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Teacher guide — Grade 10, Unit 4: Time series basics

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

# Lesson Time
1 Trend, season and noise 40–45 min
2 Fitting a trend 40–45 min
3 Anomalies 40–45 min
P Unit project: Climate or weather? 2 periods

Before you start

  • Materials: Notebook notebooks/time_series.ipynb.
  • Read docs/pedagogy/lesson-anatomy.md and docs/pedagogy/ai-use-policy.md.

If you have no computers / no internet

Plot 12 monthly values by hand; mark the seasonal peak; compute a yearly average.

Common misconceptions

  • A warm month proves climate change; weather ≠ climate.
  • Trend lines from short series are unreliable.

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: Trend, season and noise 1. Is a yearly warm summer a trend?
Answer: No, it is seasonality. 2. Why use annual means for trend?
Answer: They average out the seasonal cycle. 3. What is noise?
Answer: Random variation not explained by trend or season.

Lesson 2: Fitting a trend 1. Slope 0.03 °C/yr is how much per decade?
Answer: 0.3 °C. 2. Why try different start years?
Answer: To check how sensitive the trend is. 3. Weather vs climate?
Answer: Weather is short-term; climate is long-term pattern.

Lesson 3: Anomalies 1. Anomaly = ?
Answer: Observed − usual (baseline) value for that month. 2. Why subtract a monthly baseline?
Answer: To remove the seasonal cycle. 3. Positive anomaly means…
Answer: Warmer than usual.

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 Grade 10: Python programming, databases and AI & contemporary technology; compulsory Maths data handling/statistics.

Answers: practice exercises

  1. Trend: tourism growth; seasonality: monsoon peak in umbrella sales; noise: unusual weeks (a dry July).
  2. 0.45 °C per decade; 1.8 °C over 40 years.
  3. +0.6 °C.
  4. Synthetic: highest 2010 (≈ 2,886 mm), lowest 2007 (≈ 825 mm) — a factor of 3.5 (the synthetic rain is very noisy).
  5. Trend ≈ +111 mm per decade, but the SD of monsoon totals is ≈ 420 mm: the trend is small compared with year-to-year variation over 30 years — no confident claim.
  6. January ≈ +0.40 °C/decade, July ≈ −0.13 °C/decade: winter warms faster in this table (real Himalayan records also often show stronger winter warming — a nice link, but check sources).
  7. climate.set_index("date")["mean_temp_c"].resample("YS").mean() gives the same 30 values.
  8. Every anomaly shifts by the same amount (+0.22 °C) because the baseline is cooler; the trend (0.28 °C/decade) does not change.
  9. Annual anomalies 2015–2020: 0.76, 0.33, 0.68, 0.08, 0.15, 0.29 — fitting from 2015 gives −1.0 °C/decade, because 2015 was the warmest year (a cherry-picked start). From 1991 the trend is +0.28.
  10. Check: df.groupby("month") of the anomaly within the baseline years ≈ 0 (floating-point tiny values).

Lesson 1 Make: monsoon share of annual rain ≈ 87% on average in the synthetic table. Lesson 2 Make: fitting the monthly series directly gives ≈ 0.32 °C/decade (the seasonal cycle adds noise and the series starts in January and ends in December, which nudges the slope); residuals show the seasonal wave. Lesson 3: largest monthly anomaly June 2019 (+2.3 °C); weakest monsoon 2007.

Real-data exercises: notes

  • R1 NASA POWER (MERRA-2 model) trends for Nepal grid cells are typically a few tenths of a °C per decade; values differ by place and are model-based, not station data.
  • R2 The world has warmed ≈ 0.2 °C per decade since the 1970s; recent years are the warmest on record.
  • R3 Dips appear in years of conflict and political crises; 2015 (earthquake) is just after this dataset ends — newer MoCTCA reports show it.