Lesson 23

The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting. The expressions are explicitly chosen to encourage students to use their understanding of the 10 + n structure of teen numbers to subtract (MP7). This method will be discussed in more depth is this lesson's activities.

• 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.

• “Did anyone approach the problem in a different way?”

The purpose of this activity is to play the same game from the previous lesson, with a focus on using the ten in the teen number to help find the difference. This time, all students use the double 10-frame to represent the teen number to encourage students to use a ten to help them subtract.

Students may start by taking away the ones from the teen number and then take additional ones from the 10-frame to determine the answer. Students may use a different method and take away the single digit number from the full 10-frame, then count the remaining counters across both 10-frames. Or, students may may count on from the one-digit number to the teen number. In each case, students write an equation to show the difference. Students may write subtraction equations or missing addend equations.

• Each group of 2 needs a set of Number Cards 0 - 10 and a set of Number Cards 11-20 used in a previous lesson.

• Groups of 2
• Give each group a set of number cards 0–10, a set of number cards 11–20, double 10-frames, and connecting cubes or two-color counters.
• “We’re going to play the same subtraction game as yesterday, but this time you will represent your teen number on the double 10-frame.”
• If needed, play a round of the game with the class, demonstrating using the double 10-frame.

• 7 minutes: partner work time
• Monitor for students who:
  • take away to 10, then take away some more
  • take away from the 10, then count what is left
• “On your own, pick your favorite round. Show how you found the value of the difference using drawings, words, or numbers.”
• 3 minutes: independent work time

• Invite previously identified students to share.
• “How is the game different from yesterday?” (Yesterday we could solve any way we want, today we used 10-frames to build numbers and take away.)
• “Did the double 10-frames help? Why?” (They helped me see how I could use 10 to take away easier.)

The purpose of this activity is for students to analyze different take away methods used to find the difference between two numbers. During the launch, students discuss the two different methods to subtract. Then they solve two problems using one of the methods they discussed. Given the first step toward a calculation, students make sense of and then complete the calculation (MP3).

During the activity synthesis, the teacher records equations to match the method shared. It is important that each step is written as its own equation. For example, when solving \(13 - 6 = \boxed{\phantom{3}}\), the teacher records:

• \(13 - 3 = 10\)
• \(10 - 3 = 7\)

• Groups of 2
• Give students access to double 10-frames and connecting cubes or two-color counters.
• “Have you ever started solving a math problem, and then had trouble finishing? Today we’re going to see some ways that students started to find the difference, and suggest ways they could finish.”
• Display the first problem with Diego's work.
• “What did Diego do?” (He put 15 on his 10-frames and crossed out 5 to get to 10.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• “What could Diego do next to find the difference?” (He already took away 5, so he needs to take 3 more away so that he subtracts 8 altogether.)
• 1 minute: quiet think time
• 1 minute: partner discussion
• Demonstrate crossing off three more.
• “What is the difference?”
• Repeat the discussion with Andre’s work. (Andre took 8 away from the full 10-frame and has 2 left. He needs to combine the 2 with the 5 in the other 10-frame to find the difference.)

• Read the task statement.
• 4 minutes: independent work time
• 2 minutes: partner discussion
• Monitor for a student who uses and can explain each way to subtract \(14-5\).

If students take away without using the ten, consider asking:

• “Can you explain how you found the difference?”
• “How many counters would you take away to make 10? Then how many more would you need to take away?”

• Invite previously identified students to share.
• As each student shares, ask them to explain why they chose their method.
• “Did anyone solve it a different way? Why?”