Building Dot Plots

Overview

Students organise raw data and create labelled dot plots, then describe and compare distributions. The lesson develops statistical thinking through a familiar context and asks students to justify claims using features of a visualisation.

Learning intentions

• We are learning to create accurate dot plots from raw data.
• We are learning to describe variables, units, context and features of a data visualisation.
• We are learning to interpret and compare data displays.

Success criteria

• I can organise data in a frequency table.
• I can make a correctly scaled and labelled dot plot.
• I can identify the mode, range and total number of values.
• I can describe what the graph shows using evidence.

Curriculum links

• Te Mātaiaho Mathematics and Statistics, Phase 3 (Years 7–8): Statistics — Visualisation of data.
• Te Mātaiaho Mathematics and Statistics, Phase 3 (Years 7–8): Statistics — Interpretation of data.
• Categorical data can be visualised through dot plots and bar graphs; students describe the variable, units, context and features of a visualisation.
• This lesson supports mathematical communication, reasoning and critical evaluation of representations.

Key vocabulary

Data, variable, numerical data, categorical data, frequency, dot plot, scale, mode, range, distribution, cluster, gap, outlier, context.

Prior knowledge and preparation

Students should be able to count, order whole numbers, read a number line and describe simple patterns. Prepare one worksheet per student or pair, a slide deck, board space and rulers. Use mixed-ability pairs of two or three within the class of 25.

Lesson structure (60 minutes)

1. 0–5 min · Warm-up. Open with the hook and warm-up slides and ask, “How could we show how many books a group has read?” Students estimate the most common value, then explain how a graph could make this visible.

2. 5–18 min · Explicit teaching. Display the dot plot modelling slides. Explain that a dot plot shows data values along a number line, with one dot for each observation; repeated values are stacked. Numerical data are counts or measurements, while categorical data are groups or labels. Model ordering raw data, making a frequency table, choosing an even scale, labelling the variable and units, placing dots, adding a title, and interpreting the graph. Think aloud: “I need a scale that includes every value, and I must count every dot once.” Address misconceptions: unequal intervals, missing zeroes, joining dots into a line graph, and treating a stack as one observation.

Worked example: books read = 0, 2, 1, 3, 2, 4, 1, 2, 5, 3, 2, 1.

Books	0	1	2	3	4	5
Frequency	1	3	4	2	1	1

The dot plot has one dot above 0, three above 1, four above 2, two above 3, and one each above 4 and 5. The mode is 2 books, the range is 5 books, and there are 12 data values. The context is students’ books read; the unit is books.

3. 18–28 min · Guided practice. Work through the temperature example on the guided example slides: daily temperatures in °C are 18, 20, 19, 21, 20, 18, 22, 20. Students help construct the frequency table and dot plot. Ask: “What is the mode?” “What is the range?” “How many days were at least 20°C?” Answers: mode 20°C; range 4°C (18 to 22); four days.

4. 28–42 min · Collaborative practice. Distribute the dot plot practice worksheet. Pairs complete Questions 1–3, checking that each dot represents one value. Partners use the prompt “I notice… because…” to discuss clusters, gaps and comparisons. Circulate and use the observation checklist.

5. 42–53 min · Independent practice. Students complete Questions 4–5 independently, including the misleading-scale task. Remind them to state the variable, unit and context before making a claim. Early finishers write one accurate comparison sentence using data evidence.

6. 53–60 min · Plenary and exit task. Return to the discussion and exit slides. Students complete the exit task: “Data are 2, 3, 3, 4, 5, 5, 5, 6. State the mode, range and total number of values. What would the tallest stack be above?” Answers: mode 5; range 4; 8 values; the tallest stack is above 5, with three dots.

Resources

• the complete dot plot lesson deck
• the dot plot practice worksheet
• Whiteboard and markers
• Rulers and pencils
• Projector or interactive display
• Exercise books

Ready-to-use worksheet

Dot Plots: student instructions For each task, organise the data first. Use an evenly spaced number line, one dot per value, stacked dots for repeats, a title, and labels including units where needed. Show calculations and answer in complete sentences.

1. Construct and interpret. Number of goals scored: 0, 1, 2, 1, 3, 2, 2, 0, 4, 1. Draw a dot plot on a number line from 0 to 4. Find the mode, range and total values. 2. Construct and describe. Travel times to school (minutes): 10, 15, 20, 15, 25, 10, 15, 30, 20, 10. Draw a dot plot from 10 to 30, using intervals of 5 minutes. Find the mode and range. Describe one feature of the distribution. 3. Compare data sets. Team A scores: 2, 3, 3, 4, 4, 5. Team B scores: 1, 2, 3, 4, 5, 6. Without drawing, compare their modes and ranges. Which team has the greater spread? Explain. 4. Spot the problem. A dot plot of favourite fruit uses a number line labelled 1, 2, 4, 5, with equal spaces between labels. Explain why this is misleading and suggest a correction. 5. Challenge. Create a data set of eight whole numbers from 0 to 6 with mode 3 and range 6. Draw its dot plot.

Answer key

1. Frequencies: 0:2, 1:3, 2:3, 3:1, 4:1. Modes 1 and 2; range 4; 10 values.
2. Frequencies: 10:3, 15:3, 20:2, 25:1, 30:1. Modes 10 and 15; range 20 minutes. Possible description: data cluster at 10–15 minutes and become less frequent as time increases.
3. Team A modes are 3 and 4; range 3. Team B has no mode because every value occurs once; range 5. Team B has the greater spread.
4. The scale has unequal numerical intervals represented by equal spaces: the gap from 2 to 4 hides the missing 3. Use equal intervals, such as 1, 2, 3, 4, 5, or clearly mark a broken axis.
5. Answers vary. Example: 0, 1, 3, 3, 3, 4, 5, 6. Mode 3 and range 6.

Assessment

• Observe whether students order data, use an even scale, place every dot and label the context and units.
• Question pairs: “How do you know?” and “What does the tallest stack represent?”
• Collect the worksheet and exit task; check accuracy and the quality of written interpretations.

Teacher observation checklist: frequency table accurate; scale even; one dot per observation; repeated values stacked; title and labels included; mode/range correct; interpretation uses evidence; can explain a misleading display.

Differentiation

• Support: provide a pre-drawn number line, allow counters before drawing, highlight each raw value as it is counted, and use sentence starters such as “The mode is ___ because ___.”
• EAL/SEN: pre-teach vocabulary with simple examples, read instructions aloud, use enlarged graph paper and pair students with a supportive peer.
• Challenge: ask students to create two data sets with the same mode but different ranges, then explain how the distributions differ.