Foundations of Mathematical Thinking · 1st Class · Sorting and Collecting Data · Summer Term

Chance: Likely and Unlikely

Calculate the theoretical probability of simple events as fractions, decimals, and percentages, understanding sample spaces and mutually exclusive events.

• 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

About This Topic

Chance: Likely and Unlikely helps first class students grasp basic ideas of probability using simple terms: certain (always happens), likely (often happens), unlikely (rarely happens), and impossible (never happens). They explore these through hands-on tools such as spinners with unequal sections, bags with different numbers of colored counters, and coin tosses. Students predict outcomes, perform multiple trials, and record tallies on class charts, directly answering key questions like what likely means or examples of certain events.

This topic fits the Sorting and Collecting Data unit in the NCCA Foundations of Mathematical Thinking curriculum. It develops prediction skills, data recording, and early understanding of sample spaces by listing possible results from simple events. Repeated trials show how more attempts give reliable patterns, preparing students for data analysis later.

Active learning suits this topic perfectly. When students make spinners in pairs, draw from bags in small groups, and compare whole-class results, abstract chance becomes concrete. They see predictions match or differ from trials, sparking discussions that build mathematical language and confidence.

Key Questions

1. What does it mean to say something is likely or unlikely to happen?
2. How do you know if something will always happen, never happen, or might happen?
3. Can you give an example of something that is certain and something that is impossible?

Learning Objectives

• Classify simple events as certain, likely, unlikely, or impossible based on given scenarios.
• Predict the outcome of simple chance events, such as coin tosses or spinner results.
• Record and tally the results of multiple trials for chance events.
• Compare predicted outcomes with actual results from chance experiments.

Before You Start

Counting and Cardinality

Why: Students need to be able to count objects accurately to record results from chance experiments.

Sorting and Classifying Objects

Why: Students must be able to sort objects by attributes (like color) to set up chance experiments with different items.

Key Vocabulary

Certain	An event that is guaranteed to happen. For example, the sun rising tomorrow is certain.
Impossible	An event that cannot happen. For example, a cat flying without assistance is impossible.
Likely	An event that has a high probability of happening, but is not guaranteed. For example, it is likely to rain if the sky is full of dark clouds.
Unlikely	An event that has a low probability of happening, but could still occur. For example, it is unlikely to win the lottery.
Outcome	The result of a chance event. For example, when tossing a coin, the outcomes are heads or tails.

Watch Out for These Misconceptions

Common Misconception

All outcomes from spinners or bags are equally likely.

What to Teach Instead

Young learners assume equal sections or items mean equal chance, ignoring size or quantity. Creating and testing unequal spinners in pairs shows frequent outcomes for larger parts. Group tallies reveal patterns, helping students revise ideas through evidence.

Common Misconception

A single trial proves what is likely or unlikely.

What to Teach Instead

Students think one spinner landing on blue means blue is likely. Multiple trials in small groups demonstrate variability and closer matches to proportions over time. Discussing class data corrects this by showing reliability from repetition.

Common Misconception

Certain events might still not happen.

What to Teach Instead

Confusing certain with likely leads to doubt about always outcomes. Activities with bags containing only one color, drawn repeatedly in whole class, confirm certainty. Peer explanations reinforce the distinction.

Active Learning Ideas

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.

30 min·Pairs

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.

35 min·Small Groups

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.

25 min·Whole Class

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.

20 min·Individual

Real-World Connections

• Weather forecasters use probability to describe the chance of rain or snow, helping people decide if they need an umbrella or a warm coat.
• Game designers use chance elements in board games and video games to make them exciting and unpredictable, ensuring players have a different experience each time they play.
• Manufacturers of products like cereal boxes sometimes include surprise toys or prizes, creating an element of chance for consumers.

Assessment Ideas

Quick Check

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.

Exit Ticket

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.

Discussion Prompt

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.

Frequently Asked Questions

How to teach likely and unlikely events in first class?

Start with familiar contexts like weather or games. Use spinners and bags for predictions and trials. Students record 10-20 outcomes, then classify as likely if over half occur. Class charts compare predictions to results, building intuition for chance without numbers. This approach keeps it concrete and engaging.

What activities work best for certain and impossible events?

Use sorting cards with real-world examples: certain like 'the sun rises', impossible like 'it snows in summer in Ireland'. Follow with prediction tools like all-red bags for certain draws. Small group trials and shares help students articulate differences, connecting to daily life for retention.

How can active learning help students understand chance?

Active methods like making spinners or drawing from bags let students predict, test, and observe firsthand. Pairs and small groups encourage talk about why results vary, revealing patterns invisible in lectures. Whole-class data displays show consensus, turning chance from abstract to experiential and boosting participation.

What are common misconceptions in early probability lessons?

Pupils mix likely with certain or think one trial sets likelihood. They overlook unequal chances in tools. Hands-on unequal spinners and repeated bag draws, plus group discussions, expose these. Tracking tallies over trials corrects views, as students see evidence contradict initial beliefs.