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Worksheet Grade 7 Math

Stonefall Dam's Powerhouse Records: A Proportionality Worksheet

A grade 7 worksheet where students test two tables from a fictional dam for proportionality, find the constant, and write an equation for the powerhouse.

Objectives

  1. Students will test a table of paired values for a constant ratio.
  2. Students will identify a constant of proportionality and write its equation.
  3. Students will explain why a table with a fixed starting amount is not proportional.

Vocabulary

Acre-foot
The amount of water it takes to cover one acre of land, about the size of a football field, one foot deep. Western states use acre-feet to measure large amounts of water.

Also: proportional, constant of proportionality, powerhouse, standby load

Teacher overview

A dam's powerhouse turns falling water into electricity, and over a narrow range of conditions the electricity produced is close to proportional to the water sent through the turbines. Not every table at the same site behaves that way, which is what makes the pair of records in this worksheet useful. Students test a fictional powerhouse table and a fictional pump station table, find the constant of proportionality for the one that has it, and explain the fixed standby amount that spoils the other. The error to plan for is calling any table proportional when both columns increase together: the pump station's numbers rise steadily, yet its ratios fall from 95 to 83.75, because 30 kilowatt-hours of standby power are used before the pump moves any water at all.

Stonefall Dam's Powerhouse Records: A Proportionality Worksheet — Grade 7 Math
Name: ____________________________ Date: ______________

Student Worksheet

Stonefall Dam is a fictional dam. Table A shows water released through its powerhouse and the electricity that release produced.

Table A. Water released, in acre-feet: 20, 35, 50, 80.
Table A. Electricity, in kilowatt-hours: 4,400, 7,700, 11,000, 17,600.

Table B shows the electricity used by the fictional pump station next to the dam.

Table B. Hours run: 2, 4, 6, 8.
Table B. Electricity used, in kilowatt-hours: 190, 350, 510, 670.

  1. In Table A, divide the electricity by the water released for the 20 acre-foot row. What is the ratio?
  2. Do the same for the 80 acre-foot row. What is the ratio?
  3. Is Table A a proportional relationship? Answer yes or no.
  4. What is the constant of proportionality for Table A, in kilowatt-hours per acre-foot?
  5. Let w stand for acre-feet released and e stand for kilowatt-hours produced. Write an equation for Table A.
  6. How much electricity would a release of 65 acre-feet produce?
  7. How many acre-feet must the dam release to produce 8,800 kilowatt-hours?
  8. In Table B, divide the electricity by the hours for the 2-hour row. What is the ratio?
  9. Do the same for the 8-hour row. What is the ratio?
  10. Is Table B a proportional relationship? Explain how the ratios show your answer.
  11. In Table B, each extra hour adds the same amount of electricity. If the pattern holds, how much electricity would 10 hours use?

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: 220 kilowatt-hours per acre-foot.
    Divide 4,400 by 20 to get 220.
  2. Answer: 220 kilowatt-hours per acre-foot.
    Divide 17,600 by 80 to get 220, the same ratio as the first row.
  3. Answer: Yes.
    All four rows give the same ratio: 4,400 over 20, 7,700 over 35, 11,000 over 50, and 17,600 over 80 each equal 220.
  4. Answer: 220 kilowatt-hours per acre-foot.
    The shared ratio is the constant of proportionality.
  5. Answer: e = 220w.
    Multiply the acre-feet released by the constant of 220 to get the kilowatt-hours produced.
  6. Answer: 14,300 kilowatt-hours.
    Substitute 65 for w: 220 times 65 equals 14,300.
  7. Answer: 40 acre-feet.
    Substitute 8,800 for e and divide: 8,800 divided by 220 equals 40.
  8. Answer: 95 kilowatt-hours per hour.
    Divide 190 by 2 to get 95.
  9. Answer: 83.75 kilowatt-hours per hour.
    Divide 670 by 8 to get 83.75.
  10. Answer: No.
    The ratios are 95, 87.5, 85, and 83.75, so they are not the same. The pump uses 30 kilowatt-hours before it runs an hour, and that fixed amount shrinks as a share of the total.
  11. Answer: 830 kilowatt-hours.
    Each extra hour adds 80 kilowatt-hours, since 350 minus 190 equals 160 across 2 hours. Then 670 plus 80 plus 80 equals 830 kilowatt-hours at 10 hours.

Differentiation

Support

Give these students a table with a third column already labeled for the ratio, so the only task in items 1, 2, 8, and 9 is one division per row. Assign items 1 through 6 and item 8.

Extension

Ask these students to write an equation for Table B in the form electricity equals a number times hours plus a number, then to explain in two sentences how the graph of that equation differs from the graph of the Table A equation.

ELL supports

Pre-teach "released," "produced," "ratio," and "constant" with two columns of matched cards that students pair and divide. Provide the frame "___ divided by ___ equals ___, so the ratio is ___" for items 1, 2, 8, and 9.