Mathematics · Year 2

Active learning ideas

Identifying Possible Outcomes

Active learning works for identifying possible outcomes because students need concrete, hands-on experience with chance experiments to move from abstract ideas to clear understanding. When Year 2 students manipulate objects like coins, spinners, and dice, they turn probability concepts into tangible experiences that build lasting memory.

• ACARA Content Descriptions
• AC9M2P01

• 15–30 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Plan-Do-Review
• 20 min · Pairs

Pairs: Coin Flip Listing

Partners flip a coin 10 times and list all possible outcomes first, then record actual results. They draw a simple tree diagram showing heads and tails branches. Compare predictions to trials and adjust lists if needed.

What are all the possible results when flipping a coin?

Facilitation Tip

During the Coin Flip Listing activity, circulate and prompt pairs to explain why they think heads and tails are equally likely before recording.

What to look for

Give students a drawing of a spinner with four equal sections: red, blue, green, yellow. Ask them to list all the possible outcomes if the spinner is spun once. Then, ask them to draw a different spinner and list its possible outcomes.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 02

• Plan-Do-Review
• 30 min · Small Groups

Small Groups: Custom Spinner Challenge

Groups divide paper plates into equal sections with colours, then list all possible spin outcomes. Test spinners 20 times, tally results, and discuss if all outcomes appeared. Share findings with the class.

Predict all the possible colours you could spin on a spinner with three colours.

Facilitation Tip

In the Custom Spinner Challenge, remind groups to measure sections carefully so outcomes remain fair for accurate comparisons.

What to look for

Present students with a scenario: 'You have a bag with one red ball and one blue ball. You close your eyes and pick one ball.' Ask students to hold up fingers to show how many possible outcomes there are. Then, ask them to name each outcome.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 03

• Plan-Do-Review
• 25 min · Whole Class

Whole Class: Die Roll Prediction

Display a six-sided die. Class brainstorms and votes on all possible outcomes together on a shared chart. Roll the die repeatedly, marking tallies. Review the complete list and note equal chances.

Explain why some outcomes might be more likely than others in a chance experiment.

Facilitation Tip

For the Die Roll Prediction, model how to create a tally chart by recording predictions first, then actual results, to highlight the difference between expectation and reality.

What to look for

Pose the question: 'Imagine you roll a special six-sided die that has the number 1 on three faces, the number 2 on two faces, and the number 3 on one face. What are all the possible outcomes you could roll?' Facilitate a class discussion to confirm the outcomes are 1, 2, and 3.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

Activity 04

• Plan-Do-Review
• 15 min · Individual

Individual: Card Draw Sort

Give each student a deck of four cards (two red, two blue). List outcomes for drawing one card. Simulate draws with replacement, record in personal tables. Identify overlooked outcomes through self-check.

What are all the possible results when flipping a coin?

Facilitation Tip

During the Card Draw Sort, ask students to sort cards physically before writing outcomes to reinforce sorting as a method of organizing data.

What to look for

Give students a drawing of a spinner with four equal sections: red, blue, green, yellow. Ask them to list all the possible outcomes if the spinner is spun once. Then, ask them to draw a different spinner and list its possible outcomes.

• Remember
• Apply
• Analyze
• Self-Management
• Decision-Making
• Self-Awareness

A few notes on teaching this unit

Start by modeling how to list outcomes systematically, using clear visuals like drawings or simple tables. Avoid rushing to theoretical explanations; instead, let students discover patterns through repeated trials. Research shows that young learners build probabilistic reasoning best when they first experience chance through physical manipulatives before moving to abstract representations. Keep discussions focused on observable data rather than assumptions about luck.

Students will confidently list all possible outcomes from simple chance experiments, explain why some outcomes are more likely than others, and demonstrate systematic thinking in their recordings. Success looks like complete lists, accurate predictions, and clear reasoning during group discussions.

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Watch Out for These Misconceptions

• During the Custom Spinner Challenge, watch for students who assume all outcomes are equally likely even when spinner sections differ in size.

  Direct students to measure each section with a ruler and discuss how the size affects the chance of landing on that color. Have them spin 20 times and tally results, then compare tallies to the section sizes to correct assumptions.

• During the Coin Flip Listing activity, watch for students who only list one outcome, such as just heads.

  Ask partners to check each other's lists and prompt them to think aloud about what would happen if they flipped the coin again. Provide sentence stems like 'The coin can land on...' to guide completeness.

• During the Die Roll Prediction, watch for students who believe a previous roll affects the next one, such as saying 'the die is due for a 6.'

  Run a whole-class simulation with 30 rolls, recording results publicly. Pause after each roll to ask if the next roll depends on the previous one, using the data to demonstrate independence through collective observation.

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Methods used in this brief

• Plan-Do-Review