Teacher guide — Grade 11, Unit 6: Time series and seasonality¶

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

#	Lesson	Time
1	Seasonal indices	40–45 min
2	Trend with a fitted line	40–45 min
3	Trend with uncertainty	40–45 min
P	Unit project: Climate or weather?	2 periods

Before you start¶

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

If you have no computers / no internet¶

Plot 3 years of monthly values on one sheet of graph paper with years overlaid.

Common misconceptions¶

A cold winter disproves warming (weather vs climate).
A trend line from 5 years shows the long-run trend.

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: Seasonal indices 1. Seasonal indices sum to…
Answer: About 0 (if defined relative to the mean). 2. Why de-seasonalise?
Answer: To see the trend without the yearly cycle. 3. Is a cold January evidence against warming?
Answer: No: weather varies.

Lesson 2: Trend with a fitted line 1. Slope 0.03/yr → per decade?
Answer: 0.3. 2. Why try different start years?
Answer: To test sensitivity. 3. Short series risk?
Answer: Unreliable trend.

Lesson 3: Trend with uncertainty 1. Why resample whole years?
Answer: Months within a year are related. 2. Interval excludes 0 means…
Answer: A non-zero trend is likely in this series. 3. Does it prove cause?
Answer: No: it describes the trend, not the reason.

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¶

Enrichment aligned to NEB Grade 11–12 Computer Science (databases, programming) and Maths/Statistics.

Answers: practice exercises¶

10.2 − (−7.8) = 18.0 °C; below the overall mean of about 18.5 °C, so a slightly cold January.
3.67 × 132.7 ≈ 487 mm.
Months in the same year are related (autocorrelated); resampling them separately pretends there is more independent information and makes intervals too narrow.
Additive rain indices: about −105 to −113 mm in dry months and +354 mm in July. An additive index would predict negative rain for a dry month in a dry year; rain's seasonal swing scales with the level, so ratios fit better.
Trends (°C/decade, de-seasonalised): Dec–Feb 0.42, Sep–Nov 0.30, Jun–Aug 0.22, Mar–May 0.17 — winter fastest.
January only: 0.40 °C/decade, CI ≈ 0.15 to 0.67 — wider because one month per year is noisier than an annual mean of 12 months.
October 2020 (78.3 mm, adjusted ≈ 456 mm): an exceptionally wet October relative to a normal October (like a late monsoon).
In our simulation 9% of the intervals excluded 0 (should be about 5%): percentile-bootstrap intervals on 30 points are a little too narrow. Good discussion of methods having error rates too.
A −1 °C jump in 2005 turns the +0.28 °C/decade trend into about −0.22 °C/decade: a careless analyst would announce cooling. Station metadata and homogenisation matter.
Seasonally adjusted: same level as the data, season removed (for reading month-to-month change). Anomaly: difference from the month's baseline (for comparing places/periods). 12-month rolling mean: smooth trend, delayed (for seeing the long-run direction).

Lesson 2 sensitivity: trends from 1991 0.28, 1996 0.30, 2001 0.34, 2006 0.31, 2011 0.10 °C/decade. Lesson 1 Make: an average July carries about 31% of the year's rain (synthetic).

Real-data exercises: notes¶

R1 Expect positive trends of a few tenths of a degree per decade, CIs depend on the grid cell.
R2 Nepal's peak months are typically October–November and March–April; 2015 (earthquake) and 2020–21 (COVID-19) show as huge negative residuals.
R3 Tomato prices are often lowest in the winter harvest months and highest in the monsoon; check with the data.