The shape of the lesson
By the end of the lesson, learners can
- Types of data and tally tables: Open the lab and look at the frequency table: each value is listed once with how often it occurs.
- Two-way tables: A two-way table sorts the same people by two things at once, for example gender and how they travel to school.
- Comparing data and its limits: The lab shows test marks for two classes.
- Classify: words are qualitative; counts are discrete; measurements are continuous.
- Tally: one pass through the data, gates of five, then check the frequencies add to the total.
- Two-way tables: fill any row or column with only one gap, then check the last row or column.
- Fractions: the total after 'of' goes on the bottom.
- Compare: one average and one spread, each in context.
One picture every idea returns to
Classify first (qualitative or quantitative, discrete or continuous), count with a tally, and read every fraction from the right row or column. To compare two data sets, always compare one average AND one measure of spread, and say what each means in context.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Sort it, count it, read it.. Before any average or chart, data has to be sorted into types and counted into tables. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Types of data and tally tables | Open the lab and look at the frequency table: each value is listed once with how often it occurs. Project tab 2 of the lab (Averages and charts lab, frequency tables) and let a student drive it while the class predicts. Model the worked example Classify the data on the board, one line at a time. | Whole class, then pairs |
| 13 to 21 min | Teach and check: Two-way tables | A two-way table sorts the same people by two things at once, for example gender and how they travel to school. Model the worked example Complete a two-way table on the board, one line at a time. Your turn: In a club of 50 members, 22 are adults. 30 members can swim, and 18 of the swimmers are children. How many adults cannot swim? | Pairs |
| 21 to 30 min | Teach and check: Comparing data and its limits | The lab shows test marks for two classes. Project tab 5 of the lab (Averages and charts lab, comparing data) and let a student drive it while the class predicts. Model the worked example Compare two classes on the board, one line at a time. | Connect-Extend-Challenge |
| 30 to 36 min | Check | The four Stage 1 questions from the student lesson, answered on mini whiteboards or by show of fingers. Re-teach the one most get wrong. | Individual, then whole class |
| 36 to 43 min | Plenary | The exam-style questions from Stage 2, one at a time: thirty seconds alone, then a random call. The feedback lines in the key give the examiner's wording. | Individual, random call |
| 43 to 45 min | Exit and homework | Set the worksheet below (6 questions, 17 marks). Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Comparing data and its limits, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Connect-Extend-Challenge
After the new idea, each student writes three lines: how it connects to what they knew, how it extends their thinking, and what still challenges them. Pairs compare, then the challenges become the plenary.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| Always check that the frequencies add up to the total number of data values. | A missing or double-counted value is the most common way to lose the mark for a frequency table. |
| Read the words after 'of'. 'What fraction of the girls...' divides by the girls' total, not by the grand total of 60. | Using the wrong total is the examiner's favourite trap in two-way tables. |
| With times, a LOWER mean is better (faster). | With spread, a smaller range means MORE consistent, not 'worse'. Always say what the numbers mean in context, not just 'the mean is bigger'. |
Classifying and interpreting data: worksheet
6 questions, 17 marks. Written in the style of the papers; no past paper question is reproduced.
State whether each type of data is qualitative, discrete or continuous.
(a) The number of text messages sent in a day (b) The length of a leaf (c) The make of a phone (d) The temperature at noon
The numbers of goals scored in 16 football matches are
2 0 1 3 1 1 0 2 4 1 2 0 1 3 1 2
(a) Make a frequency table. (b) In how many matches were more than 2 goals scored?
Complete the two-way table.
| Left-handed | Right-handed | Total | |
|---|---|---|---|
| Boys | 4 | ||
| Girls | 17 | 20 | |
| Total | 7 | 36 |
Using your table from the previous question, find (a) the fraction of the boys who are left-handed (b) the percentage of the left-handed students who are girls.
In June, Town P had a median daily rainfall of 4 mm with range 9 mm. Town Q had a median of 7 mm with range 3 mm. Make two comparisons between the rainfall in the two towns.
A cafe records the drinks bought by its 200 customers on one Saturday.
| Hot drink | Cold drink | Total | |
|---|---|---|---|
| Morning | 85 | 120 | |
| Afternoon | 48 | ||
| Total | 200 |
(a) Complete the table. (b) What percentage of the hot drinks were sold in the morning? (c) The manager says 'Afternoon customers always prefer cold drinks.' Comment on this claim.
Answer key and marking notes
- (a) discrete (counted)
- (b) continuous (measured)
- (c) qualitative (a category)
- (d) continuous (measured)
- (a) 0 goals: 3, 1 goal: 6, 2 goals: 4, 3 goals: 2, 4 goals: 1.
- Check: \(3 + 6 + 4 + 2 + 1 = 16\).
- (b) More than 2 means 3 or 4 goals: \(2 + 1 = 3\) matches.
- Girls left-handed: \(20 - 17 = 3\). Check left column: \(4 + 3 = 7\).
- Boys total: \(36 - 20 = 16\), so boys right-handed: \(16 - 4 = 12\).
