Quiz & test questions Grade 7 Math

Byrne Hollow Farm Irrigation Records: A Grade 7 Math Quiz

A 25-point quiz on one fictional farm's records, mixing complex-fraction pump rates, percent decrease in nitrogen runoff, and a probability drawn from field samples.

Grade: Grade 7
Subject: Math
Material: Quiz & test questions
Time: 30 min
Prep: No prep
Materials: Calculator

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 and 2 divide fractional acre-inches by fractional hours, which is the complex-fraction unit rate this standard requires, and item 3 compares the two rates that result.

All materials for 7.RP.A.1 →

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: Items 4, 5, 6, and 9 apply percent of a quantity and percent decrease to nitrogen runoff and monthly irrigation totals at the fictional farm.

All materials for 7.RP.A.3 →

7.SP.C.5 Common Core Math

Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring, with larger numbers indicating greater likelihood.

How this material aligns: Items 7 and 8 ask students to state a probability between 0 and 1 from sample counts and to interpret what that number means.

All materials for 7.SP.C.5 →

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

Objectives

Students will compute and compare unit rates formed from ratios of fractions.
Students will calculate percent of a quantity and percent decrease from farm records.
Students will state and interpret a probability drawn from a set of field samples.

Vocabulary

Key words: acre-inch, runoff, percent decrease, probability

Teacher overview

This quiz is worth 25 points and covers one fictional farm's season of records, so students meet unit rates, percent decrease, and probability in a single setting rather than as three unrelated topics. The mix runs to six computation items, two multiple-choice items, and two short written explanations, which is enough range to separate students who can carry out a procedure from those who can also say what the result means. A recurring error is that students take a percent decrease from the wrong base, dividing the change by the ending value rather than the starting value, so item 10 asks them to name the base directly.

Byrne Hollow Farm Irrigation Records: A Grade 7 Math Quiz — Grade 7 Math

Name: ____________________________ Date: ______________

Assessment

Byrne Hollow Farm is fictional, and all of these records were written for this quiz. The farm waters its fields from Pikewater Creek. Show your work on the computation items.

(2 points) One pump moved 3/4 of an acre-inch of water in 1/2 of an hour. What is its rate in acre-inches per hour?
(2 points) A second pump moved 5/8 of an acre-inch in 1/4 of an hour. What is its rate in acre-inches per hour?
(2 points) Which pump is faster? Choose one.
- A. the first pump
- B. the second pump
- C. they are the same
- D. there is not enough information
(3 points) The farm spread 240 pounds of nitrogen on one field. A storm washed 15 percent of it into the creek. How many pounds washed off?
(3 points) The next year the farm planted a cover crop. Runoff fell from 36 pounds to 27 pounds. What is the percent decrease?
(3 points) The farm pumped 1,200,000 gallons in July and 1,020,000 gallons in August. What is the percent decrease from July to August?
(2 points) The farm tested 40 field samples. Six of them were above the state nitrate limit. What is the probability that one sample chosen at random was above the limit? Choose one.
- A. 0.06
- B. 0.15
- C. 0.60
- D. 1.5
(3 points) Explain what a probability of 0.15 tells the farm about its field samples. Use the words "chance" and "samples" in your answer.
(3 points) The farm plans to cut its nitrogen use by 20 percent from the 240 pounds in item 4. How many pounds will it use?
(2 points) In item 5, the percent decrease is found by dividing the change by 36 pounds and not by 27 pounds. Explain why 36 is the correct number to divide by.

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 acre-inches per hour.
Divide the water by the time: (3/4) / (1/2) = (3/4) x 2 = 1.5 acre-inches per hour.
Answer: 2.5 acre-inches per hour.
Divide the water by the time: (5/8) / (1/4) = (5/8) x 4 = 20/8 = 2.5 acre-inches per hour.
Answer: B, the second pump.
The second pump moves 2.5 acre-inches per hour against the first pump's 1.5, so it is faster. Choice A tempts students who compare 3/4 with 5/8 and stop there, since 3/4 is the larger amount of water, yet it took twice as long to move.
Answer: 36 pounds.
Multiply the nitrogen by the percent as a decimal: 240 x 0.15 = 36 pounds washed into the creek.
Answer: 25 percent.
The change is 36 - 27 = 9 pounds. Divide by the starting amount: 9 / 36 = 0.25, which is 25 percent.
Answer: 15 percent.
The change is 1,200,000 - 1,020,000 = 180,000 gallons. Divide by July's total: 180,000 / 1,200,000 = 0.15, which is 15 percent.
Answer: B, 0.15.
Divide the samples above the limit by the total samples: 6 / 40 = 0.15. Choice A comes from reading 6 out of 100, and choice C comes from dividing 6 by 10.
Answer: About 15 out of every 100 samples would be expected above the limit.
A probability of 0.15 means there is a 15 percent chance that one randomly chosen sample is above the limit. Across many samples, the farm should expect roughly 15 of every 100 to test high, though any single set of samples can differ.
Answer: 192 pounds.
A 20 percent cut leaves 80 percent of the original: 240 x 0.80 = 192 pounds. Students may also find 240 x 0.20 = 48 and subtract, giving 240 - 48 = 192 pounds.
Answer: 36 pounds is the amount the farm started with.
Percent decrease compares the change with the original amount, so the denominator must be the earlier value. Dividing 9 by 27 gives 33.3 percent, which answers a different question about how much larger 36 is than 27.

Differentiation

Support

Allow students to use a reference card during the quiz with the percent decrease formula written out and one worked example that does not use the fictional Byrne Hollow numbers. Students may also be given the reciprocal step for items 1 and 2 shown once, so that dividing by 1/2 is displayed as multiplying by 2.

Extension

Ask students who finish early to find what the runoff at the fictional farm would have to fall to for the percent decrease in item 5 to reach 40 percent, then to explain why cutting that new amount by another 40 percent does not produce an 80 percent decrease overall.

ELL supports

Provide a small labeled picture of the fictional Byrne Hollow Farm showing a pump, a field, and the creek, with "runoff," "acre-inch," and "sample" glossed. Allow students to answer items 8 and 10 with a labeled diagram plus a short sentence, and provide the frame "The probability means that out of ____ samples, about ____ would be above the limit."

Extensions

Students can convert the fictional farm's July and August totals into acre-inches applied to a stated field size, then check whether the percent decrease is the same in both units. A second follow-on has students put 40 counters in a bag, 6 of them marked to stand for the high samples, draw samples of ten, and compare how often their sample proportion lands near 0.15, which sets up the sampling variability work in the grade 7 statistics standards.