Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Measures of Central Tendency: Mean, Median, Mode

Active learning lets children experience numbers as real things they can touch, count, and share. When students move items, line up heights, or divide sweets, they build lasting mental models of mean, median, and mode that paper-and-pencil tasks cannot match. The body and voice turn abstract symbols into lived understanding.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - S.1.4

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

Activity 01

• Inquiry Circle
• 25 min · Pairs

Tally Hunt: Classroom Favorites

Children survey classmates on favorite colors or animals using picture tally charts. Tally marks reveal the mode. Order the frequencies for median, add totals and divide by class size for mean. Share findings on a large chart.

Differentiate between the mean, median, and mode as measures of central tendency.

Facilitation Tip

During Tally Hunt, keep the tally marks large enough for the whole class to see from their seats so everyone can join the counting.

What to look for

Provide students with a small set of numbers, such as the number of stickers each child in a group has (e.g., 3, 5, 3, 7, 3). Ask them to find the mode and explain in one sentence why it is the mode. Then, ask them to find the median and explain how they found it.

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

Activity 02

• Inquiry Circle
• 35 min · Whole Class

Height Line-Up: Median March

Line up whole class by height using string markers. Identify the middle position as median. Measure heights with blocks for mean calculation. Note if tallest skews the mean. Record on group posters.

Analyze how outliers affect the mean compared to the median.

Facilitation Tip

When lining up for Height Line-Up, ask students to whisper their height to a partner before ordering so they own the data they are moving.

What to look for

Give students a data set with a clear outlier, like the ages of children at a party (e.g., 5, 6, 6, 7, 15). Ask them to calculate the mean and the median. Then, ask them to write one sentence explaining which number (mean or median) better represents the typical age of most children at the party and why.

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

Activity 03

• Inquiry Circle
• 20 min · Small Groups

Sharing Circle: Mean Sweets

Distribute 20 sweets among 5 children unevenly. Discuss fair sharing for mean. Repeat with outlier bag of 10 extra. Compare to median of amounts. Draw before-and-after bars.

Justify which measure of central tendency is most appropriate for a given data set.

Facilitation Tip

In Sharing Circle, use small, countable items so remainders are visible and children can physically split 2.5 items between two friends.

What to look for

Present a scenario: 'A baker made 10 cupcakes. He sold 8 cupcakes for €2 each and 2 special cupcakes for €10 each.' Ask students: 'Would it be better to tell someone the average price was €2, or €4? Why?' Guide them to discuss how the higher-priced cupcakes affect the mean and median.

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

Activity 04

• Inquiry Circle
• 30 min · Small Groups

Toy Sort: Mode Match

Sort class toys by type in baskets. Count and circle the fullest basket for mode. Line counts for median, average per basket for mean. Vote on best measure for toys.

Differentiate between the mean, median, and mode as measures of central tendency.

Facilitation Tip

For Toy Sort, provide identical counting bears or blocks so color or shape becomes the only variable to tally.

What to look for

Provide students with a small set of numbers, such as the number of stickers each child in a group has (e.g., 3, 5, 3, 7, 3). Ask them to find the mode and explain in one sentence why it is the mode. Then, ask them to find the median and explain how they found it.

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

A few notes on teaching this unit

Start with the mode because it is the most concrete; children already use 'most' in daily talk. Move to the median next because ordering a small set is quick and builds number sense. Finish with the mean last because it requires division and can feel abstract, but concrete sharing makes it tangible. Avoid teaching formulas until students have built their own understanding through repeated use of the same objects.

By the end of these activities, every child can identify the mode as the most frequent item, the median as the middle value in an ordered line, and the mean as the fair share when items are split equally. You will see students pointing to objects, ordering themselves, and using words like 'most,' 'middle,' and 'fair' with confidence.

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Watch Out for These Misconceptions

• During Sharing Circle, watch for students who insist the mean must be a whole number.

  Pause the sharing and ask the group to split five sweets between two friends. Let them see the two whole sweets each receive and the remaining one split in half. Ask them to name the amount each friend gets, writing 2.5 on the board as the mean.

• During Height Line-Up, listen for students who say the median is the same as the mean.

  Place a very tall and a very short student at the ends of the line. Ask the group to find the middle child and compare it to the average height. Guide them to notice that the median stays in the middle even when extremes change.

• During Toy Sort, observe students who pick the biggest pile as the mode.

  Gather the class and ask them to count each pile aloud together. Write the totals on the board and circle the highest number. Ask, 'Is it the biggest pile or the one that appears most often?' Have students recount to confirm the mode is the most frequent, not the largest.

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Methods used in this brief

• Inquiry Circle