Worksheet Grade 7 Math

Moorhen Bend's Five Rain Gauges: A Grade 7 Intensity Worksheet

A grade 7 worksheet where students divide fractions of an inch by fractions of an hour to compare rainfall rates at a fictional town's five rain gauges.

Grade: Grade 7
Subject: Math
Material: Worksheet
Time: 30 min
Prep: No prep
Materials: None

Standards

7.RP.A.1 Common Core Math

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units.

How this material aligns: Items 1 through 5 divide a fraction of an inch by a fraction of an hour, producing unit rates from ratios of fractions.

All materials for 7.RP.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: Items 8, 9, and 11 multiply, divide, and subtract with mixed numbers and decimals to extend and compare the rates found earlier.

All materials for 7.NS.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 2026-09-23.

Objectives

Students will compute a rainfall rate in inches per hour from fractional amounts and times.
Students will compare rainfall rates written as fractions and as decimals.
Students will use a rate to predict rainfall over a longer or shorter time.

Vocabulary

Storm drain: A storm drain is the grate at the edge of a street that swallows rainwater and sends it through pipes to the nearest creek or river. That water is usually not treated, so only rain belongs down the drain.

Also: rain gauge, rainfall rate, unit rate, intensity

Teacher overview

Two storms can drop the same total rain and still put very different loads on a drainage system, because what floods a street is the rate at which rain arrives rather than the total depth. Utilities therefore record both the depth in a gauge and the length of time it took to collect, then divide to get inches per hour. This worksheet uses five gauges in the fictional town of Moorhen Bend, each reporting a fraction of an inch collected over a fraction of an hour. The predictable error is multiplying instead of dividing: a student who multiplies three-quarters of an inch by one-half hour reports three-eighths of an inch per hour, when dividing gives the correct 1.5 inches per hour.

Moorhen Bend's Five Rain Gauges: A Grade 7 Intensity Worksheet — Grade 7 Math

Name: ____________________________ Date: ______________

Student Worksheet

Moorhen Bend is a fictional town with five rain gauges. Each gauge reports how much rain it caught and how long the rain took to fall.

Gauge 1 caught 3/4 inch in 1/2 hour.
Gauge 2 caught 1/2 inch in 1/4 hour.
Gauge 3 caught 5/8 inch in 3/4 hour.
Gauge 4 caught 1 1/4 inches in 1 1/2 hours.
Gauge 5 caught 7/8 inch in 5/8 hour.

What is Gauge 1's rainfall rate, in inches per hour?
What is Gauge 2's rainfall rate, in inches per hour?
What is Gauge 3's rainfall rate, in inches per hour? Give a fraction.
What is Gauge 4's rainfall rate, in inches per hour? Give a fraction.
What is Gauge 5's rainfall rate, in inches per hour?
Which gauge had the fastest rate?
Two gauges had the same rate. Which two?
Rain keeps falling at Gauge 1's rate for 2 1/2 hours. How many inches fall?
At Gauge 3's rate, how many hours would it take to collect 2 inches?
The storm drains in Moorhen Bend can carry rain falling up to 1 3/4 inches per hour. Which gauge recorded a rate above that?
How much slower is Gauge 5's rate than Gauge 1's rate, in inches per hour?

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: 1.5 inches per hour.
Divide 3/4 by 1/2. Multiply 3/4 by 2 to get 3/2, which is 1.5 inches per hour.
Answer: 2 inches per hour.
Divide 1/2 by 1/4. Multiply 1/2 by 4 to get 2 inches per hour.
Answer: 5/6 inch per hour.
Divide 5/8 by 3/4. Multiply 5/8 by 4/3 to get 20/24, which reduces to 5/6, or about 0.83 inch per hour.
Answer: 5/6 inch per hour.
Rewrite the mixed numbers as 5/4 inch and 3/2 hours. Multiply 5/4 by 2/3 to get 10/12, which reduces to 5/6 inch per hour.
Answer: 1.4 inches per hour.
Divide 7/8 by 5/8. Multiply 7/8 by 8/5 to get 7/5, which is 1.4 inches per hour.
Answer: Gauge 2.
Its rate of 2 inches per hour is larger than the rates of 1.5, 5/6, and 1.4.
Answer: Gauge 3 and Gauge 4.
Both work out to 5/6 inch per hour, even though their depths and times look different.
Answer: 3.75 inches.
Multiply the rate by the time: 1.5 times 2 1/2 equals 1.5 times 2.5, which is 3.75 inches.
Answer: 2.4 hours.
Divide the depth by the rate: 2 divided by 5/6 is 2 times 6/5, which is 12/5, or 2.4 hours.
Answer: Gauge 2.
Its rate of 2 inches per hour is above 1 3/4, which is 1.75. Gauge 1 at 1.5 and Gauge 5 at 1.4 both stay below that line.
Answer: 0.1 inch per hour.
Subtract the two rates: 1.5 minus 1.4 equals 0.1 inch per hour.

Differentiation

Support

Give these students a worked card showing that dividing by a fraction means multiplying by its reciprocal, using a gauge that is not on the worksheet. Assign items 1 through 6 and item 11. Most of these answers land on friendly decimals, and item 6 needs the rates from items 3 and 4.

Extension

Ask these students to invent a sixth gauge whose depth and time are both fractions and whose rate matches Gauge 1 exactly, then to show the division that proves it. Have them explain why many different pairs of numbers give the same rate.

ELL supports

Pre-teach "gauge," "caught," "rate," and "per hour" with a picture of a marked cylinder beside a clock face divided into quarters. Provide the frame "Gauge ___ caught ___ inch in ___ hour, so its rate is ___ inches per hour" for items 1 and 2.