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.

• Secondary 2
• Mathematics
• 4 activities
• 35 min–50 min

Learning Objectives

1. Construct a stem and leaf plot from a given data set, ensuring correct ordering and notation.
2. Compare the effectiveness of stem and leaf plots versus bar charts for representing data distribution and identifying outliers.
3. Explain the advantages of using pie charts for showing proportional data and the disadvantages when comparing segments.
4. Create a pie chart from categorical data, calculating the correct angles for each sector.
5. Analyze and interpret data presented in both stem and leaf plots and pie charts to answer specific questions about the data.

Concept Mapping

⏱ 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.

Prepare & details

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.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 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.

Prepare & details

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.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 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.

Prepare & details

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.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Concept Mapping

⏱ 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.

Prepare & details

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.

Setup: Tables with large paper, or wall space

Materials: Concept cards or sticky notes, Large paper, Markers, Example concept map

• Understand
• Analyze
• Create
• Self-Awareness
• Self-Management

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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.

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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

Assessment Ideas

Exit Ticket

After Sports Scores Stem-and-Leaf, provide each student with a stem-and-leaf plot of 10 scores. Ask them to list all scores in the 80s and calculate the percentage of scores below 70%. Collect these to check for accuracy in reading the plot and computing percentages.

Discussion Prompt

During Graph Showdown: Stem vs Pie, present students with a data set (e.g., favorite fruits) displayed as both a bar chart and a pie chart. Ask: 'Which graph better shows the difference between votes for apples and oranges? Why?' Facilitate a quick pair-share before whole-class discussion.

Quick Check

After Real Data Dash: Heights Plot, display a pre-made stem-and-leaf plot of heights. Ask students to identify the lowest and highest values, the range, and list all values between 150 cm and 160 cm. Use a whiteboard or digital tool for immediate feedback.

Extensions & Scaffolding

• Challenge students to create a stem-and-leaf plot with two-digit stems after completing Sports Scores Stem-and-Leaf.
• For students struggling with Real Data Dash, provide pre-sorted data sets with clear ranges (e.g., 140-150 cm).
• Deeper exploration: Have students research how stem-and-leaf plots are used in sports analytics or medicine, then present findings to the class.

Key Vocabulary

Stem and Leaf Plot	A display of quantitative data that separates each data value into a stem (the leading digit or digits) and a leaf (the last digit).
Leaf	The last digit of a data value in a stem and leaf plot, typically representing the ones place.
Stem	The leading digit or digits of a data value in a stem and leaf plot, representing place values higher than the ones place.
Pie Chart	A circular chart divided into sectors, where each sector represents a proportion or percentage of the whole.
Sector	A portion of a pie chart that represents a specific category's proportion of the total data.