Mathematics · Secondary 2

Active learning ideas

Stem and Leaf Plots and Pie Charts

Active learning helps students grasp how stem-and-leaf plots and pie charts reveal patterns in raw data. When students build their own graphs, they see how these tools preserve or summarize values, making abstract statistics concrete and memorable.

• MOE Syllabus Outcomes
• MOE: Data Analysis - S2
• MOE: Statistics and Probability - S2

• 35–50 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Placemat Activity
• 40 min · Pairs

Survey and Pie: Class Favorites

Students survey 20 classmates on favorite sports in pairs, tally responses, calculate percentages, and draw pie charts on paper or GeoGebra. Pairs present one advantage and one limitation of their pie chart to the class. Discuss as a group which data suits pie charts best.

When is a stem and leaf plot more useful than a standard bar chart?

Facilitation Tip

During Survey and Pie: Class Favorites, circulate to ensure groups tally votes before plotting, preventing inconsistent totals.

What to look for

Provide students with a small data set (e.g., 10 test scores). Ask them to construct a stem and leaf plot and calculate the percentage of students who scored above 80%. Collect these to check for accuracy in construction and calculation.

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

Activity 02

• Placemat Activity
• 35 min · Small Groups

Sports Scores Stem-and-Leaf: Build and Analyze

Provide scores from recent basketball games; small groups sort data into a stem-and-leaf plot, identify median and range. Groups swap plots to interpret a peer's data, noting how it shows outliers better than a list. Share findings whole class.

Explain the advantages and disadvantages of using a pie chart.

Facilitation Tip

When students Build and Analyze Sports Scores Stem-and-Leaf, ask them to circle the median and explain its position to reinforce central tendency.

What to look for

Present students with two graphs representing the same data: one bar chart and one pie chart. Ask: 'Which graph better shows how many students prefer apples versus oranges? Why?' Facilitate a class discussion comparing the strengths and weaknesses of each visual.

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

Activity 03

• Placemat Activity
• 45 min · individual then small groups

Graph Showdown: Stem vs Pie

Give mixed data sets; individuals choose and construct either a stem-and-leaf or pie chart, justifying their pick. In small groups, critique each other's graphs for suitability. Vote class-wide on best representations.

Construct a stem and leaf plot from a given data set.

Facilitation Tip

In Graph Showdown: Stem vs Pie, provide a checklist for students to compare graph types before debating strengths.

What to look for

Display a pre-made stem and leaf plot. Ask students to identify the lowest score, the highest score, and the range of the data. Then, ask them to list all data points that fall within a specific range (e.g., 70-79).

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

Activity 04

• Placemat Activity
• 50 min · whole class then small groups

Real Data Dash: Heights Plot

Measure heights of all students whole class, record raw data. Divide into small groups to create back-to-back stem-and-leaf plots comparing boys and girls. Discuss distribution patterns and when this beats a bar chart.

When is a stem and leaf plot more useful than a standard bar chart?

Facilitation Tip

For Real Data Dash: Heights Plot, give students measuring tapes so they collect their own data before plotting.

What to look for

Provide students with a small data set (e.g., 10 test scores). Ask them to construct a stem and leaf plot and calculate the percentage of students who scored above 80%. Collect these to check for accuracy in construction and calculation.

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

A few notes on teaching this unit

Teachers should emphasize that stem-and-leaf plots require exact values, while pie charts show proportions. Model both constructions step-by-step, then let students struggle slightly with messy data to build resilience. Avoid over-reliance on templates; instead, have students draft by hand to internalize structure. Research shows students learn best when they connect visuals to real contexts, so tie graphs to topics like sports or surveys that students care about.

Successful learning looks like students constructing accurate plots, interpreting distributions correctly, and justifying their choice of graph for different data sets. Evidence includes clear explanations, precise labels, and thoughtful comparisons between stem-and-leaf plots and pie charts.

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Watch Out for These Misconceptions

• During Graph Showdown: Stem vs Pie, watch for students who treat stem-and-leaf plots as bar charts by summarizing frequencies in bars.

  Have students in pairs plot the same data first as a bar chart, then as a stem-and-leaf plot. Ask them to compare how the bar chart hides individual scores while the stem-and-leaf plot preserves them.

• During Survey and Pie: Class Favorites, watch for students who use pie charts to compare class totals across different days instead of showing parts of a whole.

  Provide a mismatched data set (e.g., votes from Monday and Tuesday combined). Ask groups to redraw the pie chart and explain why it is misleading, then redesign with a bar chart.

• During Real Data Dash: Heights Plot, watch for students who round leaf values to whole numbers, losing precision.

  Give each group a ruler and ask them to plot exact measurements, including decimals. Circulate to check their original data entries against the plot.

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Methods used in this brief

• Placemat Activity