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Common Core Standards: Math See All Teacher Resources

Grade 7

Geometry 7.G.A.1

1. Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

There's a reason why everyone with a heart loves mini-horses. (Honestly, if you don't think they're lovable, you might be a cold, soulless cyborg.) Since we're so used to seeing regular-sized horses, it's just naturally hilarious and adorable when we see one built on the same dimensions, but at a much smaller scale factor.

It might be slightly less cute, but we can also shrink or expand geometric figures into their mini- or maxi-horse counterparts. It's all about the scale factor—a constant by which a shape is multiplied to change its size (scale) while maintaining its dimensions. Since those dimensions stay the same, the new shape will always be similar (geometrically speaking) to the original, like a mini-horse and a Clydesdale.

The name of the game here is proportions. Students should know they can use equivalent ratios to find the measurements of an actual-sized shape (both simple polygons and composite shapes) if they know the measurements of its scale drawing and what the scale factor is.

In fact, working with scale factors is essentially just a visual version of all the work your students have done with proportions and ratios in the past. The only tricky part is to make sure they pick sides that actually correspond to each other. It's all fun and games when two similar shapes are sitting right next to each other, but rotating one of the shapes can throw a real monkey wrench in the works. Remind them to keep a careful eye on which side is where in each drawing—textbook writers love to be tricky like that (and so do we).

It's also a good idea to add increasingly complex steps into these types of problems, which you can do by asking students to find the new figure's area instead of its side lengths.

This standard also asks students to blow up or shrink down drawings at a different scale, and this can take a couple different forms. You can either give 'em the scale factor itself (e.g., "expand this triangle by a scale factor of 3.5") or give them the equivalent measurement (e.g., "if each centimeter in the original drawing represents 3 inches, reproduce the scale drawing at actual size"). Either way, students should know what they're doing.

Be careful with using scale factors to find area, though. If your students have a scale drawing of a rectangle and need to find the area when it's expanded by a scale factor of 3, make sure they know that they can't just multiply the original area by 3. It's the side lengths that we're multiplying by 3, not the area! (They'll get into dilation's relationship with area and volume in high school, so don't focus too much on that.)

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