Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Representing Data: Line Plots and Stem-and-Leaf Plots

Active learning works well for line plots and stem-and-leaf plots because students need to physically group, sort, and place data to see patterns clearly. When children handle real objects or their own measurements, abstract numerical relationships become concrete, building confidence and reducing confusion between frequency and value.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - S.1.3

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 20 min · Pairs

Pairs: Hand Span Line Plot

Partners measure each other's hand spans in centimetres using a ruler and string. They tally frequencies then plot Xs on a shared number line from 10 to 20. Pairs discuss and share the most common span with the class.

Explain when a line plot is a more appropriate representation than a bar graph.

Facilitation Tip

During Pairs: Hand Span Line Plot, circulate and ask each pair to explain their process aloud while building the plot to reinforce the connection between measurement and frequency.

What to look for

Provide students with a simple data set (e.g., number of stickers each child has). Ask them to draw a line plot for this data and then answer: 'What is the most common number of stickers?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 02

• Think-Pair-Share
• 30 min · Small Groups

Small Groups: Sibling Stem-and-Leaf

Each student reports total family members including self, data from 1 to 6. Groups sort numbers into stems (0,1) and leaves, draw the plot on chart paper. They identify the smallest and largest families.

Analyze the information that can be quickly gleaned from a stem-and-leaf plot.

Facilitation Tip

For Small Groups: Sibling Stem-and-Leaf, provide number cards so students physically sort and rearrange before plotting to avoid ordering errors.

What to look for

Give students a small set of numbers (e.g., 12, 15, 11, 18, 14). Ask them to construct a stem-and-leaf plot. Then, ask: 'What is the smallest number in the data?' and 'What is the largest number in the data?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 03

• Think-Pair-Share
• 25 min · Whole Class

Whole Class: Birthday Line Plot

Collect months born as numbers 1-12, teacher records on board. Class adds tally marks then converts to line plot with dots. Discuss peaks for most common months.

Construct a stem-and-leaf plot from a given set of numerical data.

Facilitation Tip

In Whole Class: Birthday Line Plot, assign a recorder to note each student’s birthday month on the board first, then have the class collaboratively build the line plot to ensure accuracy.

What to look for

Show students two graphs representing the same data: one a bar graph, the other a line plot. Ask: 'Which graph makes it easier to see how many students got a certain score? Why?' and 'Which graph makes it easier to see the lowest and highest scores? Why?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Activity 04

• Think-Pair-Share
• 15 min · Individual

Individual: Toy Count Line Plot

Students count a type of toy at home (0-10), draw personal line plot. Bring to school, combine into class plot. Note changes in the big picture.

Explain when a line plot is a more appropriate representation than a bar graph.

Facilitation Tip

For Individual: Toy Count Line Plot, give students sticky notes to arrange before transferring to the number line, allowing for easy adjustments and peer feedback.

What to look for

Provide students with a simple data set (e.g., number of stickers each child has). Ask them to draw a line plot for this data and then answer: 'What is the most common number of stickers?'

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

A few notes on teaching this unit

Start with hands-on sorting using objects or sticky notes before any graphing to help students see data as a collection that can be rearranged. Teach line plots before stem-and-leaf plots, as the number line provides a more intuitive bridge from counting to scaling. Avoid rushing to abstract symbols; always link marks on the plot back to a physical count or measurement.

Successful learning looks like students accurately plotting data points, identifying clusters and gaps, and explaining why a line plot or stem-and-leaf plot fits the data better than other graphs. They should also articulate the range, mode, and distribution using the visual structure of their plots.

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Watch Out for These Misconceptions

• During Pairs: Hand Span Line Plot, watch for students placing Xs or dots to represent the size of the hand rather than the count of how many hands measured 12 cm.

  Have students first create a tally chart on paper, then stack blocks for each measurement before drawing Xs on the line plot, linking physical counts to plot marks.

• During Small Groups: Sibling Stem-and-Leaf, watch for students plotting data in the order collected rather than sorted numerically.

  Provide number cards for students to sort into stems and leaves first, then place them in a pocket chart or on the table before transferring to paper.

• During Whole Class: Birthday Line Plot, watch for students treating the line plot like a bar graph by making bars instead of individual Xs for each data point.

  Model one data point at a time, emphasizing that each X represents one student’s birthday month, and compare the line plot to a bar graph to highlight the difference in structure.

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Methods used in this brief

• Think-Pair-Share