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Worksheet Grade 7 Math

Copperline Creek's Watershed Map: A Grade 7 Scale-Drawing Worksheet

A grade 7 worksheet where students use a watershed map's scale to find real distances and areas, then redraw the main channel at a new map scale.

Objectives

  1. Students will calculate actual distances and areas from a scaled map using a given scale factor.
  2. Students will redraw a measured distance at a new map scale.

Vocabulary

Watershed
A watershed is all the land where rain that falls will drain to the same stream, river, or lake. Everyone lives in a watershed, no matter how far from the water they live.

Also: scale drawing, drainage basin, scale factor

Teacher overview

Copperline Creek drains a rural watershed that a mapping crew has sketched at a fixed scale, with every inch on the paper standing for a set number of feet on the ground (a fictional watershed and map created for this worksheet). Because the crew measured the creek and its drainage basin directly on the map, students have to work backward from map measurements to real-world lengths and areas using the map's stated scale, and then apply the same reasoning in reverse to redraw a measurement at a different scale. A common misconception in this math is forgetting to square the scale's linear factor when converting an area, or squaring it incorrectly, since area scales by the square of a linear scale factor rather than by the factor itself.

Copperline Creek's Watershed Map: A Grade 7 Scale-Drawing Worksheet — Grade 7 Math
Name: ____________________________ Date: ______________

Student Worksheet

Copperline Creek's watershed map (a fictional map created for this worksheet) uses a scale of 1 inch = 1,500 feet. Use this scale for all problems unless a problem states a different scale.

  1. On the map, Copperline Creek's main channel measures 4.5 inches from its headwaters to its mouth. Find the creek's actual length in feet.
  2. One mile equals 5,280 feet. Convert your answer from problem 1 to miles, rounded to the nearest hundredth of a mile.
  3. The map's scale means that every 1 square inch on the map represents a certain number of square feet on the ground. Find that number of square feet per square inch. (Hint: square the scale's feet-per-inch value.)
  4. On the map, the watershed's drainage basin covers an area of 3.2 square inches. Using your answer to problem 3, find the basin's actual area in square feet.
  5. One acre equals 43,560 square feet. Convert your answer from problem 4 to acres, rounded to the nearest tenth of an acre.
  6. City planners want a new, more detailed map at a scale of 1 inch = 1,000 feet. Using the creek's actual length from problem 1, find how many inches long the creek would be drawn on this new map.
  7. A survey crew marks a proposed monitoring station 2.1 inches along the main channel from the headwaters, measured on the original 1 inch = 1,500 feet map. How far, in feet, is the station from the headwaters?
  8. How far, in feet, is the monitoring station from the creek's mouth? (Use your answers to problems 1 and 7.)
  9. Write the monitoring station's distance from the headwaters as a fraction of the creek's total length, in simplest form. (Use your answers to problems 1 and 7.)
  10. In your own words, explain why multiplying a map distance by the scale's feet-per-inch value gives the real-world distance. Use problem 1 as your example.

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: 6,750 ft.
    4.5 inches × 1,500 feet per inch = 6,750 feet.
  2. Answer: 1.28 mi.
    6,750 ÷ 5,280 = 1.278..., which rounds to 1.28 miles.
  3. Answer: 2,250,000 sq ft.
    Square the scale's feet-per-inch value: 1,500 × 1,500 = 2,250,000 square feet per square inch.
  4. Answer: 7,200,000 sq ft.
    3.2 square inches × 2,250,000 square feet per square inch = 7,200,000 square feet.
  5. Answer: 165.3 acres.
    7,200,000 ÷ 43,560 = 165.29..., which rounds to 165.3 acres.
  6. Answer: 6.75 in.
    6,750 feet ÷ 1,000 feet per inch = 6.75 inches.
  7. Answer: 3,150 ft.
    2.1 inches × 1,500 feet per inch = 3,150 feet.
  8. Answer: 3,600 ft.
    6,750 total feet minus 3,150 feet from the headwaters = 3,600 feet from the mouth.
  9. Answer: 7/15.
    3,150/6,750 simplifies by dividing both numbers by their greatest common factor, 450: 3,150 ÷ 450 = 7 and 6,750 ÷ 450 = 15, giving 7/15.
  10. Answer: each inch stands for 1,500 real feet.
    Because the scale states that every inch on the map equals 1,500 feet on the ground, multiplying any measured map distance (in inches) by 1,500 converts it into the matching real-world distance (in feet), which is exactly what problem 1 does with the creek's 4.5-inch map length.

Differentiation

Support (below grade level)

Provide a printed scale strip showing "1 in = 1,500 ft" with three worked practice conversions (not on the worksheet) before problem 1. Allow students to use a calculator for the multiplication and division steps, and provide the area scale factor (2,250,000 sq ft per sq in) already calculated before problem 4.

Extension (above grade level)

Ask students to explain, using problem 3's numbers as a specific case, why any linear scale factor k produces an area scale factor of k squared. Then have them find what map scale (in feet per inch) would make the drainage basin's area exactly 1 square inch on a redrawn map.

ELL supports

Provide a labeled diagram of the watershed map showing the headwaters, main channel, mouth, and drainage-basin outline, with the words "scale," "channel," and "basin" defined next to simple icons. Allow students to show scale conversions as a labeled multiplication chain rather than full sentences.

Extensions

Have students measure a real local creek, road, or trail on an online map's built-in scale bar and calculate its actual length using the same multiplication method practiced in problem 1.