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Classroom activity Grade 8 Math

Birchhollow Creek Human Scatter Plot: Rain and Turbidity

A grade 8 activity in which students stand on a taped floor grid to build a class scatter plot of rainfall and turbidity from a fictional creek's sample cards.

Objectives

  1. Students will build a class scatter plot by standing at the coordinates on a sample card.
  2. Students will describe the association between rainfall and turbidity and locate the outlier.
  3. Students will use a given line of fit to predict turbidity and judge the prediction.

Vocabulary

Turbidity
Turbidity is a measure of how cloudy or murky water looks because of tiny particles floating in it. Clear water has low turbidity, and muddy water has high turbidity.

Also: scatter plot, association, outlier, line of fit

Teacher overview

Turbidity measures how cloudy water is, and it rises when rain washes soil into a stream. Sampling crews record both the rain in the past day and the turbidity of the sample, which makes a natural pair of variables for a scatter plot. In this activity the class becomes the plot: each pair of students holds one sample card from the fictional Birchhollow Creek and stands at the matching spot on a taped floor grid, so the pattern appears before anyone draws an axis. Teaching note: eighth graders often call any point at the edge of a plot an outlier, including the highest and lowest rainfall values, when an outlier is a point far from the pattern rather than far along an axis. The card at 0.4 inch of rain is placed deliberately to make that distinction visible.

Activity Directions

Setup, about 10 minutes before class. Lay masking tape on the floor to form a grid for the fictional Birchhollow Creek data. Mark the horizontal axis from 0 to 2.5 inches of rain in steps of 0.1 inch, and the vertical axis from 0 to 45 in steps of 5. Write each of the sixteen sample cards from the handout on an index card.

  1. Hand one sample card to each pair of students. If the class has fewer than sixteen pairs, give some pairs a second card and have them set it on the floor at its point.
  2. Ask each pair to read its card aloud, naming the rain first and the turbidity second, so the class hears sixteen ordered pairs before anyone moves.
  3. Send pairs to the grid one at a time, in order of rainfall from least to greatest. Have each pair stand at the point their card names and stay there.
  4. Once every pair is standing, ask the class from the side of the room whether the points rise or fall from left to right, and whether they follow a line or a curve.
  5. Stretch a length of string across the room so that it passes through the points at 0.0 inch and 2.0 inches of rain. Tell the class this string represents the line t = 3 + 19r.
  6. Ask every student who is standing above the string to raise a hand, and then every student below it. Point out that one pair stands far above the string while the rest stand close to it.
  7. Have that far pair read its card aloud, and tell the class that this sample came from a site just downstream of a construction project in the fictional town of Birchhollow.
  8. Send students back to their seats with the handout and have them redraw the class plot on graph paper before answering the items.
Birchhollow Creek Human Scatter Plot: Rain and Turbidity — Grade 8 Math
Name: ____________________________ Date: ______________

Student Handout

Birchhollow Creek is fictional. A sampling crew recorded the rain in the 24 hours before each sample and the turbidity of the sample in NTU.

Card Rain (inches) Turbidity (NTU)
A 0.0 3
B 0.1 5
C 0.2 6
D 0.3 9
E 0.4 22
F 0.5 12
G 0.6 14
H 0.7 16
I 0.8 18
J 0.9 20
K 1.0 21
L 1.1 25
M 1.2 26
N 1.4 30
O 1.6 33
P 2.0 41

The class agreed on the line of fit t = 3 + 19r, where r is the rain in inches and t is the turbidity in NTU.

  1. Describe the association between rain and turbidity for this fictional creek.
  2. One card sits far above the pattern. How much rain is on that card?
  3. Use the class line to find the turbidity it predicts for 1.5 inches of rain.
  4. What does the number 19 in the equation mean for Birchhollow Creek?
  5. What does the number 3 in the equation mean?
  6. Use the class line to predict the turbidity after 3.0 inches of rain.
  7. Explain why the prediction in item 6 is less trustworthy than the prediction in item 3.
  8. Finished drinking water must stay at or below 0.3 NTU in nearly all samples. Explain what a treatment plant must do on a day when this fictional creek reaches 41 NTU.

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: Positive and roughly linear.
    As rain increases, turbidity increases, and the points follow a straight path rather than a curve. Apart from one card, the points sit close to the line.
  2. Answer: 0.4 inch.
    Card E pairs 0.4 inch of rain with 22 NTU, while the line predicts 3 + 19(0.4) = 10.6 NTU. The gap of about 11.4 NTU is far larger than any other gap in the table.
  3. Answer: 31.5 NTU. t = 3 + 19(1.5) = 3 + 28.5 = 31.5 NTU.
  4. Answer: 19 NTU per inch.
    Each additional inch of rain in the past day raises the predicted turbidity by about 19 NTU, so 19 is the slope.
  5. Answer: 3 NTU.
    With no rain in the past day, the line predicts about 3 NTU, which is the creek's ordinary clear-weather cloudiness.
  6. Answer: 60 NTU. t = 3 + 19(3.0) = 3 + 57 = 60 NTU.
  7. Answer: 3.0 inches is outside the data.
    The samples run from 0.0 inch to 2.0 inches of rain, so 1.5 inches sits inside that range while 3.0 inches sits well beyond it. Nothing in the data shows whether the pattern continues that far.
  8. Answer: Treat the water much harder before it leaves the plant.
    Raw water at 41 NTU is far cloudier than the 0.3 NTU that finished water must meet, so the plant must add more coagulant, allow more settling time, and watch its filters closely. Some plants slow production on very muddy days to keep the finished water within the limit.

Differentiation

Support

Give students a printed grid for the fictional Birchhollow data with the line t = 3 + 19r already drawn, and ask them to plot only the sixteen points. Provide a worked example for item 3 using 1.0 inch of rain so the substitution pattern is visible before they try 1.5 inches.

Extension

Ask students to remove card E from the fictional data set, draw a new line of fit by eye, and explain in writing how much the removal changed the slope. Have them argue whether a sampling crew should keep or discard a reading taken next to a construction site.

ELL supports

Pre-teach turbidity, outlier, and line of fit by comparing two jars of water, one clear and one stirred with soil, and by pointing to one point far from a drawn line. Provide the sentence frame for item 1: "When rain goes ___, turbidity goes ___, so the association is ___."

Extensions

With adult supervision, have students collect turbidity readings from the bank of a local stream using a simple turbidity tube on several days with different weather, and add their own points to a copy of the fictional Birchhollow plot. Students should stay out of the water, skip any visit when the stream is high or fast-moving, and wash their hands after handling samples. Ask them to decide whether their local points follow the same slope and to explain what soil type or land use might account for a difference.