Mathematics · Year 3

Active learning ideas

Balancing Equations

Active learning helps Year 3 students grasp balancing equations because concrete experiences build an intuitive understanding of equality that abstract symbols alone cannot. When students physically manipulate objects and observe balance scales, they directly connect mathematical operations to real-world equivalence.

• ACARA Content Descriptions
• AC9M3A02

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

Activity 01

• Experiential Learning
• 35 min · Small Groups

Manipulatives: Balance Scale Equations

Provide balance scales, counters, and number cards. Students place known addends on one side and find the unknown to balance, then swap sides and predict outcomes. Record equations and solutions on mini-whiteboards for sharing.

Justify why both sides of an equation must be equal.

Facilitation Tip

During Manipulatives: Balance Scale Equations, circulate and ask guiding questions like 'What happens when you add two counters to this side?' to reinforce the concept of balance.

What to look for

Provide students with a balance scale drawing. On one side, draw 3 apples and 2 bananas. Ask students to draw the correct number of oranges on the other side to make the scale balance. Write the equation represented.

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

Activity 02

• Experiential Learning
• 25 min · Pairs

Pairs: Build and Balance

Partners select two numbers, build an equation with an unknown using blocks on paper mats. One partner changes a number; the other adjusts to rebalance and explains the inverse operation. Switch roles twice.

Construct a simple equation with an unknown that balances.

Facilitation Tip

During Pairs: Build and Balance, listen for partner discussions that include phrases like 'I need to add three here to match the five there' to assess understanding.

What to look for

Present students with the equation 7 + 2 = ? + 4. Ask them to use counters or draw pictures to find the missing number and explain how they know the equation balances.

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

Activity 03

• Experiential Learning
• 30 min · Whole Class

Whole Class: Equation Chain

Start with a simple equation on the board using class counters. Call students to adjust one side; the class predicts and verifies the change needed on the other side. Continue chaining five equations.

Analyze how changing one number in an equation affects the other side to maintain balance.

Facilitation Tip

During Whole Class: Equation Chain, write student equations on the board and ask the class to verify balance before moving to the next, ensuring collective engagement.

What to look for

Pose the question: 'If I have 5 + 3 on one side of a balance, and I change the 3 to a 5, what must I do to the other side to keep it balanced?' Facilitate a discussion where students explain their reasoning using the concept of equality.

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

Activity 04

• Experiential Learning
• 20 min · Individual

Individual: Concrete to Abstract

Students use personal sets of blocks to solve five given equations, draw representations, then write symbolic versions. Self-check with a partner mirror balance.

Justify why both sides of an equation must be equal.

What to look for

Provide students with a balance scale drawing. On one side, draw 3 apples and 2 bananas. Ask students to draw the correct number of oranges on the other side to make the scale balance. Write the equation represented.

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

A few notes on teaching this unit

Start with concrete manipulatives to establish the concept of balance, then gradually move to pictorial and symbolic representations. Avoid rushing to abstract equations before students can physically demonstrate balance. Research shows that students who explore equality through hands-on experiences develop stronger number sense and problem-solving skills.

Students will confidently explain why both sides of an equation must be equal and use manipulatives to model, solve, and create balanced equations with unknowns. They will justify their reasoning using the language of balance and equality.

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Watch Out for These Misconceptions

• During Manipulatives: Balance Scale Equations, watch for students who believe they can add or subtract from only one side of the equation.

  Have students physically add or subtract the same amount from both sides of the balance scale and observe the result. Ask them to explain why the scale tips if they do not adjust both sides equally.

• During Pairs: Build and Balance, watch for students who think any number can be the unknown to make both sides equal.

  Ask partners to test multiple numbers with counters and discuss why only one value balances the equation perfectly. Encourage them to record each attempt and the outcome.

• During Whole Class: Equation Chain, watch for students who confuse equality with identical numerals rather than equal totals.

  Model an equation like 2 + 3 = 1 + 4 using blocks, then ask students to regroup counters to show how different numerals can represent the same total. Discuss part-whole relationships.

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Methods used in this brief

• Experiential Learning