Lesson 8

The purpose of this How Many Do You See is to allow students to use grouping strategies to describe amounts represented with base-ten diagrams. Students look for and make use of structure (MP7) when they describe how many they see in terms of place value and how they mentally compose new units to name how many they see.

• 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 were the images the same? How were they different?” (The first two had the same number of tens. I saw a group of three ones in each image. They each showed different values. The last image had more than 10 tens.)
• “What would you need to do to show the value of the third image with the least amount of blocks?” (If you were using blocks, you could exchange 10 tens for 1 hundred. Use one hundred instead of 10 tens.)

The purpose of this activity is for students to find the sum of a two-digit and a three-digit number when both a ten and a hundred are composed when adding by place. They find the value of each sum in a string of expressions, where the first addend remains the same, but the second addend changes. These variations result in composing a ten, composing a hundred, and composing both a ten and a hundred.

Although the number choices encourage students to consider adding by place, they may use any method that makes sense to them when finding the value of each sum. Students share their thinking with a partner and explain why their method works (MP3). The lesson synthesis focuses on students sharing and making sense of strategies based on place value and using place value language to describe what they noticed about the sums and composing larger units (MP7).

This activity uses MLR8 Discussion Supports. Advances: conversing

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

• “Find the value of each sum. Show your thinking using diagrams, symbols, or other representations. Use base-ten blocks if it helps. After you find each sum, compare your method to your partner’s.”

MLR8 Discussion Supports

• Display sentence frames to support students when they compare methods:
  • “We have the same sum, but ...”
  • “We have different sums because …”
  • “Our thinking is the same because …”
  • “Our thinking is different because …”
• 12 minutes: partner work time
• Monitor for students who find the sum of \(273 + 88\) by grouping by place value using base-ten blocks or a base-ten diagram.

• Invite previously identified students to share their work for \(273 + 88\).
• “How did _____ find the sum?”
• “What was the same and different about what you did to find the value of each sum?” (We had to make a ten and a hundred for the last one. For the first 2, we just had to make a ten or a hundred.)

The purpose of this activity is for students to make sense of different representations of student thinking when adding at three-digit number and a two-digit number. First, students analyze base-ten diagrams and corresponding equations that represent the sum that requires composing a ten and a hundred when adding by place. They make connections between the methods and discuss how they are the same and different. In the synthesis, students compare and connect their own methods for adding within 1,000 using their understanding of place value.

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

• “Priya and Lin were asked to find the value of \(358 + 67\). They represented their thinking in different ways. What is the same and different about their representations?” (Priya used the diagrams and wrote equations. Priya circled the new units she made in her diagram. Lin wrote the units and added them first. They found the same value.)
• 5 minutes: partner discussion
• “Where do you see each student composing new units?” (Priya circled 10 tens to show a new hundred and circled 10 ones to show a new ten. Lin added the units and has 11 tens and 11 ones. 11 tens is the same as 1 hundred and 1 ten and 11 ones is the same as 1 ten and 1 one.)
• 30 seconds: quiet think time
• 1 minute: partner discussion
• Share and record responses.
• “Now you are going to find the value of \(546 + 86\) and represent your thinking.”
• 5 minutes: independent work time
• Monitor for students who represent place value strategies using:
  • base-ten blocks or base-ten diagrams
  • equations in unit form
  • equations with only numbers

If students create diagrams or other representations to show how they added by place, but it is unclear how they composed hundreds or tens, ask students to explain their representation. Consider asking, “How can you show others that you composed a ten or hundred here?”

• Invite previously identified students to share their work.
• “What’s the same across these representations? What is different?” (They all got the same answer. They all made a ten and a hundred. Some used words, some used diagrams, and some used only numbers.)