Build the Graph

Overview

This is lesson 22 of 28 in Year 4 Maths Across Aotearoa. Learners organise categorical data in a frequency table and represent it in a picture graph, building on prior work with sorting, counting and recording data. They interpret the graph and explain how the title, labels and key help a reader understand it.

Learning intentions

• WALT organise categorical data in a frequency table.
• WALT represent data accurately in a picture graph.
• WALT use a title, labels and a key to communicate information.
• WALT explain what a picture graph tells us.

Success criteria

• I can count each category and record its frequency.
• I can draw the correct number of symbols for each category.
• I can add a clear title and labels.
• I can use a key where one symbol represents two students, and explain what the graph shows.

Curriculum links

• Mathematics and Statistics — Mathsteasers: challenging questions that deepen mathematical understanding for Year 4 learners.
• Mathematics and Statistics — Mathsteasers / Alignment: connecting challenge activities with familiar mathematics content.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, representation and explanation through a non-routine data task.
• Te Mātaiaho capabilities: communicating mathematical thinking, using representations, and justifying conclusions from data.

Lesson structure (60 minutes)

1. 0–5 min · Hook and connect. Display the opening data challenge: “Which category might have the most students, and how could we show this so another class understands it?” Students make a quick prediction, then share what they remember about tables, categories and picture graphs.

2. 5–15 min · Model the data. Use the worked example slides to model five categories with frequencies 9, 6, 5, 3 and 2, ensuring the total is 25 and Reading is the highest category. Think aloud while recording a frequency table, checking that the frequencies add to 25, then build a picture graph with one symbol per student. Ask: “What must the title tell us?”, “Which labels does a reader need?” and “How can we check the graph is accurate?” Students help count, identify the highest and lowest categories, and explain the connection between the table and graph.

3. 15–20 min · Compare representations. Show an incomplete and a completed version in the representation-check slides. Students turn and talk to identify missing or inaccurate features, including the title, category labels, number of symbols and total. Take brief responses and establish the class checklist: title, labels, key if needed, accurate symbols and a total of 25.

4. 20–42 min · Build the graph. Distribute the tables and picture graphs worksheet. Students complete the frequency table and then create the graph using cubes, drawn symbols or a digital representation. They begin with one symbol per student. Circulate and ask, “How do you know this row needs nine symbols?” and “How does your graph show that Reading is the highest category?” Provide tactile raised symbols, large-print copies and opportunities for oral or drawn explanations. Students who are ready try the key: one symbol = two students, considering how to represent odd frequencies such as 9, 5 and 3 accurately.

5. 42–52 min · Pair-check and interpret. Display the partner-check and discussion slides. In pairs, students check that each row matches the table, the total is 25, and the title and labels make sense. They ask and answer: “How many students chose Reading?”, “How many more chose Reading than the category with 2?” and “What does one symbol represent in your graph?” Students revise their work in a different-coloured pencil.

6. 52–60 min · Plenary and exit check. Revisit the plenary slides and invite two students to explain different ways of making an accurate graph. Students complete the final box on the tables and picture graphs worksheet: draw or describe the symbols needed for a category of 5 when one symbol represents two students, and name one feature every picture graph needs. Collect responses to identify next steps.

Resources

• the complete lesson slide deck
• the tables and picture graphs worksheet
• Linking cubes or counters, approximately 25 per pair
• Tactile raised symbols or textured stickers
• Large-print graph and table copies
• Pencils, coloured pencils and rulers
• Optional tablet or computer graphing tool
• Board or modelling space

Assessment

• Observe whether students transfer each frequency correctly from the table to the graph; ask individuals to justify one row.
• Check partner reviews for accurate totals, category labels, titles and symbol counts.
• Use the exit response to assess understanding of one-symbol-per-student and one-symbol-for-two-students representations, including the need to show odd numbers accurately.

Differentiation

• Support learners with a partially completed table, category labels already provided, a symbol bank and a counting strip to 25. Work with a small group to build the graph physically before drawing it.
• Offer sentence starters: “The highest category is ___ because…”, “The key means…” and “I checked my graph by…”.
• Allow students to respond orally, by pointing, drawing or using tactile symbols; provide large print, uncluttered layouts and a peer or adult scribe where appropriate.
• Extend confident learners by requiring the key of one symbol = two students and asking them to explain how half-symbols or paired symbols can represent odd numbers without changing the data.