Reading Data Clearly

Overview

This is lesson 9 of 30 in Exploring Statistics and Probability. Students build on prior work with organising and describing data by learning how a stem-and-leaf plot displays numerical data in order while preserving every original value.

Learning intentions

• WALT create an accurate stem-and-leaf plot from an unordered data set.
• WALT read and interpret information from a stem-and-leaf plot.
• WALT explain how a stem-and-leaf plot helps us see the distribution of data.
• WALT communicate statistical thinking clearly with a partner and a group.

Success criteria

• I can identify suitable stems and leaves for a data set.
• I can arrange leaves in ascending order and include a key.
• I can use a plot to find values, the range, the median and the mode where appropriate.
• I can explain one feature of the data using evidence from the plot.

Curriculum links

• Mathematics and Statistics — statistical investigation and communicating findings from data.
• Mathematics and Statistics — representing, describing and interpreting numerical data.
• Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathsteasers: aligned challenge resources supporting extension and deeper mathematical reasoning.

Lesson structure (60 minutes)

1. 0–5 min · Hook and retrieval. Display a mixed list of Year 9-friendly data, such as travel times in minutes: 12, 18, 21, 14, 27, 22, 19, 31, 25, 16. Open with the data mystery hook and ask, “What can we notice quickly, and what is difficult to see?” Students discuss in pairs, then suggest ways to organise the values.

2. 5–15 min · Explicit teaching. Use the stem-and-leaf modelling slides to model ordering the data, choosing tens as stems and ones as leaves, placing leaves from smallest to largest, and writing a key such as 2 | 7 = 27. Think aloud about why no values may be omitted and how a plot differs from a frequency-only display. Students help complete a partially built example and respond to quick checks using mini-whiteboards.

3. 15–25 min · Collaborative reading. Display a completed plot on the interpretation prompt slides. In groups of four, students take roles of reader, checker, explainer and recorder. They answer questions such as: What is the smallest value? What is the range? Which value occurs most often? How many values are greater than 25? Groups must point to the relevant stem and leaf before giving an answer.

4. 25–43 min · Paired construction task. Distribute the stem-and-leaf practice worksheet. Students independently order a small data set, then compare with a partner before completing a larger set. They create a plot, add a key, and answer interpretation questions. Circulate to check that students use consistent place value, include repeated values and order the leaves correctly. Pause for a two-minute whole-class check after the first question.

5. 43–52 min · Compare representations. Return to the representation challenge slides. Pairs convert one stem-and-leaf plot into a suitable display such as a dot plot or column graph, then discuss what information is easier or harder to see in each representation. Advanced students justify which display would best communicate the distribution and why.

6. 52–58 min · Error analysis and feedback. Show two flawed plots on the common errors slides: one with unordered leaves and one with a missing key or omitted value. Students identify, explain and correct the errors. Invite responses using the sentence frame, “The plot is inaccurate because…, so I would…”.

7. 58–60 min · Exit check. Students complete the final question on the reflection and exit question: create a plot for 14, 11, 18, 15, 21, 17, 12 and state one feature of the data. Collect responses to identify who is ready for independent interpretation next lesson.

Resources

• the complete stem-and-leaf teaching deck
• the stem-and-leaf practice worksheet
• Mini-whiteboards and pens
• Projector or interactive display
• A3 paper and coloured pens for group work
• Highlighters in two or three contrasting colours
• Optional calculator for checking, not constructing, answers

Assessment

• Check mini-whiteboard responses during modelling for correct stems, leaves and keys.
• Confer with pairs during the worksheet task, asking students to explain how they know their plot is complete and accurate.
• Use the exit question to assess construction, ordering, key conventions and interpretation; group students for the next lesson based on the error pattern.

Differentiation

• Support learners with a prepared place-value table, a reduced data set and the sentence frames “The smallest value is…” and “The plot shows…”. Model one value at a time before releasing students to work independently.
• For dyslexia-friendly access, use a clear sans-serif font, uncluttered slides, increased spacing and read instructions aloud. Use colour-coded stems and leaves consistently, while ensuring colour is not the only way information is communicated.
• Pair students strategically and allow oral explanations, pointing or speech-to-text instead of requiring all reasoning to be written.
• Challenge advanced learners to compare the same data in a stem-and-leaf plot and another graph type, then explain which representation best reveals centre, spread, clusters or unusual values.

Extension

• Create a back-to-back stem-and-leaf plot comparing two groups, such as two sets of travel times, and write two evidence-based comparisons.
• Design a data set that produces a specified median, range and repeated value, then swap with another pair to test.