standard_description: Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
problem_activity: Narrative
The purpose of this card sort is for students to connect words and phrases to visual representations of partitioned shapes. Students begin by sorting the cards in a way that makes sense to them, and then are invited to sort the shapes based on the language that can be used to describe them. In the activity synthesis, the phrases “two of the halves” and “four of the fourths” are introduced to describe shapes where all pieces are shaded in.
Keep cards D and N available to use during the lesson synthesis.
As students sort the shape cards they look for structure, namely the number of pieces making up each shape, whether or not the pieces are equal, and the number of those pieces that are shaded (MP7).
MLR2 Collect and Display.
Circulate, listen for and collect the language students use as they describe the shapes. On a visible display, record words and phrases such as: “shaded,” “half,” “fourth,” “quarter,” “equal,” “not equal,” “whole,” “shape.” Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Speaking
Required Materials
Materials to Copy
Shaded Parts Cards
Required Preparation
Create a set of Shaded Parts Cards for each group of 2.
Launch
Groups of 2
Give each group a set of cards.
“Sort your cards in a way that makes sense to you. Then explain how you sorted them.”
3 minutes: partner work time
Share responses.
Activity
“Now, sort the cards into the categories shown on your paper. Think about what words you can use to describe the shape on each card. Write the letter of each card in the space for it's category.”
5 minutes: partner work time
Student Facing
Sort the cards into categories in a way that makes sense to you. Explain how you sorted the cards.
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Sort your cards into these categories.
Write the letter of each card in the space for its category.
A fourth or quarter is shaded
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A half is shaded
The whole shape is shaded
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Not equal pieces
Student Response
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Activity Synthesis
Display card J.
“How can we describe this shape?” (It is a square. It is cut into halves. The whole shape is shaded.)
“When a shape is split into halves and they are both shaded, we say the whole shape is shaded or two of the halves are shaded.”
Repeat with card E.
“When a shape is split into fourths and they are all shaded, we say the whole shape is shaded or four of the fourths are shaded.”


aligns: no