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Project Grade 8 Math

Vaudry Bend Outfall Study: A Storm Data Scatter Plot Report

A five-session grade 8 project where teams plot twenty fictional storms, fit a line by eye, and report a rain and turbidity finding to a local board.

Objectives

  1. Students will construct and label a scatter plot from twenty paired storm measurements.
  2. Students will fit a straight line by eye and write its equation in slope-intercept form.
  3. Students will interpret the slope and intercept of their line in the language of the scenario.
  4. Students will explain why a prediction outside the range of the data is not supported.

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, line of fit, slope, intercept, outfall, outlier

Teacher overview

A storm drain outfall is the pipe mouth where street runoff reaches a stream, and the cloudiness of that runoff, measured as turbidity, tells a town how much soil is washing off its surfaces. The driving question of this project is whether bigger storms produce cloudier runoff at the fictional Vaudry Bend outfall, and by how much. Teams work with twenty recorded storms, build one scatter plot, fit a line by eye, and interpret what its slope and intercept mean on the ground. The final deliverable is a two-page data report and a five-minute presentation to a fictional advisory board.

Vaudry Bend Outfall Study: A Storm Data Scatter Plot Report — Grade 8 Math
Name: ____________________________ Date: ______________

Project Brief

You are a student data team. Your client is the fictional Vaudry Bend Stormwater Advisory Board. The board wants to know whether a larger storm brings cloudier water to the outfall.

The town monitored the outfall for one year. For each storm it recorded the rain depth in inches and the turbidity of the runoff. Turbidity is measured in units called NTU. Higher numbers mean cloudier water.

Storm Rain depth (inches) Turbidity (NTU)
1 0.2 12
2 0.3 15
3 0.4 19
4 0.5 24
5 0.6 22
6 0.7 31
7 0.8 35
8 0.9 33
9 1.0 41
10 1.1 45
11 1.2 44
12 1.3 52
13 1.4 55
14 1.5 58
15 1.6 63
16 1.7 61
17 1.8 70
18 1.9 74
19 2.0 78
20 0.9 96

Storm 20 fell while a builder was grading a bare lot upstream of the outfall.

Your work must meet these constraints.

  • Plot all twenty storms. Label both axes with their units.
  • You may leave at most one storm out of your line of fit. Name it and give your reason in writing.
  • Draw the line with a ruler. Write its equation in slope-intercept form.
  • Make predictions only for rain depths from 0.2 inch to 2.0 inches.
  • The report is two pages at most. The presentation is five minutes at most.

Your report must include the labeled scatter plot, a written description of the pattern, your line and its equation, a sentence on what the slope means, a sentence on what the intercept means, two predictions with your work shown, and one recommendation to the board.

Milestones

  1. Session 1, build the plot. Draw and scale both axes. Plot all twenty storms from the fictional Vaudry Bend record. Output: one labeled scatter plot with units on both axes.
  2. Session 2, describe the pattern. Write whether the association is positive or negative. Say whether it looks linear. Name any clustering. Name the one point that sits away from the rest and state which storm it is. Decide whether to leave it out of your line and give your reason. Output: a half page of writing.
  3. Session 3, fit the line. Lay a ruler so that points fall on both sides of it and the gaps are small. Draw the line. Pick two points on the line, find the slope, and write the equation in slope-intercept form. Then write one sentence on what the slope means for the outfall and one sentence on what the intercept means. Output: an annotated graph and two sentences.
  4. Session 4, predict and check. Use your equation to predict the turbidity for a 0.75-inch storm and for a 1.65-inch storm. Show the substitution for each. Then write a short paragraph on why your line should not be used to predict the turbidity of a 4.0-inch storm. Output: a prediction sheet with work shown.
  5. Session 5, report and present. Assemble the two-page report. Present for five minutes to the fictional Vaudry Bend Stormwater Advisory Board, played by classmates. Close with one recommendation the board could act on. Output: the report and the presentation.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Rubric

Score each criterion from 4 down to 1.

Scatter plot construction. 4: All twenty storms are plotted correctly, both axes are scaled evenly, and both carry a label with units. 3: All storms are plotted with one minor scaling or labeling flaw. 2: Several points are misplaced, or one axis lacks units. 1: The plot is incomplete or the axes are unscaled.

Description of the pattern. 4: The description names the direction of association, judges linearity, addresses clustering, identifies storm 20 as the outlier, and gives the grading work as the reason. 3: The description covers direction, linearity, and the outlier but omits one element. 2: The description names the direction only. 1: The description is missing or contradicts the plot.

Line of fit and equation. 4: The line has points on both sides with small gaps, the slope is computed from two points on the line, and the equation is correct in slope-intercept form. 3: The line is reasonable and the equation is correct, but the slope work is not shown. 2: The line is drawn through only the highest and lowest points, or the equation has one error. 1: No line is drawn, or no equation is written.

Use of the constraints in prediction. 4: Both predictions fall inside the stated range, the substitution is shown for each, and the paragraph explains that a 4.0-inch storm lies far outside the recorded data. 3: Both predictions are correct but the explanation of the range is thin. 2: One prediction is outside the allowed range, or no work is shown. 1: Predictions are absent or unsupported.

Report and presentation. 4: The report holds every required element within two pages, the recommendation follows from the line, and the presentation runs within five minutes. 3: One required element is thin, or the presentation runs slightly long. 2: Two or more elements are missing, or the recommendation does not follow from the data. 1: The report is incomplete and the presentation is not delivered.

Differentiation

Support

Give these teams graph paper with both axes already scaled for the fictional Vaudry Bend data and the first five storms already plotted. Supply a line-of-fit guide strip of clear plastic so the line can be positioned before it is drawn, and provide the sentence frames "As rain depth increases, turbidity ___" and "The slope means that each extra inch of rain adds about ___ units of turbidity."

Extension

Ask these teams to split the record into storms under one inch and storms of one inch or more, fit a separate line to each half, and compare the two slopes. They should then write a short paragraph arguing either that one line describes the fictional Vaudry Bend outfall well enough or that two lines describe it better, citing the gaps between their lines and the points.

ELL supports

Pre-teach outfall, turbidity, runoff, and grading with a labeled drawing of a street, a storm drain, a pipe, and a stream, plus two jars of water, one clear and one cloudy. Post a word bank with positive association, negative association, outlier, slope, and intercept, each beside a small sketch. Allow the session 2 description to be recorded orally before it is written, and provide a partly completed presentation outline for session 5.

Extensions

Have teams design the next year of monitoring for the fictional Vaudry Bend outfall. They should state how many storms to sample, which rain depths are missing from the current record, and what extra measurement would help explain points such as storm 20. Ask them to write the plan as a one-page memo to the board and to name the single change that would most improve the line of fit.