Worksheet Grade 7 Math

Marlstone Pressure Zone: A Grade 7 Scale-Drawing Worksheet

A grade 7 worksheet where students read a scaled map of a fictional water system's pressure zone to find real pipe lengths and area, then redraw it at a new scale.

Grade: Grade 7
Subject: Math
Material: Worksheet
Time: 35 min
Prep: No prep
Materials: Calculator, Ruler

Standards

7.G.A.1 Common Core Math

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.

How this material aligns: Students compute actual pipe lengths and the true area of the zone from a scaled map in items 1 through 6, then reproduce the map at a new scale in items 7 and 8, exactly what this standard names.

All materials for 7.G.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will use a map scale to find actual lengths and distances from measured map lengths.
Students will compute the actual area of a rectangular pressure zone from its map dimensions.
Students will reproduce map lengths and areas at a different scale and explain how they change.

Vocabulary

Pressure zone: A pressure zone is a section of a water system that a utility manages separately because it sits at a different elevation than the rest of the town. Utilities create pressure zones so that water pressure stays safe and steady for everyone, whether they live at the bottom of a hill or near the top.
Water main: A big underground pipe that carries drinking water beneath the streets to a neighborhood. Smaller service lines branch off it to reach each building.

Also: scale, area

Teacher overview

Utilities split a town into pressure zones and keep scaled maps of the water mains inside each one. This worksheet gives students a scaled map of a fictional zone and asks them to recover true lengths, a true area, and a redrawn map at a new scale. The common error to watch for is students treating an area the way they treat a length: when the scale doubles, lengths on the map halve, but the map area shrinks to one fourth, and items 8 and 10 make that difference explicit.

Marlstone Pressure Zone: A Grade 7 Scale-Drawing Worksheet — Grade 7 Math

Name: ____________________________ Date: ______________

Student Worksheet

Marlstone is a fictional town used for this worksheet. Its water system has an East Pressure Zone, and the utility keeps a scaled map of that zone. On the map, the scale is 1 centimeter = 250 meters. Every map length below has already been measured for you with a ruler.

Map measurements:

Main Street water main: 6 cm long
Oak Avenue water main: 4.4 cm long
The zone is drawn as a rectangle: 8 cm wide by 5 cm tall
The pump-to-tank distance: 3.2 cm

The Main Street main measures 6 cm on the map. What is its actual length in meters?
Convert your answer to item 1 into kilometers.
The Oak Avenue main measures 4.4 cm on the map. What is its actual length in meters?
The zone is drawn 8 cm wide by 5 cm tall. What are its actual width and height in meters?
Using your item 4 answers, find the actual area of the zone in square meters.
The pump-to-tank distance is 3.2 cm on the map. What is the actual distance in meters?
The utility redraws the map at a new scale, 1 cm = 500 meters. How long will the Main Street main be on the new map?
On the new map at 1 cm = 500 meters, what are the zone rectangle's new width and height in centimeters?
When the scale changes from 1 cm = 250 meters to 1 cm = 500 meters, do the map lengths get longer or shorter? Explain why in one sentence.
On the first map the zone rectangle covers 8 × 5 = 40 square centimeters. On the new map it covers 4 × 2.5 = 10 square centimeters. Explain why the map area dropped to one fourth when the lengths were cut in half.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Answer: 1,500 meters.
6 cm × 250 meters per cm = 1,500 meters.
Answer: 1.5 kilometers.
1,500 meters ÷ 1,000 = 1.5 kilometers.
Answer: 1,100 meters.
4.4 cm × 250 meters per cm = 1,100 meters.
Answer: 2,000 meters by 1,250 meters.
Width: 8 cm × 250 = 2,000 meters. Height: 5 cm × 250 = 1,250 meters.
Answer: 2,500,000 square meters.
2,000 meters × 1,250 meters = 2,500,000 square meters.
Answer: 800 meters.
3.2 cm × 250 meters per cm = 800 meters.
Answer: 3 cm.
The main is 1,500 meters long. 1,500 ÷ 500 meters per cm = 3 cm on the new map.
Answer: 4 cm by 2.5 cm.
Width: 2,000 ÷ 500 = 4 cm. Height: 1,250 ÷ 500 = 2.5 cm.
Answer: Shorter.
Each centimeter now stands for 500 meters instead of 250, so the same real distance needs fewer centimeters on the map.
Answer: Area depends on two lengths, so halving each cuts it twice.
Both the width and the height were cut in half, and one half times one half is one fourth, so 40 square centimeters became 10 square centimeters.

Differentiation

Support

Provide the scale as a labeled rule at the top of the page, "1 cm on the map = 250 meters in real life," and let students set up each length problem as a multiplication before they compute. Pre-fill item 4's setup so students only carry out the two multiplications.

Extension

Ask students to redraw the map at a third scale, 1 cm = 1,000 meters, list the new length of every feature, and describe the pattern they notice in how the map lengths shrink each time the scale number doubles.

ELL supports

Pair the words "width," "height," "length," and "distance" with arrows drawn on a sample rectangle. Provide a two-column table labeled "map length (cm)" and "real length (meters)" so students can organize items 1, 3, and 6 before writing sentences.