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Lesson plan Grade 8 Math

Twin Forks' Elevated Tank: Building a Linear Function for Water Level

A 45-minute grade 8 lesson where students use overnight tank-level data to find a rate of change and initial value, build a linear function, and predict a target level.

Objectives

  1. Students will determine the rate of change and initial value of a tank's water level from a data table.
  2. Students will construct a linear function modeling a tank's water level over time and use it to make predictions.
  3. Students will use a linear function to find the time at which a tank reaches a specified water level.

Vocabulary

Key words: rate of change, initial value, linear function, net rate

Teacher overview

Twin Forks (a fictional town used for this lesson) operates an elevated storage tank whose water level was measured every 10 minutes overnight, showing a steady rise even though a small, unrepaired leak was draining water the whole time. This lesson has students find the tank's rate of change and initial value from that data table and build a linear function to model and predict its level. A common misconception is assuming a tank's rate of change must equal its inlet valve's fill rate alone; the net rate recorded in the data already accounts for the competing leak, and that net rate is what actually predicts future readings.

Procedure

Hook (5 min): Show students the data table for the fictional town of Twin Forks' elevated tank water level at four times overnight (t = 0, 10, 20, and 30 minutes, with levels of 12, 15, 18, and 21 feet) and ask, "If this pattern continues, what do you think the level will be after 60 minutes?" Collect a few predictions without confirming them.

Direct instruction (12 min): Explain that the tank's inlet valve adds water faster than a small leak drains it, producing a steady net rate of increase. Model finding the rate of change from the table: the level rises 3 feet every 10 minutes, so the rate is 0.3 feet per minute. Identify the initial value as 12 feet at t = 0. Construct the linear function L(t) = 12 + 0.3t together as a class, and confirm it matches all four data points.

Guided practice (13 min): In pairs, students use the function to predict the tank's level at two future times, then check their predictions by extending the original table two more rows using the same 3-foot-per-10-minute pattern.

  1. What is the tank's predicted level at t = 60 minutes?
  2. What is the tank's predicted level at t = 90 minutes?

Independent practice (10 min): Each student answers two questions on a handout.

  1. Twin Forks' operators want to know when the tank will reach 35 feet. Using the function, at what time, in minutes, does the tank reach 35 feet?
  2. If the leak were repaired so no water was lost, and the inlet alone adds water at 0.5 feet per minute, write a new function for the tank's level starting from the same 12-foot initial value.

Closure / exit ticket (5 min): Students answer one question on an index card.

  1. A different tank starts at 8 feet and rises at 0.4 feet per minute. Write its linear function and predict its level after 25 minutes.

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: 30 ft.
    Guided practice, t = 60 minutes: L(60) = 12 + 0.3(60) = 12 + 18 = 30 feet.
  2. Answer: 39 ft.
    Guided practice, t = 90 minutes: L(90) = 12 + 0.3(90) = 12 + 27 = 39 feet. Both predictions match the pattern of the level rising 3 feet every 10 minutes in the original table.
  3. Answer: about 77 min.
    Independent practice question 1: set 35 = 12 + 0.3t. Subtract 12 from both sides: 23 = 0.3t. Divide by 0.3: t ≈ 76.7, which rounds to about 77 minutes.
  4. Answer: L(t) = 12 + 0.5t.
    Independent practice question 2: the initial value stays 12 feet, but the rate of change becomes 0.5 feet per minute once the leak no longer subtracts from the inlet's rate.
  5. Answer: 18 ft.
    Exit ticket: L(t) = 8 + 0.4t, so L(25) = 8 + 0.4(25) = 8 + 10 = 18 feet.

Differentiation

Support (below grade level)

Give students the rate of change (0.3 feet per minute) and initial value (12 feet) already labeled from the table, so they only need to substitute values of t into the function rather than deriving the function from scratch.

Extension (above grade level)

Ask students to determine how many minutes it would take the original tank (starting at 12 feet, rising at 0.3 feet per minute) to reach the same 18-foot level that the exit-ticket tank reaches at t = 25 minutes (18 = 12 + 0.3t, so t = 20 minutes), and compare which tank gets there faster despite its lower rate.

ELL supports

Pre-teach "rate of change," "initial value," and "linear function" using a simple everyday example, such as a savings jar that starts with some coins and gains a fixed number each day, before applying the same structure to the tank. Allow students to show the guided practice predictions as a continued table instead of function notation.

Extensions

Have students measure or research a real rate of change they can observe, such as a classroom sink's fill rate or a plant's growth over several days, build a linear function for it, and compare its structure to the Twin Forks tank function.