Worksheet Grade 6 Engineering & Design

Corrigan Bend Water-Quality Sampling Plan Worksheet

Nine items where students size a river water-quality sampling plan against a coverage rule and a fixed budget, then compare a bulk-price alternative.

Grade: Grade 6
Subject: Engineering & Design
Material: Worksheet
Time: 35 min
Prep: No prep
Materials: None

Standards

MS-ETS1-1 NGSS

Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

How this material aligns: Items 1 through 4 require students to define how many sampling locations satisfy the every-2-mile coverage rule and test that plan against the $900 sampling budget constraint.

All materials for MS-ETS1-1 →

6.RP.A.3 Common Core Math

Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations, including finding a percent of a quantity and converting measurement units.

How this material aligns: Items 5 and 9 ask students to find percents of a quantity, such as what percent of the original plan's coverage or the sampling budget a revised plan represents, and item 7 finds a unit price per test.

All materials for 6.RP.A.3 →

Download Word file

This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will calculate how many sampling locations are needed to meet a stated coverage requirement along a river.
Students will check a sampling plan's total cost against a fixed budget.
Students will calculate percents of a quantity to compare an original sampling plan with a revised plan.

Vocabulary

Key words: sampling, coverage, constraint, bulk discount

Teacher overview

Corrigan Bend's water utility (a fictional utility used for this worksheet) wants to test water quality along a stretch of river and needs a sampling plan that covers the river thoroughly without going over budget. This worksheet has students calculate how many sampling locations a coverage rule requires, check that plan's cost against a fixed budget, and compare the coverage and cost of an adjusted plan using percents, the kind of budget-versus-coverage tradeoff a real monitoring program must work through.

Corrigan Bend Water-Quality Sampling Plan Worksheet — Grade 6 Engineering & Design

Name: ____________________________ Date: ______________

Student Worksheet

All distances, prices, and budgets on this worksheet are fictional, invented for the Corrigan Bend scenario. The utility's rule is to test the river every 2 miles along its 20-mile length, starting at mile 0 (the source) and continuing through mile 20 (the river's mouth). Each water-quality sampling kit costs $85. The utility's sampling budget is $900.

How many sampling locations are needed to test the river every 2 miles from mile 0 through mile 20, counting a location at both mile 0 and mile 20?
Find the total cost of testing every location from problem 1, at $85 per kit.
Does the plan in problem 2 fit within the $900 budget? By how many dollars is it over or under?
To fit the $900 budget, the utility considers testing fewer locations. At $85 per kit, what is the greatest number of locations it can afford with a $900 budget?
If the utility tests only 10 locations instead of the 11 from problem 1, what percent of the original 11-location plan's coverage is that? Round to the nearest whole percent.
Instead of removing a location, the utility asks a lab for a bulk price: all 11 tests for one flat fee of $800 instead of $85 each. Does this bulk fee fit within the $900 budget? By how many dollars is it under or over?
Find the bulk per-test price in problem 6 by dividing the $800 flat fee by 11 tests. Round to the nearest cent.
How much does the utility save per test with the bulk deal (problem 7) compared with the regular $85 price? Round to the nearest cent.
Using the bulk deal from problem 6, what percent of the $900 budget does the sampling plan use? Round to the nearest whole percent.

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

Answer Key

Answer: 11 locations. Testing every 2 miles from mile 0 through mile 20 gives locations at 0, 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20, which is 11 locations in all, since the location at mile 0 must be counted along with every 2-mile mark after it.
Answer: $935. 11 locations times $85 per kit equals $935.
Answer: Over by $35. $935 minus $900 equals $35 over budget.
Answer: 10 locations. $900 divided by $85 equals 10.588, so the utility can afford 10 full-price locations (10 times $85 equals $850), with $50 left over; an 11th location would bring the total to $935, which is over budget.
Answer: 91 percent. 10 divided by 11 equals 0.9091, which rounds to 91 percent.
Answer: Under by $100. $900 minus $800 equals $100 under budget, so the bulk fee fits.
Answer: $72.73 per test. $800 divided by 11 equals $72.7272, which rounds to $72.73.
Answer: $12.27 per test. $85.00 minus $72.73 equals $12.27 saved per test.
Answer: 89 percent. $800 divided by $900 equals 0.8889, which rounds to 89 percent.

Differentiation

Support

Provide a printed number line from mile 0 to mile 20 marked every 2 miles, so students can count sampling locations directly from the diagram before calculating problem 1, and allow a calculator for every division problem.

Extension

Ask students to find a coverage rule (testing every how many miles) that would require exactly 6 sampling locations along the same 20-mile river, including a location at both mile 0 and mile 20.

ELL supports

Provide a labeled river diagram showing the 20-mile stretch with sampling dots already placed every 2 miles, connecting the vocabulary word "location" to a visual point on the map. Allow students to show their division and percent work as numbers in a simple two-column chart rather than full sentences.

Extensions

Have students research, using a teacher-provided map, a real river or stream near their school and propose their own every-so-many-miles sampling rule for it, calculating how many locations that rule would require.