Teacher guide — Grade 9, Unit 7: Percent, rate and per-capita¶

Time: 3 lessons + project (about 5 periods). Track: A/B.

#	Lesson	Time
1	Share, percent and per 1,000	40–45 min
2	Choosing a denominator	40–45 min
3	Percent change and percentage points	40–45 min
P	Unit project: Rate detective	2 periods

Before you start¶

Materials: Notebook notebooks/rates.ipynb (or spreadsheet).
Read docs/pedagogy/lesson-anatomy.md and docs/pedagogy/ai-use-policy.md.

If you have no computers / no internet¶

Spreadsheet units can be done as a paper grid: draw the table, write formulas as words ('sum of column C').

Common misconceptions¶

A rate with the wrong denominator misleads (girls enrolled ÷ all enrolled ≠ ÷ girls of school age).
Percent of a percent confusion.

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: Share, percent and per 1,000 1. 12 of 200 as a percent?
Answer: 6%. 2. 12 of 200 per 1,000?
Answer: 60 per 1,000. 3. Why per 1,000 for rare things?
Answer: Small percents are hard to read; per 1,000 gives readable numbers.

Lesson 2: Choosing a denominator 1. Girls' share of enrolment divides by…
Answer: Total enrolment (girls + boys). 2. Why can two 'girls' percentages differ?
Answer: Different denominators answer different questions. 3. Always state the denominator in…
Answer: The chart title or caption.

Lesson 3: Percent change and percentage points 1. 48% → 50%: points?
Answer: 2 points. 2. Relative change?
Answer: 2 ÷ 48 ≈ 4.2%. 3. Fair headline wording?
Answer: State 'percentage points' for the difference.

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¶

Optional Computer Science (Grades 9–10): databases/SQL and introductory programming; compulsory ICT/Maths data handling.

Answers: practice exercises¶

0.025; 2.5%; 25 per 1,000.
840 ÷ 28 = 30 students per teacher.
100 × 1,180 ÷ 1,250 = 94.4 males per 100 females.
Passes: 18 + 28 + 5 = 51 of 70 → 72.9%. Simple average of rates = 70%: the big class (70%) and small class (50%) are wrongly given equal weight with the small 90% class.
(a) literate people aged 5+ ÷ people aged 5+; (b) remittances received ÷ GDP; (c) hospital beds ÷ population × 10,000; (d) students ÷ computers.
+10.3 percentage points; percent change 10.3 ÷ 65.9 ≈ 15.6%. Headline: "Literacy rose from 65.9% to 76.2% between the 2011 and 2021 censuses, up about 10 percentage points."
+20% over the decade; annual growth (1.2)^(0.1) − 1 ≈ 1.84% per year.
Vehicles may have grown much faster than deaths: deaths per vehicle can fall while deaths per person (and the total) rise. Check deaths per 100,000 people and the counts.
Synthetic sums: Hill 84.4, Mountain 87.9, Terai 97.2 males per 100 females; Hill lowest. In real data, hill districts with heavy male labour migration have low sex ratios.
No: 1.1 × 1.1 = 1.21 → 21%.

Lesson 2 activity: weighted girls' share by belt — Hill 50.16%, Mountain 50.15%, Terai 50.11%; mean of district shares — Hill 50.24%, Mountain 50.05%, Terai 49.80%. Small differences because district shares are all close to 50%; the method matters much more when rates vary a lot. Lesson 3 activity: 400,000 → 460,000 is +15%, about 1.41% per year. Rice index = 92 ÷ 80 × 100 = 115 (15% rise).

Real-data exercises: notes¶

R1 Nepal's remittances are among the highest shares in the world (around a quarter of GDP in recent years); % of GDP compares economies of different sizes.
R2 Census 2021 vs 2011: Bagmati and Madhesh had the largest increases in count; some hill/mountain districts lost people (provincial totals all grew modestly; check the portal). Annual growth national 0.92% (NSO).
R3 Index with 2014 = 100; spikes appear in years with supply shocks (e.g. 2015 blockade period). Let students find and explain them.