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Worksheet Grade 7 Math

Skelder Reservoir's Depth Profile: A Scale Drawing Worksheet

A grade 7 worksheet where students read a fictional reservoir cross-section drawn with one scale across and a different scale down, then rescale one measurement.

Objectives

  1. Students will compute actual lengths and depths from a scale drawing that uses two scales.
  2. Students will convert an actual measurement back into a drawing length.
  3. Students will explain why a reservoir profile uses a different vertical scale.

Vocabulary

Reservoir
A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.

Also: profile, cross-section, horizontal scale, vertical scale

Teacher overview

Engineers who study reservoirs draw a profile, which is a side view cut straight across the water from one shore to the other. A reservoir is far wider than it is deep, so a profile drawn at a single scale would show the depth as a thin line, and drawings of this kind normally use one scale across the page and a more expanded one down it. This worksheet gives students the two scales for a fictional reservoir and asks them to work in both directions. The error to watch for is applying the horizontal scale to a vertical measurement, which is the mistake item 9 is built around.

Skelder Reservoir's Depth Profile: A Scale Drawing Worksheet — Grade 7 Math
Name: ____________________________ Date: ______________

Student Worksheet

Suppose the fictional Skelder Dam holds back Skelder Reservoir. An engineer drew a profile of the reservoir on graph paper. The profile uses two scales. Across the page, 1 centimeter stands for 50 meters. Down the page, 1 centimeter stands for 5 meters. Use those two scales for every item.

  1. On the drawing, the water surface is 14.0 centimeters wide. How wide is the reservoir in meters?
  2. At the deepest point, the drawing shows 4.6 centimeters from the surface line down to the reservoir floor. How deep is the water in meters?
  3. A sampling buoy is drawn 3.2 centimeters from the left shore. How far is the buoy from the shore in meters?
  4. The face of the dam is drawn 5.8 centimeters tall. How tall is the dam face in meters?
  5. A second arm of the reservoir is 480 meters long. How long would it be on this drawing?
  6. The intake tower stands 18 meters above the reservoir floor. How tall would the tower be on this drawing?
  7. The engineer redraws the profile so that 1 centimeter stands for 100 meters across the page. How wide is the water surface on the new drawing?
  8. Explain why the profile does not use the same scale across the page and down it.
  9. A student measured the deepest point as 4.6 centimeters and used the horizontal scale by mistake. What depth did that student report?
  10. How many meters too deep was that student's answer?

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

Answer Key
  1. Answer: 700 meters. Multiply the drawing width by the horizontal scale: 14.0 times 50 equals 700 meters.
  2. Answer: 23 meters. Multiply the drawing depth by the vertical scale: 4.6 times 5 equals 23 meters.
  3. Answer: 160 meters. This is a distance across the page, so use the horizontal scale: 3.2 times 50 equals 160 meters.
  4. Answer: 29 meters. The dam face is a height, so use the vertical scale: 5.8 times 5 equals 29 meters.
  5. Answer: 9.6 centimeters. Divide the actual length by the horizontal scale: 480 divided by 50 equals 9.6 centimeters.
  6. Answer: 3.6 centimeters. Divide the actual height by the vertical scale: 18 divided by 5 equals 3.6 centimeters.
  7. Answer: 7 centimeters. The surface is 700 meters wide, and 700 divided by 100 equals 7 centimeters at the new scale.
  8. Answer: Because the reservoir is much wider than it is deep. At 1 centimeter for 50 meters, a depth of 23 meters would be under half a centimeter and hard to read, so the vertical scale is stretched to show the shape of the bottom.
  9. Answer: 230 meters. Using the horizontal scale gives 4.6 times 50, which equals 230 meters.
  10. Answer: 207 meters. The correct depth is 23 meters, and 230 minus 23 equals 207 meters too deep.

Differentiation

Support

Give these students a labeled sketch with an arrow across the page marked "use 50" and an arrow down the page marked "use 5," and let them write the matching number beside each item before computing. Allow calculators and accept items 5 and 6 answered as a division sentence with the result.

Extension

Ask students to redraw the whole profile at a vertical scale of 1 centimeter for 10 meters, list the new drawing measurements for items 2, 4, and 6, and describe in writing how the shape of the reservoir bottom changes on the page.

ELL supports

Pre-teach "profile," "scale," "across," and "down" by holding a sheet of paper flat and tracing the two directions while naming each scale aloud. Provide the frame "This is a length across, so I multiply by ___" for items 1 and 3.