Mathematics · Grade 9

Active learning ideas

Box Plots and Outliers

Active learning works here because box plots require students to physically manipulate data, which builds both procedural fluency and conceptual understanding. When students construct these visuals themselves, they move beyond abstract definitions to see how quartiles divide data and how outliers behave in context.

• Ontario Curriculum Expectations
• CCSS.MATH.CONTENT.6.SP.B.4
• CCSS.MATH.CONTENT.HSS.ID.A.1

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Case Study Analysis
• 30 min · Pairs

Pairs: Class Data Box Plot Build

Pairs collect heights from 20 classmates, sort data, calculate quartiles and IQR, then sketch box plots on graph paper. They mark potential outliers and discuss impacts on the plot. Switch partners to verify calculations.

Interpret the five-number summary represented in a box plot.

Facilitation Tip

During Pairs: Class Data Box Plot Build, circulate to ensure students label each component of the five-number summary on their plots.

What to look for

Provide students with a dataset. Ask them to calculate the five-number summary and the IQR. Then, have them identify any potential outliers using the 1.5 × IQR rule and write one sentence explaining their findings.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 02

• Case Study Analysis
• 45 min · Small Groups

Small Groups: Histogram vs Box Plot Match

Provide datasets; groups create histograms and box plots side-by-side. They list three differences in conveyed information and present one example to the class. Use digital tools like Desmos for efficiency.

Differentiate between a box plot and a histogram in terms of information conveyed.

Facilitation Tip

For Histogram vs Box Plot Match, give groups two minutes to defend why a histogram or box plot better represents a given dataset before revealing answers.

What to look for

Present students with two box plots representing different datasets (e.g., test scores from two classes). Ask: 'What can you conclude about the spread and central tendency of each dataset? What are the advantages of using box plots over histograms for this comparison?'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 03

• Case Study Analysis
• 20 min · Whole Class

Whole Class: Outlier Investigation

Display multiple box plots on the board from sports stats. Class votes on outlier status using IQR rule, then debates if outliers are errors or extremes. Tally votes and refine rule application.

Justify the method for identifying outliers using the IQR.

Facilitation Tip

During Outlier Investigation, ask guiding questions like, 'What might cause this point to be an outlier?' to push students beyond yes/no answers.

What to look for

Show students a pre-made box plot with a few data points marked. Ask: 'Is this point (point A) likely an outlier? Justify your answer using the IQR rule and the information shown in the box plot.'

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

Activity 04

• Case Study Analysis
• 35 min · Individual

Individual: Interpretation Stations

Set up stations with box plots from different contexts. Students rotate, answering prompts on spread, median comparison, and outlier justification in journals. Debrief key insights as a group.

Interpret the five-number summary represented in a box plot.

Facilitation Tip

At Interpretation Stations, provide a checklist of key terms students must use in their written responses to ensure precision.

What to look for

Provide students with a dataset. Ask them to calculate the five-number summary and the IQR. Then, have them identify any potential outliers using the 1.5 × IQR rule and write one sentence explaining their findings.

• Analyze
• Evaluate
• Create
• Decision-Making
• Self-Management

A few notes on teaching this unit

Teach this topic by starting with raw data so students see how quartiles emerge from sorting. Use concrete examples like student heights to make quartiles tangible. Avoid rushing to the IQR rule; let students derive it by comparing distances between quartiles first. Research shows students grasp spread better when they construct box plots by hand before analyzing pre-made ones.

Successful learning looks like students confidently identifying quartiles, calculating IQR, and justifying outliers using the 1.5 × IQR rule. They should explain data spread and skewness in their own words and select appropriate visuals for comparisons.

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Watch Out for These Misconceptions

• During Pairs: Class Data Box Plot Build, watch for students assuming outliers are always errors.

  Redirect pairs to the IQR rule and ask them to discuss whether the outlier makes sense in context, such as a height measurement in a class with a student who is significantly taller due to growth spurts.

• During Histogram vs Box Plot Match, watch for students confusing the two plots as showing the same information.

  Have groups compare their matched pairs and explain in writing how histograms show frequency while box plots show quartiles, using the raw data to support their reasoning.

• During Outlier Investigation, watch for students treating the median as the mean.

  Prompt groups to calculate both the median and mean of their dataset and compare them, noting how skewness affects the relationship between these measures.

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Methods used in this brief

• Case Study Analysis