Lesson plan Grade 12 Math

Kettleridge Reservoir Hydrograph: Reading a Drought Year

A grade 12 lesson where students read key features off a fictional reservoir's water-level graph and compute average rates of change across a drought and recovery.

Grade: Grade 12
Subject: Math
Material: Lesson plan
Time: 50 min
Prep: Low prep
Materials: Projector, Printed data-and-grid handout, Calculator

Standards

HSF-IF.B.4 Common Core Math

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

How this material aligns: In direct instruction and guided practice students identify the graph's starting value, its steepest decreasing interval, and its relative minimum in reservoir terms, the key-feature interpretation this standard names.

All materials for HSF-IF.B.4 →

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: Students calculate the average rate of change of the reservoir level over the full decline, the steepest month, and the recovery, interpreting each rate as a drawdown or refill speed, exactly what this standard requires.

All materials for HSF-IF.B.6 →

Download Word file

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 identify the intercept, steepest decline, and relative minimum of a reservoir hydrograph.
Students will compute the average rate of change of the level over stated intervals.
Students will interpret each rate as a drawdown or refill speed in the drought's context.

Vocabulary

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.

Also: hydrograph, relative minimum, average rate of change, interval

Teacher overview

A reservoir's water level over a year is a function students can read the way a water manager does, pulling the starting level, the fastest month of decline, and the low point straight off the curve. This lesson uses a year of monthly water-surface readings from the fictional Kettleridge Reservoir through a drought and its recovery. A common misconception this lesson addresses is that the average rate of change over a long interval equals the rate in its worst single month; students see that a season-long average of a few feet per month can hide a much steeper drop packed into one month.

Procedure

Hook (5 min): Project the Kettleridge level curve (a line graph of the monthly readings below, plotted in advance) and ask students to point to the month the reservoir was in the most trouble, then to the month it started to recover. Take a few answers without confirming, so the graph reading in the next steps settles the question.

Direct instruction (12 min): Present the monthly water-surface readings for the fictional Kettleridge Reservoir, in feet above the intake:

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Level (ft)	92	90	87	82	75	66	55	52	58	67	76	83

Define the key features: the January value of 92 ft is the starting level (the intercept), the interval where the curve drops fastest is the steepest decline, and the lowest point before recovery is the relative minimum. Then introduce average rate of change over an interval as the change in level divided by the change in months, and work June-to-July as a model: (55 − 66) ÷ 1 = −11 ft per month.

Guided practice (14 min): In pairs, students find the relative minimum, then compute the average rate of change over the full decline from January to August and confirm that the steepest single month is June to July. Circulate to check that pairs are dividing by the correct number of months.

Formative check (4 min): Ask each pair to hold up a card with the month of the relative minimum and its level. Confirm the class agrees on August at 52 ft before continuing; reteach the relative-minimum idea to any pair that named July.

Independent practice (10 min): Each student computes the average rate of change over the recovery from August to December and writes one sentence comparing that refill speed to the decline speed found in guided practice.

Closure / exit ticket (5 min): Students answer on a card: "From March (87 ft) to June (66 ft), what was the average rate of change in feet per month?" Collect on the way out.

Kettleridge Reservoir Hydrograph: Reading a Drought Year — Grade 12 Math

Name: ____________________________ Date: ______________

Student Handout

The table below gives the monthly water-surface level of the fictional Kettleridge Reservoir, in feet above the intake, across one drought year. Answer each question from this table alone, and show the subtraction and division you use for every rate.

Month	Jan	Feb	Mar	Apr	May	Jun	Jul	Aug	Sep	Oct	Nov	Dec
Level (ft)	92	90	87	82	75	66	55	52	58	67	76	83

State the reservoir's starting level, the January reading that the graph uses as its intercept.
Identify the relative minimum: name the month with the lowest level before the reservoir recovers, and give that level in feet.
Find the single month over which the level falls the most, and give that month's average rate of change in feet per month.
Compute the average rate of change of the level over the full decline, from January to August, in feet per month.
Compute the average rate of change of the level over the recovery, from August to December, in feet per month.
Compute the average rate of change of the level from March to June, in feet per month.

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: starting level 92 ft. The January reading of 92 ft is the graph's intercept, the reservoir's level at the start of the year before the drought deepened.
Answer: relative minimum is August at 52 ft. The level falls every month through August, then rises, so August is the low point before recovery.
Answer: steepest month is June to July at −11 ft per month. From 66 ft to 55 ft is a drop of 11 ft in one month, the largest single-month change in the table.
Answer: about −5.7 ft per month over the full decline. From January (92 ft) to August (52 ft) is a change of −40 ft across 7 months: −40 ÷ 7 = −5.71, about −5.7 ft per month. This season-long average is much gentler than the −11 ft of the worst month.
Answer: about 7.75 ft per month over the recovery. From August (52 ft) to December (83 ft) is +31 ft across 4 months: 31 ÷ 4 = 7.75 ft per month, so the reservoir refilled faster than it drew down on average.
Exit ticket answer: −7 ft per month. From March (87 ft) to June (66 ft) is −21 ft across 3 months: −21 ÷ 3 = −7 ft per month.

Differentiation

Support

Provide the level differences between consecutive months already filled in a row beneath the table, so students can spot the steepest month and set up rate-of-change fractions without first subtracting. Pre-mark the axes on the grid handout.

Extension

Ask students to sketch a plausible curve for the following year if the drought returns but is half as severe in its steepest month, keeping the same starting level, and to state the average rate of change their sketch implies over its decline. Have them explain which feature of the original graph they changed and why.

ELL supports

Pre-teach "hydrograph," "decline," "relative minimum," and "rate of change" with a simple rising-and-falling line labeled at its start, low point, and recovery. Provide sentence frames for the independent practice, such as "The reservoir refilled at about ___ feet per month, which is ___ than the decline."