Chance graphs

Overview

In this lesson, students build simple graphs to display data from a chance investigation. They learn how to choose an appropriate graph, read it, and use it to describe patterns.

Learning intentions

• Students will represent collected data using a bar graph or a simple line plot.
• Students will label graphs clearly (title, axes/category labels, and scale).
• Students will interpret graphs to make simple statements about outcomes and variability.
• Students will compare results from their class data with another group’s graph using appropriate mathematical language.

Success criteria

• I can sort my data and count frequencies for each category or value.
• I can create a bar graph or line plot that matches my data (correct labels and scale).
• I can read my graph to answer questions such as “Which outcome happened most/least?”
• I can explain how the graph shows variation in experimental results.

Curriculum links

• Collect, organise, and display data in tables and graphs, choosing appropriate representations.
• Interpret data displays to answer questions and describe patterns.
• Use chance language to discuss likelihood and to compare outcomes from repeated trials.

Lesson structure (45 minutes)

1. 5 min – Starter: Quick recall and purpose

• Display 1–2 sample graphs (simple bar graph and line plot) and ask: “What do we notice? What does each part tell us?”
• Briefly recap: graphs help us see patterns quickly, not just raw numbers.

2. 10 min – Teach: Bar graphs vs line plots

• Model with teacher-collected or recent class data: for categorical outcomes (e.g., spinner results), use a bar graph; for ordered numbers (e.g., number of heads), use a line plot.
• Explicitly point to essentials: title, labels, scale (counting by 1, 2, or 5 as appropriate), and consistent spacing.
• Use a short worked example: “If ‘Red’ occurs 6 times, the bar for Red must reach 6 on the scale.”

3. 15 min – Create: Students graph their data

• In pairs, students use their own group’s results from the unit investigation.
• They choose the graph type and complete it on grid paper or a prepared template.
• Teacher circulates to check: correct tally-to-frequency conversion, clear labels, and that the graph matches the data.

4. 10 min – Interpret: Read and answer

• Students answer 3 prompts on their sheet:
• Which outcome happened most often?
• Which happened least often?
• Name one way the results vary from what you expected (using “sometimes”, “often”, “not always”).
• Students then compare with another pair: “Does your graph show a similar pattern or a different one?”

5. 5 min – Share: Class reflection

• Quick “gallery walk” or 2–3 volunteer shares.
• Teacher reinforces key idea: different trials can produce different results, and graphs help us see that variability.

Resources

• Group data sheets from the earlier chance investigation
• Graph paper or pre-drawn bar graph/line plot templates
• Coloured pencils/textas and rulers (for neat, straight axes)
• Tally marks worksheets (optional quick reference)
• A small set of example graphs (teacher-prepared)
• Display screen/whiteboard for modelling
• Sentence starters for interpreting graphs (e.g., “Most often was…”, “Least often was…”)
• Data prompt card for the interpretation questions

Assessment

• Formative checks during graph construction: correct frequency representation, accurate labels, appropriate graph choice.
• Short written responses to interpretation prompts to gauge understanding of reading graphs and describing variability.
• Teacher observation during pair comparison: use of mathematical language and simple reasoning from the graph.

Differentiation

• Support:
• Provide partially completed graph templates with axis titles and a suggested scale.
• Offer a step-by-step checklist (count outcomes, choose graph type, label, draw bars/plots).
• Use small-group teacher conferencing for students needing help converting tallies to frequencies.
• Extension:
• Ask students to add an extra question: “How many more times did the most common outcome occur than the least common?”
• Encourage comparing two graphs by stating differences and similarities in counts.
• EAL/SEN:
• Use visual sentence starters and word banks for chance and comparison (e.g., “most”, “least”, “more”, “less”, “sometimes”).
• Allow oral explanation recorded by the teacher or on an adapted response sheet.
• Choice and accessibility:
• Let students choose between bar graph or line plot based on their data type, ensuring they can still access the representation and interpretation task.