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IM K-5 Math
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6-8 Accelerated 6 Unit 1 Lesson 6

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K-5 Math •6-8 Math 9-12 Math

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•Accelerated 6 Accelerated 7

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•Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 •Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11 Lesson 12 Lesson 13

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Lesson 6

6.1 Warm-up 6.2 Activity 6.3 Activity Student Lesson Summary

Unit 1, Lesson 6

From Parallelograms to Triangles

Accelerated 6

6.1

Warm-up

Same Parallelograms, Different Bases

Here are two copies of a parallelogram. Each copy has one side labeled as the base and a segment drawn for its corresponding height and labeled .

The base of the parallelogram on the left is 2.4 centimeters; its corresponding height is 1 centimeter. Find its area in square centimeters.
The height of the parallelogram on the right is 2 centimeters. How long is the base of that parallelogram? Explain your reasoning.

Are You Ready for More?

6.2

Activity

A Tale of Two Triangles (Part 1)

Standards Alignment

Building On

Addressing

Building Toward

6.G.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

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Two shapes are identical if they match up exactly when placed one on top of the other.

Draw one line to decompose each shape into two identical triangles, if possible. Use a straightedge to draw your line.
Which quadrilaterals can be decomposed into two identical triangles?

Pause here for a small-group discussion.
Study the quadrilaterals that can, in fact, be decomposed into two identical triangles. What do you notice about them? Write a couple of observations about what these quadrilaterals have in common.

Are You Ready for More?

6.3

Activity

A Tale of Two Triangles (Part 2)

Standards Alignment

Building On

Addressing

Building Toward

6.G.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

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Your teacher will give your group several pairs of triangles. Each group member should take 1 or 2 pairs.

1. Which pair(s) of triangles do you have?
2. Can each pair be composed into a rectangle? A parallelogram?
Discuss with your group your responses to the first question. Then, complete each statement with All, Some, or None. Sketch 1 or 2 examples to illustrate each completed statement.
1. ________________ of these pairs of identical triangles can be composed into a rectangle.
2. ________________ of these pairs of identical triangles can be composed into a parallelogram.

Are You Ready for More?

Student Lesson Summary

A parallelogram can always be decomposed into two identical triangles by a segment that connects opposite vertices.

Three parallelograms showing decompositions into two identical triangles.

Going the other way around, two identical copies of a triangle can always be arranged to form a parallelogram, regardless of the type of triangle being used. To produce a parallelogram, we can join a triangle and its copy along any of the three sides that match, so the same pair of triangles can make different parallelograms. Here are examples of how two copies of both Triangle A and Triangle F can be composed into three different parallelograms.

Three parallelograms composed from two identical triangles.

Three parallelograms composed from two identical triangles.

This special relationship between triangles and parallelograms can help us reason about the area of any triangle.

Glossary

None

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Standards Alignment

Building On

Addressing

6.G.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

View Full Standard

Building Toward