standard_description: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
problem_activity: Narrative
The purpose of this activity is for students to begin to distinguish triangles from other shapes. By working with variants and non-examples of triangles, students begin to develop their understanding of what makes a shape a triangle. Students may more easily identify equilateral triangles as triangles but may also identify other examples as triangles. When students discuss with their group which group a shape should be placed in, students informally describe the attributes of the shape (MP6).
Required Materials
Materials to Copy
Triangle Sort Cards
Required Preparation
Cut out triangle cards from the blackline master. Each group of 4 needs 1 set of cards.
Launch
Groups of 4
Give each group a set of cards.
“Work with your group to sort the shapes into 2 groups. Put the shapes that are triangles on the left side of your page. Put the shapes that are not triangles on the right side of your page. When you place a shape, tell your group why you think the shape belongs in that group.”
Activity
4 minutes: small-group work time
Monitor for students who discuss attributes of triangles when sorting.
“Write a number to show how many shapes are in each group.”
1 minute: independent work time
“Walk around to see how the other groups organized their shapes. Did they organize them the same way that your group did?”
6 minutes: work time
Student Facing
Let’s put the shapes into 2 groups.
Triangle
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Not a Triangle
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Student Response
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Advancing Student Thinking
I
f students put shapes other than triangles into the group of triangles, consider asking:
“How did you choose which group to put this shape in?”
“What is alike, or the same, about all of the shapes in this group?”
Activity Synthesis
Display cards O, K, and G next to each other.
“Noah says that the shape in the middle is not a triangle because it is pointing down and triangles have to point up. Do you agree with Noah? Why or why not?“


aligns: no