Unit 2: Scale Drawings, Similarity, and Slope

Students study scaled copies of plane figures and scale drawings of real-world objects, extend their work to dilations and similarity, and use similar triangles to understand slope and write equations for lines.

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What this unit covers

A Scaled Copies · 3 lessons

Goals

• Determine whether a figure is a scaled copy of another figure, by examining corresponding side lengths and angle measures.
• Draw a scaled copy of a figure using a given scale factor.

Lessons

1. What Are Scaled Copies?
2. Scale Factors and Making Scaled Copies
3. Scaled Relationships

B Scale Drawings · 4 lessons

Goals

• Create a scale drawing given the actual measurements of the object or given another scale drawing at a different scale.
• Explain how to use scales and scale drawings to calculate actual distances and areas.

Lessons

1. Scale Drawings
2. Creating Scale Drawings
3. Changing Scales in Scale Drawings
4. Units in Scale Drawings

C Dilations · 4 lessons

Goals

• Create a dilation of a figure given a scale factor and center of dilation.
• Describe a figure on a coordinate grid and its image under a dilation, using coordinates to refer to points.
• Identify the center, scale factor, and image of a dilation.

Lessons

1. Projecting and Scaling
2. Dilations
3. Dilations on a Square Grid
4. More Dilations

D Similarity · 3 lessons

Goals

• Calculate unknown side lengths in similar triangles using the ratios of side lengths within the triangles and the scale factor between similar triangles.
• Justify that two triangles are similar by finding a sequence of transformations that takes one triangle to the other or by checking that two pairs of corresponding angles are congruent.

Lessons

1. Similarity
2. Similar Triangles
3. Side Length Quotients in Similar Triangles

E Slope · 3 lessons

Goals

• Comprehend the term “slope” to mean a number that tells how steep a line is.
• Create an equation relating the quotient of the vertical and horizontal side lengths of a slope triangle to the slope of a line and use it to justify whether a point is on the line by verifying that the values of x and y satisfy the equation.

Lessons

1. Meet Slope
2. Writing Equations for Lines
3. Using Equations for Lines

F Let's Put It to Work · 2 lessons

Lessons

1. Draw It to Scale (Optional)
2. The Shadow Knows (Optional)

Helpful to know first

The curriculum says this unit builds on these.

Grade 7 Math · Unit 1 Scale Drawings

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