Comparing Categorical Data

Overview

In this 45-minute lesson, students organise data about two categorical variables in a two-way table. They build on earlier work collecting, sorting and representing data, then calculate row and column totals, compare groups and describe relationships using evidence.

Learning intentions

• WALT organise data about two categorical variables in a two-way table.
• WALT calculate and check row, column and grand totals.
• WALT compare groups and identify relationships in categorical data.
• WALT explain conclusions using evidence from a table.

Success criteria

• I can place each piece of data in the correct cell.
• I can calculate accurate row, column and overall totals.
• I can compare categories using numbers from the table.
• I can describe a relationship without claiming that one variable causes another.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: relevant challenge connected to familiar mathematics content.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Statistical investigation: organising, analysing and communicating information from categorical data.

Lesson structure (45 minutes)

1. 0–5 min · Hook and notice. Teacher opens with the question and data hook slides and displays a quick class scenario: “Do students who prefer fiction also tend to prefer reading at home?” Students make an individual prediction, then share what two categories they think could be compared.

2. 5–12 min · Explicit teaching. Teacher models a two-way table using a fictional survey of 20 Year 5 students. The two variables are preferred book type (fiction/non-fiction) and preferred reading place (home/library). Teacher demonstrates how each student contributes to one cell, then adds row totals, column totals and the grand total. Students help check that each row and column total matches the original data.

3. 12–17 min · Guided interpretation. Teacher uses the worked-table and discussion slides to ask: “Which book type is more common?”, “Where do more students prefer to read?”, and “How many fiction-preferring students chose the library?” Students discuss answers with a partner and justify each response by pointing to a cell or total.

4. 17–32 min · Paired investigation. Teacher distributes the two-way tables investigation worksheet and explains that students will complete two tables from given data, calculate totals and answer comparison questions. Pairs first sort the information into the correct cells, then independently calculate totals before checking together. Teacher circulates, asking, “How do you know this total is correct?” and “Which numbers are you comparing?”

5. 32–39 min · Reasoning challenge. Teacher returns to the comparison challenge slides and presents two completed tables about favourite lunchtime fruit and whether students bring lunch from home or buy it at school. Students identify one similarity, one difference and one possible relationship, recording numerical evidence. Invite pairs to share different valid conclusions and discuss why a relationship does not prove that one variable causes the other.

6. 39–45 min · Plenary and exit check. Teacher displays the plenary and exit-question slide and asks students to complete the final question on their worksheet: “What does the table suggest, and what evidence supports your answer?” Students submit their response, then explain one way to check a two-way table for accuracy.

Resources

• the two-way tables introduction and teaching deck
• the two-way tables investigation worksheet
• Whiteboard or interactive display
• Pens or pencils
• Calculators, optional for checking totals
• Prepared fictional survey data
• Highlighters in two colours

Assessment

• During modelling, check whether students understand that each response belongs in one cell and that totals represent combined categories.
• During paired work, listen for accurate use of “row total”, “column total”, “grand total”, “more than”, “fewer than” and “difference”.
• Use the written comparison and evidence response as an exit check. Look for an accurate conclusion supported by values from the table.

Differentiation

• Support students with a partially completed table, colour-coded row and column headings, and a small set of data to place one item at a time. Provide the sentence stems: “The largest group is ___ because ___” and “There are ___ more ___ than ___.”
• Pair students strategically and allow counters or tally marks to represent each response before recording totals. Read instructions aloud and provide a worked example for students who need language or processing support.
• For EAL learners, pre-teach and display “category”, “cell”, “total”, “compare”, “difference” and “relationship”; accept oral explanations before written responses.
• Challenge confident students to create a third question about the table, calculate a difference between two groups, or explain why the data suggests a relationship but does not prove causation.