Project Grade 11 Math

Does Turbidity Predict Bacteria? A Creek Monitoring Regression Project

A grade 11 investigation pairing turbidity and bacteria readings from a fictional creek to fit a regression, assess the fit, and evaluate a data-based safety claim.

Grade: Grade 11
Subject: Math
Material: Project
Time: 4 sessions, ~220 min total
Prep: Moderate prep
Materials: Turbidity tube or meter, Sample bottles, Disposable gloves, Graphing technology, Provided dataset and safety protocol

Standards

HSS-ID.B.6 Common Core Math

Represent data on two quantitative variables on a scatter plot, and describe how the variables are related, including fitting a function to the data, using functions fitted to data to solve problems, and informally assessing the fit of a function by plotting and analyzing residuals.

How this material aligns: In the analysis milestone, teams fit a least-squares line to paired turbidity and bacteria data, use it to predict, and assess the fit by plotting and reading residuals.

All materials for HSS-ID.B.6 →

HSS-IC.B.6 Common Core Math

Evaluate reports based on data.

How this material aligns: In the final milestone, teams evaluate a developer's data-based safety claim, judging its sample size and reasoning against their own regression before presenting a verdict.

All materials for HSS-IC.B.6 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-23.

Objectives

Students will fit a regression line to paired turbidity and bacteria data and assess its fit with residuals and a correlation coefficient.
Students will evaluate a data-based claim about creek safety for statistical soundness.

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: regression line, residual, correlation coefficient

Teacher overview

Cloudy water often carries more bacteria, because the same runoff that stirs up sediment also washes in waste. Water agencies sometimes use turbidity, which is quick and cheap to measure, as a stand-in for bacteria, which takes a lab and a day to count. This project asks whether that shortcut holds up for one fictional creek. Over four sessions, teams collect or use paired turbidity and bacteria readings, fit a regression line, judge how well it fits, and then test a real-world style claim against their own data. The driving question is whether turbidity is a trustworthy predictor of bacteria in this creek.

Does Turbidity Predict Bacteria? A Creek Monitoring Regression Project — Grade 11 Math

Name: ____________________________ Date: ______________

Project Brief

Driving question: In Hollow Brook, does turbidity predict the bacteria count well enough to use as a warning signal?

Scenario: Hollow Brook (a fictional creek used for this project) runs past a proposed housing site. A developer has claimed the creek is safe for a planned swimming area, citing a single clear-water sample. A fictional watershed council has asked student teams to investigate whether turbidity and bacteria move together in the creek, and to weigh the developer's claim.

Hypothesis and variables: Each team writes a testable hypothesis, such as "higher turbidity is associated with higher bacteria counts." The independent variable is turbidity (measured in NTU), and the dependent variable is the bacteria count (measured as E. coli, in MPN per 100 milliliters).

Constraints:

Teams use at least 8 paired samples, gathered across different sites or different weather days so the turbidity values span a wide range.
All sampling follows the provided safety protocol under adult supervision; students never enter moving water, handle samples with gloves, never taste or drink creek water, and wash their hands afterward.
Teams without lab access use the provided Hollow Brook dataset instead of collecting their own bacteria counts.

Final deliverable: A short written report and a class presentation to the fictional watershed council that includes the scatter plot, the fitted line, the correlation coefficient, a residual check, and a clear judgment on the developer's single-sample claim.

Milestones

Session 1 (Question and plan): Teams write their driving question, hypothesis, and variables, and draft a sampling plan naming sites, the number of paired samples, and safety steps. Output: a one-page research plan.
Session 2 (Collect the data): Teams gather at least 8 paired turbidity and bacteria readings, or record the provided Hollow Brook dataset below, and organize the pairs in a table. Output: a completed data table. The provided fallback dataset pairs turbidity in NTU with E. coli in MPN per 100 milliliters: (3, 40), (5, 75), (8, 120), (12, 210), (15, 260), (20, 410), (28, 590), (35, 720).
Session 3 (Fit and check): Teams make a scatter plot, fit a least-squares line with technology, compute the correlation coefficient, and plot residuals to judge the fit. Output: a scatter plot with the line, the correlation coefficient, and a short residual note.
Session 4 (Evaluate and present): Teams use their line and fit to weigh the developer's single clear-water claim, decide whether one sample can support a safety conclusion, and present their verdict to the class acting as the watershed council. Output: the written report and presentation.

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

Rubric

Criterion	Emerging	Developing	Proficient	Advanced
Investigation design	No clear hypothesis or variables	States a hypothesis but the sampling plan misses the range or safety constraint	Clear hypothesis, named variables, and a plan meeting the 8-sample and safety constraints	Design also justifies why the chosen sites span a wide turbidity range for a stronger fit
Regression analysis	No line or correlation reported	Line drawn but no residual or correlation coefficient	Fitted line, correlation coefficient, and a residual check are all present and correct	Analysis interprets the correlation coefficient and residual pattern to state how far the line can be trusted
Evaluating the claim	Restates the developer's claim without testing it	Notes the single sample but does not connect it to the data	Uses the team's data to explain why one clear-water sample cannot establish safety	Weighs sample size and the residual spread to give a measured, evidence-based verdict
Presentation and report	Report is incomplete or hard to follow	Report covers the analysis but omits the plot or the verdict	Report and talk clearly present the plot, fit, and verdict to the council	Presentation also anticipates a likely council question and answers it with the data

Differentiation

Support

Provide the fallback dataset already entered in graphing technology and a screenshot showing where the fitted line and correlation coefficient appear, so teams can focus on interpreting rather than setting up the tool. Give a checklist for the research plan in Session 1.

Extension

Ask teams to predict the bacteria count at a turbidity the dataset does not include, then explain why extrapolating beyond the sampled range is riskier than predicting within it, tying the argument to their residual plot.

ELL supports

Pre-teach "turbidity," "bacteria," "predict," and "residual" with a labeled image of clear and cloudy water samples. Provide a report template with headed sections and sentence frames such as "Our correlation coefficient was ___, which means the fit is ___."

Extensions

Teams can invite a local watershed or utility staff member to hear the presentations and comment on how the agency actually uses turbidity as an early warning, turning the project's verdict into a question the class can ask a working professional.