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Unit 8

Symmetry in Figures (Part 2)

Lesson 5

Properties of Two-dimensional Shapes

Expressions and Equations

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Let’s draw some figures that have lines of symmetry.

Unit 8 ● Lesson 5

Learning

Goal

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Keeping Track

Unit 8 ● Lesson 5 ● Warm-up

Find the value of each expression mentally.

43 + 57 + 50 + 7 + 3 + 40
243 + 57 + 43 + 257
1,043 + 257 + 57 + 200 + 43 + 1,000
1,943 + 257 + 1 + 257 + 1,000 + 943

How did you use the first expression to help solve the expressions that follow?

Number Talk

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Half-drawn Figures

Unit 8 ● Lesson 5 ● Activity 1

Each shaded triangle is half of a whole figure that has a line of symmetry shown by the dashed line.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Half-drawn Figures

Unit 8 ● Lesson 5 ● Activity 1

Clare drew in some segments to show the missing half of each figure.

Do you agree that the dashed line is a line of symmetry for each figure Clare completed? Explain your reasoning. If you disagree with Clare's work, show a way to complete the drawing so the dashed line is a line of symmetry.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Half-drawn Figures

Unit 8 ● Lesson 5 ● Activity 1

Let’s look at some of our drawings and compare them to Clare’s.
What might be a possible reason for thinking that Clare’s drawings show the correct whole figures?
How can we tell that Clare’s completed figures do not have line symmetry?

Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What’s the Whole Picture?

Unit 8 ● Lesson 5 ● Activity 2

Here are three figures. Each figure is half of a whole figure. The dashed line is a line symmetry of that figure.

Use patty paper to help you draw the whole figure.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What’s the Whole Picture?

Unit 8 ● Lesson 5 ● Activity 2

Each figure on the grid is half of a whole figure that has a line of symmetry. The dashed line shows the line of symmetry. Use the grid to help you draw the whole figure. Be as precise as possible.

Here is another figure that is half of a whole figure with a vertical line of symmetry. Draw the whole figure. Be as precise as possible.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What’s the Whole Picture?

Unit 8 ● Lesson 5 ● Activity 2

How did you use the patty paper and other tools to complete the figures with the triangle, trapezoid, and rhombus halves?
How did the tools support you in drawing the whole figures?
Did you use tools when drawing the whole figures that were on the grid? Why or why not?

Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What Could the Whole Figure Be?

Unit 8 ● Lesson 5 ● Activity 3

Trace a triangle cutout from your teacher.

If the triangle is half of a whole figure that has line symmetry, what could the whole figure look like? Can you show two possibilities? Three possibilities?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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What Could the Whole Figure Be?

Unit 8 ● Lesson 5 ● Activity 3

Let’s look at some of your completed drawings.
Are there other possible whole figures that are not yet shown?
Did anyone use a strategy other than flipping the cutout along one side and tracing it? What was the strategy? How did it help you?
Where is the line of symmetry in each completed drawing?

Activity Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Symmetry in Figures (Part 2)

Unit 8 ● Lesson 5

Today we saw that, if given half of a figure and a line of symmetry, we can draw a full figure. If we wanted to, we can do that quite precisely.

Here’s half of a figure you saw earlier. What are some ways to find the other half so that the whole figure has line symmetry?

How would you know if your drawing is correctly drawn?

Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Make Them Whole

Unit 8 ● Lesson 5

Do you agree that Kiran's drawing shows the correct whole figure? Explain or show your reasoning. If you disagree, you can also show the correct whole figure by drawing.

The shaded figure is half of a whole figure with a line of symmetry, shown by the dashed line.

Here's Kiran's drawing to show the whole figure.

Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.