Lesson 7

The purpose of this How Many Do You See is to build on what students know about place value to make sense of visual representations of two-digit numbers. When students describe how many they see by grouping tens with tens and ones with ones or composing a ten, they show how they look for and make use of base-ten structure (MP7). This will be helpful when students use base-ten representations to compose and decompose a ten during the lesson.

• Groups of 2
• “How many do you see? How do you see them?”  
• Display the image.
• 30 seconds: quiet think time

• Display the image.
• “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Record responses.
• Repeat for each image.

• “Which two images have the same value? How do you know?”(The first image and the second image both have the same amount. The first one shows 5 tens and 5 ones. I know Image 2 is the same because I know 2 groups of 5 is the same as 1 ten. So it's the same as 5 tens and 5 ones.)

The purpose of this activity is for students to subtract a two-digit number from a two-digit number in a way that makes sense to them. Students build on their understanding of decomposing a ten when subtracting a one-digit number from a two-digit number to subtract two-digit numbers. The synthesis is devoted to presenting and comparing techniques students use to find the difference, including diagrams and equations (MP3).

This activity uses MLR8 Discussion Supports. Advances: listening, speaking, conversing

• Groups of 2
• Give students access to connecting cubes and base-ten blocks.

• “Find the value of each difference and share your method and solution with your partner.”
• 7 minutes: independent work time

MLR8 Discussion Supports

• “After your partner shares their method, repeat back what they told you.”
• Display the sentence frames:
  • “I heard you say . . . .”
  • “Our methods are alike because . . . .”
  • “Our methods are different because . . . .”
• 5 minutes: partner discussion
• Monitor for students who use base-ten blocks to show decomposing a ten.

Some students may not use base-ten blocks to find the difference. Prompt them to show their thinking in a way that could help others understand. Ask them to write expressions to show the steps they took when appropriate. Consider asking:

• “How did you find the value of the difference?”
• “What could you add to your diagram to help your partner understand what you did?”
• “How could you use equations to show the steps you used?”

• Invite previously identified students to share.
• “What did _____ do to solve the problem? How can we record it?”
• 30 seconds: quiet think time
• Share responses.
• Show how to represent solving with base-ten blocks with drawings and equations.
• “How are these representations like the way _____ used base-ten blocks to find the value of the difference? How are they different?”

The purpose of this activity is for students to subtract a two-digit number from a two-digit number. In the first activity, students used any method that made sense to them to find the difference. In this activity, they use base-ten blocks to represent the starting number and subtract amounts that require a ten to be decomposed.

• Create a set of cards from the blackline master for each group of 4.

• Groups of 4
• Give each group a set of cards and access to base-ten blocks.

• “Now you are going to play a card game using base-ten blocks.”
• “First, each member of your group will choose a different player card, Diego, Lin, Jada, or Han.”
• “Write down the name you picked. Mix up the other cards and put them face down.”
• “Now you each have a player and your starting number.”
• “Use the blocks to represent your starting numbers.”
• 2 minutes: group work
• Guide students through the rest of the steps:
  • “Take turns picking a card and read the card to the group.”
  • “Listen for your player’s name and follow the directions on the card.”
  • “Share your thinking while your group members listen. Write an equation to show the new number.”
  • “Before picking a new card, make sure your group works together to agree on the new number.”
  • “You will keep playing until all of the cards have been read. Your player‘s number should change two times.”
• 15 minutes: group work time
• Monitor for students who:
  • discuss decomposing a ten using precise language
  • work together to give feedback and resolve any disagreements
  • compose tens when adding the ending numbers

• Invite 1–2 previously identified students to share with their group.
• Consider asking:
  • "What questions do you have for __ about their method?"
  • "How was their method the same as how you found your player's new numbers? How was it different?"