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Teacher guide — Grade 8, Unit 6: Comparing groups

Time: 3 lessons + project (about 5 periods). Track: A (no-code).

# Lesson Time
1 Counts versus rates 40–45 min
2 Comparing two groups 40–45 min
3 Percent change and percentage points 40–45 min
P Unit project: Two places, fair comparison 2 periods

Before you start

  • Materials: Printed extract of the (synthetic) district table: 10 districts; calculators.
  • Read docs/pedagogy/lesson-anatomy.md and docs/pedagogy/ai-use-policy.md.

If you have no computers / no internet

All eight units run on paper, calculators and the blackboard. Computers are optional (spreadsheet or CODAP, https://codap.concord.org); every activity below has a paper version.

Common misconceptions

  • A bigger district with more school children is 'better at education'. Compare shares, not counts.
  • Percent change vs percentage points.

Differentiation

  • Support: give a partially filled table / sentence starters; pair with a data-steward role.
  • Stretch: ask "what would change your conclusion?" and "who is missing?"

Answer key (check questions)

Lesson 1: Counts versus rates 1. District P: 900 of 1,800 children enrolled; Q: 600 of 1,000. Which has the higher enrolment rate?
Answer: P 50%, Q 60% → Q. 2. Why is a count unfair across districts?
Answer: Bigger districts have bigger counts just by being bigger. 3. Convert 45 per 1,000 to a percent.
Answer: 4.5%.

Lesson 2: Comparing two groups 1. What do you compute for each group before comparing?
Answer: The same summary, e.g. the median. 2. If belt medians are 66 and 77, what is the difference?
Answer: 11 percentage points. 3. Why draw both on the same axis?
Answer: To compare fairly at a glance.

Lesson 3: Percent change and percentage points 1. 60% to 66%: change in percentage points?
Answer: 6 points. 2. Same change as relative percent?
Answer: 6 ÷ 60 = 10%. 3. Why do headlines sometimes pick the bigger-sounding one?
Answer: To make a change seem more dramatic; always ask which one is used.

Assessment

Starter quiz each lesson (3 questions, one recalling the previous lesson); unit quiz in quiz.yml; project marked with the rubric in docs/pedagogy/assessment.md; 2-minute oral check per group.

Alignment

Extends the Grade 8 compulsory Maths statistics chapter (pie chart, mean, median, mode) with question-forming, data collection and interpretation.

Note (2026-10-11 revision): Lesson 1 now uses six named districts (Terai-09, Terai-15, Hill-05, Hill-03, Mountain-08, Hill-13) chosen so that the count and rate rankings really differ. The first six rows of the table rank the same both ways, so do not use them for this activity.

Answers: practice exercises

  1. Girls 216/240 = 90%; boys 221/260 = 85%. Girls did better although more boys passed.
  2. 8 per 1,000 = 0.8%; 2.5% = 25 per 1,000; 0.3 per 100 = 300 per 100,000.
  3. (176 − 160) ÷ 160 × 100 = 10% increase.
  4. X: 150 ÷ 1,500,000 × 100,000 = 10 per 100,000; Y: 40 ÷ 200,000 × 100,000 = 20 per 100,000. Y is more dangerous per person.
  5. +30 percentage points; percent change (70 − 40) ÷ 40 = 75%. Report: "Households with a toilet rose from 40% to 70%, up 30 percentage points."
  6. A: median 33, range 18; B: median 32, range 8. Similar centres; A is much more spread out (both the weakest and strongest students are in A). Dot plots on one 20–40 axis show this.
  7. Count of schools reflects size (Kathmandu has many people). Compute schools (or seats) per 1,000 school-age children, and consider distance/travel time, which matters more in remote districts.
  8. Rs 1,000 → Rs 800 (−20%) → Rs 960 (+20% of 800). Not back: 4% lower than the start.
  9. "From how many to how many cases?" (base size) and "Over what period, and has testing changed?" Also: compared with other wards/years?
  10. Mountain 65.5, Hill 77.5, Terai 70.35. The 10-district extract includes only 2 Terai and 3 Mountain districts, so its medians depend on which districts happen to be included: small groups give shaky summaries.

Real-data exercises: notes

  • R1 Census 2021 final: 29,164,578 people and about 6.67 million households → about 4.4 persons per household (check exact household count on the results page). Mountain and western Terai districts tend to have larger households, Kathmandu valley smaller; let students discover this.
  • R2 India has by far the largest count; rates are closer and change year to year (Bhutan's rate is high). Values change with each WDI update, so check them on the day.
  • R3 69.1 − 54.8 = 14.3 years; percent change ≈ 26%.