Mathematics · 6th Grade

Active learning ideas

Interpreting Data Displays

Active learning works well for interpreting data displays because students need to physically engage with visuals to notice patterns and limitations. Moving between different graph types helps them see how each display shapes understanding in different ways.

• Common Core State Standards
• CCSS.Math.Content.6.SP.B.4
• CCSS.Math.Content.6.SP.B.5

• 25–40 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Gallery Walk
• 40 min · Small Groups

Gallery Walk: What's the Story?

Post six data displays (mix of dot plots, histograms, box plots) with context labels removed. Groups write a one-paragraph narrative about what each display shows , center, spread, shape, outliers , without being told what the data is about. Debrief compares narratives across groups.

Critique how the scale of a graph can be used to mislead an audience.

Facilitation Tip

During the Gallery Walk, position students so they can’t see others’ notes until they’ve recorded their own interpretations first.

What to look for

Provide students with two versions of the same data displayed on graphs with different scales. Ask: 'Which graph makes the difference between Group A and Group B seem larger? Explain why, referencing the scale.'

• Understand
• Apply
• Analyze
• Create
• Relationship Skills
• Social Awareness

Activity 02

• Think-Pair-Share
• 25 min · Pairs

Think-Pair-Share: Spot the Misleading Graph

Show students a histogram with a truncated y-axis that makes a small difference look dramatic. Pairs analyze the graph, identify the design choice that misleads, and redraw a fair version. Class discusses how scale choices influence perception.

Construct a narrative about a data set based on its graphical representation.

Facilitation Tip

In Think-Pair-Share, assign roles (e.g., graph reader, claim checker) to ensure both students contribute to the discussion.

What to look for

Present a scenario, such as 'A local news report claims that most students in our school get less than 3 hours of sleep.' Show a histogram of student sleep data. Ask: 'Does this graph support the claim? How could the graph be changed to make the claim look stronger or weaker?'

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

Activity 03

• Inquiry Circle
• 40 min · Small Groups

Inquiry Circle: Best Display for the Question

Groups receive three versions of the same data (dot plot, histogram, box plot) and a set of five interpretation questions. They determine which display answers each question most efficiently and explain their reasoning in writing.

Evaluate the effectiveness of different data displays for different types of questions.

Facilitation Tip

For Collaborative Investigation, provide a set of pre-selected questions that require students to match data to the most informative display format.

What to look for

Give students a box plot showing the heights of students in two different classes. Ask them to write one sentence comparing the typical height and one sentence comparing the spread of heights for the two classes.

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

A few notes on teaching this unit

Experienced teachers approach this topic by shifting focus from reading graphs to reasoning about them. Avoid letting students stop at identifying the median or mode; always ask how these values connect to the real-world scenario. Research suggests that students benefit from comparing poorly constructed graphs to well-made ones to internalize design principles.

Successful learning looks like students explaining how shape, center, and spread relate to the data context. They should justify which displays best answer specific questions and critique misleading representations with evidence.

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Watch Out for These Misconceptions

• During Gallery Walk: What's the Story?, watch for students assuming taller bars in any histogram mean more data values.

  Use the Gallery Walk materials to point out histograms with unequal bin widths. Ask students to calculate actual frequencies by multiplying height by bin width to reveal the misconception.

• During Think-Pair-Share: Spot the Misleading Graph, watch for students believing all graph formats lead to the same conclusions.

  Have students revisit their paired discussions and specifically compare what a box plot hides versus what a dot plot reveals, using the provided misleading graphs as evidence.

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Methods used in this brief

• Gallery Walk
• Think-Pair-Share
• Inquiry Circle