The shape of the lesson
By the end of the lesson, learners can
- Bar charts and pictograms: In the lab's charts tab, change the numbers of each fruit and watch the bar chart, the pictogram and the pie chart all redraw from the same table.
- Pie charts and 360°: A pie chart shows how a whole is shared out.
- Stem-and-leaf diagrams: Open the stem-and-leaf tab: the stem is the tens digit and the leaf is the units digit.
- Pie chart angles: \(\dfrac{360^\circ}{\text{total}}\) per item, then check the angles add to \(360^\circ\).
- Reading a pie chart: number \(= \dfrac{\text{angle}}{360} \times \text{total}\).
- Pictograms: symbols \(\times\) key value; part-symbols are fractions of it.
- Composite bars: section size = top reading \(-\) bottom reading.
- Stem-and-leaf: ordered leaves and a key, every time.
One picture every idea returns to
In a pie chart the whole circle, \(360^\circ\), is the total frequency, so each item gets \(\dfrac{360^\circ}{\text{total}}\). In a pictogram, always use the key. A stem-and-leaf diagram must be ordered and must have a key.
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, Data you can see.. Bar charts, pictograms, pie charts and stem-and-leaf diagrams each show a frequency table as a picture. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 13 min | Teach and check: Bar charts and pictograms | In the lab's charts tab, change the numbers of each fruit and watch the bar chart, the pictogram and the pie chart all redraw from the same table. Project tab 3 of the lab (Averages and charts lab, charts) and let a student drive it while the class predicts. Model the worked example Read a pictogram on the board, one line at a time. Your turn: In a composite bar chart, the bar for Year 10 reaches 60 students. The 'walk' section goes from 0 to 25, 'bus' from 25 to 48 and 'car' from 48 to 60. How many Year 10 students travel by bus? | Whole class, then pairs |
| 13 to 21 min | Teach and check: Pie charts and 360° | A pie chart shows how a whole is shared out. Model the worked example Draw a pie chart on the board, one line at a time. | Pairs |
| 21 to 30 min | Teach and check: Stem-and-leaf diagrams | Open the stem-and-leaf tab: the stem is the tens digit and the leaf is the units digit. Project tab 4 of the lab (Averages and charts lab, stem-and-leaf) and let a student drive it while the class predicts. Model the worked example Build and use a stem-and-leaf diagram on the board, one line at a time. | Think-Pair-Share |
| 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, 16 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 Stem-and-leaf diagrams, 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.
Think-Pair-Share
Pose the question, give thirty seconds of silent thinking, then a minute to compare with a partner before a few pairs share with the class. The silent minute is the part that cannot be cut.
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 |
|---|---|
| In a composite bar chart, read the size of each section, not the height of its top. | The bus section that ends at 48 is \(48 - 25 = 23\) students. |
| A bigger angle does not always mean more people when two pie charts have different totals. \(80^\circ\) of 72 people and \(64^\circ\) of 90 people are both 16 people. | Return to Pie charts and 360°: ask a pair to state the correct version and show it on the lab before moving on. |
| No key, no marks: the examiner must know whether 5 | 1 means 51, 5.1 or 510. | And an unordered stem-and-leaf diagram also loses a mark. |
Statistical charts and diagrams: worksheet
6 questions, 16 marks. Written in the style of the papers; no past paper question is reproduced.
40 students chose their favourite sport: football 14, netball 10, hockey 9, tennis 7. Calculate the angle of each sector of a pie chart.
In a pie chart, a sector of \(54^\circ\) represents 27 people. (a) How many people does the whole pie chart represent? (b) How many people does a \(100^\circ\) sector represent?
The ages of 12 members of a club are
34 27 41 38 29 45 33 27 50 36 42 31
(a) Draw an ordered stem-and-leaf diagram with a key. (b) Find the median age.
In a composite bar chart, the bar for one shop reaches 60 sales. The sections are: phones from 0 to 25, tablets from 25 to 48, laptops from 48 to 60. How many more tablets than laptops were sold?
In a pictogram, one symbol represents 12 visitors. (a) How many symbols should be drawn for 30 visitors? (b) How many visitors do \(4\tfrac{1}{4}\) symbols represent?
180 people were asked how they travel to work. The pie chart has a \(150^\circ\) sector for bus and a \(90^\circ\) sector for car. The rest travel by cycle or on foot, and the angle for cycle is twice the angle for walk.
(a) Find the angle for walk. (b) How many people cycle?
Answer key and marking notes
- Each student is \(\dfrac{360^\circ}{40} = 9^\circ\).
- Football \(126^\circ\), netball \(90^\circ\), hockey \(81^\circ\), tennis \(63^\circ\).
- Check: \(126 + 90 + 81 + 63 = 360^\circ\).
- (a) Each person is \(\dfrac{54}{27} = 2^\circ\), so the total is \(\dfrac{360}{2} = 180\) people.
