Math problem set Grade 6 Engineering & Design

Bellcreek Filter Club Budget and Unit-Cost Problems

Eight problems where a fictional engineering club tracks filter-material costs, budget percentages, and bulk pricing using a fixed $6.00 team budget.

Grade: Grade 6
Subject: Engineering & Design
Material: Math problem set
Time: 40 min
Prep: No prep
Materials: calculator (optional)

Standards

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: Problems 3 and 7 ask students to find what percent of the $6.00 team budget a purchase represents or leaves unspent, and problem 4 compares a bulk unit price with the regular unit price, applying ratio, rate, and percent reasoning to a real budgeting constraint.

All materials for 6.RP.A.3 →

6.NS.B.3 Common Core Math

Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.

How this material aligns: Every problem requires fluent decimal addition, subtraction, multiplication, or division of dollar amounts such as the $0.75 and $1.25 scoop prices on the club's supply list.

All materials for 6.NS.B.3 →

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

Objectives

Students will calculate the total cost of a filter design using given per-scoop and per-item prices.
Students will find what percent of a fixed budget a purchase represents or leaves unspent.
Students will compare a bulk unit price with a regular unit price to determine which is cheaper.

Vocabulary

Key words: unit price, budget, percent, bulk price

Teacher overview

The Bellcreek Middle School engineering club (a fictional after-school club used for this problem set) is designing model water filters for an upcoming school design fair. Each team works within a fixed $6.00 materials budget (a fictional club budget) and buys gravel, sand, activated charcoal, cotton layers, and coffee filters from a supply price list. A common misconception in this set is finding "percent of budget spent" by dividing the budget by the cost instead of the cost by the budget, which produces a number greater than 1 instead of a proper percent; watch for that reversed division in problems 3 and 7.

Bellcreek Filter Club Budget and Unit-Cost Problems — Grade 6 Engineering & Design

Name: ____________________________ Date: ______________

Problems

The club's supply price list: gravel $0.75 per scoop, sand $0.50 per scoop, activated charcoal $1.25 per scoop, cotton layer $0.40 each, coffee filter $0.60 each. Every team has a $6.00 budget (fictional prices used for this problem set).

Team A buys 2 scoops of gravel, 1 scoop of sand, and 1 coffee filter. Find the total cost.
How much of Team A's $6.00 budget is left after the purchase in problem 1?
What percent of the $6.00 budget did Team A spend in problem 1? Round to the nearest whole percent.
Gravel normally costs $0.75 per scoop, but the club can buy it in bulk: 5 scoops for $3.25. Find the bulk price per scoop, and state whether the bulk price is cheaper or more expensive than the regular price.
Team C builds a five-part filter: 1 scoop each of gravel, sand, and activated charcoal, plus 1 cotton layer and 1 coffee filter. Find the total cost.
Does Team C's design in problem 5 stay within the $6.00 budget? By how many dollars is it under or over?
What percent of Team C's $6.00 budget remains unspent after the purchase in problem 5? Round to the nearest whole percent.
Team D wants a charcoal-heavy filter and plans to spend as close to the full $6.00 budget as possible. If Team D buys 3 scoops of activated charcoal first, how many coffee filters, at most, can they add without going over the $6.00 budget?

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: $2.60. 2 scoops of gravel (2 x $0.75 = $1.50), plus 1 scoop of sand ($0.50), plus 1 coffee filter ($0.60): $1.50 + $0.50 + $0.60 = $2.60.
Answer: $3.40. $6.00 minus $2.60 equals $3.40.
Answer: 43 percent. $2.60 divided by $6.00 equals 0.4333, which rounds to 43 percent. Dividing the cost by the budget, not the budget by the cost, gives a number less than 1, which converts to a proper percent.
Answer: $0.65 per scoop, cheaper. $3.25 divided by 5 equals $0.65 per scoop, which is $0.10 less than the regular $0.75-per-scoop price.
Answer: $3.50. Gravel ($0.75) plus sand ($0.50) plus charcoal ($1.25) plus cotton ($0.40) plus coffee filter ($0.60) equals $0.75 + $0.50 + $1.25 + $0.40 + $0.60 = $3.50.
Answer: Under by $2.50. $6.00 minus $3.50 equals $2.50 under budget.
Answer: 42 percent. $2.50 divided by $6.00 equals 0.41667, which rounds to 42 percent.
Answer: 3 coffee filters. 3 scoops of charcoal cost 3 x $1.25 = $3.75, leaving $6.00 minus $3.75, or $2.25. Three coffee filters cost 3 x $0.60 = $1.80, which fits, but 4 coffee filters would cost 4 x $0.60 = $2.40, which does not fit in $2.25, so the most Team D can add is 3 coffee filters, leaving $0.45 unspent.

Differentiation

Support

Provide a printed price list card with every item's cost already written next to it, and let students use a calculator for every addition, subtraction, and division step so the focus stays on choosing the correct operation.

Extension

Ask students to design their own five-item filter that spends between $5.00 and $6.00 of the fictional club budget, list its items and total cost, and calculate what percent of the budget it uses.

ELL supports

Provide a labeled picture price list showing each material (gravel, sand, charcoal, cotton, coffee filter) next to its price, so the vocabulary and the numbers are visually connected. Allow students to show their work as a simple running total list rather than full sentences.

Extensions

Have students compare their own team's total filter cost with a partner's design that uses different materials in different amounts, and discuss which design gets more layers of filtration per dollar spent.