Cover lesson · Humanities · Year 6 · Advanced
LNF: Numeracy → Learning that statistics represent data and that probability models chance helps us make informed inferences and decisions → Interpreting data
Name: Class: Date:
What this practises: interpreting data in geography. Pupils read a bar chart, a line graph and a table of monthly rainfall for two invented weather stations, one in the mountains of Eryri and one on the Pembrokeshire coast. They find the wettest and driest months and the range, work out totals and the mean, compare winter with summer, spot why a chart with an axis starting at 40 mm misleads, judge conclusions as true, false or cannot tell, and use the data to give holiday advice. The rainfall numbers are invented but follow the real pattern of rain in Wales.
Print: this sheet, one per pupil, and the stimulus sheet “Rainfall at two weather stations in Wales”, one between two. Colour printing helps but is not needed. Pupils need a pencil and a ruler. Calculators are allowed for checking only.
Run: 5 min read the stimulus sheet together, including the box “Why do mountains get more rain?” · 7 min Step 1 · 5 min Step 2 · 8 min Step 3 · 6 min Step 4 · 10 min Step 5 · 7 min Step 6 · 8 min Step 7. Total 56 minutes.
Collect: this sheet. Quick checks: Station A total 2760 mm, mean 230 mm, range 210 mm (January 340 mm, June 130 mm); Station B total 900 mm, mean 75 mm, range 65 mm (November 110 mm, May 45 mm). Winter and summer totals: Station A 910 mm and 460 mm, Station B 280 mm and 170 mm. On Chart 3 the November bar looks 14 times as tall as May’s, but November really had only about 2.4 times as much rain. Step 6: true, cannot tell, false, cannot tell.
A family wants to go on holiday in Wales, and they want to stay dry. They have found rainfall data for two places: a valley in the mountains of Eryri and a beach village on the Pembrokeshire coast. Your job is to read the charts, do the maths and give them good advice. Watch out: one of the charts is trying to trick you!
Cover the table (section 5 of the stimulus sheet) with a piece of paper. Use only the charts to answer. Then uncover the table and tick each answer that matches.
| # | Question | Answer | Tick |
|---|---|---|---|
| 1 | Chart 1: how much rain fell at Station A in March? | ||
| 2 | Chart 1: in which month did Station A get exactly 300 mm? | ||
| 3 | Chart 1: how much rain fell at Station A in August? Hint: each faint line is 10 mm. | ||
| 4 | Chart 2: how much rain fell at Station B in August? Hint: each faint line is 5 mm. | ||
| 5 | Chart 2: between which two months did the rain at Station B go up the most? By how much? |
The range tells you how spread out the data is. Range = wettest month − driest month.
| Station | Wettest month and amount | Driest month and amount | Range (mm) |
|---|---|---|---|
| A (Eryri) | |||
| B (Pembrokeshire) |
Which station has rain that changes more from month to month? How does the range show this?
(a) Add up all 12 months to find the total rain for the year. Tip: add the months in pairs first. Then find the mean: share the total equally between the 12 months (total ÷ 12).
| Station | Total for the year (mm) | Mean rain per month (mm) |
|---|---|---|
| A (Eryri) | ||
| B (Pembrokeshire) |
Show your working here:
(b) Someone says “Station A is about 3 times as wet as Station B.” Check by working out 3 × Station B’s total. Are they right?
(c) In which months did Station A get more than its mean? How many months is that?
Winter is December, January and February. Summer is June, July and August. Add the 3 months for each season.
| Station | Winter total (mm) | Summer total (mm) | Difference (mm) |
|---|---|---|---|
| A (Eryri) | |||
| B (Pembrokeshire) |
Finish the sentences. At both stations, winter is _____________ than summer. At Station A, winter is about _____ times as wet as summer.
Does this match what the stimulus sheet says about rain in the west of Wales? Explain.
Look at Chart 3, made by the holiday website. It uses the same Station B numbers as Chart 2.
(a) What number does the side (vertical) axis of Chart 3 start at? What number should a fair bar chart start at?
(b) Count the faint lines. On Chart 3, how many times as tall as the May bar is the November bar?
(c) Now use the table. How many times as much rain really fell in November as in May? Tip: try 2 × 45 and 3 × 45.
(d) Why could Chart 3 trick a visitor? Why might a holiday website do this?
(e) Draw a fair bar chart for Station B on the grid below. Use a ruler. The axis starts at 0 and each faint line is 10 mm. Write the number on top of each bar.
| Month | February | May | August | November |
|---|---|---|---|---|
| Station B rain (mm) | 75 | 45 | 65 | 110 |
(f) Compare the November and May bars on your fair chart with the same bars on Chart 3. What do you notice?
Read each conclusion. Write true, false or cannot tell. Then give evidence from the data. “Cannot tell” means the data does not give us enough information to know.
| Conclusion | True, false or cannot tell? | Evidence |
|---|---|---|
| (a) Station A is wetter than Station B in every month. | ||
| (b) It rains every day in Eryri. | ||
| (c) At Station B, November is more than 5 times as wet as May. | ||
| (d) Next January, Station A will get exactly 340 mm of rain. |
The Morgan family (invented) want a holiday week in Wales with as little rain as possible. They can choose Station A’s valley in Eryri or Station B’s beach village, in any month. Write them a short note (4 to 6 sentences). You must:
Sentence starters: I advise you to go to ... because ... · The data shows that ... · However, the data cannot tell you ...