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Lesson plan Grade 8 Math

Alderbrook Water Tank: Reading and Sketching Level Graphs

A 50-minute grade 8 lesson where students describe and sketch qualitative graphs of a fictional town's water-tank level rising, holding, and falling across a day.

Objectives

  1. Students will describe qualitatively how a graph increases, stays constant, and decreases.
  2. Students will sketch a graph that matches a verbal description of a tank filling and draining.

Vocabulary

Key words: increasing, decreasing, constant, rate of change

Teacher overview

The water level in an elevated tank rises overnight when demand is low, holds steady, then falls quickly during the morning peak before the pumps refill it, which makes its level over a day a clear story to read from a graph. This lesson has students describe those intervals qualitatively and sketch a graph from a verbal description, using a fictional town's tank. A common misconception this lesson addresses is reading a higher point on the graph as a faster change; students learn that steepness, not height, shows how fast the level is changing.

Procedure

Hook (5 min): Project a simple line graph of a water tank's level over 24 hours without labels and ask students to describe, in plain words, what is happening to the water at three different parts of the graph. Collect two or three descriptions aloud without judging them.

Direct instruction (12 min): Introduce the language of qualitative graphs: increasing, decreasing, and constant, and the idea that a steeper part of the line means a faster rate of change. Work the Alderbrook example: from midnight to 6 a.m. the level holds at 40 feet (constant), from 6 to 9 a.m. it falls from 40 feet to 22 feet (decreasing, and steep), and from 3 to 9 p.m. it rises back to 40 feet (increasing). Show how the average rate of change from hour 6 to hour 9 is (22 - 40) / (9 - 6) = -6 feet per hour.

Guided practice (13 min): As a class, sketch a graph for a verbal description of a different tank: it fills steadily all morning, holds at midday, and drains steadily all afternoon. Have students name which parts are increasing, constant, and decreasing as you draw, and mark where the line is steepest.

Independent practice (15 min): Students complete the Student Handout, describing the Alderbrook graph and sketching a graph from a verbal story.

Closure and exit ticket (5 min): On an index card, students answer: "A tank's level graph is flat for three hours. What is happening to the water during that time?" Collect and check that students connect a flat line to a constant level. If more than a few miss it, revisit the constant interval before the next lesson.

Alderbrook Water Tank: Reading and Sketching Level Graphs — Grade 8 Math
Name: ____________________________ Date: ______________

Student Handout

Alderbrook is a fictional town. Its water tank was measured every three hours for one day. The level, in feet, is shown below. Read the table from left to right, as you would read a graph.

Time Midnight 3 a.m. 6 a.m. 9 a.m. Noon 3 p.m. 6 p.m. 9 p.m.
Level (ft) 40 40 40 22 16 16 34 40
  1. During which time periods is the tank level staying about the same (constant)?
  2. During which three-hour interval does the level fall the fastest?
  3. Between 6 a.m. and 9 a.m. the level drops from 40 feet to 22 feet. Find the average rate of change in feet per hour.
  4. During which hours is the tank refilling (the level increasing)?
  5. Is the whole day's graph a single straight line, or does it bend? Explain how you know.
  6. Sketch a graph for a second tank described this way: it fills steadily from empty all morning, holds steady at midday, then drains steadily to empty by evening. Label which parts are increasing, constant, and decreasing.

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: Midnight to 6 a.m., and noon to 3 p.m.
    The level holds at 40 feet from midnight to 6 a.m., and at 16 feet from noon to 3 p.m., so it is constant during those periods.
  2. Answer: 6 a.m. to 9 a.m.
    The level drops 18 feet (from 40 to 22) in that interval, the largest drop of any three-hour period, so it is the steepest, fastest fall.
  3. Answer: -6 feet per hour.
    (22 - 40) / (9 - 6) = -18 / 3 = -6 feet per hour. The negative sign shows the level is falling.
  4. Answer: 3 p.m. to 9 p.m.
    The level rises from 16 feet at 3 p.m. to 34 feet at 6 p.m. and 40 feet at 9 p.m., so it is increasing across those hours.
  5. Answer: It bends; the graph is not a single straight line.
    Different intervals have different slopes (flat, then steeply down, then up), so the graph is made of several segments rather than one straight line.
  6. Answer: A graph that rises, then is flat, then falls.
    The morning part slopes upward (increasing), the midday part is a flat horizontal segment (constant), and the afternoon part slopes downward (decreasing) back to zero.

Differentiation

Support

Provide the Alderbrook data already plotted as a line graph so students describe the shape rather than build it, and give them a word bank (increasing, decreasing, constant, steep) to label each interval.

Extension

Ask students to write their own verbal story for a tank that has four different intervals, trade with a partner, and each sketch the other's graph. They should then compare sketches and resolve any differences by pointing to the words in the story.

ELL supports

Pair each vocabulary word with a hand motion (rising hand for increasing, flat hand for constant, lowering hand for decreasing) and use them while describing the graph. Provide sentence frames such as "From ___ to ___ the level is ___."

Extensions

If your facilities team can share a real tank-level trend chart, or a photo of one from a public works report, have students describe its increasing, constant, and decreasing parts using the same language, and identify the steepest interval of the real day.