Lesson 7

The purpose of this How Many Do You See is for students to use grouping strategies to describe the images they see. It gives the teacher an opportunity to hear how students use place value terminology to talk about how many they see and the value represented by a base-ten diagram.

Students may describe how many of each unit they see or may describe the total value of the blocks. In the synthesis, students compare different ways each image represents the same number and describe the ways they could see when larger units could be composed. This understanding will be helpful in the lesson activities when students compose tens and hundreds and anticipate when they may need to compose units.

• Groups of 2
• “How many do you see? How do you see them?”
• Flash 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.

• “How are these images the same? How are they different?” (They each represent the same number. They have different amounts of hundreds, tens, and ones.)
• “How could you tell when you could compose a ten or a hundred?” (When there were ten of a unit. I saw two rows of 5 tens, so I knew I had enough to count it as 1 hundred.)

The purpose of this activity is for students to find sums that require composing a ten or hundred when adding by place. The numbers in the expressions share the same digits, but one expression requires composing a ten and the other requires composing a hundred when adding by place. Students may use the methods that make sense to them when finding the value of each sum. Monitor for students who use base-ten blocks, base-ten diagrams, or equations to show adding by place and composing new units. The synthesis focuses on representations that show composing a ten and a new hundred.

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

• “Find the value of each expression. Use the base-ten blocks or show your thinking using a diagram, symbols, or other representations.”
• “When you and your partner are finished, compare your thinking.”
• 5 minutes: independent work time
• 5 minutes: partner discussion
• Monitor for students who use base-ten blocks or diagrams to show adding by place and composing hundreds or tens.

• “Will you explain your representation to me?”
• “What is the value of the sum? How could you write it as a three-digit number?”
• “Can you use base-ten blocks to show me the total using as few blocks as possible?”

• “How was finding the value of the expressions the same? How was it different?” (In both of them you have to make a unit. In the first one you made a ten with 10 ones and in the second one you made a hundred with 10 tens.)
• Invite previously identified students to share their methods.
• “How did _____ represent composing a ten to find the value of \(364 + 28\)?”
• “How did _____ represent composing a hundred to find the value of \(364 + 82\)?”
• Consider asking, “When did you notice that you would need to compose a unit?” (I could tell because I knew that there would be more than 10 ones once I started adding. I knew when I got the blocks that there were more than 10 tens.)

The purpose of this activity is for students to practice adding a two-digit number and a three-digit number in sums that require composing a ten or hundred when adding by place. Students are given a card with a three-digit number or a two-digit number. Students with three-digit numbers find a partner with a two-digit number. When students first discuss whether they would need to compose a ten or a hundred when adding their numbers, they look for and make use of place value structure and construct viable arguments (MP3, MP7).

This activity uses MLR8 Discussion Supports. Advances: conversing

• Create a set of cards from the blackline master so that each student will receive 1 card.

• Groups of 2
• Give students access to base-ten blocks.
• Give half of the students three-digit cards (A) and the other half two-digit cards (B).

• “If you have a card with the letter A on it, find someone with a B. Write an expression to show the sum of the numbers on your cards.”
• “Then, before you find the value of the sum, decide whether you think you would compose a ten or a hundred if you added ones to ones and tens to tens. Explain your thinking. You can use base-ten blocks or diagrams to help explain.”

• Display sentence frames to support students when they explain their strategy and listen to others:
  • “I noticed _____ so I think that …”
  • “I heard you say …”
  • “I agree because …”
  • “I disagree because …”
• “After you discuss, work together to find the sum. Then trade cards and find another partner.”
• As needed, demonstrate one round with a student.
• 15 minutes: partner work time
• Monitor for students who:
  • use base-ten blocks or diagrams to show that a new unit will be composed
  • use what they know about adding by place and sums of 10 to explain why they knew a new unit would be composed (I know \(8 + 3\) is more than 10, so I know a hundred will be composed when we add 8 tens and 3 tens)
  • add 10 or 100 more using a mental strategy

• “What do you notice about the hundreds, tens, and ones?”
• “How could you represent your numbers with base-ten blocks and show where you would compose a unit?”

• Invite 2–3 previously identified groups to share how they decided if a ten or hundred would be composed.
• Invite 1–2 previously identified groups to share an expression that resulted in a hundred being composed. Have them share their method for finding the sum.