Lesson 8

The purpose of this warm-up is for students to compare and contrast ways of representing quantities. This warm-up prepares students to represent shapes they sort in a way that makes sense to them.

• Groups of 2
• Display the image.
• “Pick one that doesn’t belong. Be ready to share why it doesn’t belong.”
• 1 minute: quiet think time

• “Discuss your thinking with your partner.”
• 2–3 minutes: partner discussion
• Share and record responses.

• “Which representation is easiest for you to see how many? Why?” (The three triangles because I can just look at it and know how many. The number 5 because I don't have to count.)

The purpose of this activity is for students to organize shape cards into three categories and name the categories. Students describe how they sorted and how many shapes are in each category. Students choose and describe different attributes of their shapes and how those attributes determine the different ways they sorted their shapes (MP3). Students create a representation of how they sorted in the next activity.

• Create a set of shape cards from the blackline master for each group of 2.
• Have extra copies of the three-column table from a previous lesson available for students. 

• Groups of 2
• Give each group a set of shape cards and access to copies of the three-column table.
• “Look at all of your shape cards. Take a minute to look over the cards by yourself first and think about how you would sort them.”
• 1 minute: quiet think time

• “Work with your partner to sort the cards into three categories in any way that you want. You do not need to use all of the cards.”
• 5 minutes: partner work time
• “Share with another group. Explain how you sorted the shapes. Tell how many shapes are in each category and how many shapes there are altogether.” (There are 5 white shapes. There are 12 shapes altogether.)
• 2 minutes: small group discussion
• Monitor for two groups who sorted their cards in different ways.

• Invite previously identified students to share.
• “How did this group sort their shapes? How many shapes are in each category?” (They sorted by color. There are 6 white shapes, 3 black shapes, and 3 gray shapes.)

The purpose of this activity is for students to represent how they sorted their shapes in the previous activity and tell how many in each category and how many in all. At the end of the activity, display each representation on tables or walls, to use during the gallery walk in the next activity.

• Have extra copies of the three-column table from a previous lesson available for students. 

• Give students access to colored pencils or crayons and copies of the three-column table.

• Read the task statement.
• 10 minutes: independent work time

If students make a representation that doesn’t show three categories, consider asking,

• “Can you explain how you showed your sort on the paper?”
• “How could you show each category in your representation?”

• “Now we will have a chance to look at and interpret each other's representations.”

The purpose of this activity is for students to interpret different representations created based on their shape sorts. Students use the different representations to determine how many shapes are in each category. During the synthesis, students discuss aspects of representations that make them easier to interpret.

• Display students’ representations of their shape sorts on tables or walls so they are easily seen as students walk around.

• Groups of 2

• “With your partner, look at each representation. Discuss how each group sorted the shapes, how many shapes are in each category, and how you know.”
• 10 minutes: partner discussion 
• As students work, consider asking:
  • “How does this representation show how many shapes are in the first category?”
  • “What makes this representation easy to interpret?”
• Monitor for representations that use shapes, tally marks, numbers, and labels. 

• Display previously identified representations. 
• “How did this group sort their shapes? How many are in each category? How do you know?”
• Repeat with different student work as time allows. 
• “Which representation was easiest to interpret? What made it easier than the others?” (The one with numbers was easiest because I didn’t have to count. The one with labels was easiest because I knew what the groups were.)