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Worksheet Grade 7 Math

Thornapple Aquifer Levels: A Grade 7 Signed-Number Worksheet

A grade 7 worksheet where students add and subtract positive and negative monthly changes to track a fictional aquifer's water level across a season.

Objectives

  1. Students will add positive and negative monthly changes to find a running water level.
  2. Students will separate and total the gains and the losses in a season of data.
  3. Students will interpret a net signed change as a rise or a fall in the water level.

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.
Recharge
Recharge is water soaking down through the ground to refill an aquifer, the way rain refills an underground sponge. Aquifers stay healthy only if recharge keeps up with pumping.

Also: water level, net change

Teacher overview

An aquifer is an underground layer of rock or sand that holds water that towns pump from wells, and its water level rises when rain soaks in and falls when wells pump it out. This worksheet tracks a fictional aquifer over one season, with each month reported as a positive change (a rise) or a negative change (a fall). The common error here is adding all six numbers as if they were positive; students who lose track of the signs will report a rise of 13.5 feet when the season actually ended only 3.0 feet higher, so the running-total items are built to catch that slip.

Thornapple Aquifer Levels: A Grade 7 Signed-Number Worksheet — Grade 7 Math
Name: ____________________________ Date: ______________

Student Worksheet

Thornapple is a fictional aquifer used for this worksheet. Its water level is measured in feet, compared with the level in September. September is the starting point, so its level is 0 feet. Each month after that has a change. A positive change means the level rose. A negative change means the level fell.

Monthly changes, in feet:

  • October: +2.5
  • November: +1.75
  • December: −0.5
  • January: −3.25
  • February: +4.0
  • March: −1.5
  1. Find the water level at the end of October. Start from 0 and add October's change.
  2. Find the level at the end of November by adding November's change to your item 1 answer.
  3. Find the level at the end of December.
  4. Find the level at the end of January.
  5. Find the level at the end of February.
  6. Find the level at the end of March. This is the level at the end of the season.
  7. Add all six monthly changes directly: 2.5 + 1.75 + (−0.5) + (−3.25) + 4.0 + (−1.5). Show that your total matches your item 6 answer.
  8. Which single month had the largest fall in level? Give the month and its change.
  9. Add together only the months with a fall (the negative changes). What is their total?
  10. Add together only the months with a rise (the positive changes). What is their total?
  11. The season ended above the September level. Explain in one sentence what that means for the town's wells.

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: 2.5 feet above the September level.
    0 + 2.5 = +2.5 feet.
  2. Answer: 4.25 feet above the September level.
    2.5 + 1.75 = +4.25 feet.
  3. Answer: 3.75 feet above the September level.
    4.25 + (−0.5) = 4.25 − 0.5 = +3.75 feet.
  4. Answer: 0.5 feet above the September level.
    3.75 + (−3.25) = 3.75 − 3.25 = +0.5 feet.
  5. Answer: 4.5 feet above the September level.
    0.5 + 4.0 = +4.5 feet.
  6. Answer: 3.0 feet above the September level.
    4.5 + (−1.5) = 4.5 − 1.5 = +3.0 feet.
  7. Answer: 3.0 feet above the September level.
    2.5 + 1.75 = 4.25; 4.25 − 0.5 = 3.75; 3.75 − 3.25 = 0.5; 0.5 + 4.0 = 4.5; 4.5 − 1.5 = 3.0. The total is +3.0 feet, which matches item 6.
  8. Answer: January, at −3.25 feet.
    January's −3.25 is the most negative change, so it is the largest single fall.
  9. Answer: −5.25 feet.
    (−0.5) + (−3.25) + (−1.5) = −5.25 feet.
  10. Answer: 8.25 feet of rises.
    2.5 + 1.75 + 4.0 = +8.25 feet.
  11. Answer: The aquifer holds more water than in September.
    A level of +3.0 feet means the water sits higher than the starting point, so the wells have more water to draw from than they did at the start of the season.

Differentiation

Support

Provide a vertical number line from −6 to +6 feet and have students mark each running total as they go, so the direction of every change is visible. Color rises in one shade and falls in another before any addition happens.

Extension

Ask students to write the one monthly change that would have been needed in March to bring the season's net change to exactly 0 feet, and to explain how they found it from the February total.

ELL supports

Pre-teach "rise," "fall," "recharge," and "net change" with up and down arrows. Provide a running table with columns "month," "change," and "new level" so students track the sign of each step in one place before writing item 11.