standard_description: Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
problem_activity: Narrative
The purpose of this activity is for students to identify shapes as flat and solid as they sort shapes into groups. A sorting task gives students opportunities to analyze the structure of the shapes and identify common properties and characteristics (MP7).
If the sorting mat provided in the student workbook is too small for students to sort the shapes, consider giving students two pieces of construction paper, or ask students to put the solid shapes on one side of the table and the flat shapes on the other side.
MLR8 Discussion Supports.
Invite each partner to identify each shape aloud: Flat shape or solid shape. Encourage students to challenge each other when they disagree.
Advances: Conversing
Action and Expression: Internalize Executive Functions.
Invite students to plan a strategy for how they will sort the shapes.
Supports accessibility for: Conceptual Processing, Organization
Required Materials
Materials to Gather
Geoblocks
Solid shapes
Materials to Copy
Flat Shapes Cards K
Required Preparation
Each group of 2 needs a set of solid shapes and a set of cards.
Launch
Groups of 2
Give each group of students a set of solid shapes and a set of flat shapes cards.
Activity
“Work with your partner to sort the shapes into two groups. Write a number to show how many shapes are in each group.”
3 minutes: partner work time
“Pair up with another group. Show them how you sorted your shapes. Did you sort all of the shapes in the same way?”
3 minutes: small-group work time
“What could you call each group of shapes to show why you put those shapes together?”
Monitor for a group that sorts by flat shapes and solid shapes.
Student Facing
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Student Response
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Advancing Student Thinking
If students identify a pyramid as flat because “it looks like a triangle,” consider asking:
“What is the same about all of the shapes in this group?”
Display a pyramid and a triangle next to each other and ask “What do you notice about these shapes? What is different about them?”
Activity Synthesis
Invite previously selected students to share the way they sorted the shapes into flat shapes and solid shapes.
“This group has flat shapes. This group has solid shapes.”
Display a square.
“Should this shape go with the flat shapes or the solid shapes? Why?” (It is a flat shape. If we put it on our desk, it doesn’t stick up.)
Display a cube.
“Should this shape go with the flat shapes or the solid shapes? Why?” (It is a solid shape. It sticks up and takes up space.)


aligns: no