What students learn
Two figures are similar when one is a dilation of the other: corresponding angles are equal and corresponding sides are proportional. The scale factor k = image side ÷ pre-image side. When k > 1 the figure grows; when k < 1 it shrinks. Once students know k, any missing side is one multiplication or division away.
The five levels
- Find the scale factor between two figures.
- Use a given scale factor to find a missing side by multiplying or dividing.
- Turned and flipped figures with only one matching pair of sides labeled, so students find k first.
- Nested and overlapping triangles, and "Similar or Not Similar?" questions.
- Everything mixed, including fractional scale factors like 3/2 and 2/3, and algebra in the side lengths.
Equal sides share tick marks and a color, and corresponding sides share a color, so students match sides by their position in the figure, not by where they sit on the screen.
Between questions, students jump and duck past obstacles that are real reasons bridges don't get built: permits, protected wildlife, unstable soil and flooding. Correct answers earn coins for a crew shop of engineers, architects, electricians and more. Practice mode removes the obstacles and hearts and lets students pick the question types.
Worked examples
Level 1: a triangle with sides 3, 4, 5 is enlarged to 9, 12, 15.
k = 9 / 3 = 3
Level 2: k = 4, and the pre-image side is 6. Find the image side.
6 × 4 = 24
Level 4, nested triangles: a line parallel to the base cuts a small triangle with base 4 from a big triangle with base 10. The small triangle's side is 6. Find the matching side of the big triangle.
k = 10 / 4 = 2.5 6 × 2.5 = 15
Common mistakes
Adding instead of multiplying (3 → 9 is "+6", so 4 → 10). The bridge comes out the wrong size and fails. The missed question comes back as a picture with a scale-factor arrow on each pair of sides.
Matching sides by screen position when the figure is turned. The color coding shows which sides really correspond.
Dividing the wrong way (pre-image ÷ image), which gives 1/k. Ask: "Is the new shape bigger or smaller? So should k be more or less than 1?"
Ways to use it in class
- Printables. A free worksheet with an answer key and a two-to-a-page exit ticket match this game, ready to print or save as a PDF.
- Start in Practice. Let students play Level 1 questions with no obstacles until they can explain what k means.
- Level goals. Set a target distance for the class to reach on a given level.
- Draw the bridge. After a miss, students sketch the two figures and label k.
- Exit ticket. "A 4 × 6 rectangle is dilated to 10 × 15. What is k? Is it an enlargement or a reduction?"
Discussion questions
- Are all squares similar? All rectangles? Why?
- If the scale factor is 1, what do you know about the two figures?
- How could you use a shadow to find the height of a flagpole?
Real-world connections
Blueprints, scale models, maps, photo resizing, and finding a building's height from its shadow all use similar figures. A map scale of 1 inch : 10 miles is a scale factor.
Standards
CCSS.MATH.CONTENT.8.G.A.4Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations.
CCSS.MATH.CONTENT.7.G.A.1Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing.
Access and privacy
No accounts, no student data. Progress and coins save only in that browser. Plays with the keyboard or touch; on a phone, turn it sideways.