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Worksheet Grade 8 Math

Glassmere Chlorine Residual: A Distribution-System Scatter Plot

A grade 8 worksheet where students plot a fictional utility's chlorine readings against distance, then describe the negative association and spot an outlier.

Objectives

  1. Students will construct a scatter plot from a table of paired measurements.
  2. Students will describe the association as positive or negative and identify an outlier.

Vocabulary

Chlorine residual
Chlorine residual is the small amount of chlorine still left in the water after it leaves the treatment plant. It keeps protecting the water from germs all the way to your faucet.

Also: scatter plot, association, outlier

Teacher overview

Glassmere is a fictional town whose water crew tests the chlorine level, called the chlorine residual, at ten points along one pipe route leaving the plant. Chlorine is added at the plant and slowly used up as water travels, so the readings drop with distance. This worksheet has students plot that data, name the pattern, and find the one point that does not fit. A common mistake is calling a single off-trend point a change in the pattern; students should learn to mark it as an outlier and look for a reason behind it.

Glassmere Chlorine Residual: A Distribution-System Scatter Plot — Grade 8 Math
Name: ____________________________ Date: ______________

Student Worksheet

The fictional Glassmere water crew measured the chlorine residual at ten test points along one pipe. Distance is measured in miles from the plant. Use this table for every item.

Distance from plant (miles) Chlorine residual (mg/L)
0.5 1.8
1.0 1.6
1.5 1.5
2.0 1.3
2.5 1.2
3.0 1.0
3.5 0.9
4.0 1.7
4.5 0.6
5.0 0.5
  1. Plot all ten points on a grid, with distance on the horizontal axis and chlorine residual on the vertical axis.
  2. As distance from the plant increases, does the chlorine residual generally go up or down?
  3. Is the association between distance and residual positive or negative?
  4. Does the pattern look roughly linear or clearly nonlinear?
  5. One point does not fit the pattern. Give its distance and its residual.
  6. The off-trend point was sampled at a tap on a short side line fed by a small booster station that adds more chlorine. Explain why that point is higher than the pattern around it.
  7. Ignore the off-trend point. Estimate the residual you would expect at 2.75 miles.
  8. Ignore the off-trend point. By about how much does the residual drop from 0.5 mile to 5.0 miles?
  9. The crew wants the residual to stay at or above 0.5 mg/L everywhere. Does the point at 5.0 miles meet that target?
  10. Explain your reasoning: Why does the chlorine residual tend to fall as water travels farther from the plant?

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: a scatter plot of the ten points.
    Points are plotted at (0.5, 1.8), (1.0, 1.6), (1.5, 1.5), (2.0, 1.3), (2.5, 1.2), (3.0, 1.0), (3.5, 0.9), (4.0, 1.7), (4.5, 0.6), and (5.0, 0.5). Distance goes on the horizontal axis and residual on the vertical axis.
  2. Answer: down.
    The residual generally decreases as distance increases, from about 1.8 near the plant to 0.5 at the far point.
  3. Answer: negative.
    When one quantity goes up while the other goes down, the association is negative.
  4. Answer: roughly linear.
    Apart from one point, the readings fall at a fairly steady rate, so a straight line would fit them well.
  5. Answer: 4.0 miles, 1.7 mg/L.
    The point (4.0, 1.7) sits well above the falling trend, so it is the outlier.
  6. Answer: That tap gets water that was just re-chlorinated at the booster station, so its residual is higher than the readings on the main route around it, which is why the point sits above the pattern.
  7. Answer: about 1.1 mg/L.
    At 2.5 miles the residual is 1.2 and at 3.0 miles it is 1.0, so a point at 2.75 miles should be about halfway between, near 1.1 mg/L.
  8. Answer: 1.3 mg/L.
    The residual drops from 1.8 at 0.5 mile to 0.5 at 5.0 miles: 1.8 - 0.5 = 1.3 mg/L.
  9. Answer: yes.
    The reading at 5.0 miles is exactly 0.5 mg/L, which meets the "at or above 0.5" target, though only just.
  10. Answer: Chlorine reacts with material in the pipes and in the water as it travels, so the amount left keeps getting used up, and the residual falls the farther the water is from where the chlorine was added.

Differentiation

Support

Provide a grid with the axes already labeled and scaled, and plot the first two points as worked examples. Let students use a straightedge to see the trend before answering items 3 and 4.

Extension

Ask students to sketch a straight line that fits the data with the outlier removed, then use the line to predict the residual at 6 miles and explain whether they trust a prediction beyond the measured range.

ELL supports

Pre-teach "residual," "association," and "outlier" with a simple picture: a line of dots going down and one dot jumping above the line. Provide sentence frames for items 2 and 3: "As distance goes up, residual goes ___," and "The association is ___."