A scale copy has every length multiplied by the same number. That number is the scale factor.
Scale factor is the number every length is multiplied by to make the copy.
Step 1: Picture It
Start with something you already know.
A funhouse mirror
- A flat mirror shows you in your own shape.
- A funhouse mirror stretches you taller but not any wider.
- Your arms look long and thin, and your face looks narrow.
- You look like a different shape, not a bigger copy of you.
A scale copy keeps the shape: every length grows or shrinks by the same number.
Stretch only one way, like that mirror, and you get a distortion, not a scale copy.
Step 2: Let's Learn
Read it, or press Listen and follow the words.
Try it first
A photo is 3 cm wide and 5 cm tall. A bigger print keeps the same shape. The print is 6 cm wide. Every length was multiplied by the same number. How tall is the print, in cm?
cm
Stuck is fine. Let’s Learn shows the way next. Got it first time? You can jump ahead to Watch an Example.
Every length, not some
If one side doubles and another triples, the result is a distortion, not a scale copy.
Angles do not change
Scaling changes lengths but leaves every angle exactly as it was.
A factor under 1 shrinks
A scale factor of 1/2 makes a copy half the size. It is still a scale copy.
Step 3: Try It Yourself
Tap and try it out.
| Original | Copy |
|---|---|
| 3 | 6 |
| 6 | 12 |
Every row is the same ratio. 3 to 6 is the same comparison as 6 to 12.
Step 4: In Real Life
A model car
A model car is 1/24 the size of the real one. Every length is scaled by the same factor. That is why the model looks right and a squashed one looks wrong.
Step 5: Watch an Example
One step at a time.
Watch Ana Find a Scale Factor
A right triangle with sides 6, 8 and 10 cm is copied. The copy has sides 9, 12 and 15 cm.
- Step 1
Ana matches the sides by position before she divides anything. The shortest goes with the shortest: 6 cm with 9 cm. In both triangles the square corner sits between the two shorter sides. That is how she knows the matching is right.
Watch Leo Check Two Rectangles
A rectangle 5 cm by 8 cm, and a second one 15 cm by 24 cm. Leo works out whether the second is a scale copy. He starts, and you finish.
- Step 1
Leo lines the matching sides up first: the width 5 cm goes with the width 15 cm, and the height 8 cm goes with the height 24 cm.
Step 6: Your Turn
Practice makes it stick.
The Poster
Problem 1 of 16
Maya has a poster 3 ft wide and 4 ft tall. The print shop makes a scale copy 12 ft wide. Printing the tall side costs $2 for every foot. What does the tall side of the big poster cost?
dollars
The Flag
Problem 2 of 16
A flag is 8 in wide and 20 in tall. Sam makes a small scale copy that is 5 in tall. Ribbon along the short side of the small copy costs $3 for every inch. What does the ribbon cost?
dollars
Scale It
Multiply to make a copy. Divide a matching pair to find a factor.
Problem 3 of 16
A 7 cm side is scaled by 3. How long is the matching side on the copy, in cm?
cm
Problem 4 of 16
A 6 cm side becomes 18 cm on the copy. What is the scale factor?
Problem 5 of 16
A 20 cm side is scaled by 1/2. How long is the matching side on the copy, in cm?
cm
Problem 6 of 16
A 6 cm side is scaled by 2.5. How long is the matching side on the copy, in cm?
cm
Problem 7 of 16
A 4 cm side becomes 10 cm on the copy. What is the scale factor?
Whose Step?
One line in each piece of working is a slip. Find it, then fix it.
Problem 8 of 16
Priya scaled a rectangle 5 cm by 8 cm using a factor of 3. One line is a slip. Which?
Priya's copy of a 5 cm by 8 cm rectangle, factor 3
- 1Original 5 cm by 8 cm, factor 3
- 25 × 3 = 15
- 38 + 3 = 11
- AnswerCopy is 15 cm by 11 cm
Problem 9 of 16
Priya's line 3 should scale the 8 cm side. What does it give, in cm?
cm
Problem 10 of 16
Dev found the scale factor from a 5 cm side to a 20 cm side. One line is a slip. Which?
Dev's scale factor from 5 cm to 20 cm
- 1Original side 5 cm, copy side 20 cm
- 2Scale factor = 5 ÷ 20
- 3= 0.25
- AnswerEvery length on the copy is 0.25 times the original
Problem 11 of 16
What is the scale factor from a 5 cm side to a 20 cm side?
Pick the Move
Choose the move before you make it.
Problem 12 of 16
A rectangle 6 cm by 9 cm is copied, and the 6 cm side becomes 15 cm. Which move finds the copy's other side?
Problem 13 of 16
You have a triangle and a second triangle. Which check tells you whether they are scale copies?
Same Shape?
Decide without drawing anything. Divide the matching pairs, and ask what scaling leaves untouched.
Problem 14 of 16
A rectangle is 4 cm wide and 10 cm tall. Select every rectangle below that is a scale copy of it.
Problem 15 of 16
Select every statement that is true of a scale copy.
Problem 16 of 16
A triangle has a 40° corner. A scale copy of it is made with a factor of 3. What is the matching corner on the copy, in degrees?
degrees
Step 7: Quick Check
Show what you know.
Question 1 of 2
A 9 cm side becomes 27 cm. What is the scale factor?
Question 2 of 2
What makes a copy a scale copy?
Ready for more?Optional. Past the lesson, for anyone who wants it.
Stretch 1 of 2
A rectangle is 5 cm by 12 cm. A scale copy of it has one side of 30 cm. The other side could be one of two lengths. What is the larger of the two, in cm?
cm
Stretch 2 of 2
A rectangle is 4 cm by 6 cm. A scale copy of it has a perimeter of 60 cm. How long is the copy's longer side, in cm?
cm
What You Learned
- A scale copy multiplies every length by the same factor.
- Angles stay exactly the same.
- A factor under 1 shrinks and still counts as a scale copy.
For the grown-up
The misconception this lesson targets is that a copy is made by adding the same amount to every length rather than multiplying by the same factor. Adding keeps the sides the same distance apart and quietly changes the shape, which is why a child who adds often cannot see anything wrong with the answer. Two smaller slips ride alongside it: dividing the original by the copy instead of the copy by the original, which turns an enlargement into a number below 1, and deciding by eye whether two shapes look alike. The cure for all three is the same habit — divide a matching pair of sides, then test that factor on a second pair.
What makes a copy a scale copy — A scale copy has all its lengths multiplied by the same number and all its angles unchanged. Both conditions matter. Stretch a photo horizontally only and the angles change — the result is a distortion, not a scale copy.
The scale factor — The number every length is multiplied by is the scale factor. A factor above 1 enlarges, below 1 shrinks, and exactly 1 leaves the figure unchanged. To find it, divide a length on the copy by the matching length on the original.
Testing whether two figures are scale copies — Divide each pair of matching lengths. If every division gives the same number, the figures are scale copies; if the ratios differ, they are not. One inconsistent pair is enough to rule it out.
Match the parts before dividing — The longest side of the original corresponds to the longest side of the copy, and so on. Dividing mismatched sides gives a meaningless ratio. On a rotated or reflected copy the matching is not obvious, so identify corresponding parts first.
Every length by the same factor — A rectangle 4 by 6. Scale by 2: 8 by 12. Both sides doubled. The shape is unchanged. Now add 2 to each instead: 6 by 8. That is a different shape. A scale copy multiplies every length by the same number.