Foundations of Mathematical Thinking · 1st Class

Active learning ideas

Chance: Likely and Unlikely

Active learning works for this topic because young children build intuitive understanding through physical experience. When they spin, draw, and toss, they connect abstract words like 'likely' to real evidence in their hands. This hands-on approach makes probability concrete before moving to symbols or numbers.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - SP.3.1
• NCCA: Junior Cycle - Strand 3: Statistics and Probability - SP.3.2

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

Activity 01

• Think-Pair-Share
• 30 min · Pairs

Pairs Activity: Unequal Spinner Trials

Pairs draw and color spinners with unequal sections, such as three-quarters blue and one-quarter red. They predict the likely color, spin 20 times each, and tally outcomes on a sheet. Pairs then explain their results to another pair.

What does it mean to say something is likely or unlikely to happen?

Facilitation Tip

During Unequal Spinner Trials, circulate and ask pairs to explain which color they think will come up most and why before they spin.

What to look for

Present students with a set of picture cards showing different scenarios (e.g., a pig flying, a sun rising, a full moon, a rain cloud). Ask students to hold up a green card for 'certain', red for 'impossible', yellow for 'likely', and blue for 'unlikely' as you describe each scenario.

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

Activity 02

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

Small Groups: Color Bag Predictions

Provide bags with varying ratios of colored counters, like 4 red and 1 blue in one bag. Groups predict the likely draw, perform 15 draws with replacement, record tallies, and graph results. Groups share why one color was more likely.

How do you know if something will always happen, never happen, or might happen?

Facilitation Tip

In Color Bag Predictions, remind small groups to agree on a prediction before taking out counters to test their ideas.

What to look for

Give each student a small bag with 3 red counters and 1 blue counter. Ask them to draw a counter 5 times, recording the color each time. On their exit ticket, they should write one sentence about whether it was 'likely' or 'unlikely' to draw the blue counter and why.

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

Activity 03

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

Whole Class: Coin Toss Tracker

Display a chart for heads and tails. Class predicts outcomes for 20 tosses, teacher tosses while students mark results live. Discuss if predictions matched and why multiple tosses matter.

Can you give an example of something that is certain and something that is impossible?

Facilitation Tip

During Coin Toss Tracker, model how to record tallies with tall marks and a line crossing every fifth mark to build data literacy.

What to look for

Pose the question: 'If I have a spinner with 4 equal sections, and 3 are green and 1 is red, what is likely to happen if we spin it 10 times?' Facilitate a class discussion where students share their predictions and reasoning, encouraging them to use the vocabulary learned.

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

Activity 04

• Think-Pair-Share
• 20 min · Individual

Individual: Chance Sort Cards

Give students cards describing events, such as 'It rains in Ireland' or 'Pigs fly'. They sort into certain, likely, unlikely, impossible piles individually, then justify choices in a class share.

What does it mean to say something is likely or unlikely to happen?

Facilitation Tip

For Chance Sort Cards, observe students as they justify their sorts aloud to check their grasp of the terms.

What to look for

Present students with a set of picture cards showing different scenarios (e.g., a pig flying, a sun rising, a full moon, a rain cloud). Ask students to hold up a green card for 'certain', red for 'impossible', yellow for 'likely', and blue for 'unlikely' as you describe each scenario.

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

A few notes on teaching this unit

Teach this topic by letting students experience the contrast between expectation and reality first. Avoid giving definitions upfront; instead, let them discover the meanings through repeated trials. Research shows that young learners grasp probability best when they collect their own data and see patterns emerge over time. Avoid rushing to formal labels before they have enough evidence to support them.

Successful learning looks like students using the vocabulary of chance correctly to describe outcomes they observe. They should justify predictions with evidence from trials, such as pointing to a larger section on a spinner as the reason it is likely. By the end, they can classify events as certain, likely, unlikely, or impossible with clear reasoning.

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Watch Out for These Misconceptions

• During Unequal Spinner Trials, watch for students who assume all sections have the same chance regardless of size.

  Have students predict which color they think will appear most often and why, then spin 20 times and tally results as a pair. Point to the larger section and ask, 'Does the size of the section change how often that color lands?'

• During Color Bag Predictions, watch for students who think one draw tells the whole story about likely or unlikely.

  Ask groups to draw a counter 10 times, recording each result. Then gather class data to show that the blue counter appears about one-quarter of the time, matching the proportion in the bag.

• During Coin Toss Tracker, watch for students who confuse 'certain' with 'likely' when only one outcome is possible.

  Use a bag with only green counters and draw repeatedly as a whole class. Ask, 'Can we ever draw a color that is not green? Why or why not?'

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Methods used in this brief

• Think-Pair-Share