Classroom activity Grade 11 Math
Thistlewood Well Field Sampling Relay: A Sampling Distribution
A grade 11 activity where teams draw repeated random samples from a fictional well field to build a class sampling distribution and estimate its spread.
Objectives
- Students will draw repeated random samples from a fixed population and calculate each sample's mean.
- Students will build a class dot plot of sample means and describe its spread as an estimate of sampling variability.
Vocabulary
Key words: random sample, sampling distribution, population mean, sample mean
Teacher overview
This is a whole-class simulation activity for 24 to 32 students working in eight teams of three or four. The fictional Thistlewood well field's twenty wells become twenty index cards, and each team repeatedly draws a small random sample from those cards, calculates its mean, and adds that mean to a shared class dot plot. The activity teaches the concept directly: as the class watches dots accumulate, sample means cluster far more tightly than the individual well readings did, turning the abstract idea of a sampling distribution into something the class builds together.
Activity Directions
- Before class, write each of Thistlewood's twenty fictional well nitrate readings (in mg/L) on its own index card: 3, 4, 4, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 10. Place all twenty cards into a bag. Do not reveal the true population mean to students until the debrief.
- Organize students into eight teams of three or four. Give each team a bag containing a shuffled copy of the twenty cards (or have all teams share one bag and reshuffle between draws).
- Each team draws one card, records its value, returns the card to the bag, and shuffles before drawing again, repeating until the team has drawn four values (sampling with replacement).
- Each team calculates the mean of its four drawn values and records it as its "Round 1 sample mean."
- Each team places a sticky dot above its Round 1 sample mean on a shared class dot plot drawn on the board (a number line running from 2 to 11 mg/L).
- Each team repeats the draw-four-and-average process for a Round 2 and a Round 3, adding one new dot to the class plot after each round.
- Once every team has added three dots to the plot (24 dots total), stop drawing and look at the completed class dot plot together as a group.
- As a class, describe where the dots cluster and how far the most extreme dots stray from that cluster.
- Reveal the true population mean, calculated from all twenty original well cards, and compare it to the center of the class dot plot.
From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.
Answer Key
The first item below is numbered to match step 9 of the Activity Directions, where its answer is revealed (steps 1 through 8 are setup and procedure with no single numeric answer of their own). Items 10 and 11 are debrief questions to pose after step 9.
Answer: 6.5 mg/L.
The true population mean of all twenty wells, revealed in step 9: sum of the readings (3 + 4 + 4 + 5 + 5 + 5 + 6 + 6 + 6 + 6 + 7 + 7 + 7 + 7 + 8 + 8 + 8 + 9 + 9 + 10) = 130; 130 ÷ 20 = 6.5 mg/L.Debrief question: Why do the individual well readings on the original twenty cards spread out more widely than the teams' sample means?
Answer: Averaging four draws smooths out the extremes, since a high draw in a sample is often balanced by a lower one drawn in the same round, so sample means cluster closer to the true population mean than individual well readings do on their own.Debrief question: If each team had sampled ten wells instead of four, would you expect the class dot plot's spread to tighten or loosen?
Answer: Tighten. Larger samples average out more of the individual variation, producing sample means that cluster more closely around the true population mean, which is exactly why bigger samples produce a smaller margin of error.
Differentiation
Support (below grade level)
Reduce the sample size from four draws to three draws per round to simplify the mean calculation, and provide a printed recording sheet with a labeled space for each draw, the sum, and the final mean so students can follow the same steps every round.
Extension (above grade level)
Have advanced teams run a fourth round with a sample size of eight draws instead of four, plot those larger-sample means in a different color on the same class dot plot, and compare how tightly the eight-draw dots cluster compared to the four-draw dots.
ELL supports
Pre-teach "sample," "population," and "distribution" with a simple visual: a jar of twenty labeled marbles (the population) next to a small scoop holding four marbles (a sample), showing that the scoop's average can differ from the jar's true average. Allow teams to record their draws and means using numbers and a simple diagram rather than written sentences.