Comparing Data Spread

Overview

In this 60-minute lesson, learners compare two small dot plots connected to familiar Aotearoa contexts. They identify the most common, lowest and highest values, then use everyday language and range to describe whether data values are clustered or spread out. This is lesson 25 of 28 and extends earlier learning about reading and describing data displays.

Learning intentions

• WALT identify the most common, lowest and highest values in a dot plot.
• WALT describe how much data values vary using everyday language.
• WALT calculate and use range to compare data sets.
• WALT explain our thinking using evidence from a data display.

Success criteria

• I can state the most common value in a dot plot.
• I can identify the lowest and highest values.
• I can find the range by subtracting the lowest value from the highest value.
• I can explain which group is more spread out and use data to support my answer.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers / Alignment: applying relevant mathematical ideas to unfamiliar or challenging problems.
• Mathematics and Statistics — Mathsteasers / Additional resources for advanced learners: reasoning, explaining and comparing mathematical ideas.

Lesson structure (60 minutes)

1. 0–7 min · Hook and prior knowledge. Open with the opening comparison slides showing two dot plots about the number of manu seen by two groups at a local wetland visit. Ask: “Both groups have the same highest value. Do they have the same amount of variation?” Learners quietly notice one feature, then share with a partner. Clarify that variation means how different or spread out the values are.

2. 7–17 min · Model reading a dot plot. Use the dot plot teaching slides to model two small data sets. Think aloud while locating the lowest value, highest value and most common value. Circle the tallest stack and explain that the most common value is the value appearing most often, not necessarily the largest value. Learners use fingers or mini-whiteboards to show each answer before discussing the evidence.

3. 17–27 min · Model range and spread. Reveal the range on the range modelling slide. Demonstrate: range = highest value − lowest value, using counters on a number line before recording the subtraction. Compare a tightly clustered plot with a more spread-out plot. Emphasise that a larger range usually means the values are more spread out, while range alone does not tell us the most common value. Learners calculate one range with a partner and complete the sentence: “The range is __ because __ − __ = __.”

4. 27–45 min · Compare the Data activity. Distribute the Compare the Data worksheet to pairs. Learners read two dot plots based on everyday Aotearoa contexts, first completing the Must Do: state the most common value. They then complete the Can Do: identify the lowest, highest and range. Finally, they attempt the Try: compare the spread of both groups and explain which is more spread out. Provide counters or allow learners to stand along a floor number line to physically represent each data set. Partners must point to evidence before writing an answer.

5. 45–54 min · Compare and justify. Display the discussion and reasoning slides and invite pairs to compare answers. Ask: “Can two groups have the same range but look different?” and “Can the most common value help us decide which group is more spread out?” Select different strategies, including a counter model, subtraction and a verbal explanation. Revoice imprecise statements into mathematical language while accepting everyday descriptions such as “packed together”, “spread across” and “a big gap”.

6. 54–60 min · Plenary and exit check. Show the final challenge slide with a new dot plot. Learners independently answer on the bottom of the final reflection section: “The most common value is __. The range is __. This group is/is not very spread out because __.” Collect responses to identify who is ready to compare two ranges in the next lesson.

Resources

• the complete lesson slide deck
• the Compare the Data worksheet
• Mini-whiteboards and pens
• Linking counters or small blocks
• Masking tape floor number line
• Pencils and coloured pencils
• Prepared dot plots displayed or projected
• A4 paper for learners needing additional working space

Assessment

• Listen for accurate use of most common value, lowest, highest and range during modelling and partner work.
• Check worksheet responses, especially whether learners use the dot plots as evidence rather than guessing from the shape.
• Use the final reflection to group learners for the next lesson: secure, developing or needing support with range and spread.

Differentiation

• Support learners with a highlighted lowest and highest value, a partially completed subtraction sentence, counters and the sentence frames: “The most common value is __ because __ appears __ times” and “Group __ is more spread out because its range is __.”
• Read the worksheet aloud, enlarge dot plots and allow learners to explain orally before recording. Pair learners thoughtfully and pre-teach “common”, “range”, “cluster” and “spread”.
• For learners ready for challenge, provide two groups with equal ranges but different clusters and ask them to explain why range is useful but does not describe every feature of a data set.
• EAL learners may draw arrows to the lowest and highest values, rehearse responses with a partner and use the everyday comparison words displayed on the slides.