Math problem set Grade 7 Math

Halstead's Water Main Map: Scale Drawing Problems for Grade 7

A grade 7 math problem set using measurements from a scaled map of a neighborhood's water mains to find real lengths and areas, then convert one length to a new scale.

Grade: Grade 7
Subject: Math
Material: Math problem set
Time: 40 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: Problems 1 through 7 compute actual lengths and an actual area from a scale map of water mains and reproduce one length at a different map scale.

All materials for 7.G.A.1 →

7.RP.A.2 Common Core Math

Recognize and represent proportional relationships between quantities, including identifying the constant of proportionality and representing proportional relationships by equations.

How this material aligns: The map scale of 1 inch to 200 feet is the constant of proportionality students apply throughout, converting between map inches and real feet in both directions.

All materials for 7.RP.A.2 →

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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 real lengths from map measurements.
Students will find a real area from a scale drawing's dimensions.
Students will redraw a length at a different scale using proportional reasoning.

Vocabulary

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, proportional, area

Teacher overview

Utilities keep scale maps of their pipe networks so crews can find real distances without measuring the ground. This problem set uses a map of the Halstead neighborhood, a fictional service area, so students convert between map inches and real feet, find a real area, and redraw one main at a smaller scale. A common misconception this set corrects is scaling an area by multiplying just once by the scale; both the length and the width must be scaled, so the area grows by the scale used twice.

Halstead's Water Main Map: Scale Drawing Problems for Grade 7 — Grade 7 Math

Name: ____________________________ Date: ______________

Problems

Halstead's water department keeps a map drawn at a scale of 1 inch = 200 feet. Use that scale for every problem.

On the map, the Main Street water main measures 6 inches. How long is the real main, in feet?
The Oak Avenue main measures 3.5 inches on the map. How long is the real main, in feet?
How much longer is the real Main Street main than the real Oak Avenue main, in feet?
A planned new pipe will be 850 feet long in real life. How many inches long will it be drawn on this map?
The map shows the service area as a rectangle measuring 4 inches by 2.5 inches. What are the real length and width of the service area, in feet?
Using your real length and width from problem 5, find the real area of the service rectangle in square feet.
The town prints a smaller map at a scale of 1 inch = 400 feet. On this new map, how many inches long is the Main Street main, whose real length you found in problem 1?
Explain how the same real Main Street main can measure 6 inches on the first map and only 3 inches on the smaller map. What changed, and what stayed the same?

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: 1,200 feet. 6 inches x 200 feet per inch = 1,200 feet.
Answer: 700 feet. 3.5 inches x 200 feet per inch = 700 feet.
Answer: 500 feet. 1,200 - 700 = 500 feet longer.
Answer: 4.25 inches. 850 feet / 200 feet per inch = 4.25 inches on the map.
Answer: 800 feet by 500 feet. Length: 4 x 200 = 800 feet; width: 2.5 x 200 = 500 feet.
Answer: 400,000 square feet. 800 feet x 500 feet = 400,000 square feet.
Answer: 3 inches. 1,200 feet / 400 feet per inch = 3 inches on the smaller map.
Answer: The real main is the same length both times; only the scale changed. The smaller map uses more feet per inch (400 instead of 200), so the same distance takes fewer inches to draw.

Differentiation

Support

Give students an arrow reminder card: "map inches to real feet: multiply by 200; real feet to map inches: divide by 200." Work problem 1 together, then let students try the rest. Allow a calculator for every step.

Extension

Ask students to find the real perimeter of the service rectangle from problem 5, then redraw the whole rectangle's dimensions at the 1 inch = 400 feet scale and confirm the area shrinks to one-fourth on paper.

ELL supports

Pre-teach "scale," "map inch," and "real feet" with a picture of a ruler over a small map. Provide a two-column table labeled "map (inches)" and "real (feet)" for students to fill as they solve, and accept numeric answers with units only.