4 = 8$$