Worksheet Grade 7 Math
Ashen Hollow Aquifer Recharge: A Grade 7 Proportional Worksheet
A grade 7 worksheet where students test a fictional town's recharge data for proportionality, find the constant of proportionality, and write and use an equation.
Objectives
- Students will decide whether a recharge data set is proportional by checking for a constant ratio.
- Students will identify the constant of proportionality and write and use an equation for it.
Vocabulary
- Aquifer
- An aquifer is an underground layer of rock, sand, or gravel that holds water in the tiny spaces between its grains. Wells reach down into aquifers to bring water up to the surface.
Also: recharge zone, constant of proportionality, proportional
Teacher overview
The fictional town of Ashen Hollow gets its water from an aquifer below a grassy recharge zone. When rain soaks into that zone, the aquifer gains water, and the gain is proportional to the amount of rain. This worksheet gives students a small recharge table, asks them to test it for proportionality, and has them find the constant of proportionality and turn it into an equation. Watch for the common error of writing the equation as x = ky instead of y = kx, which flips the two quantities.
Student Worksheet
The recharge zone at Ashen Hollow has been measured. This table shows how much water the aquifer gained for four different amounts of rain.
| Rain (inches) | Water added (gallons) |
|---|---|
| 0.5 | 6,000 |
| 1 | 12,000 |
| 2 | 24,000 |
| 4 | 48,000 |
- Is the water added proportional to the rain? Check the ratio of gallons to inches for each row, then explain what you find.
- What is the constant of proportionality for this recharge zone? Give it in gallons per inch of rain.
- Let x be the rain in inches and y be the gallons added. Write an equation that gives y for any value of x.
- A storm drops 3 inches of rain. Use your equation to find the gallons added to the aquifer.
- In a dry month, only 0.25 inch of rain falls. How many gallons does the aquifer gain?
- One month the aquifer gained 54,000 gallons from rain. How many inches of rain fell?
- The town pumps 9,000 gallons a day out of the aquifer for homes. How many gallons is that over a 30-day month?
- During that same month, 6 inches of rain fell. How many gallons did recharge add, and was that enough to replace all the water pumped out?
- A new parking lot will pave part of the zone and drop the constant to 9,000 gallons per inch. Write the new equation and find the gallons a 3-inch storm adds now.
- Explain, using the constant of proportionality, why paving the recharge zone lowers how much water reaches the aquifer for the same rain.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
- Answer: Yes, it is proportional. Each row gives the same ratio: 6,000 ÷ 0.5 = 12,000; 12,000 ÷ 1 = 12,000; 24,000 ÷ 2 = 12,000; 48,000 ÷ 4 = 12,000. A constant ratio means the two quantities are proportional.
- Answer: 12,000 gallons per inch. The steady ratio of gallons to inches found in item 1 is the constant of proportionality.
- Answer: y = 12,000x. Multiply the rain in inches by 12,000 to get the gallons added.
- Answer: 36,000 gallons. Using y = 12,000x with x = 3: 12,000 × 3 = 36,000 gallons.
- Answer: 3,000 gallons. Using x = 0.25: 12,000 × 0.25 = 3,000 gallons.
- Answer: 4.5 inches. Solve 54,000 = 12,000x by dividing: 54,000 ÷ 12,000 = 4.5 inches.
- Answer: 270,000 gallons. 9,000 gallons per day × 30 days = 270,000 gallons pumped out.
- Answer: 72,000 gallons, which was not enough. Recharge added 12,000 × 6 = 72,000 gallons, but 270,000 gallons were pumped out, so pumping removed far more than the rain replaced.
- Answer: y = 9,000x, so 27,000 gallons. With the lower constant, a 3-inch storm adds 9,000 × 3 = 27,000 gallons.
- Answer: Paving lowers the constant of proportionality, the gallons added per inch of rain. A smaller constant means every inch of rain adds fewer gallons, because water runs off the pavement instead of soaking into the aquifer.
Differentiation
Support
Give students a filled-in ratio column beside the table so they can see the 12,000 pattern before item 1. Provide the equation frame "y = ___ times x" for item 3, and allow a calculator for the multiplication and division in items 4 through 9.
Extension
Ask students to build a second recharge zone with a different constant of proportionality, write its equation, and then compare how many more gallons their zone gains than Ashen Hollow's for a 5-inch storm.
ELL supports
Pre-teach "aquifer," "recharge zone," and "proportional" with a simple labeled sketch of rain soaking down into an underground layer. Provide the sentence frame "The water added is ___ times the rain, so the constant is ___" for items 1 and 2.