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Worksheet Grade 8 Art & Music

Comparing Pump Rates as Slopes: A Well-Field Line-Graph Worksheet

A grade 8 art-design worksheet where students graph two well pumps' fill rates, compare the slopes as unit rates, and plan a clear two-line comparison chart.

Objectives

  1. Students will graph two proportional fill relationships on one grid.
  2. Students will read each pump's unit rate as the slope of its line and compare the two.
  3. Students will name design choices that make a two-line comparison chart easy to read.

Vocabulary

Pump
A pump is a machine that adds energy to water to move it or push it uphill, doing the job gravity cannot do on its own. Water systems use many different kinds of pumps to move water from wells, through treatment, and out to customers.

Also: slope, unit rate, proportional, legend

Teacher overview

At the fictional Ridgeline well field in the town of Ashford, two pumps fill the same storage tank at steady but different rates. When a designer draws both fill rates on one grid, the steeper line is the faster pump, and the slope of each line is its rate in gallons each minute. This worksheet has students build the two lines from data tables, read each slope as a unit rate, and compare them. The last item turns the math into a design task: deciding what makes a two-line chart easy to read at a glance.

Comparing Pump Rates as Slopes: A Well-Field Line-Graph Worksheet — Grade 8 Art & Music
Name: ____________________________ Date: ______________

Student Worksheet

Both pumps start filling an empty tank at 0 minutes. Their steady rates are shown in the tables.

Pump A:

Minutes Gallons added
0 0
1 12
2 24

Pump B:

Minutes Gallons added
0 0
1 20
2 40
  1. Pump A adds 12 gallons each minute. How many gallons has it added after 5 minutes?
  2. Pump B adds 20 gallons each minute. How many gallons has it added after 5 minutes?
  3. What is the slope of Pump A's line, in gallons per minute?
  4. What is the slope of Pump B's line, in gallons per minute?
  5. Which pump's line is steeper, and what does a steeper line mean here?
  6. Both lines pass through the point (0, 0). Explain why.
  7. The tank needs 240 gallons. How many minutes does Pump A take to add that much?
  8. How many minutes does Pump B take to add 240 gallons?
  9. After 4 minutes, how many more gallons has Pump B added than Pump A?
  10. You will draw both lines on one grid. Name two design choices that help a reader tell the two lines apart, and say how the two slopes should look.

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: 60 gallons. Pump A adds 12 gallons each minute, and 12 times 5 equals 60.
  2. Answer: 100 gallons. Pump B adds 20 gallons each minute, and 20 times 5 equals 100.
  3. Answer: 12 gallons per minute. The line rises 12 gallons for every 1 minute, so the slope is 12.
  4. Answer: 20 gallons per minute. The line rises 20 gallons for every 1 minute, so the slope is 20.
  5. Answer: Pump B is steeper. A steeper line means the pump fills faster, adding more gallons each minute.
  6. Answer: At 0 minutes, no water has been added yet, so both pumps start at 0 gallons, which is the point (0, 0).
  7. Answer: 20 minutes. 240 gallons divided by 12 gallons per minute equals 20 minutes.
  8. Answer: 12 minutes. 240 gallons divided by 20 gallons per minute equals 12 minutes.
  9. Answer: 32 gallons. After 4 minutes Pump B has 80 gallons and Pump A has 48 gallons, and 80 minus 48 equals 32.
  10. Answer: Any two clear choices, such as using two different colors with a labeled legend, or labeling each line directly. The steeper line, Pump B with slope 20, should rise faster than Pump A with slope 12, and gridlines with labeled axes help the reader compare them.

Differentiation

Support

Provide a grid with the axes already labeled and scaled and with Pump A's line drawn, so students plot only Pump B and compare. Let students extend each table to 5 minutes before answering items 1 and 2.

Extension

Ask students to add a third pump that adds 16 gallons each minute, place its line between the other two, and explain how its slope and steepness compare without drawing the grid first.

ELL supports

Pre-teach "slope" and "steeper" using two ramps of different steepness. Provide sentence frames for items 5 and 6, and allow item 10 to be answered as a labeled sketch of a two-line chart with a legend.