Grade 7 · Math

7th grade How scaling changes area worksheet

6 printable versionsChallenge Me10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version

How scaling changes area

Grade 7 Math Worksheet - Challenge Me

NameDate

Circle the best answer, or write your answer on the line.

Pia's bedroom plan has the scale 1 cm : 2 m. The real bedroom covers how many times as much area as the plan?
Ren's model castle has the scale 1 inch : 4 feet. The real castle wall covers how many times as much area as the model wall?
Tala's town map has the scale 1 cm : 5 m. The real town covers how many times as much area as the map?
Ari measures a lake on a map with the scale 1 cm : 400 m. The lake is 5 cm by 6 cm on the map. How many square kilometers is the real lake?
Bo measures a forest on a map with the scale 1 cm : 250 m. The forest is 10 cm by 3 cm on the map. How many square kilometers is the real forest?
Esme's school plan has the scale 1 cm : 3 m. The building has a square courtyard cut out of its middle, as shown. How many square meters does the real building cover?
Jun's park plan has the scale 1 cm : 2 m. The lawn has a square pond cut out of it, as shown. How many square meters of real grass is there?
Kira's playground plan has the scale 1 cm : 5 m. The playground has a square sandpit cut out of it, as shown. How many square meters of real ground is there?
Side 1 | ?, area 1 | 1/9 (the picture is not printed to size). Ren shrinks a kite design A onto a sticker B, similar shapes. B covers 1/9 as much area as A. What is the scale factor from A to B?
Side 1 | ?, area 1 | 4/9 (the picture is not printed to size). Tala shrinks a poster A onto a flyer B, similar rectangles. B covers 4/9 as much area as A. What is the scale factor from A to B?

7th grade How scaling changes area worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

How scaling changes area. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find a real area from a plan: change the scale to square units first (1 cm stands for 3 m, so 1 cm² stands for 9 m²).
I can say how many times as much area a copy has when every side is a number of times as long (the factor times itself).
I can work back from an area to the scale factor, and keep the units straight when the scale mixes cm and m, or m and km.

Standard: 7.G.A.1 (areas)

Words to know

scale: What 1 cm (or 1 inch) on a plan stands for in real life, like 1 cm : 3 m.

scale factor: How many times as long the real thing is as the plan, in one unit.

area factor: How many times as much area: the scale factor times itself.

square cm (cm²): The area of a square that is 1 cm on each side.

cutout: A part of a rectangle that is not there, like a courtyard in the middle.

Common mistakes

Your child multiplied or divided the area by the scale only once.

Your child gave the number for lengths when the question asked about area.

Your child doubled the factor instead of multiplying it by itself. Try it together: a square with sides 3 times as long covers how many of the small squares?

What to say

Ask: if a room is twice as long and twice as wide, how many times as much floor is there?

Ask: if a square's sides get 3 times as long, how many of the small squares fit inside the big one?

Questions parents ask

What is the most common mistake with how scaling changes area?

Your child multiplied or divided the area by the scale only once.

How can I help my child with how scaling changes area?

Ask: if a room is twice as long and twice as wide, how many times as much floor is there?

Are these 7th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 7 math

See all grade 7 math

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records