standard_description: Know and apply the Binomial Theorem for the expansion of (x + y)^(n )in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle. (The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument.)
problem_activity: Narrative
The purpose of this activity is for students to sort triangles into more specific categories. This requires students to attend to an attribute other than the number of sides. As students sort the triangles, monitor for students who sort by the number of equal side lengths or the presence of a right angle (MP7). Although the terms “equilateral,” “isosceles,” and “scalene” are not introduced in this lesson it is fine if students already know them and use them to describe the groups of triangles.
MLR2 Collect and Display.
Direct attention to words collected and displayed from the previous lesson. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading
Representation: Access for Perception.
Synthesis: Use gestures during explanation of triangle sorting to emphasize side lengths of triangles.
Supports accessibility for: Visual-Spatial Processing
Required Materials
Materials to Copy
Triangle Cards Grade 3
Required Preparation
Create a set of cards from the blackline master for each group of 2 or 4.
When copying the card sort triangles, use colored paper to distinguish these cards from the cards in the next activity.
Launch
Groups of 2 or 4
Distribute one set of pre-cut cards to each group of students.
“What do you notice about the shapes on the cards?” (The shapes are all triangles. They all look different. Some of them have sides that are the same length.)
1 minute: quiet think time
Activity
“Work with your partner to sort the triangles into categories. Be sure to explain your categories.”
8 minutes: partner work time
Monitor for students that sort the triangles into groups based on:
the number of sides with equal length (all, two, none)
the sides and corners having the same size (the triangles being identical)
the presence of right angles
Student Facing
Sort the triangles into categories. Record your categories and be prepared to explain how you sorted the shapes.
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Student Response
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Advancing Student Thinking
If students say they aren’t sure how to sort the shapes because they are all triangles, consider asking:
“What other attributes have you used before to sort shapes?”
“How are some of the triangles different?”
Activity Synthesis
Select groups to share their categories and how they sorted their cards.
Allow as many categories to be presented as time permits, but be sure to highlight categories based on the number of sides with equal length.
Highlight the use of terms like “equal side lengths” and “angles.”
Record and display the attributes students use to categorize the triangles.


aligns: no