Math problem set Grade 8 Science

Verdigris Aquifer: Scientific Notation for Groundwater

A grade 8 science problem set where students write huge aquifer and city-use volumes in scientific notation, compare magnitudes, and reason about groundwater depletion.

Grade: Grade 8
Subject: Science
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: Calculator

Standards

8.EE.A.3 Common Core Math

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

How this material aligns: Every problem has students write very large groundwater volumes in scientific notation and state how many times as much one quantity is than another, the exact skill this standard names.

All materials for 8.EE.A.3 →

MS-ESS3-1 NGSS

Construct a scientific explanation based on evidence for how the uneven distributions of Earth's mineral, energy, and groundwater resources are the result of past and current geoscience processes.

How this material aligns: Problem 8 has students construct an evidence-based explanation for why a slowly recharging aquifer can be drawn down within decades, addressing this standard's focus on groundwater as a limited resource whose stored volume changes through human withdrawal.

All materials for MS-ESS3-1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will write large water volumes in scientific notation and divide them to compare magnitudes.
Students will use scientific notation to estimate how long an aquifer's stored water would last.

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.
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: scientific notation, withdrawal

Teacher overview

Groundwater volumes are enormous, and scientific notation is the tool that keeps them manageable. In this set, students work with the fictional Verdigris Aquifer, which supplies the fictional city of Ashford, writing its stored water and the city's daily use in scientific notation and comparing them. A common misconception in this math is treating the powers of ten like the leading digits; when dividing 8.4 × 10^10 by 4.2 × 10^6, students must divide 8.4 by 4.2 and subtract the exponents, not divide the exponents. The set builds from writing single values to estimating how many years the aquifer's water would last.

Verdigris Aquifer: Scientific Notation for Groundwater — Grade 8 Science

Name: ____________________________ Date: ______________

Problems

In this scenario, the fictional Verdigris Aquifer holds an estimated 84,000,000,000 gallons of water, and the fictional city of Ashford withdraws about 4,200,000 gallons per day. Use these figures throughout.

Write the aquifer's stored volume, 84,000,000,000 gallons, in scientific notation.
Write Ashford's daily withdrawal, 4,200,000 gallons, in scientific notation.
About how many times as much water does the aquifer hold as the city withdraws in one day? Show the division using your answers from problems 1 and 2.
How many gallons does Ashford withdraw in a full year (365 days)? Write your answer in scientific notation, rounded to two significant figures.
Ignoring any recharge, about how many years of water does the aquifer hold at that yearly withdrawal? Use your answers from problems 1 and 4.
One acre-foot equals 325,851 gallons. How many acre-feet is Ashford's daily withdrawal of 4,200,000 gallons? Round to the nearest tenth.
Recharge adds about 3,000,000 gallons per day to the aquifer while Ashford removes 4,200,000 gallons per day. What is the net daily change in the aquifer's storage? Write it in scientific notation.
Explain why an aquifer that took thousands of years to fill can be drawn down within a few decades if withdrawals stay larger than recharge.

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: 8.4 × 10^10 gallons.
84,000,000,000 has the decimal moved 10 places to give 8.4 × 10^10 gallons.
Answer: 4.2 × 10^6 gallons.
4,200,000 has the decimal moved 6 places to give 4.2 × 10^6 gallons.
Answer: 20,000 times.
(8.4 × 10^10) ÷ (4.2 × 10^6) = (8.4 ÷ 4.2) × 10^(10−6) = 2 × 10^4 = 20,000 times.
Answer: 1.5 × 10^9 gallons.
4.2 × 10^6 × 365 = 1,533,000,000 = 1.533 × 10^9, which rounds to 1.5 × 10^9 gallons.
Answer: About 55 to 56 years.
(8.4 × 10^10) ÷ (1.533 × 10^9) = 54.8, about 55 years of stored water. Using the rounded 1.5 × 10^9 from problem 4 gives (8.4 × 10^10) ÷ (1.5 × 10^9) = 56 years; accept 55 or 56.
Answer: 12.9 acre-feet.
4,200,000 ÷ 325,851 = 12.89, about 12.9 acre-feet per day.
Answer: −1.2 × 10^6 gallons per day.
3,000,000 − 4,200,000 = −1,200,000 = −1.2 × 10^6 gallons per day, a net loss because withdrawals exceed recharge.
Answer: Recharge is far slower than pumping.
Water moves slowly through rock and soil, so an aquifer refills over a very long time. If withdrawals stay larger than recharge, stored water leaves faster than it returns, and even a huge supply that took millennia to accumulate can fall sharply within decades.

Differentiation

Support

Provide a place-value chart for moving the decimal point, and work problem 1 together before students continue. For problem 3, remind students in writing to divide the leading digits and subtract the exponents as two separate steps.

Extension

Ask students to find how many years the aquifer's water would last if recharge were included, using the net loss of 1.2 × 10^6 gallons per day from problem 7 instead of the full withdrawal, and to compare that with their problem 5 answer.

ELL supports

Pre-teach "aquifer," "recharge," and "withdrawal" with a simple cross-section drawing of water stored underground. Provide a worked model of one division in scientific notation, labeled step by step, for students to follow on the other problems.