Quiz & test questions Grade 4 Engineering & Design

Calderbrook Mill Waterwheel: A Paddle Design Review Quiz

A grade 4 quiz on choosing among three model waterwheel paddle designs, using a test table of turns, lifted washers, and supply-token costs.

Grade: Grade 4
Subject: Engineering & Design
Material: Quiz & test questions
Time: 30 min
Prep: No prep
Materials: None

Standards

4-PS3-4 NGSS

Apply scientific ideas to design, test, and refine a device that converts energy from one form to another.

How this material aligns: The quiz assesses a build in which model waterwheels turn falling water into lifting motion, with item 2 reading the lift results and item 9 planning the one-change test that would refine the wheel.

All materials for 4-PS3-4 →

3-5-ETS1-2 NGSS

Generate and compare multiple possible solutions to a problem based on how well each is likely to meet the criteria and constraints of the problem.

How this material aligns: Items 6 and 7 require students to weigh three paddle designs against the same washer target, turn target, and token limit before naming one.

All materials for 3-5-ETS1-2 →

4.NBT.B.5 Common Core Math

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

How this material aligns: Items 3, 4 and 8 multiply a two-digit count by a one-digit number to find lifted weight, turns in seven minutes, and total cups poured.

All materials for 4.NBT.B.5 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-09-23.

Objectives

Students will tell a constraint apart from a criterion in a waterwheel design problem.
Students will compare three waterwheel designs against stated targets and a token limit.
Students will multiply and divide whole numbers to find lifted weight, turn counts, and cost.

Vocabulary

Key words: criteria, constraint, waterwheel, fair test, paddle

Teacher overview

This 30-minute quiz is worth 25 points and mixes three multiple-choice items, four computation items, and two short-answer items. Every number a student needs appears in the test table or in the item itself, so no outside knowledge is required. The misconception worth planning for is the belief that the design with the single best test number must be the best design overall. Fourth graders regularly pick the wheel that lifted the most washers or spun the fastest and then ignore the spending limit the problem set out, which is why items 6 and 7 send them back to the cost column before they name a winner.

Calderbrook Mill Waterwheel: A Paddle Design Review Quiz — Grade 4 Engineering & Design

Name: ____________________________ Date: ______________

Assessment

The town of Calderbrook is a made-up town used for this quiz. Its old grain mill has a waterwheel that no longer turns. A class built three model waterwheels to find out which paddles work best. Each model was fed by the same jug of water. Each model lifted a string of metal washers. The table below shows what the class wrote down.

Design	Paddles	Cost in supply tokens	Turns in one minute	Washers lifted
A	6 flat	8	24	6
B	10 flat	12	30	9
C	6 cupped	10	22	10

The mill owner gave the class three rules for the new wheel:

The wheel must lift at least 8 washers.
The wheel must turn at least 20 times in one minute.
The wheel must cost no more than 10 supply tokens.

(2 points) The rule "no more than 10 supply tokens" is an example of which one?
- A) a test result
- B) a constraint
- C) a lucky guess
- D) a data table
(2 points) Which design lifted the most washers?
- A) Design A
- B) Design B
- C) Design C
- D) All three lifted the same number
(3 points) Design C lifts 10 washers at one time. Each washer weighs 5 grams. How many grams does Design C lift at one time?
(3 points) Design B turns 30 times in one minute. At that same rate, how many times does Design B turn in 7 minutes?
(3 points) The class has 60 supply tokens to spend. One Design C wheel costs 10 supply tokens. How many Design C wheels can the class build with 60 tokens?
(4 points) Design B lifted 9 washers and turned 30 times in one minute. Both of those numbers pass the mill owner's rules. Explain why the class still did not choose Design B.
(2 points) Name the one design that follows all three of the mill owner's rules.
(3 points) The class poured 24 cups of water through Design A during its test. They poured the same amount through each of the 3 designs. How many cups of water did they pour in all?
(3 points) The class wants to find out whether cupped paddles lift more than flat paddles. They will build one more wheel. Which plan gives a fair test?
- A) Use cupped paddles and 10 paddles instead of 6.
- B) Use cupped paddles, keep 6 paddles, and pour the same amount of water as before.
- C) Use cupped paddles and pour the water from a much taller jug.
- D) Use flat paddles and hang more washers on the string.

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: B) a constraint.
A constraint is a limit on what a team may spend or use. The token rule limits spending, while the washer rule and the turn rule describe what the wheel must do.
Answer: C) Design C.
The table shows Design C lifted 10 washers, which is more than Design A's 6 and Design B's 9.
Answer: 50 grams.
10 washers × 5 grams = 50 grams.
Answer: 210 turns.
30 turns in one minute × 7 minutes = 210 turns.
Answer: 6 wheels.
60 tokens ÷ 10 tokens per wheel = 6 wheels.
Answer: Design B costs more than the rules allow.
Design B costs 12 supply tokens, and the mill owner allows no more than 10. A design that misses even one rule is out, no matter how strong its other numbers look.
Answer: Design C.
Design C lifted 10 washers, which clears the target of 8. It turned 22 times in one minute, which clears the target of 20. It cost 10 supply tokens, which is not above the limit of 10. Design A misses the washer target and Design B misses the token limit.
Answer: 72 cups.
24 cups × 3 designs = 72 cups. Pouring the same amount through each model is what made the test fair.
Answer: B) Use cupped paddles, keep 6 paddles, and pour the same amount of water as before.
A fair test changes one thing at a time. Choice B changes only the paddle shape, so any change in the result points back to the cupped paddles. Choices A and C change a second thing, and choice D does not test cupped paddles at all.

Differentiation

Support

Print the three rules on a separate strip so students can lay it beside the table while they work. Set up the first step of items 3, 4, and 8 for them, as in 10 × 5 = ____, and allow a calculator on every computation item. For item 7, have students first cross out each design that breaks a rule, one rule at a time, rather than judging all three rules at once.

Extension

Ask students to sketch a fourth wheel that would lift more than 10 washers while still costing 10 supply tokens or fewer. They should label what they would give up to stay inside the limit, such as fewer paddles or a smaller wheel, and name the one number they would watch during the test.

ELL supports

Provide a labeled drawing of a model waterwheel showing the paddle, the axle, the string, and the washers, and keep it visible during the quiz. Offer a sentence frame for item 6: "Design B did not win because its ____ was ____ than the rule allows." Accept a labeled sketch in place of written words for item 7.

Extensions

Connect the quiz to the machines a modern hydropower plant uses by pointing out that a turbine is a descendant of the mill wheel, spun by falling water and connected to a generator instead of a grindstone. Ask students what other rules a real village might add to the mill owner's three, such as keeping a fish path open or keeping the repair work simple enough for one person, and have them mark whether each new rule is a criterion or a constraint.