- Right-handed total: \(12 + 17 = 29\) (check: \(36 - 7 = 29\)).
- (a) \(\dfrac{4}{16} = \dfrac{1}{4}\)
- (b) \(\dfrac{3}{7} \times 100 = 42.9\%\) (3 s.f.)
- Average: Town Q had more rain on average (higher median, \(7 > 4\)).
- Spread: Town Q's rainfall was more consistent (smaller range, \(3 < 9\)).
- (a) Morning cold: \(120 - 85 = 35\). Afternoon total: \(200 - 120 = 80\).
- Afternoon hot: \(80 - 48 = 32\). Hot total: \(85 + 32 = 117\). Cold total: \(35 + 48 = 83\) (check: \(117 + 83 = 200\)).
- (b) \(\dfrac{85}{117} \times 100 = 72.6\%\) (3 s.f.)
- (c) On this day \(\dfrac{48}{80} = 60\%\) of afternoon customers chose cold drinks, so most did.
- But the data come from one Saturday only (perhaps a hot day), so 'always' is not justified.
6 multiple-choice questions on this lesson
From the topic question bank. Assign them in the app for a marked score in your gradebook, or run the topic as a class game.
Which of these is discrete data?
- AThe number of goals scored in a hockey match
- BThe time taken to run 400 m
- CThe mass of a newborn baby
- DThe favourite colour of a student
A tally reads |||| |||| |||| |||. What is the frequency?
- A18
- B15
- C13
- D4
The two-way table shows the sport chosen by 80 students.
| Football | Tennis | Swimming | Total | |
|---|---|---|---|---|
| Year 9 | 18 | 7 | 11 | 36 |
| Year 10 | 14 | 12 | 18 | 44 |
| Total | 32 | 19 | 29 | 80 |
- A\(\dfrac{18}{29}\)
- B\(\dfrac{18}{44}\)
- C\(\dfrac{18}{80}\)
- D\(\dfrac{11}{29}\)
A council wants to know whether the people of a town support building a new car park. It asks 200 people who are parking at a busy supermarket. 82% say yes. Which is the best reason why this result may not represent the whole town?
- AThe sample is biased: people who are already parking are more likely to want more parking.
- B200 people is too many for a survey to be accurate.
- CThe answers are qualitative, so no conclusion can be drawn.
- D82% is not a whole number of people.
(Extended) A gardener grows two groups of sunflowers. Group A: median height 34 cm, interquartile range 6 cm. Group B: median height 31 cm, interquartile range 14 cm. Which statement is correct?
- AGroup A is taller on average and more consistent in height.
- BGroup A is taller on average, but Group B is more consistent in height.
- CGroup B is more consistent, because a larger IQR means the heights are higher.
- DGroup B is taller on average, because its heights are more spread out.
250 people are surveyed. 40% of them are under 30. Of the people under 30, 65% use a social media app every day. Of the people aged 30 or over, 30% use it every day. What percentage of the daily users are under 30?
- A59.1%
- B65%
- C26%
- D40%
Quiz key
Goals are counted: a match can have 2 or 3 goals but never 2.4, so the data are quantitative and discrete. Time and mass are measured and can take any value in a range, so they are continuous (the time is the most tempting wrong answer, but 52.37 s is a perfectly possible time). A colour is a category, so it is qualitative.
Each crossed gate is 5 (four upright strokes and one across them), so \(5 + 5 + 5 + 3 = 18\). Counting only the four upright strokes in each gate gives \(4 + 4 + 4 + 3 = 15\). 13 misses a whole gate, and 4 is the number of groups, not the frequency.
'Of the students who chose swimming' means the swimming total, 29, goes on the bottom, and 18 of them are in Year 10: \(\dfrac{18}{29}\). The tempting \(\dfrac{18}{44}\) is the fraction of YEAR 10 students who chose swimming (the wrong total). \(\dfrac{18}{80}\) uses the grand total, and \(\dfrac{11}{29}\) is the Year 9 swimmers.
Only drivers at a supermarket were asked, and they are the people most likely to want a car park, so the sample is not representative of the town: it is biased. A larger sample makes results more reliable, not less, so '200 is too many' is wrong. Yes/no answers are qualitative but can still be counted and turned into a percentage, and 82% of 200 is 164 people, a whole number.
Average: \(34 > 31\), so Group A is taller on average. Spread: \(6 < 14\), so Group A's heights are closer together, which means more consistent. The tempting second option gets the spread backwards: a LARGER interquartile range means the middle half of the data is more spread out, so less consistent. The spread says nothing about which group is taller.
Under 30: \(0.4 \times 250 = 100\) people, of whom \(0.65 \times 100 = 65\) are daily users. Aged 30 or over: \(150\) people, of whom \(0.3 \times 150 = 45\) are daily users. Daily users altogether: \(65 + 45 = 110\). So \(\dfrac{65}{110} \times 100 = 59.1\%\) (3 s.f.). The tempting 65% is the percentage of the UNDER-30s who are daily users: the wrong total. 26% divides 65 by everybody (250), and 40% is just the share of the whole survey that is under 30.
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.