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Math problem set Grade 5 Math

Tracking Amber Falls Reservoir Through a Dry Summer

A grade 5 math problem set graphing a reservoir's daily water level during a dry summer on a coordinate grid and finding each day's decimal drawdown.

Objectives

  1. Students will graph a set of daily measurements as ordered pairs on a coordinate grid.
  2. Students will subtract decimal water-level readings to find daily and total change.

Vocabulary

Reservoir
A human-made lake, usually created by a dam, that stores water for later. Reservoirs supply cities and farms and help control floods.
Drawdown
Drawdown is how far the water level in a well drops when a pump pulls water out. The harder and longer you pump, the bigger the drawdown gets.
Drought
A long stretch of drier-than-normal weather that leaves too little water for people, farms, and nature. Droughts build slowly and can last for years.

Also: coordinate grid, ordered pair

Teacher overview

Amber Falls Reservoir, a fictional reservoir used for this problem set, is monitored daily during dry summer months because its water level drops steadily without regular rain to refill it. This problem set gives students six days of water-level readings, measured in feet above a fixed reference marker at the reservoir's base, to graph on a coordinate grid and analyze using subtraction. A common misconception in this math is assuming the water level drops by the same amount every day; the daily readings in this set are close but not identical, and students should notice the pattern changes slightly from day to day rather than forcing every difference to match.

Tracking Amber Falls Reservoir Through a Dry Summer — Grade 5 Math
Name: ____________________________ Date: ______________

Problems

Amber Falls Reservoir's water level was recorded once each day for six days:

Day Water level (ft)
1 42.0
2 41.5
3 40.8
4 40.0
5 39.4
6 38.5
  1. Plot each day's reading as an ordered pair (day, water level) on a coordinate grid, using the day number as the x-value and the water level in feet as the y-value. Which day had the highest water level, and which day had the lowest?
  2. Find how many feet the water level dropped from Day 1 to Day 2.
  3. Find how many feet the water level dropped from Day 2 to Day 3.
  4. Find how many feet the water level dropped from Day 3 to Day 4.
  5. Find how many feet the water level dropped from Day 4 to Day 5.
  6. Find how many feet the water level dropped from Day 5 to Day 6.
  7. Add your five daily drops from problems 2 through 6. Then check your total by subtracting the Day 6 reading directly from the Day 1 reading. Do the two totals match?
  8. If the reservoir keeps dropping at about the same rate as it did from Day 5 to Day 6, predict the water level on Day 7. Show your work.
  9. Challenge. Amber Falls reaches a drought-watch level once it falls to 35.0 feet. Using your Day 7 prediction from problem 8 and the same daily drop rate, about how many more full days after Day 7 would it take to reach 35.0 feet?

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: Day 1 highest, Day 6 lowest.
    The six ordered pairs are (1, 42.0), (2, 41.5), (3, 40.8), (4, 40.0), (5, 39.4), and (6, 38.5). Day 1 has the highest y-value, 42.0 ft, and Day 6 has the lowest, 38.5 ft.
  2. Answer: 0.5 ft.
    42.0 − 41.5 = 0.5 ft.
  3. Answer: 0.7 ft.
    41.5 − 40.8 = 0.7 ft.
  4. Answer: 0.8 ft.
    40.8 − 40.0 = 0.8 ft.
  5. Answer: 0.6 ft.
    40.0 − 39.4 = 0.6 ft.
  6. Answer: 0.9 ft.
    39.4 − 38.5 = 0.9 ft.
  7. Answer: 3.5 ft, and yes, the totals match.
    0.5 + 0.7 + 0.8 + 0.6 + 0.9 = 3.5 ft. Subtracting directly, 42.0 − 38.5 = 3.5 ft, which matches the sum of the five daily drops.
  8. Answer: 37.6 ft.
    Using the Day 5 to Day 6 drop of 0.9 ft, 38.5 − 0.9 = 37.6 ft predicted for Day 7.
  9. Answer: about 3 more days.
    From the Day 7 prediction of 37.6 ft down to 35.0 ft is a drop of 2.6 ft. At about 0.9 ft per day, 2.6 ÷ 0.9 ≈ 2.9, which rounds up to about 3 more full days before the reservoir reaches 35.0 feet.

Differentiation

Support (below grade level)

Provide a pre-drawn coordinate grid with the x-axis already labeled 1 through 7 and the y-axis already labeled from 35 to 43 in whole-foot increments, so students only need to plot the six points rather than build the grid themselves.

Extension (above grade level)

Ask students to calculate the average daily drop across all six days (total drop divided by five intervals) and compare that average to the actual Day 5 to Day 6 drop used in problem 8, discussing which number gives a more reliable prediction and why.

ELL supports

Pre-teach "reservoir," "drawdown," and "ordered pair" with a simple labeled picture of a reservoir and a water-level marker. Allow problem 1's comparison question (highest and lowest day) to be answered by pointing to the completed graph rather than writing a full sentence.

Extensions

Research whether a reservoir near your own community publishes its water level online, and if so, have students graph one week of real readings using the same coordinate-grid method practiced with Amber Falls Reservoir.