Lesson 4
Decompose Even and Odd Numbers
Warmup: Number Talk: Equal Addends (10 minutes)
Narrative
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
 Record answers and strategy.
 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
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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.
Advances: Reading, Writing
Supports accessibility for: Organization, VisualSpatial Processing, Conceptual Processing
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to counters.
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

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

Can both bags have the same amount of cookies?
\(12 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

Can both bags have an even number of cookies?
\(12 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

Can both bags have an odd number of cookies?
\(12 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

Can one bag have an even number of cookies and the other have an odd number of cookies?
\(12 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)


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

Can both bags have the same amount of cookies?
\(14 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

Can both bags have an even number of cookies?
\(14 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

Can both bags have an odd number of cookies?
\(14 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

Can one bag have an even number of cookies and the other have an odd number of cookies?
\(14 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)


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

Can both bags have the same amount of cookies?
\(15 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

Can both bags have an even number of cookies?
\(15 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

Can both bags have an odd number of cookies?
\(15 = \underline{\hspace{1 cm}} + \underline{\hspace{1 cm}}\)

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
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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
Required Materials
Materials to Gather
Launch
 Groups of 2
 Give students access to counters.
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
 Pick a number between 0 and 20.
 Decide with your partner whether the number is even or odd.
 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
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Advancing Student Thinking
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?” (\(4 + 4 = 8\), \(8 = 4 + 4\))
Cooldown: Two Equal Addends (5 minutes)
CoolDown
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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
\(4 + 4 = 8\)