Mathematics · Senior Infants

Active learning ideas

Introduction to Variables and Expressions

Active learning helps young children grasp variables and expressions by connecting abstract symbols to concrete actions. When students use counters to represent unknown amounts, they see how expressions describe real situations. Drawing stories and acting out number tales make symbolic math feel like play, building confidence before formal notation.

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

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

Activity 01

• Stations Rotation
• 25 min · Small Groups

Manipulative Play: Counter Variables

Provide counters and story cards with unknowns, like 'some apples plus 3'. Children build expressions using boxes for variables, act out the story, and count to find the total. Discuss as a group what the box represents.

Can you tell me a number story using these 5 counters?

Facilitation Tip

During Manipulative Play: Counter Variables, circulate and ask, 'How would you show 3 more counters if this box stands for some?' to encourage flexible thinking about the unknown.

What to look for

Present students with a story like 'There were some apples in the basket. 3 were eaten. Now there are 5 apples. How many were there at first?' Ask students to draw a box for 'some apples' and write the number sentence: □ - 3 = 5. Then, ask them to show with counters how many apples were there initially.

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

Activity 02

• Stations Rotation
• 30 min · Pairs

Drawing Workshop: Story Pictures

Children listen to a verbal story with unknowns, draw pictures using symbols for variables, then label with expressions like □ + 2 = 5. Pairs share drawings and explain their symbols.

There are 4 birds on a wall and 2 fly away , how many are left?

Facilitation Tip

In Drawing Workshop: Story Pictures, ask students to explain their drawings aloud while you note how they assign symbols to quantities.

What to look for

Give each student a card with a simple expression, like 6 + □ = 10. Ask them to write a number story that matches this expression and draw a picture to show the answer. They should also write what the box represents.

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

Activity 03

• Stations Rotation
• 35 min · Whole Class

Story Circle: Verbal to Expression

In a circle, one child shares a number story with an unknown; others represent it with symbols on whiteboards. Rotate roles and vote on the best expression as a class.

Can you draw a picture to show this number story?

Facilitation Tip

In Story Circle: Verbal to Expression, model using a puppet to act out stories so students focus on the numbers, not performance.

What to look for

Ask students: 'If I say I have a box of crayons, and I give 2 away, and now I have 7 crayons, what does the box stand for? How can we write that as a number story?' Listen for their use of 'some' or 'unknown' and their ability to represent it with a symbol.

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

Activity 04

• Stations Rotation
• 20 min · Pairs

Partner Puzzles: Expression Matching

Pairs match verbal stories to pre-made expressions with variables, using counters to verify. They create one new match together and present to the class.

Can you tell me a number story using these 5 counters?

Facilitation Tip

In Partner Puzzles: Expression Matching, provide only one set of cards per pair to prompt collaboration and justification.

What to look for

Present students with a story like 'There were some apples in the basket. 3 were eaten. Now there are 5 apples. How many were there at first?' Ask students to draw a box for 'some apples' and write the number sentence: □ - 3 = 5. Then, ask them to show with counters how many apples were there initially.

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

A few notes on teaching this unit

Start with concrete experiences before introducing symbols. Research shows that young learners need to see variables as temporary placeholders, not fixed numbers. Avoid rushing to solve for variables; instead, emphasize representing and testing. Use peer discussion to normalize mistakes as part of problem-solving, and always connect expressions back to stories to maintain meaning.

Successful learning shows when children can represent unknown quantities with symbols, translate verbal stories into expressions, and explain their reasoning using both words and symbols. They should move from guessing to testing values, showing flexibility in thinking about variables as placeholders for any number.

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Watch Out for These Misconceptions

• During Manipulative Play: Counter Variables, watch for students defaulting to zero when placing counters in boxes.

  Prompt them to test different numbers by asking, 'What happens if the box has 1 counter? How about 2?' and have them adjust the total to match the story.

• During Drawing Workshop: Story Pictures, watch for students avoiding symbols and writing full counts instead of using boxes.

  Model replacing a drawn group with a box, saying, 'This picture shows 5 apples, but the story says some were eaten. Let’s use this box to stand for the unknown apples.'

• During Story Circle: Verbal to Expression, watch for students treating unknowns as unsolvable problems.

  Act out the story with counters while narrating, 'We don’t know how many there were at first, but we can find out by removing 3 from the total. Now we know the box stood for 10.'

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Methods used in this brief

• Stations Rotation