Math problem set Grade 9 Science

Pinch Creek Reservoir: Graphing Two Drought Conservation Paths

A grade 9 math problem set where students build and graph linear equations for a fictional reservoir's storage under current withdrawal versus a conservation order.

Grade: Grade 9
Subject: Science
Material: Math problem set
Time: 45 min
Prep: Low prep
Materials: calculator, graph paper

Standards

HSA-CED.A.2 Common Core Math

Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

How this material aligns: Item 7 has students write and graph two linear equations relating reservoir storage to elapsed time on the same labeled, scaled coordinate axes, exactly the equation-and-graph task this standard describes.

All materials for HSA-CED.A.2 →

HSF-IF.B.6 Common Core Math

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

How this material aligns: Items 1 and 4 have students calculate the reservoir's average daily rate of change in storage under two withdrawal scenarios, the rate-of-change calculation this standard requires.

All materials for HSF-IF.B.6 →

HS-ESS3-3 NGSS

Create a computational simulation to illustrate the relationships among the management of natural resources, the sustainability of human populations, and biodiversity.

How this material aligns: Items 1 through 8 build a simplified reservoir water budget from inflow, evaporation and seepage, and withdrawal, then run it forward under two management choices to compare how long the supply stays above the emergency threshold.

All materials for HS-ESS3-3 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will calculate a reservoir's net daily change in storage from inflow, evaporation, and withdrawal data.
Students will write and solve linear equations projecting when a reservoir reaches a critical storage level.
Students will graph two storage projections on the same labeled coordinate axes and compare their slopes.

Vocabulary

Key words: reservoir storage, inflow, withdrawal, net rate of change, conservation order

Teacher overview

Pinch Creek Reservoir (a fictional reservoir used for this problem set) supplies the city of Rowan Bend. A multi-year drought has left the reservoir's inflow far below what the city withdraws each day, and city officials are deciding whether to issue a mandatory conservation order that would cut withdrawal significantly. This problem set has students build a water budget for the reservoir, project when it would reach a critical storage level under current conditions, and compare that projection with one under mandatory conservation.

A common misconception in this math is calculating the reservoir's net daily change using only inflow and withdrawal, forgetting that evaporation and seepage also remove water from an open reservoir even when no one draws from it. Every problem in this set requires accounting for all three terms, inflow, evaporation and seepage, and withdrawal, before the net rate of change is correct.

Pinch Creek Reservoir: Graphing Two Drought Conservation Paths — Grade 9 Science

Name: ____________________________ Date: ______________

Problems

Pinch Creek Reservoir currently holds 4,500 million gallons (MG) of stored water. Use these facts for all problems:

Inflow from Pinch Creek adds 15 MG per day.
Evaporation and seepage remove a steady 5 MG per day, regardless of withdrawal.
The city currently withdraws 40 MG per day for its water supply.
State rules require Rowan Bend to activate emergency water-use restrictions if storage falls to 1,500 MG.

Calculate the reservoir's current net daily change in storage: net change = inflow − evaporation/seepage − withdrawal.
Using your answer to item 1, write a linear equation for the reservoir's storage, S, after t days under current conditions: S = 4,500 + (net change) × t.
Solve your equation from item 2 for the value of t when S = 1,500 MG, the emergency threshold. Round to the nearest whole day.
City officials propose a mandatory conservation order that would cut withdrawal from 40 MG per day to 25 MG per day, with inflow and evaporation/seepage unchanged. Calculate the new net daily change in storage under this order.
Write a new linear equation for storage under the proposed conservation order, using your answer to item 4.
Solve your equation from item 5 for the value of t when S = 1,500 MG under the conservation order. Round to the nearest whole day.
Graph both equations, from items 2 and 5, on the same coordinate axes. Put days (t) on the horizontal axis and storage in MG on the vertical axis, and label and scale both axes so the 1,500 MG threshold and both projected crossing days are visible. Describe in one or two sentences how the two lines compare.
Calculate how many additional days the conservation order buys the city before reaching the emergency threshold, using your answers to items 3 and 6.
Challenge. Suppose the city council only approves half of the proposed cut, reducing withdrawal to 32.5 MG per day (halfway between 40 and 25) instead of the full 25 MG per day. Write a third linear equation for this partial-conservation scenario and solve for the day the reservoir would reach the 1,500 MG threshold.

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: -30 MG/day.
Net change = 15 − 5 − 40 = −30 MG per day, meaning the reservoir currently loses about 30 million gallons of stored water every day.
Answer: S = 4,500 − 30t.
Starting storage is 4,500 MG, and it decreases by 30 MG for every day, t, that passes: S = 4,500 − 30t.
Answer: 100 days.
Set S = 1,500: 1,500 = 4,500 − 30t. Subtracting 4,500 from both sides gives −3,000 = −30t, so t = 100 days.
Answer: -15 MG/day.
Net change = 15 − 5 − 25 = −15 MG per day under the proposed conservation order, half the current rate of loss.
Answer: S = 4,500 − 15t.
S = 4,500 − 15t, using the reduced net rate of change from item 4.
Answer: 200 days.
Set S = 1,500: 1,500 = 4,500 − 15t. Subtracting 4,500 from both sides gives −3,000 = −15t, so t = 200 days.
Answer: description, not a single number.
Both lines start at the same point, (0, 4,500), since both scenarios begin from today's storage level. The current-conditions line (item 2) has a steeper downward slope, −30 MG per day, and crosses the 1,500 MG threshold at t = 100 days, while the conservation-order line (item 5) has a gentler slope, −15 MG per day, and stays above the current-conditions line for every day after t = 0, crossing the threshold much later, at t = 200 days.
Answer: 100 days.
200 − 100 = 100 additional days before the reservoir reaches the emergency threshold under the conservation order, compared to current conditions.
Answer: about 133 days.
Net change = 15 − 5 − 32.5 = −22.5 MG per day. Equation: S = 4,500 − 22.5t. Setting S = 1,500: 1,500 = 4,500 − 22.5t, so −3,000 = −22.5t, and t = 3,000 ÷ 22.5 ≈ 133.3 days, which rounds to about 133 days before the reservoir reaches the threshold under partial conservation. That is only about one-third of the way from the 100-day projection to the 200-day projection, even though the withdrawal is halfway between the two scenarios.

Differentiation

Support (below grade level)

Provide items 2 and 5's equations already written with the net-change values substituted, so students only need to solve for t in items 3 and 6. Provide pre-scaled graph paper with the axes already labeled "Days" and "Storage (MG)" for item 7.

Extension (above grade level)

Ask students to calculate exactly what withdrawal rate, in MG per day, would let the reservoir maintain a stable storage level (net change of 0) given the current 15 MG per day inflow and 5 MG per day evaporation and seepage, and to explain what that withdrawal rate means for the city's water planning.

ELL supports

Pre-teach "inflow," "withdrawal," and "net change" using a simple bathtub diagram: water flowing in from a faucet (inflow), draining out two drains of different sizes (evaporation and withdrawal), labeled in English and students' home languages where possible. Allow item 7's comparison to be answered with the completed graph plus one short sentence instead of a full paragraph.