Unit 7

Building Polygons (Part 1)

Angles, Triangles, and Prisms

Lesson 6

Expressions and Equations

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Let’s build shapes.

Unit 7 ● Lesson 6

Learning

Goal

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True or False: Signed Numbers

Unit 7 ● Lesson 6 ● Activity 1

Decide whether each equation is true or false. Be prepared to explain your reasoning.

4 • (-6) = (-6) + (-6) + (-6) + (-6)

-8 • 4 = (-8 • 4) + 4

6 • (-7) = 7 • (-7) + 7

-10 – 6 = -10 – (-6)

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

What Can You Build?

Unit 7 ● Lesson 6 ● Activity 2

Your teacher will give you some strips of different lengths and fasteners you can use to attach the corners.

1. Use the pieces to build several polygons, including at least one triangle and one quadrilateral.
2. After you finish building several polygons, select one triangle and one quadrilateral that you have made.
1. Measure all the angles in the two shapes you selected.
2. Using these measurements along with the side lengths as marked, draw your triangle and quadrilateral as accurately as possible.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

What Can You Build?

Unit 7 ● Lesson 6 ● Activity 2

How can you tell when two shapes are identical copies?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Building Diego’s and Jada’s Shapes

Unit 7 ● Lesson 6 ● Activity 3

1. Diego built a quadrilateral using side lengths of 4 in, 5 in, 6 in, and 9 in.
1. Build such a shape.
2. Is your shape an identical copy of Diego’s shape? Explain your reasoning.
2. Jada built a triangle using side lengths of 4 in, 5 in, and 8 in.
• Build such a shape.
• Is your shape an identical copy of Jada’s shape? Explain your reasoning.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Building Diego’s and Jada’s Shapes

Unit 7 ● Lesson 6 ● Activity 3

• Is this what you thought Jada and Diego’s shapes looked like?
• Which shape did you make an identical copy of? Why do you think your shapes are identical copies of this shape?
• Why did you not make an identical copy of Diego’s shape?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Building Han’s Shape

Unit 7 ● Lesson 6 ● Activity 4

Han built a polygon using side lengths of 3 in, 4 in, and 9 in.

1. Build such a shape.
2. What do you notice?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Building Han’s Shape

Unit 7 ● Lesson 6 ● Activity 4

• Did anyone try to make a triangle first? What happened?
• What length did you choose to use for your fourth side? Would another choice have worked?
• If another group used the same length for their fourth side as you, does their polygon have to be an identical copy of yours? How do you know?
• Did any group choose to have more than 4 sides on their polygon? Does such a shape fulfill the given conditions?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Building Polygons (Part 1)

Unit 7 ● Lesson 6

• What kinds of shapes could you build with side lengths 4 inches, 4 inches, and 4 inches?
• What kinds of shapes could you not build with this set of side lengths and fasteners?
• How is building a triangle with three given side lengths different from building a quadrilateral with four given side lengths?

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Unit 7 ● Lesson 6

• I can show that the 3 side lengths that form a triangle cannot be rearranged to form a different triangle.
• I can show that the 4 side lengths that form a quadrilateral can be rearranged to form different quadrilaterals.

Learning

Targets

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An Equilateral Quadrilateral

Unit 7 ● Lesson 6 ● Activity 5

When asked to draw a quadrilateral with all four sides measuring 5 cm, Jada drew a square.

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1. Do you agree with Jada’s answer?
2. Is there a different shape Jada could have drawn that would answer the question? Explain your reasoning.

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7

Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

Word:

Unique Triangle

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Definition:

A unique triangle is a triangle that can be drawn in only one specific way given a set of conditions (side lengths or angles).

Example:

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Lesson Video

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