Lesson plan Grade 8 Science
Sunflower Flats Aquifer: A Linear Model of Storage Loss
A 50-minute grade 8 science lesson where students build a linear function for a fictional aquifer's storage as pumping outpaces recharge, then interpret its slope.
Objectives
- Students will construct a linear function that models an aquifer's storage as recharge and pumping change it over time.
- Students will interpret the slope as the net depletion rate and explain why heavy pumping draws down a limited resource.
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: storage, linear function
Teacher overview
Fictional Sunflower Flats draws its water from an aquifer that refills slowly from rain but is pumped hard for farms and homes. When pumping takes out more water each year than recharge puts back, the amount in storage falls by the same amount every year, which is exactly the pattern of a linear function. This lesson has students build that function, read its slope as the yearly loss, and use it to predict when storage crosses a chosen limit. A common misconception it addresses is that an aquifer is like an endless underground river rather than a limited store that can be spent faster than it refills.
Procedure
Hook (5 min): Ask students what happens to a savings account if you take out more money each month than you put in. Connect that to an aquifer, where recharge is the deposit and pumping is the withdrawal.
Direct instruction (12 min): Define recharge, pumping, and storage. Establish that if pumping and recharge stay steady, the net change each year is constant, so storage over time forms a straight line. Introduce the form: storage = starting storage + (net yearly change) × years, and note that a net loss makes the slope negative.
Worked example (8 min): Model a different aquifer than the handout uses. Suppose it starts with 40,000 acre-feet, recharges 500 acre-feet per year, and is pumped 900 acre-feet per year. The net change is 500 − 900 = −400 acre-feet per year, so storage = 40,000 − 400t. Show that after 5 years, storage = 40,000 − 2,000 = 38,000 acre-feet. This example is for instruction only; students do not answer it.
Independent practice (18 min): Students work the Sunflower Flats handout individually or in pairs, building and interpreting the linear function for that aquifer.
Formative check and exit (7 min): Review handout question 2's function as a class and have each student write, on the back of the handout, what the slope means in plain words. Collect and scan for the idea that storage drops by a fixed amount each year.
Student Handout
Use the fictional Sunflower Flats aquifer for every question. It currently holds 60,000 acre-feet of water. Each year, recharge adds 800 acre-feet and pumping removes 1,300 acre-feet.
- What is the net change in storage each year?
- Write a linear function for the storage S, in acre-feet, after t years.
- How much water will the aquifer hold after 10 years?
- What does the slope of your function mean in this situation?
- What does the initial value of your function mean in this situation?
- After how many years will storage drop to 50,000 acre-feet?
- What yearly pumping amount would keep the aquifer's storage steady?
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: −500 acre-feet per year. Recharge minus pumping is 800 − 1,300 = −500 acre-feet each year.
- Answer: S = 60,000 − 500t. Storage starts at 60,000 acre-feet and falls 500 acre-feet for each year t.
- Answer: 55,000 acre-feet. S = 60,000 − 500 × 10 = 60,000 − 5,000 = 55,000 acre-feet.
- Answer: The slope −500 means storage drops by 500 acre-feet every year because pumping removes that much more than recharge replaces.
- Answer: The initial value 60,000 is the storage at year 0, the amount of water in the aquifer before this period of pumping begins.
- Answer: 20 years. Set 60,000 − 500t = 50,000, so 500t = 10,000 and t = 20 years.
- Answer: 800 acre-feet per year. If pumping equals the 800 acre-feet of yearly recharge, the net change is zero and storage stays steady.
Differentiation
Support
Provide a table with the years 0, 5, 10, 15, and 20 already listed so students can fill in storage values before writing the function, letting the constant drop become visible as a pattern first. Allow a calculator for every step.
Extension
Ask students to graph both the Sunflower Flats function and the worked-example function on the same axes, then explain which aquifer runs low first and why, using both the starting amounts and the slopes (the worked-example aquifer starts with less water and runs low first, even though its slope is less steep).
ELL supports
Pre-teach "recharge," "pumping," "storage," and "slope" with a labeled picture of an underground water store with an inflow arrow and a larger outflow arrow. Provide the sentence frame "Storage goes down by ___ acre-feet each year because ___" for questions 4 and 5.