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Computing Actual Lengths from a Scale Drawing

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Examples, solutions, and videos to help Grade 7 students learn how to compute actual lengths from a scale drawing.

New York State Common Core Math Grade 7, Module 1, Lesson 18

Download the Worksheets for Grade 7, Module 1, lesson 18 (pdf)

Lesson 18 Student Outcomes

Given a scale drawing, students compute the lengths in the actual picture using the scale. Students identify the scale factor in order to make intuitive comparisons of size then devise a strategy for efficiently finding actual lengths using the scale.

Example 1: Basketball at Recess?

Vincent proposes an idea to the Student Government to install a basketball hoop along with a court marked with all the shooting lines and boundary lines at his school for students to use at recess. He presents a plan to install a half- court design as shown below. After checking with school administration, he is told it will be approved if it will fit on the empty lot that measures 25 feet by 75 feet on the school property. Will the lot be big enough for the court he planned? Explain.

Example 2

The diagram shown represents a garden. The scale is 1 cm for every 20 meters of actual length. Find the actual length and width of the garden based upon the given drawing. Each square in the drawing measures 1 cm by 1 cm.

Example 3

A graphic designer is creating an advertisement for a tablet. She needs to enlarge the picture given here so that 0.25 inches on the scale picture will correspond to 1 inch on the actual advertisement. What will be the length and width of the tablet on the advertisement?

Lesson 18 Exercises
1. Students from the high school are going to perform one of the acts from their upcoming musical at the atrium in the mall. The students want to bring some of the set with them so that the audience can get a better feel of the whole production. The backdrop that they want to bring has panels that measure 10 feet by 10 feet. The students are not sure if they will be able to fit these panels through the entrance of the mall since the panels need to be transported flat (horizontal). They obtain a copy of the mall floor plan, shown below, from the city planning office. Use this diagram to decide if the panels will fit through the entrance. Use a ruler to measure.

Lesson 18 Problem Set
1. A toy company is redesigning their packaging for model cars. The graphic design team needs to take the old image shown below and resize it so that 1/2 inch on the old packaging represents 1/3 inch on the new package. Find the length of the image on the new package.

2. The city of St. Louis is creating a welcome sign on a billboard for visitors to see as they enter the city. The following picture needs to be enlarged so that 1/2 inch represents 7 feet on the actual billboard. Will it fit on a billboard that measures 14 feet in height?

5. The portrait company that takes little league baseball team photos is offering an option where a portrait of your baseball pose can be enlarged to be used as a wall decal (sticker). Your height in the portrait measures 3 1/2 inches. If the company uses a scale where 1 inch on the portrait represents 20 inches on the wall decal, find the height on the wall decal. Your actual height is 55 inches. If you stand next to the wall decal, will it be larger or smaller than you?

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