- (b) \(\dfrac{100}{2} = 50\) people.
- (a) 2 | 7 7 9 3 | 1 3 4 6 8 4 | 1 2 5 5 | 0 with Key: 3 | 4 means 34 years.
- (b) \(n = 12\): the median is halfway between the 6th and 7th values, 34 and 36, so 35 years.
- Tablets: \(48 - 25 = 23\). Laptops: \(60 - 48 = 12\).
- \(23 - 12 = 11\) more tablets.
- (a) \(\dfrac{30}{12} = 2.5\), so two and a half symbols.
- (b) \(4.25 \times 12 = 51\) visitors.
- (a) Angles left: \(360 - 150 - 90 = 120^\circ\). Walk \(= x\), cycle \(= 2x\), so \(3x = 120\) and \(x = 40^\circ\).
- (b) Cycle angle \(= 80^\circ\). Each person is \(\dfrac{360}{180} = 2^\circ\), so \(\dfrac{80}{2} = 40\) people cycle.
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.
72 people were asked to name their favourite season. 20 of them chose summer. What angle should the summer sector have in a pie chart?
- A\(100^\circ\)
- B\(20^\circ\)
- C\(18^\circ\)
- D\(27.8^\circ\)
The pie chart shows how 180 students travel to school. How many students walk?
- A50
- B100
- C200
- D27.8
The composite bar chart shows how the students in three year groups travel to school. How many Year 10 students travel by bus?
- A30
- B55
- C25
- D70
The stem-and-leaf diagram shows the marks of 16 students.
| 1 | 2 5 8 |
| 2 | 0 3 3 6 9 |
| 3 | 1 4 4 7 |
| 4 | 0 2 5 8 |
- A30
- B29
- C31
- D8.5
A pie chart shows the favourite clubs of the 540 students in a school. The drama sector has an angle of \(48^\circ\). Then 60 new students join the school, and all of them choose drama. A new pie chart is drawn for all 600 students. What is the new angle for drama?
- A\(79.2^\circ\)
- B\(88^\circ\)
- C\(53.3^\circ\)
- D\(132^\circ\)
In a pie chart, the angles for options A, B and C are in the ratio \(2 : 3 : 4\). The only other option, D, has a sector of \(90^\circ\) and represents 45 people. How many people chose option C?
- A60
- B120
- C80
- D45
Quiz key
Each person gets \(\dfrac{360^\circ}{72} = 5^\circ\), so 20 people get \(20 \times 5 = 100^\circ\). The tempting \(20^\circ\) gives each person only \(1^\circ\), ignoring that the whole circle is \(360^\circ\). \(18^\circ\) is \(360 \div 20\), dividing by the wrong number, and 27.8 is the PERCENTAGE who chose summer (\(\dfrac{20}{72} \times 100\)), not an angle.
Walk has an angle of \(100^\circ\). Number of students \(= \dfrac{100}{360} \times 180 = 50\). (Or: each student is \(\dfrac{360}{180} = 2^\circ\), and \(100 \div 2 = 50\).) The tempting 100 is the angle itself, not the number of students. 200 comes from \(\dfrac{100 \times 360}{180}\), the fraction upside down, and 27.8 is the percentage who walk.
In the Year 10 bar, the bus section starts at 25 (the top of the walk section) and ends at 55. So \(55 - 25 = 30\) Year 10 students travel by bus. The tempting 55 reads only the top of the bus section. 25 is the number who walk, and 70 is the total for Year 10.
The median is at position \(\dfrac{16+1}{2} = 8.5\), halfway between the 8th and 9th values. Counting: 12, 15, 18, 20, 23, 23, 26, 29, 31, so the median is \(\dfrac{29 + 31}{2} = 30\). The tempting 29 and 31 are just the 8th or the 9th value on its own, and 8.5 is the position, not the mark.
Drama students at first: \(\dfrac{48}{360} \times 540 = 72\). After the new students join: \(72 + 60 = 132\) out of 600. New angle \(= \dfrac{132}{600} \times 360 = 79.2^\circ\). The tempting \(88^\circ\) adds the angle for 60 students from the OLD chart (\(60 \times \dfrac{360}{540} = 40^\circ\)) to \(48^\circ\), but every degree now stands for more students. \(53.3^\circ\) only scales \(48^\circ\) by \(\dfrac{600}{540}\), and 132 is the number of drama students, not an angle.
Angles for A, B and C: \(360 - 90 = 270^\circ\), shared \(2 : 3 : 4\), so one part is \(270 \div 9 = 30^\circ\) and C is \(4 \times 30 = 120^\circ\). D shows that \(90^\circ\) is 45 people, so each person is \(2^\circ\), and C is \(120 \div 2 = 60\) people. The tempting 120 is C's angle, not its number of people. 80 shares a total of 180 people as if D were part of the ratio (\(\tfrac{4}{9} \times 180\)), and 45 is the number who chose D.
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.