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.

• 2nd Year
• Foundations of Mathematical Thinking
• 4 activities
• 20 min–40 min

Learning Objectives

1. Predict the most likely outcome of a simple probability experiment involving coins or dice.
2. Compare experimental results from multiple trials to initial predictions.
3. Record and organize data from probability experiments using tally marks.
4. Explain the difference between a prediction and an experimental outcome.
5. Classify events as likely or unlikely based on experimental data.

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

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.

Prepare & details

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.

Setup: Varies; may include outdoor space, lab, or community setting

Materials: Experience setup materials, Reflection journal with prompts, Observation worksheet, Connection-to-content framework

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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

Common Misconception

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

What to Teach Instead

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

Assessment Ideas

Exit Ticket

After Pairs Prediction: Coin Flip Trials, give each student a coin to flip 10 times and record results with tally marks. Ask them to write one sentence comparing their prediction to the actual results.

Discussion Prompt

During Small Groups: Dice Roll Challenge, pose the question: 'If you rolled a standard die 100 times, would you expect the same number of each outcome?' Facilitate a class discussion where students reference their group data to support their reasoning.

Quick Check

During the Bag Draw Experiment, observe students recording results. Ask individual students: 'What is your prediction for the most frequent color?' and 'How are you keeping track of your draws?' to assess their approach.

Extensions & Scaffolding

• Challenge early finishers to design their own spinner with unequal sections and predict outcomes before testing.
• Scaffolding for struggling students involves pre-tallied charts with partial data to help them see patterns.
• Deeper exploration asks students to graph class results and compare individual predictions to the group total.

Key Vocabulary

Probability	The chance that a specific event will happen. It is often expressed as a fraction or percentage.
Outcome	A possible result of an experiment. For example, when rolling a die, the outcomes are the numbers 1 through 6.
Prediction	A statement about what you think will happen in an experiment before you conduct it.
Tally Marks	A way to record data by making a mark for each item counted. Usually, four marks are made vertically, and the fifth mark crosses them to make a group of five.
Fairness	In probability, a situation is fair if all outcomes have an equal chance of occurring, like a fair coin or a fair die.