Mathematics · Junior Infants

Active learning ideas

Solving One-Step Equations: Multiplication & Division

Active learning helps young students grasp one-step multiplication and division equations by connecting abstract symbols to hands-on experiences. Using physical objects lets children see equal grouping and sharing, which builds an intuitive sense of balance in equations before moving to symbolic notation.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Algebra - A.1.6

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

Activity 01

• Stations Rotation
• 30 min · Small Groups

Balance Scale Equations: Grouping Challenges

Provide pan balances, counters, and cards showing equations like '□ x 3 = 12'. Children place groups on one side and total on the other, adjusting until balanced. They record findings with drawings and explain to the group.

Explain why dividing by a fraction is the inverse of multiplying by that fraction.

Facilitation Tip

During Balance Scale Equations, place the equation card next to the scale so students can match the visual representation with the physical grouping.

What to look for

Give each student a card with a problem like '4 groups of □ make 12'. Ask them to draw a picture to solve it and write the number that goes in the box. Then, ask them to write the related division sentence.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 02

• Stations Rotation
• 25 min · Whole Class

Sharing Circle: Division Stories

Sit in a circle with toy fruits or sweets. Pose problems like 'Share 8 apples equally among 4 friends'. Children distribute physically, count each share, and write or draw the equation. Discuss why checking matters.

Construct an equation that requires division to solve for the variable.

Facilitation Tip

In Sharing Circle, model the language of division by saying, 'Let's share these toys fairly into two groups, so each group has the same number.'

What to look for

Present a problem on the board, such as '15 ÷ □ = 3'. Ask students to show fingers for the answer or hold up a pre-made card with the number. Observe which students can correctly identify the missing divisor.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 03

• Stations Rotation
• 20 min · Pairs

Equation Mats: Multiplication Undo

Set up mats with outlines for groups and totals. Children fill with blocks for '2 x □ = 10', then reverse by dividing. Pairs swap mats to solve and check each other's work.

Evaluate the importance of checking solutions in equations.

Facilitation Tip

On Equation Mats, ask students to whisper the inverse operation they used to undo the equation before writing the answer.

What to look for

Pose the question: 'If you know 3 x 5 = 15, how can you use that to find the answer to 15 ÷ 3?' Encourage students to explain the connection using counters or drawings.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Activity 04

• Stations Rotation
• 35 min · Small Groups

Toy Shop Problems: Real-World Equations

Use play money and toys. Children solve 'How many toys for €5 if 2 cost €10?' by grouping or sharing. They role-play buying and verify totals.

Explain why dividing by a fraction is the inverse of multiplying by that fraction.

Facilitation Tip

With Toy Shop Problems, let students act out the scenario first, then record the equation that matches their actions.

What to look for

Give each student a card with a problem like '4 groups of □ make 12'. Ask them to draw a picture to solve it and write the number that goes in the box. Then, ask them to write the related division sentence.

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

A few notes on teaching this unit

Experienced teachers begin with concrete materials to build understanding before introducing symbols, as research shows this prevents rote memorization without meaning. Avoid rushing to abstract recording; instead, encourage students to verbalize their actions while manipulating objects. Use consistent language for operations, such as 'groups of' for multiplication and 'shared into' for division, to reinforce the connection between the two.

By the end of these activities, students should confidently use counters, blocks, or drawings to solve one-step equations with multiplication and division. They should also explain why their solutions work by recombining groups or recounting objects, showing clear connections between the operations.

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Watch Out for These Misconceptions

• During Sharing Circle, watch for students who remove objects one-by-one instead of creating equal groups right away.

  Prompt them to first count the total objects, then decide how many groups they need. Ask, 'How many toys should go in each bag so both bags have the same amount?' to guide equal distribution.

• During Balance Scale Equations, watch for students who assume multiplication always increases the total without considering the group size.

  Have them recount the groups while placing objects on the scale, asking, 'Does this group of 4 make the scale balance because we added 4 more, or because we made equal parts?' to clarify the role of grouping.

• During Equation Mats, watch for students who skip checking their work after writing the answer.

  Ask them to use the same counters to recombine the groups or shares to confirm the equation balances, reinforcing the importance of verification with a peer.

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Methods used in this brief

• Stations Rotation