Comparing Bar Graphs

Overview

In this nineteenth lesson of Mapping Data and Change, students construct and interpret bar graphs for categorical data. They build on earlier work collecting, sorting and representing data, choosing a scale and using graph features to compare frequencies with evidence.

Learning intentions

• WALT organise categorical data and represent it in a bar graph.
• WALT choose a suitable scale and label a graph accurately.
• WALT compare categories by referring to frequencies shown on a graph.
• WALT explain conclusions using mathematical evidence.

Success criteria

• I can give my graph a clear title and label both axes.
• I can choose and use an equal, suitable scale.
• I can draw bars with correct heights and equal widths.
• I can make comparison statements using data from the graph.

Curriculum links

• Mathematics and Statistics — representing and interpreting categorical data.
• Mathematics and Statistics — communicating findings using tables and graphs.
• Mathematics and Statistics — selecting appropriate representations and explaining mathematical thinking.
• Mathsteasers — challenging learners to deepen understanding through higher-order questions and relevant mathematical problem solving.

Lesson structure (45 minutes)

1. 0–5 min · Hook and notice. Teacher opens with the opening comparison slide showing two bar graphs representing the same categorical data, one with a misleading scale and one with a clear scale, then asks, “Which graph gives the fairest comparison, and why?” Students discuss with a partner and identify differences in the scale, bars, labels and visual message.

2. 5–13 min · Explicit teaching. Teacher uses the graph features and modelling slides to model turning a frequency table into a bar graph: write a descriptive title, place categories on the horizontal axis, frequency on the vertical axis, select an equal scale, label both axes, and draw bars accurately. Students help decide whether scales of 1, 2, 5 or 10 are appropriate for different maximum frequencies and explain their choices.

3. 13–18 min · Guided comparison. Teacher displays a completed graph from the guided questioning slides and models precise comparison language, such as “Cycling was 4 more than walking” and “Swimming had twice the frequency of running.” Students answer questions using the graph and justify each answer by referring to bar heights or calculated differences.

4. 18–32 min · Paired graph construction. Teacher distributes the bar graph construction and comparison worksheet and the graph paper pack. Pairs use the provided categorical frequency table to construct one accurate bar graph, checking the title, axes, scale, bar widths and heights against the success criteria. They then complete comparison questions, including finding the greatest and least frequencies, the difference between two categories and one statement supported by evidence.

5. 32–39 min · Peer checking and challenge. Teacher uses the checking and discussion slides to show a checklist and asks pairs to swap graphs with a nearby pair. Students check one another’s graph for equal intervals, correct plotting, clear labels and a fair scale, then improve their own work. Fast finishers write a “Which category would you recommend and why?” response using at least two pieces of numerical evidence.

6. 39–45 min · Plenary and exit assessment. Teacher reveals the plenary and exit-question slide and presents a small categorical data set. Students independently sketch or describe a suitable bar graph scale and complete the sentence: “Category ___ is ___ more/less than category ___ because ___.” Teacher collects responses to identify who can compare frequencies and who needs further support with scales or graph conventions.

Resources

• the complete Bar Graph Comparisons slide deck
• the bar graph construction and comparison worksheet
• the graph paper pack
• Pencils, rulers and coloured pencils
• Whiteboard and markers
• Pair-check success-criteria checklist
• Projector or interactive display

Assessment

• During modelling, ask students to explain why a scale is suitable and check that they understand equal intervals.
• Circulate during paired construction, using questions such as “How do you know this bar should reach 12?” and “What does this difference tell us?”
• Use the independent exit response to assess graph interpretation, comparison language and evidence-based reasoning. Note students needing a short follow-up workshop.

Differentiation

• Support learners with a partially labelled axis, a maximum frequency already identified and a scale choice limited to two sensible options. Provide a vocabulary bank including category, frequency, scale, greater than, less than and difference.
• Pair students strategically and provide sentence starters: “The most common category is…”, “___ has ___ more than ___”, and “I know this because…”.
• For EAL learners, use the visual model, gestures and repeated oral rehearsal before written responses. Read worksheet instructions aloud and check understanding individually.
• Extend confident learners by asking them to create a second valid graph using a different suitable scale, compare the visual impact, and explain which graph communicates the data most effectively.