Lesson plan Grade 7 Math

Sampling the Trace Line Water System: A Grade 7 Statistics Lesson

A 45-minute grade 7 lesson where students compare two water-sampling plans across four zones and calculate how well each plan represents the full system.

Grade: Grade 7
Subject: Math
Material: Lesson plan
Time: 45 min
Prep: No prep
Materials: Simple map of the four zones and the treatment plant (board sketch or handout), Calculator, Index cards for the exit ticket

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: Students calculate what percentage of Trace Line's 400 homes and its four zones two competing sampling plans actually reach, evaluating which plan yields data representative of the whole population.

All materials for 7.SP.A.1 →

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This material is in the public domain (CC0) and may be copied, edited, and shared freely, without attribution. Updated 2026-07-16.

Objectives

Students will calculate the percentage of a population that a sampling plan actually reaches.
Students will explain why a sample concentrated in one location fails to represent a population with uneven characteristics.

Vocabulary

Key words: random sample, representative sample, population, sampling plan

Teacher overview

The Trace Line Water System (a fictional rural water system used for this lesson) serves 400 homes spread across four zones of 100 homes each, and Zone A's homes are older, on average, than the homes in the other three zones. Two candidate plans for testing water quality across the system are on the table: Plan A tests only at the treatment plant, and Plan B tests a set of taps spread across all four zones. This lesson has students calculate exactly what share of the system's homes each plan reaches and use those percentages to argue which plan produces data a manager could trust. A common misconception in this lesson is assuming that any sample, as long as it includes enough total taps, is automatically representative, without checking whether those taps are actually spread across the population's meaningful differences.

Procedure

Hook (5 min): Show students a simple map of the fictional Trace Line Water System with four zones (A, B, C, D) of 100 homes each, and tell them Zone A's homes are on average older than the other zones' homes. Ask: if you could only test 5 taps for the whole system, where would you put them, and why?

Direct instruction (10 min): Introduce Plan A (5 taps, all located inside the treatment plant, not in any home) and Plan B (20 taps, 5 randomly selected from each of the 4 zones). Model calculating what percentage of the system's 400 homes Plan A actually samples water from: 0 of 400 homes, or 0 percent, because none of its taps are in a home at all.

Guided practice (15 min): In pairs, students calculate: the percentage of the system's 400 homes that Plan B samples overall, the percentage of Zone A's 100 homes that Plan B samples, and, if 40 of Zone A's 100 homes (40 percent) have older service lines, about how many of Zone A's 5 sampled homes under Plan B would be expected to have those older lines.

Independent practice (10 min): Each student writes a short paragraph explaining why Plan A cannot detect a problem concentrated in Zone A, even if that problem is common there, using their percentage calculations as evidence.

Closure / exit ticket (5 min): Students answer one question on an index card: "If Zone A actually has 200 homes instead of 100, while Zones B, C, and D stay at 100 homes each, how should Plan B's 20 total taps be redistributed to keep the sample proportional to each zone's size?" Collect and check for proportional reasoning before dismissal.

From Water for Schools (waterforschools.org). This material is in the public domain (CC0) and may be copied, edited, and shared freely.

Answer Key

Items 1 through 3 answer the three guided-practice calculations, in order.

Answer: 5 percent.
Plan B samples 20 of the system's 400 homes: 20 ÷ 400 = 0.05, or 5 percent.
Answer: 5 percent.
Plan B samples 5 of Zone A's 100 homes: 5 ÷ 100 = 0.05, or 5 percent, the same rate as every other zone.
Answer: about 2 homes.
If 40 percent of Zone A's homes have older service lines, a representative sample of 5 homes would be expected to include about 0.40 × 5 = 2 homes with those lines.
Answer: about 8 taps in Zone A, 4 taps in each of the other three zones.
This is the exit-ticket answer. Zone A would then hold 200 of the system's 500 total homes, or 40 percent, so a proportional sample of 20 taps would put about 0.40 × 20 = 8 taps in Zone A; splitting the remaining 12 taps evenly across Zones B, C, and D (100 homes each, 20 percent of the total each) gives about 4 taps per zone. Accept any answer that keeps each zone's tap count proportional to its share of the system's 500 total homes.

Differentiation

Support (below grade level)

Provide a printed table with the zone names, home counts, and Plan B's tap counts already filled in, so students only need to compute the percentages rather than organize the data themselves. Work through the Plan A calculation (0 percent) together as a class before pairs begin the Plan B calculations.

Extension (above grade level)

Ask students to design a Plan C that samples the same total of 20 taps but concentrates more taps in Zone A because it is known to have more older service lines, then justify in writing why an uneven-but-informed sample can sometimes be more useful than an evenly split one.

ELL supports

Provide a labeled zone map with icons for "treatment plant" and "home" so students can see visually why Plan A's taps never touch an actual home. Allow the independent-practice paragraph to be replaced with a two-column chart comparing Plan A and Plan B side by side.