Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Measures of Variability: Range

Active learning helps Junior Infants grasp range through concrete, playful experiences that connect to their world. Measuring real objects like teddies or sticks makes the abstract idea of spread visible and meaningful. Movement and touch build the foundation for understanding variability in data sets.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - S.1.5

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Think-Pair-Share
• 25 min · Pairs

Hands-On Measuring: Teddy Heights

Provide linking cubes for students to measure five class teddies' heights. Each child records tallest and shortest, then subtracts to find range. Pairs share and compare ranges from different teddy sets.

Explain what the range tells us about a data set.

Facilitation Tip

During Teddy Heights, have students line up the teddies from shortest to tallest to clearly identify the extremes before measuring.

What to look for

Provide students with a small collection of objects (e.g., crayons of different lengths). Ask them to identify the longest and shortest crayon and then state the range of lengths in 'crayon units'. Teacher observes and provides support.

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

Activity 02

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

Outdoor Hunt: Stick Lengths

Children collect 10 sticks outside and sort by length using a line on the ground. In small groups, identify longest and shortest, calculate range by counting units between. Discuss what a big range means for their collection.

Compare the information provided by the range versus the mean.

Facilitation Tip

For Stick Lengths, provide a common unit (e.g., blocks) so comparisons are consistent and focus remains on range rather than measurement accuracy.

What to look for

Give each student a card with a simple data set, like {3, 7, 2, 5}. Ask them to write down the highest number, the lowest number, and what the range is. They can draw a picture to show the spread.

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

Activity 03

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

Game Station: Jump Distances

Mark a jump line; students jump five times, measure with tape in whole class. Record distances, find max and min as a group, compute range. Repeat with added 'giant' jumps to see change.

Predict how adding an extreme value to a data set will affect its range.

Facilitation Tip

In Jump Distances, mark end points with tape and count steps together to ensure children see the gap between the farthest and nearest jumps.

What to look for

Present two sets of teddy bear heights: Set A {5 blocks, 6 blocks, 7 blocks} and Set B {3 blocks, 7 blocks, 9 blocks}. Ask students: 'Which group of teddy bears has more difference in height? How do you know?' Guide them to use the term 'range'.

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

Activity 04

• Think-Pair-Share
• 20 min · Individual

Toy Sort: Button Counts

Examine toys with buttons; count for six items individually. Note highest and lowest counts, subtract for range. Share drawings of sets with biggest spreads.

Explain what the range tells us about a data set.

Facilitation Tip

During Toy Sort with button counts, ask students to group toys by the same number of buttons first, then identify the groups with the most and fewest buttons.

What to look for

Provide students with a small collection of objects (e.g., crayons of different lengths). Ask them to identify the longest and shortest crayon and then state the range of lengths in 'crayon units'. Teacher observes and provides support.

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

A few notes on teaching this unit

Start with physical objects to anchor the concept of range in something students can see and touch. Avoid abstract numbers until they have a clear understanding of what range represents. Use repetition and peer discussion to reinforce that range depends only on the highest and lowest values, not the number of items or middle values. Research shows that concrete experiences build the strongest foundation for later abstract reasoning.

Students will point to the highest and lowest values in a set, find their difference, and describe whether the range is large or small. They will connect the size of the range to how clustered or spread out the data points are. Successful learning includes using terms like 'biggest,' 'smallest,' and 'difference' naturally during activities.

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Watch Out for These Misconceptions

• During Teddy Heights, watch for students counting all the teddies to find the range instead of focusing on the tallest and shortest.

  Guide students to physically isolate the tallest and shortest teddies first, then measure only those two to find the range.

• During Jump Distances, watch for students thinking the range is the farthest jump rather than the difference between farthest and nearest jumps.

  Have students count the steps from the nearest jump to the farthest jump, emphasizing the gap between the two.

• During Toy Sort with button counts, watch for students assuming the range changes when a middle number of buttons is added.

  Ask students to test their prediction by adding a toy with a middle number of buttons and measuring the new range to see if it changes.

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Methods used in this brief

• Think-Pair-Share