Quiz & test questions Grade 5 Engineering & Design

Thackeray Mill Dam Fish Ladder: A Grade 5 Design Choice Quiz

A grade 5 quiz on two fish ladder designs for a fictional mill dam, mixing multiple choice, decimal computation, and a written design recommendation.

Grade: Grade 5
Subject: Engineering & Design
Material: Quiz & test questions
Time: 30 min
Prep: No prep
Materials: None

Standards

3-5-ETS1-1 NGSS

Define a simple design problem reflecting a need or a want that includes specified criteria for success and constraints on materials, time, or cost.

How this material aligns: Item 2 asks students to sort the ladder's jump height, climb height, and bank length rules into criteria and constraints, which is the problem-defining work this standard names.

All materials for 3-5-ETS1-1 →

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, 7, and 9 make students weigh Design A and Design B against the same stated criteria and constraint, then recommend one, matching this standard's compare-multiple-solutions expectation.

All materials for 3-5-ETS1-2 →

5.NBT.B.7 Common Core Math

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

How this material aligns: Item 3 divides by a decimal to hundredths, 9.0 by 0.75, and items 4, 5, and 8 multiply and divide with decimals to tenths, each answered with place-value reasoning in the key.

All materials for 5.NBT.B.7 →

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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 sort stated design rules into criteria and constraints for a fish ladder problem.
Students will divide and multiply decimals to find step counts and ladder lengths.
Students will recommend one ladder design and name the rule it meets that the others miss.

Vocabulary

Fish ladder: A series of water steps built beside a dam so migrating fish, like salmon, can swim past it. Fish leap or swim from pool to pool to reach the river above.
Dam: A strong wall built across a river to hold back water. Dams store water for people and farms, help prevent floods, and can make electricity.

Also: criterion, constraint, step rise

Teacher overview

This 30-minute quiz is worth 25 points and checks whether fifth graders can hold a design problem and its arithmetic together at the same time. It mixes two multiple-choice items, four decimal computations, and three short written responses, all built on one fictional dam and two proposed fish ladders. Students divide and multiply decimals to hundredths, then use those results to judge two designs and recommend one.

A misconception worth naming before students start: many fifth graders treat "the design that works best" as the design with the biggest or smallest number, rather than the design that meets every stated rule. On this quiz, Design B is shorter along the bank than Design A, and students who stop at that comparison will choose it, missing that its steps are too tall for the fish to jump. Tell students plainly that a design has to pass every rule the town wrote, and that a design meeting all of those rules but one still fails. A second, smaller error shows up in item 3: students who see 9.0 divided by 0.75 often misplace the decimal point and write 0.12, treating the division the way they would line up an addition. Remind them to check whether an answer makes sense, since a ladder cannot climb 9 feet in less than one step.

Thackeray Mill Dam Fish Ladder: A Grade 5 Design Choice Quiz — Grade 5 Engineering & Design

Name: ____________________________ Date: ______________

Assessment

Thackeray Mills is a fictional town on the Selbourne River. Its old mill dam is 9.0 feet tall. Fish cannot swim past it to reach their nesting gravel upstream. The town wants to add a fish ladder, which is a row of small pools that climb beside the dam. A fish jumps from one pool to the next.

The town wrote three rules for the ladder.

Each step must rise 0.80 feet or less, so small fish can jump it.
The ladder must climb the full 9.0 feet of the dam.
The ladder may be no longer than 40.0 feet along the river bank, because that is all the land the town owns.

Two designs came in.

Design A uses steps that rise 0.75 feet. Each pool is 4.0 feet long.
Design B uses 6 steps in all. Each pool is 4.0 feet long.

(2 points) What is the main job of a fish ladder?
- A) It makes the dam taller.
- B) It lets fish move past a dam to water upstream.
- C) It cleans the river water.
- D) It stores water for the town.
(2 points) Which rule is a constraint, not a criterion?
- A) Each step must rise 0.80 feet or less.
- B) The ladder must climb the full 9.0 feet.
- C) The ladder may be no longer than 40.0 feet, because that is all the land the town owns.
- D) Fish must be able to reach the gravel upstream.
(3 points) Design A uses steps that rise 0.75 feet. The ladder must climb 9.0 feet. How many steps does Design A need?
(3 points) Every pool in Design A is 4.0 feet long. Using your step count from item 3, how many feet long is Design A along the bank?
(3 points) Design B climbs the same 9.0 feet using 6 equal steps. How many feet does each step of Design B rise?
(3 points) Look at your answer to item 4. Which one of the town's three rules does Design A break?
(3 points) Look at your answer to item 5. Which one of the town's three rules does Design B break?
(3 points) The town asks for a third plan, Design C. It keeps steps that rise 0.75 feet, but each pool is shortened to 3.0 feet. Design C needs the same number of steps as Design A, which you found in item 3. How many feet long is Design C along the bank?
(3 points) Which design should Thackeray Mills build? Name it, and give one reason that points to a rule.

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) It lets fish move past a dam to water upstream.
A ladder does not change the height of the dam or treat the water; it gives fish a path around the blockage.
Answer: C) The ladder may be no longer than 40.0 feet.
A constraint is a limit on space, time, money, or materials. Choices A, B, and D describe what success looks like, so they are criteria.
Answer: 12 steps.
9.0 divided by 0.75 equals 12, because 0.75 times 12 equals 9.0. Students who wrote a number smaller than 1 divided in the wrong order.
Answer: 48.0 feet.
12 pools times 4.0 feet per pool equals 48.0 feet.
Answer: 1.5 feet.
9.0 divided by 6 equals 1.5, so each step of Design B rises 1.5 feet.
Answer: Design A breaks the 40.0-foot length limit.
It measures 48.0 feet along the bank, which is 8.0 feet more than the town has room for. Its step rise of 0.75 feet is inside the jump rule, so length is the only rule it breaks.
Answer: Design B breaks the 0.80-foot jump rule.
Its steps rise 1.5 feet each, which is nearly twice the height small fish can clear. At 24.0 feet long it fits the bank easily, so the jump rule is the only one it breaks.
Answer: 36.0 feet.
12 pools times 3.0 feet per pool equals 36.0 feet.
Answer: Design C.
Accept any answer that names Design C and points to a rule: it is 36.0 feet long, which fits inside the 40.0-foot limit, and its steps rise 0.75 feet, which is under the 0.80-foot jump rule. Do not accept Design B on the grounds that it is shortest, since it breaks the jump rule.

Differentiation

Support

Give these students a printed copy of the three rules with the word "criterion" or "constraint" already written beside each one, so item 2 checks their reading of the rule rather than their recall of the vocabulary. For items 3 and 5, supply the division sentences already set up, and let students use a calculator. A number line marked in quarters helps students see that 0.75 fits into 9.0 twelve times.

Extension

Ask these students to write a fourth design of their own that meets all three rules and uses the fewest pools possible. They should show the step rise they chose, the pool length, the step count, and the total bank length, and they should explain why no design can use fewer than 12 steps while holding the jump rule at 0.80 feet.

ELL supports

Pre-teach "step rise," "bank," and "pool" using a simple side-view sketch of a staircase beside a wall, labeling the rise of one step and the flat part of one pool. Provide a sentence frame for items 6, 7, and 9: "Design ___ breaks the rule about ___ because its number is ___." Allow students to answer item 9 by circling a design name and completing the frame.

Extensions

Students can look up whether any dam on a river near the school has a fish ladder or a fish lift, and sketch what they find. A short class discussion comparing a ladder, which fish climb on their own, with a lift, which carries fish upward in a moving hopper, gives students a second solution to weigh against the same criteria they used on this quiz.