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.

• Junior Infants
• Foundations of Mathematical Thinking
• 4 activities
• 15 min–30 min

Learning Objectives

1. Classify a given statement as an expression, an equation, or an inequality.
2. Explain verbally and symbolically what it means for a number to be a solution to a simple equation.
3. Construct a simple real-world scenario that can be represented by an inequality using 'more than' or 'less than'.
4. Compare two quantities using concrete objects to determine if they are equal, more than, or less than.

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.

Prepare & details

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.

Setup: Standard classroom seating, individual or paired desks

Materials: RAFT assignment card, Historical background brief, Writing paper or notebook, Sharing protocol instructions

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

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.

Prepare & details

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.

Setup: Standard classroom seating, individual or paired desks

Materials: RAFT assignment card, Historical background brief, Writing paper or notebook, Sharing protocol instructions

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

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.

Prepare & details

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.

Setup: Standard classroom seating, individual or paired desks

Materials: RAFT assignment card, Historical background brief, Writing paper or notebook, Sharing protocol instructions

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

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.

Prepare & details

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.

Setup: Standard classroom seating, individual or paired desks

Materials: RAFT assignment card, Historical background brief, Writing paper or notebook, Sharing protocol instructions

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

Teaching This Topic

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Exit Ticket

After Balance Scale Play, give students two small bags of counters. Ask them to count 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.

Quick Check

During Whole Class Sorting, 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.

Discussion Prompt

After Story Circle, 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?'

Extensions & Scaffolding

• Challenge: Provide unbalanced scales with more than 10 items and ask students to find multiple ways to balance them.
• Scaffolding: Offer a smaller scale and fewer items for students to manipulate, focusing on one-to-one correspondence.
• Deeper exploration: Introduce simple number sentences with missing parts, like '3 + __ = 5,' and have students use counters to solve before writing the answer.

Key Vocabulary

Equation	A mathematical statement that shows two amounts are equal, like a balanced scale.
Inequality	A mathematical statement that shows two amounts are not equal, meaning one is greater or smaller than the other.
Solution	A number or value that makes an equation or inequality true.
Equal	Having the same amount or value.
More than	A greater quantity or amount.
Less than	A smaller quantity or amount.