Scale Factor Activity + Independent Practice | 7th Grade Math | TPT - Free Printable

Let’s solve each task card one by one. We’ll use simple steps and check our work carefully.

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Task Card 1:
We have two triangles:
- Small triangle side = 2 cm
- Big triangle side = 6 cm

Scale factor means: how many times bigger (or smaller) the new shape is compared to the original.

To find scale factor from small to big → divide big side by small side:

6 ÷ 2 = 3

So, Figure B is 3 times bigger than Figure A.

✔ Scale factor = 3

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Task Card 2:
We have two trapezoids:
- Figure A has base = 4 ft
- Figure B has base = 8 ft

Again, scale factor from A to B → divide B’s side by A’s side:

8 ÷ 4 = 2

So, Figure B is 2 times bigger than Figure A.

✔ Scale factor = 2

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Task Card 3:
We have two rectangles:
- Rectangle A: length = 9 m, width = 25 m? Wait — let’s look again.

Actually, looking at the diagram description:

It says:
- Rectangle A: one side = 9 m, other side = ? (but we’re told it’s similar to B)
- Rectangle B: sides = 5 m and x (missing)

Wait — actually, in similar figures, corresponding sides are proportional.

Looking at the labels:

Probably:
- Rectangle A: height = 25 m, base = 9 m
- Rectangle B: height = 5 m, base = x

Since they are similar, the ratio of heights should equal ratio of bases.

So:

Height ratio: 5 / 25 = 1/5

That means Rectangle B is 1/5 the size of Rectangle A.

So base of B = (1/5) × base of A = (1/5) × 9 = 9/5 = 1.8 m

But wait — maybe the 25 m and 5 m are the same side? Let me double-check.

Alternative interpretation: Maybe 25 m and 5 m are corresponding sides? Then scale factor from A to B is 5/25 = 1/5.

Then if 9 m corresponds to x, then:

x = 9 × (1/5) = 1.8 m

Yes.

✔ Missing side length x = 1.8 meters

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Task Card 4:
An oak tree casts a shadow 20 ft long.
At the same time, a 3-ft tall sapling casts a 5-ft shadow.

We need to find the height of the oak tree.

This is a proportion problem using similar triangles (sun’s rays make similar right triangles).

Set up proportion:

height of sapling / shadow of sapling = height of oak / shadow of oak

3 / 5 = h / 20

Cross-multiply:

5 × h = 3 × 20
5h = 60
h = 60 ÷ 5 = 12

✔ Height of oak tree = 12 feet

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Final Answer:
1. Scale factor = 3
2. Scale factor = 2
3. Missing side = 1.8 m
4. Oak tree height = 12 ft