Worksheet Grade 8 Careers & CTE

Nordhaven's Overnight Tank Trend: Reading an Operator's Chart

A grade 8 worksheet where students read a fictional utility's overnight tank-level log, find rates of change, build a linear function, and predict an overflow time.

Grade: Grade 8
Subject: Careers & CTE
Material: Worksheet
Time: 45 min
Prep: No prep
Materials: Calculator, Graph paper

Standards

8.F.A.1 Common Core Math

Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.

How this material aligns: Item 1 asks students to justify that tank level is a function of time because each recorded hour has exactly one water level.

All materials for 8.F.A.1 →

8.F.B.4 Common Core Math

Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description, a table, or a graph, and interpret them in terms of the situation modeled.

How this material aligns: Items 3, 5, and 6 have students find the rate of change from the log table and write the linear function for the level after midnight, naming its initial value.

All materials for 8.F.B.4 →

8.F.B.5 Common Core Math

Describe qualitatively the functional relationship between two quantities by analyzing a graph, and sketch a graph that exhibits the qualitative features of a function described verbally.

How this material aligns: Item 10 asks students to describe qualitatively the falling and rising sections of the overnight graph and where the direction changes.

All materials for 8.F.B.5 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-03.

Objectives

Students will determine rates of change from an hourly tank-level log.
Students will write a linear function for a tank filling and use it to predict a later level.
Students will describe the shape of a tank-level graph and explain what causes each section.

Vocabulary

Key words: storage tank, rate of change, initial value, linear function, overflow

Teacher overview

Every water utility with an elevated tank has someone watching the tank level overnight, because that stored water is what carries a town through the morning demand peak and through a fire. Operators read the level as a trend that falls while customers use water and rises while a pump refills the tank. This worksheet gives students an hour-by-hour log from a fictional utility and asks the questions an operator answers from it. The misconception it targets is reading a negative rate of change as a smaller number rather than as a direction, which leads students to describe a tank that is emptying at 1.2 feet per hour as filling slowly.

Nordhaven's Overnight Tank Trend: Reading an Operator's Chart — Grade 8 Careers & CTE

Name: ____________________________ Date: ______________

Student Worksheet

Imagine you are the overnight operator for Nordhaven Water District, a fictional utility. The Hill Street tank is a standpipe, and the depth of water in it is recorded every hour. All readings below were invented for this worksheet. The pump that refills the tank was off at the start of the night and started later.

Time	Water depth (feet)
8:00 p.m.	32.4
9:00 p.m.	31.2
10:00 p.m.	30.0
11:00 p.m.	28.8
12:00 midnight	27.6
1:00 a.m.	28.5
2:00 a.m.	29.4
3:00 a.m.	30.3
4:00 a.m.	31.2
5:00 a.m.	32.1
6:00 a.m.	33.0

Is the tank's water depth a function of the time of night? Explain your reasoning using the log.
How much did the depth change between 8:00 p.m. and 11:00 p.m.? Write your answer as a signed number of feet.
What was the rate of change in feet per hour between 8:00 p.m. and midnight? Show your work.
Between which two readings did the depth stop falling and start rising?
What was the rate of change in feet per hour between midnight and 4:00 a.m.? Show your work.
Let h be the number of hours after midnight. Write a linear function for the depth L in feet, and state what the initial value represents.
Use your function to predict the depth at 7:00 a.m., which is 7 hours after midnight.
The tank overflows at a depth of 35.0 feet. Using your function, how many hours after midnight would the depth reach 35.0 feet if the pump kept running? Round to the nearest tenth.
Suppose the pump had never started and the depth had kept falling at the rate you found in item 3. What would the depth have been at 4:00 a.m.?
Describe the shape of a graph of depth against time for this whole night, from 8:00 p.m. to 6:00 a.m.
Explain why the depth falls during the evening and rises after midnight, using what you know about when people use water.

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: Yes.
Each time in the log has exactly one recorded depth, which is what makes the relationship a function. No hour is paired with two different depths.
Answer: -3.6 feet.
28.8 - 32.4 = -3.6, so the depth fell 3.6 feet over those three hours.
Answer: -1.2 feet per hour.
From 8:00 p.m. to midnight is 4 hours, and the depth went from 32.4 to 27.6 feet. Change is 27.6 - 32.4 = -4.8 feet, and -4.8 divided by 4 = -1.2 feet per hour. The sign shows the tank is emptying.
Answer: Between midnight and 1:00 a.m.
The depth reached its lowest reading of 27.6 feet at midnight, then rose to 28.5 feet at 1:00 a.m.
Answer: 0.9 feet per hour.
From midnight to 4:00 a.m. is 4 hours, and the depth went from 27.6 to 31.2 feet. Change is 31.2 - 27.6 = 3.6 feet, and 3.6 divided by 4 = 0.9 feet per hour.
Answer: L = 27.6 + 0.9h.
The initial value 27.6 is the depth at midnight, when h = 0, and 0.9 is the rate of change in feet per hour while the pump runs.
Answer: 33.9 feet.
L = 27.6 + 0.9(7) = 27.6 + 6.3 = 33.9 feet. The log supports the function, since h = 6 gives 27.6 + 5.4 = 33.0 feet, matching the 6:00 a.m. reading.
Answer: 8.2 hours.
Solve 27.6 + 0.9h = 35.0. Subtract 27.6 from both sides: 0.9h = 7.4. Divide by 0.9: h = 8.22, which rounds to 8.2 hours after midnight, a little after 8:00 a.m.
Answer: 22.8 feet.
Starting from 27.6 feet at midnight and falling 1.2 feet per hour for 4 hours gives 27.6 - 4(1.2) = 27.6 - 4.8 = 22.8 feet.
Answer: A V shape.
The graph falls in a straight line from 8:00 p.m. to midnight, reaches its lowest point at midnight, then rises in a straight line to 6:00 a.m. The rising side is less steep than the falling side, because 0.9 is smaller than 1.2 in size.
Answer: Customer demand is high in the evening and low overnight.
In the evening, people cook, shower, and wash dishes, so water leaves the tank faster than the pump would refill it. After midnight demand drops, so the operator runs the pump and the tank refills before the morning rush begins.

Differentiation

Support

Provide the table with a third column already labeled "change from the hour before" and the first two rows filled in, so students see the constant difference before they compute a rate. Give the function frame "L = (depth at midnight) + (feet per hour)h" for item 6.

Extension

Ask students to write a second function for the falling part of the night, using hours after 8:00 p.m. as the input, then find the time at which the two functions would predict the same depth if both continued.

ELL supports

Pre-teach "rate of change," "initial value," and "overflow" with a drawing of a standpipe marked at the lowest and highest depths from this invented log. Allow items 10 and 11 to be answered with a labeled sketch plus short phrases rather than full sentences.

Extensions

Have students graph the log on graph paper with time on the horizontal axis and depth on the vertical axis, then mark the point where the direction changes and label it as the moment the pump started. Ask them to write one sentence explaining what an operator would do if the depth kept falling after the pump was turned on.