Quiz & test questions Grade 7 Math

Cattail Bend Water Testing: A Grade 7 Sampling Quiz

A grade 7 quiz mixing multiple-choice, short-answer, and computation items on random sampling, inference, and probability for a fictional lake's water tests.

Grade: Grade 7
Subject: Math
Material: Quiz & test questions
Time: 25 min
Prep: No prep
Materials: None

Standards

7.SP.A.1 Common Core Math

Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations about a population from a sample are valid only if the sample is representative of that population.

How this material aligns: Items 1 and 2 ask why one spot may not represent a whole lake and why random sampling helps, the representative-sample reasoning this standard names.

All materials for 7.SP.A.1 →

7.SP.A.2 Common Core Math

Use data from a random sample to draw inferences about a population with an unknown characteristic of interest, generating multiple samples to gauge the variation in estimates.

How this material aligns: Items 3, 4, 7, and 8 use random-sample results to estimate a population value and explain why estimates vary, the inference work this standard requires.

All materials for 7.SP.A.2 →

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 5 and 6 express a contamination chance as a probability between 0 and 1, the meaning of probability this standard describes.

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 explain why random samples give a better estimate than one sample.
Students will estimate a population value and a probability from random-sample data.

Vocabulary

Key words: random sample, estimate, probability, sampling variation

Teacher overview

This 25-minute quiz is worth 22 points. It checks whether students can reason about random sampling, use sample data to estimate a population value, and express a chance as a probability between 0 and 1. The scenario is the fictional Cattail Bend, a lake the health department tests. The quiz mixes two multiple-choice items, two short-answer items, and four computation items.

Cattail Bend Water Testing: A Grade 7 Sampling Quiz — Grade 7 Math

Name: ____________________________ Date: ______________

Assessment

(2 points) A health worker tests water from only one spot at Cattail Bend and uses it to describe the whole lake. Why might this be a problem?
- A) One spot may not represent the whole lake.
- B) One sample is always wrong.
- C) Testing the water is not allowed.
- D) One spot is always the cleanest.
(3 points) To estimate the lake's water quality, the worker tests many random spots instead of one. Explain why random samples from many spots give a better estimate.
(3 points) In a random sample of 40 test strips, 6 show high bacteria. What fraction and what percent of the sample is high?
(3 points) Cattail Bend has 500 regular testing spots. Use the sample in item 3 to estimate how many spots would show high bacteria.
(3 points) Based on the sample in item 3, what is the probability that one randomly chosen spot shows high bacteria? Give your answer as a number between 0 and 1.
(2 points) Which value describes an event that is very unlikely but still possible?
- A) 0
- B) 0.02
- C) 0.5
- D) 1
(3 points) A second, larger random sample of 80 strips shows 10 high. What percent of this sample is high, and is it higher or lower than the first sample's 15 percent?
(3 points) The two samples gave different estimates, 15 percent and 12.5 percent. Explain why two random samples from the same lake can give different results.

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: A. One spot may not represent the whole lake, because a single spot could be unusually clean or dirty and would not stand for every part of the lake.
Answer: Random samples from many spots are more likely to represent the whole lake, so the estimate is more trustworthy. One spot could be an outlier, while many random spots balance out.
Answer: 6/40, which is 15 percent. 6 ÷ 40 = 0.15, and 0.15 is 15 percent of the sample.
Answer: 75 spots. Apply the sample rate to the population: 0.15 × 500 = 75 spots estimated to be high.
Answer: 0.15. The share high in the sample, 6 ÷ 40 = 0.15, is the estimated probability that one random spot is high.
Answer: B. A probability of 0.02 is close to 0, so the event is very unlikely, but it is greater than 0, so it is still possible.
Answer: 12.5 percent, which is lower. 10 ÷ 80 = 0.125, or 12.5 percent, and 12.5 percent is lower than the first sample's 15 percent.
Answer: Random samples vary by chance, which is sampling variation. Different spots land in each sample, so the estimates differ. Larger samples tend to vary less and come closer to the true value.

Differentiation

Support

Allow a calculator and provide the division set up for items 3 and 7, such as "6 ÷ 40," so students can focus on turning the result into a percent and a probability. Give a number line from 0 to 1 for item 6.

Extension

Ask students to combine the two samples in items 3 and 7 into one larger sample of 120 strips, find the combined percent high, and explain why the combined estimate is likely closer to the true value than either sample alone.

ELL supports

Pre-teach "random sample," "estimate," and "probability" with simple visuals, such as pulling test strips from a lake map and a 0-to-1 number line. Provide the sentence frame "The sample is ___ percent high, so the probability is about ___" for items 3 and 5.