Mathematics · Junior Infants

Active learning ideas

Introduction to Equations and Inequalities

Active learning with balance scales and everyday objects builds a strong foundation for equations and inequalities. Children see equality and balance physically, which makes abstract symbols meaningful. This hands-on approach reduces confusion and builds confidence in identifying equal and unequal amounts.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Algebra - A.1.5

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

Activity 01

• RAFT Writing
• 25 min · Pairs

Balance Scale Play: Finding Equality

Provide scales and counters for pairs to balance sides by adding or removing items. Prompt them to describe actions verbally, like 'two more makes it equal.' Record one equation per pair on chart paper.

Differentiate between an expression, an equation, and an inequality.

Facilitation Tip

During Balance Scale Play, encourage students to say, 'This side has the same as that side,' to reinforce the language of equality.

What to look for

Give students two small bags of counters. Ask them to count the counters in each bag and write or draw whether the bags are equal, one has more than the other, or one has less than the other. Then, give them a simple equation like '2 + 1 = ?' and ask them to write the number that makes it true.

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

Activity 02

• RAFT Writing
• 30 min · Small Groups

Story Circle: Inequality Scenarios

Read a story about sharing sweets unevenly, then have small groups act it out with props. Discuss 'more than' or 'less than' and draw simple pictures. Transition to symbols by labeling group drawings.

Explain what it means for a value to be a 'solution' to an equation.

Facilitation Tip

In Story Circle, pause to model the words 'more than' or 'less than' when unbalanced scales appear in the story.

What to look for

Present students with three cards: one showing '3 + 2', one showing '3 + 2 = 5', and one showing '3 + 2 > 4'. Ask students to point to the card that is an equation and the card that shows an inequality. Discuss why.

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

Activity 03

• RAFT Writing
• 20 min · Whole Class

Whole Class Sorting: Expressions vs Equations

Display cards with expressions (e.g., 'four apples') and equations (e.g., 'two plus two equals four'). Class votes and sorts them on a board, justifying with toy fruits. End with creating one new equation together.

Construct a real-world scenario that can be represented by an inequality.

Facilitation Tip

For Whole Class Sorting, remind students to check both sides of the scale before deciding if it shows an equation or expression.

What to look for

Present a scenario: 'I have 3 apples, and my friend has 5 apples.' Ask students: 'Who has more apples? How do you know?' Then ask: 'Can we say I have less than my friend? How can we show this with numbers or words?'

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

Activity 04

• RAFT Writing
• 15 min · Individual

Individual Mat Work: Solution Hunt

Each child gets a mat with an unbalanced scale picture and numeral cards. They select the solution card to balance it, then share one with a partner verbally.

Differentiate between an expression, an equation, and an inequality.

Facilitation Tip

During Individual Mat Work, ask students to explain their steps aloud as they add or remove items to balance the scale.

What to look for

Give students two small bags of counters. Ask them to count the counters in each bag and write or draw whether the bags are equal, one has more than the other, or one has less than the other. Then, give them a simple equation like '2 + 1 = ?' and ask them to write the number that makes it true.

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

A few notes on teaching this unit

Start with concrete objects before introducing symbols. Use consistent language like 'this side equals that side' to build vocabulary. Avoid rushing to written equations; let children explore balance first. Research shows young learners grasp equality better when they see and touch the concept, so keep materials varied but simple. Watch for students who focus only on the number of items without considering balance, and gently redirect their attention to the scale itself.

Children will confidently use balance scales to show equality with identical items, verbally describe unbalanced scales as 'more than' or 'less than,' and begin to match these ideas to simple written symbols. They will see solutions as logical outcomes of balancing, not random guesses.

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Watch Out for These Misconceptions

• During Balance Scale Play, watch for students who insist equality only works with numbers and ignore the physical balance of items.

  Prompt students to use identical toys or blocks on both sides, then ask, 'Does the scale balance now? How do you know?' This shifts their focus from numbers to the concept of balance.

• During Story Circle, listen for students who describe unbalanced scales as 'wrong' or 'broken.'

  After the story, hold up an unbalanced scale and ask, 'Is this scale wrong? What could it show about the two sides?' Guide the group to use 'more than' or 'less than' to describe the inequality.

• During Individual Mat Work, observe students who guess numbers without testing them on the scale.

  Ask students to place their guess on the scale and check if it balances. If not, prompt them to adjust and try again, reinforcing that solutions come from testing, not guessing.

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Methods used in this brief

• RAFT Writing