Foundations of Mathematical Thinking · 2nd Year

Active learning ideas

Predicting Outcomes of Simple Experiments

Active learning works well for this topic because predicting and testing outcomes helps students move from intuition to evidence-based reasoning. Hands-on experiments make abstract ideas like probability concrete, letting students see patterns in data they collect themselves.

• NCCA Curriculum Specifications
• NCCA: Primary - Data
• NCCA: Primary - Reasoning

• 20–40 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 20 min · Pairs

Pairs Prediction: Coin Flip Trials

Pairs discuss and predict the outcome for 20 coin flips, such as more heads or tails. One student flips while the other tallies results on a chart. Partners switch roles, then compare predictions to data and explain differences.

What do you think will happen if you flip a coin? Why?

Facilitation Tip

During the Coin Flip Trials, remind pairs to alternate flips so each student participates equally.

What to look for

Give each student a coin. Ask them to flip it 10 times and record the results using tally marks. Then, ask them to write one sentence comparing their prediction to their actual results.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 30 min · Small Groups

Small Groups: Dice Roll Challenge

Groups predict the most frequent number on a die after 30 rolls. Each member rolls 10 times and adds tallies to a group chart. Groups create a bar graph and discuss if predictions matched results.

How many different numbers can come up when you roll a dice?

Facilitation Tip

For the Dice Roll Challenge, provide one die per group and ask students to predict before rolling to reinforce initial reasoning.

What to look for

Pose the question: 'If you roll a standard die 100 times, would you expect to get the same number of each outcome?' Facilitate a class discussion where students share their predictions and reasoning, referencing their earlier experiments.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 40 min · Whole Class

Whole Class: Spinner Probability Game

Class predicts color frequencies on shared spinners divided into sections. Students take turns spinning and tallying on a large board. Review class data to check predictions and note patterns.

Can you record what happened in your experiment using tally marks?

Facilitation Tip

In the Spinner Probability Game, have students rotate roles of recorder, spinner, and predictor to keep everyone engaged.

What to look for

Observe students as they conduct a dice-rolling experiment. Ask individual students: 'What is your prediction for the most frequent outcome?' and 'How are you recording your results?'

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 25 min · Individual

Individual: Bag Draw Experiment

Each student predicts draws from a bag with colored counters. They draw with replacement 20 times, tally privately, then share results to see class trends against predictions.

What do you think will happen if you flip a coin? Why?

Facilitation Tip

For the Bag Draw Experiment, prepare identical bags with colored tiles so all students compare the same conditions.

What to look for

Give each student a coin. Ask them to flip it 10 times and record the results using tally marks. Then, ask them to write one sentence comparing their prediction to their actual results.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teach this topic by letting students experience chance firsthand before introducing vocabulary like probability or fairness. Avoid over-explaining theory upfront, as hands-on trials build intuition naturally. Research shows that repeated trials reduce misconceptions faster than lectures alone.

Successful learning looks like students using tally marks to record trials, comparing predictions to results, and explaining why outcomes vary despite initial guesses. They should articulate that probability describes long-term patterns, not single events.

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Watch Out for These Misconceptions

• During Pairs Prediction: Coin Flip Trials, watch for students who think a coin will land the same way repeatedly.

  Ask pairs to tally 20 flips, then combine their data with another pair to show how heads and tails balance over more trials.

• During Small Groups: Dice Roll Challenge, watch for students who believe a die favors certain numbers based on recent rolls.

  Have groups share their tallies on a class chart to compare individual results to the total, highlighting that fairness emerges over many rolls.

• During Whole Class: Spinner Probability Game, watch for students who think predictions must match outcomes exactly.

  After trials, lead a discussion where students explain why variability exists even when sections are equal, using their spinner data as evidence.

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Methods used in this brief

• Experiential Learning