Classroom activity Grade 7 Math
Sampling Bittern Slough: A Grade 7 Random-Sample Activity
A grade 7 activity where groups draw repeated random chips from a hidden population to estimate a fictional river's contamination and see how sampling varies.
Objectives
- Students will estimate a population's proportion from a random sample of draws.
- Students will compare single-group and combined estimates to see how larger samples vary less.
Vocabulary
Key words: random sample, estimate, sampling variation, population
Teacher overview
Water-quality staff can never test every point along a river, so they take random samples and use them to estimate the whole. This is a small-group simulation for a class working in teams of three or four. A bag of chips stands for every possible sampling spot along the fictional Bittern Slough, where some spots have nitrate above the safe level and most do not. Each group draws a random sample, estimates the share of high-nitrate spots, and then the class combines samples to see that a larger sample gives a steadier estimate. The activity maps directly onto the concept: drawing chips one at a time with replacement is a stand-in for sending a technician to randomly chosen points, and the spread of the group estimates is the sampling variation that real monitoring programs plan around.
Activity Directions
- Before class, fill a bag with 100 chips. Mark 30 of them "high," for high nitrate, and leave the other 70 blank, for safe. Keep the count of high chips secret. Tell students the bag stands for every sampling spot along the fictional Bittern Slough, and a "high" chip is a spot where nitrate is above the safe level.
- Divide the class into groups of three or four and give each group a recording sheet.
- One student draws a single chip without looking, and the group records whether it is high or safe. Return the chip to the bag and shake it. Returning each chip keeps the bag's mix the same, which is sampling with replacement.
- Each group repeats the draw until it has recorded 20 samples, taking turns so everyone draws.
- Each group counts its high draws and finds what percent of its 20 samples were high. That percent is the group's estimate for the whole river.
- Write every group's estimate on the board. Point out how far apart the estimates are from one another; that spread is sampling variation.
- Add every group's draws together into one large class sample, and find the percent high for that combined total.
- Now reveal the true share of high chips in the bag. Have groups compare their own estimate, and the combined class estimate, against the true value.
- End the activity once groups have compared the small-sample and large-sample estimates to the truth, then move to the debrief questions on the recording sheet.
Student Handout
Your bag stands for every sampling spot along the fictional Bittern Slough. Draw 20 chips, one at a time, returning each chip and shaking the bag between draws. Use the tally box, then answer the questions.
| Draw result | Tally | Total |
|---|---|---|
| High nitrate | ||
| Safe |
- How many of your 20 draws were high, and what percent of 20 is that?
- Was your group's estimate higher or lower than the combined class estimate written on the board?
- Which came closer to the true share of high spots: your group's 20 draws or the whole class's combined draws? Explain why in one or two sentences.
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: Answers vary.
The percent equals the high count divided by 20, times 100. For example, 5 high out of 20 is 5 ÷ 20 = 25%. Accept any correct count-to-percent conversion for that group's draws. - Answer: Answers vary.
Some groups land above the class estimate and some below, which is the point: single small samples scatter around the true value in both directions. - Answer: Usually the combined class draws.
The whole class's larger sample almost always lands closer to the true share, because a bigger random sample has less sampling variation than any one group's 20 draws. If a group's own estimate happened to land closer, accept it when the student explains that a small sample can land near the true value by chance, while a larger sample does so more reliably.
Differentiation
Support
Pair students who need help with a partner and give them a pre-drawn tally sheet with the 20 boxes already outlined, so recording each draw is a single mark. Do the first five draws with the whole group aloud so the routine of draw, record, return, and shake is clear before they continue on their own.
Extension
Ask one group to run two rounds of only 10 draws and another group to run two rounds of 40 draws, then compare how much more the 10-draw estimates jump around. Have them write a sentence predicting what would happen to the spread if every group drew 100 times.
ELL supports
Post a picture card for "high" (a red water drop) and "safe" (a blue water drop) at each table, and pre-teach "sample," "estimate," and "true value" with a quick demonstration draw. Provide the sentence frame "My estimate is ___ percent, and the true value is ___ percent" for the debrief.
Extensions
Have students read how a real drinking-water system decides how many samples to collect, a number that state and federal monitoring rules set largely by how many people the system serves, and connect the idea that more sampling sites give a more trustworthy result to what they just saw with the chips. A short discussion of why testing costs money ties the statistics to the practical limits monitoring programs face.