Stem-and-leaf plots

Classroom resources

Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.

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Students will be able to

• I can build an ordered stem-and-leaf plot with a key.
• I can read values, the median, the mode and the range from a stem-and-leaf plot.

Timing

Predict and Run 8 min · Investigate 12 min · Modify 12 min · Practise and Make 8 min

Before class

Do the Run board first. Students need Mean, median, mode and range.

This is a hinge: describing and comparing distributions (next lesson) reads shape from these plots. The common mistake is leaving out a stem with no leaves, which hides gaps; it is planted in Jo's working. Others: unordered leaves, and reading a leaf as a value on its own (the board's key helps).

The board shows the dot plot and the stem-and-leaf plot together in Run and Make, so students can see they show the same data.

Running the lesson

1. Predict: take a show of hands; students who chose 3, 1, 5, 5, 8 read digits, not values.
2. Run: ask where 29 goes and why it goes at the end of its row.
3. Investigate: build a plot of the class's own data (arm spans, say) on the board.
4. Modify: before the three-digit task, ask what the stems should be for 105.
5. Make: collect answers; ask whether 35 has to appear.

When students get stuck

Answers to the checks

1. read a row: In a stem-and-leaf plot, a row reads $3 \mid 1\ 5\ 5\ 8$. Which values does it show?
   31, 35, 35 and 38. The stem 3 is the tens; each leaf is the units of one value.
2. add two values: Add 44 and 29 to the data (type them in the box). Where does each go? Was your prediction right about reading a row?
   
3. Build, then read: What is the median of the data in this plot?
   27
   11 values, so the median is the 6th: 14, 18, 21, 23, 23, 27.
4. Find the mistake: Jo draws a stem-and-leaf plot. Click the line where her working goes wrong.
   line 3
   Line 3: every stem from the smallest to the largest goes in, even with no leaves: 1, 2, 3, 4. The empty 3 row shows the gap between the 20s and the 40s.
5. Range from the plot: What is the range of the data?
   31
   Highest 45, lowest 14: 45 − 14 = 31.
6. Build one: Build the stem-and-leaf plot for these quiz scores: $8, 15, 17, 22, 26, 26, 31$.
   
   Stems 0, 1, 2, 3: 0 | 8, 1 | 5 7, 2 | 2 6 6, 3 | 1. A one-digit value has stem 0.
7. The mode: What is the mode?
   63
   The leaf 3 appears three times on the 6 stem: 63.
8. Count the values: How many values are in this plot?
   10
   Each leaf is one value: 2 + 5 + 3 = 10.
9. Use the key: A plot of heights has the key $15 \mid 2 = 152$ cm. What does $16 \mid 7$ show?
   167 cm
   The key tells you the place values: 16 | 7 is 167 cm.
10. Three digits: Edge case: values $105, 112, 118, 121$. What are the stems?
    10, 11 and 12
    For three-digit values the stem is the first two digits: 10 | 5, 11 | 2 8, 12 | 1.
11. Median: What is the median?
    63
    5th and 6th values are both 63, so the median is 63.
12. Range: What is the range?
    27
    79 − 52 = 27.
13. Which stems: Values $41, 44, 62, 65$. Which stems should the plot have?
    4, 5 and 6 (5 has no leaves)
    Every stem from 4 to 6, so the empty 5 row shows the gap.
14. Review: mean: Review: find the mean of $23, 31, 35, 35$.
    31
    124 ÷ 4 = 31.
15. a plot with a given median: Make a stem-and-leaf plot of 8 two-digit values with a median of 35.
    
    For example 21, 28, 33, 34, 36, 40, 45, 52: the 4th and 5th are 34 and 36, halfway is 35.

Solutions

One possible solution for each task. Other correct programs are fine.

one change at a time › Build one

Open task: any program that does what the step asks.

one change at a time › The mode

Open task: any program that does what the step asks.

one change at a time › Count the values

Open task: any program that does what the step asks.

one change at a time › Use the key

Open task: any program that does what the step asks.

one change at a time › Three digits

Open task: any program that does what the step asks.

a plot with a given median

Open task: any program that does what the step asks.

Stretch and support

Stretch: Draw a back-to-back stem-and-leaf plot for two classes' scores (leaves going left for one, right for the other).

Support: Sort the values first, then write them in rows by tens before making the plot.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient maths coach for a Year 7 student in Australia. Help me understand ONE idea only, from the lesson "Stem-and-leaf plots".

The idea: Creating stem-and-leaf plots: I can Students construct ordered stem-and-leaf plots from a data set and read values from them accurately.

What understanding looks like:
- Constructs an ordered stem-and-leaf plot with correct stems and leaves.
- Orders the leaves within each stem.
- Includes a key explaining what the stem and leaf represent.

Mistakes students often make here:
- A student leaves out an empty stem (Jo's mistake).
- A student reads a leaf as a value.
- A student writes leaves out of order.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Stem-and-leaf plots".

Exit ticket

Draw a stem-and-leaf plot of 17, 25, 22, 41, 18, 29, 26 and find its median.

1 | 7 8, 2 | 2 5 6 9, 3 | (empty), 4 | 1. Median: the 4th of 7 values, 25.

What each step is for

• read a row: Committing to what a row means before building one tests whether they combine the stem and each leaf into one value.
• add two values: Adding values and watching them land in the right row, in order, shows the plot's rule: the tens choose the row, the units the place.
• build and read: Stems in order with none missed, leaves in order, a key; then the median, mode and range read straight off. Jo's mistake leaves out a stem with no leaves, which hides a gap.
• one change at a time: One change at a time: build a plot on the board, read the mode from a different plot, count the values, use the key, then the edge case of three-digit values.
• read the plot: Reading the median, range and number of values from plots, mixed; the missing-stem slip in a question; the review keeps the mean fresh.
• a plot with a given median: Building eight two-digit values with a median of 35 reverses reading: the 4th and 5th leaves must average 35.

Where it leads

Next: Comparing data sets (AC9M7ST02 nodes 2 and 3).

Where it leads: back-to-back plots, histograms and grouped data (Year 8 and 9).