Math problem set Grade 7 Engineering & Design

Quarrystone Hollow Fish Ladder: Scale Drawing and Pool Steps

A grade 7 problem set on a fictional dam where students size a fish ladder's pool steps, convert between drawing inches and real feet, and redraw at a second scale.

Grade: Grade 7
Subject: Engineering & Design
Material: Math problem set
Time: 45 min
Prep: No prep
Materials: Calculator, Ruler with inch markings, Graph paper

Standards

7.G.A.1 Common Core Math

Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

How this material aligns: Problems 3 through 5 convert between drawing inches and real feet on a stated scale, and problem 5 reproduces the same ladder at a second scale that halves the drawing.

All materials for 7.G.A.1 →

7.NS.A.3 Common Core Math

Solve real-world and mathematical problems involving the four operations with rational numbers.

How this material aligns: Problems 1, 2, 6 and 7 combine division by a decimal rise, whole-number multiplication, and a gallons conversion to size the pools.

All materials for 7.NS.A.3 →

7.RP.A.3 Common Core Math

Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.

How this material aligns: Problem 9 applies a stated gallons-per-minute conversion to the ladder's design flow, and problem 10 reports that flow as a percent of the river's late-summer flow.

All materials for 7.RP.A.3 →

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

Objectives

Students will compute actual lengths from a scale drawing and reproduce a length at a second scale.
Students will divide a total rise by a rise per step to find how many steps a structure needs.
Students will calculate a rectangular pool volume in cubic feet and convert it to gallons.

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.

Also: scale drawing, rise, cubic feet per second

Teacher overview

Quarrystone Hollow is a fictional mill dam on a river where migrating fish can no longer reach their spawning gravel upstream. The county is designing a fish ladder, which is a staircase of small pools that lets fish swim up past the dam one short jump at a time. Biologists on the team have set the rise between pools at three quarters of a foot, because the local fish clear that height reliably but tire on anything taller. This set has students count the pools, lay the ladder out on a scale drawing, redraw it at a second scale, and size the water the pools hold. A common error in this math is multiplying by the scale when converting a real length into drawing inches, when that direction calls for division instead.

Quarrystone Hollow Fish Ladder: Scale Drawing and Pool Steps — Grade 7 Engineering & Design

Name: ____________________________ Date: ______________

Problems

Use these figures from the fictional Quarrystone Hollow project for every problem. The water surface above the dam sits 12 feet higher than the water below it, so the ladder must climb 12 feet in all. Each pool sits 0.75 foot higher than the pool below it. Count one pool for each 0.75-foot rise. Each pool is 6 feet long, 4 feet wide, and holds water 3 feet deep. The county's first drawing uses the scale 1 inch equals 4 feet. One cubic foot of water holds 7.48 gallons.

How many pool steps does the ladder need to climb the full 12 feet?
Each pool is 6 feet long from end to end, and the pools sit in one straight line. How many feet long is the whole ladder?
On the county's drawing, 1 inch stands for 4 feet. How many inches long is the whole ladder on that drawing?
On the same drawing, how many inches tall is the 12-foot climb?
A second drawing uses the scale 1 inch equals 8 feet. How many inches long is the whole ladder on the second drawing?
One pool is 6 feet long, 4 feet wide, and holds water 3 feet deep. How many cubic feet of water does one pool hold?
Using 7.48 gallons for every cubic foot, how many gallons of water does one pool hold? Round to the nearest hundredth.
How many cubic feet of water do all of the ladder's pools hold together?
The ladder needs 4 cubic feet of water per second flowing down it. One cubic foot per second equals 448.8 gallons per minute. How many gallons per minute does the ladder need?
In late summer the river carries 120 cubic feet per second. The ladder takes 4 cubic feet per second of that. What percent of the river's flow does the ladder use? Round to the nearest tenth of a 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: 16 steps.
12 feet of total climb divided by 0.75 foot per step = 16 pool steps.
Answer: 96 feet.
16 pools x 6 feet per pool = 96 feet of ladder length.
Answer: 24 inches.
96 feet divided by 4 feet per inch = 24 inches on the drawing. Students who multiply here get 384 inches, a drawing 32 feet long that could never fit on a sheet of paper.
Answer: 3 inches.
12 feet divided by 4 feet per inch = 3 inches on the drawing.
Answer: 12 inches.
96 feet divided by 8 feet per inch = 12 inches. Doubling the feet represented by each inch halves the drawing, so 12 inches is half of the 24-inch answer from problem 3.
Answer: 72 cubic feet.
6 feet x 4 feet x 3 feet = 72 cubic feet in one pool.
Answer: 538.56 gallons.
72 cubic feet x 7.48 gallons per cubic foot = 538.56 gallons in one pool.
Answer: 1,152 cubic feet.
72 cubic feet per pool x 16 pools = 1,152 cubic feet in all sixteen pools.
Answer: 1,795.2 gallons per minute.
4 cubic feet per second x 448.8 gallons per minute for each cubic foot per second = 1,795.2 gallons per minute.
Answer: 3.3 percent.
4 divided by 120 = 0.03333, which is 3.333 percent, or 3.3 percent rounded to the nearest tenth.

Differentiation

Support

Give these students a side-view sketch of the ladder with the first three pools already drawn and labeled, so problem 1 becomes a matter of continuing a pattern before dividing. Provide a two-column conversion table headed "inches on the drawing" and "feet on the river" with two rows completed. Allow a calculator on every problem, and let students leave problem 7 rounded to the nearest whole gallon.

Extension

Ask students to redesign the ladder with a rise of 0.5 foot per pool instead of 0.75 foot, then report how many pools it needs, how long it becomes, and how many inches long it would be on the 1 inch equals 4 feet drawing. Have them write a short recommendation weighing the gentler climb against the added length and cost.

ELL supports

Pre-teach rise, pool, ladder, and scale with a labeled diagram of two stacked pools showing the rise measured between the two water surfaces. Provide the sentence frame "Every ___ feet on the river equals ___ inch on the drawing" for problems 3 through 5. Allow answers to problem 10 to be written as a number with the word percent rather than a full sentence.

Extensions

Have students draw the ladder to scale on graph paper at 1 inch equals 4 feet, showing the 16 pools in side view with the rise marked between each pair. Ask them to label the total length and total climb on the drawing, then trade drawings with a partner and check each other's measurements with a ruler. Students who finish early can add a second sketch at 1 inch equals 8 feet and write one sentence comparing what each drawing shows well.