Lesson 4

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.

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

• Record answers and strategy.
• Keep expressions and work displayed.
• Repeat with each expression.

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

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.

• Groups of 2
• Give students access to counters.

• “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

• “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.)

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.

• Groups of 2
• Give students access to counters.

• “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

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?”

• 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.”