Organising Data Clearly

Overview

In this 45-minute lesson, students organise raw data into frequency tables using categories and intervals. They build on earlier work collecting and sorting data, then identify patterns, check that frequencies match the total number of responses, and distinguish between a frequency and an individual data value.

Learning intentions

• WALT organise raw data into a frequency table.
• WALT choose suitable categories or equal intervals for a data set.
• WALT identify patterns and check that a table is accurate.
• WALT explain the difference between a data value and its frequency.

Success criteria

• I can sort raw data into sensible categories or intervals.
• I can record a tally and frequency accurately.
• I can check that the frequencies add to the total number of data values.
• I can describe at least one pattern shown by a frequency table.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: applying mathematical thinking to relevant textbook and classroom content.
• Mathematics and Statistics — Mathsteasers: additional challenge and reasoning for advanced learners.
• Mathematical practices: representing information, reasoning, communicating explanations, and checking the reasonableness of results.

Lesson structure (45 minutes)

1. 0–5 min · Hook and prior knowledge. Teacher opens with the hook and comparison slides and displays the raw data: 12, 15, 12, 18, 21, 16, 15, 19, 22, 14, 17, 15. Ask: “What could we do to make this data easier to understand?” Students think-pair-share ideas such as sorting, tallying or grouping, then explain what they already know about frequency.

2. 5–12 min · Explicit teaching. Teacher uses the frequency table teaching slides to model a table for the raw data, using intervals of 10–14, 15–19 and 20–24. Model placing each value in one interval, recording tally marks, counting the tally as the frequency, and checking that the frequencies total 12. Students help decide where selected values belong and respond to the prompts: “Is 15 a frequency?” and “What does a frequency of 5 tell us?”

3. 12–17 min · Guided reasoning. Teacher presents two partially completed tables from the guided-check slides. One has a missing tally and one has an incorrect total. Prompt students to justify which table is accurate and how they know. Students discuss with a partner, identify the error, and explain why every data value must be counted once only.

4. 17–32 min · Paired investigation. Teacher distributes the frequency tables investigation worksheet to pairs and revisits the investigation instructions. Students complete three tasks: sort a set of raw data into given categories, create suitable equal intervals for a second data set, and answer questions about the most common group, least common group and overall pattern. Partners check each tally as they work. The teacher circulates, asking, “How did you choose your intervals?” and “How can you prove your total is correct?”

5. 32–39 min · Compare and discuss. Teacher displays the comparison and discussion slides and selects two pairs to share tables, including different choices of categories where appropriate. Students compare the tables, test whether categories overlap or leave gaps, and explain how the same data can be organised in different useful ways. Emphasise that categories must be clear, consistent and exhaustive.

6. 39–45 min · Plenary and exit check. Teacher uses the plenary slides to present the raw data 3, 7, 5, 3, 8, 6, 4, 3 and asks students to sketch a frequency table using intervals 3–4, 5–6 and 7–8. Students complete the final worksheet question independently: state the frequency of 3–4, give the total number of values, and write one pattern they notice. Invite two students to explain how they checked their answer.

Resources

• the complete frequency tables slide deck
• the frequency tables investigation worksheet
• Whiteboard and markers
• Pencils and erasers
• Optional mini-whiteboards for rapid responses
• Prepared raw-data examples displayed on the board

Assessment

• Listen during the hook and guided reasoning for correct use of “data value”, “tally” and “frequency”.
• Check paired tables for accurate sorting, non-overlapping categories, correct tally marks and frequencies that total the number of data values.
• Use the independent plenary response to identify whether students can construct a table, distinguish frequency from a value, and describe a pattern.

Differentiation

• Support students with a pre-drawn table, highlighted interval boundaries, a smaller data set and the sentence starters: “The frequency is ___ because ___” and “I checked the total by ___.”
• Provide counters or small paper marks so students can physically assign each data value to one interval before recording tallies.
• Pair students thoughtfully and ask students who are ready to explain why categories must not overlap, rather than simply completing more examples.
• For EAL learners and students needing additional support, use clear visual examples, rehearse vocabulary orally, and check understanding through pointing, sorting and partner explanation before written recording.