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Math problem set Grade 7 Math

Hallowfell Basin Snowpack: A Percent-of-Average Problem Set

A grade 7 problem set where students turn April snow measurements from a fictional basin into percents of average and predict the summer water supply.

Objectives

  1. Students will express a snow measurement as a percent of its long-term average.
  2. Students will combine station readings into a basin total and find its percent of average.
  3. Students will predict runoff from a percent of average and convert acre-feet to gallons.

Vocabulary

Snowpack
The snow that piles up in the mountains over the winter. As it melts in spring and summer, it acts like a giant water tank feeding rivers and reservoirs.
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: snow water equivalent, percent of average, runoff

Teacher overview

In mountain regions the snow that piles up over winter is the water supply for the following summer, so hydrologists measure it on April 1 at fixed stations and report the snow water equivalent, meaning the depth of water the snow would make if it all melted at once. Each reading is then compared with that station's long-term average and reported as a percent of average. This set follows four stations in a fictional basin and ends with the runoff those stations predict. The misconception this set is built to correct is reading "60 percent of average" as "60 percent below average," which describes a far worse year than the measurement actually reports.

Hallowfell Basin Snowpack: A Percent-of-Average Problem Set — Grade 7 Math
Name: ____________________________ Date: ______________

Problems

Suppose the fictional Hallowfell Basin supplies the town of Redwick. Four stations reported snow water equivalent on April 1, shown beside each station's long-term average.

Station April 1 snow water equivalent (inches) Long-term average (inches)
Pinnock Ridge 18.0 24.0
Holbeck Pass 13.5 30.0
Strandmill Meadow 21.0 20.0
Tarnhollow Flat 9.6 16.0
  1. What percent of its long-term average did Pinnock Ridge measure this April?
  2. What percent of its long-term average did Holbeck Pass measure?
  3. What percent of its long-term average did Strandmill Meadow measure?
  4. What percent of its long-term average did Tarnhollow Flat measure?
  5. Add the four station readings and add the four averages. What percent of average is the basin total this year?
  6. Last year the basin produced 44,000 acre-feet of runoff in a year that measured 100 percent of average. If runoff is proportional to snowpack, how much runoff should this year produce?
  7. Redwick used 3,036 acre-feet of water last year. What percent of this year's predicted runoff is that?
  8. Write the change from the average basin total to this year's basin total as a signed number in inches.
  9. One acre-foot equals 325,851 gallons. How many gallons did Redwick use last year?

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: 75 percent. Divide the reading by the average: 18.0 divided by 24.0 equals 0.75.
  2. Answer: 45 percent. Divide the reading by the average: 13.5 divided by 30.0 equals 0.45.
  3. Answer: 105 percent. Divide the reading by the average: 21.0 divided by 20.0 equals 1.05, which is above average.
  4. Answer: 60 percent. Divide the reading by the average: 9.6 divided by 16.0 equals 0.60.
  5. Answer: 69 percent. This year's total is 18.0 plus 13.5 plus 21.0 plus 9.6, which equals 62.1 inches. The average total is 24.0 plus 30.0 plus 20.0 plus 16.0, which equals 90.0 inches. Then 62.1 divided by 90.0 equals 0.69.
  6. Answer: 30,360 acre-feet. Multiply last year's runoff by the percent of average: 0.69 times 44,000 equals 30,360 acre-feet.
  7. Answer: 10 percent. Divide the town's use by the predicted runoff: 3,036 divided by 30,360 equals 0.10.
  8. Answer: -27.9 inches. Subtract the average total from this year's total: 62.1 minus 90.0 equals negative 27.9 inches.
  9. Answer: 989,283,636 gallons. Multiply acre-feet by the conversion factor: 3,036 times 325,851. That is 977,553,000 for 3,000 acre-feet plus 11,730,636 for 36 acre-feet, giving 989,283,636 gallons.

Differentiation

Support

Give these students the four divisions already set up as fractions, with the reading on top and the average underneath, and let them convert each decimal to a percent. Allow calculators and let them skip problem 9, or supply the first partial product for it.

Extension

Ask students to find what April 1 reading Holbeck Pass would have needed for the fictional basin total to reach 90 percent of average, with the other three stations unchanged, and to explain why one station can move the basin total so much.

ELL supports

Pre-teach "snowpack," "average," "runoff," and "percent of average" with a bar drawing that shows this year's snow beside a taller bar for the average. Provide the frame "This station measured ___ inches out of an average of ___ inches, which is ___ percent of average" for problems 1 through 4.

Extensions

Have students plot the four stations on a bar graph with this year's reading and the long-term average side by side, then write a short recommendation to the fictional town of Redwick on whether to start summer watering limits in May, citing the basin percent of average from problem 5.