Evaluating Algebraic Expressions

Active learning works for evaluating algebraic expressions because children learn best through concrete manipulation before abstract thinking. Substituting values into expressions with physical objects builds confidence and clarifies the meaning of variables in a way that static worksheets cannot.

• Junior Infants
• Foundations of Mathematical Thinking
• 4 activities
• 15 min–35 min

Learning Objectives

1. Calculate the result of simple algebraic expressions by substituting given numerical values.
2. Identify the order of operations (multiplication before addition) in evaluating expressions.
3. Construct a table of values for an algebraic expression by performing multiple substitutions.
4. Explain how changing the value of a variable affects the outcome of an expression.

Stations Rotation

⏱ 25 min·Pairs

Manipulative Play: Box Substitution

Provide pairs with expression cards (□ + 2, 3 × □) and number cards (1-5). Children place a number under the box, use counters to find the total, and record in a two-column table. Switch roles after three tries.

Prepare & details

Analyse how changing the value of a variable impacts the result of an algebraic expression.

Facilitation Tip: During Manipulative Play: Box Substitution, circulate and ask pairs to explain their substitution steps using the cubes as they swap values into the box.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 35 min·Small Groups

Stations Rotation: Order Stations

Set up three stations: one for addition expressions, one for multiplication, one for mixed. Small groups rotate every 7 minutes, substituting values with linking cubes and noting results on mini-tables. Debrief as a class.

Prepare & details

Apply the correct order of operations when evaluating an expression with multiple terms.

Facilitation Tip: Set up Order Stations with visual signs showing 'First multiply, then add' to reinforce the correct sequence at each station.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 20 min·Whole Class

Whole Class: Pattern Parade

Write a class expression on the board, like 2 + □. Call numbers; children hold up that many fingers and add 2 more using body claps. Chart results together to spot the growing pattern.

Prepare & details

Construct a table of values by substituting different values of a variable into an algebraic expression.

Facilitation Tip: During Pattern Parade, invite students to present their findings to the class, encouraging them to use the word 'variable' as they describe patterns.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Stations Rotation

⏱ 15 min·Individual

Individual: Stamp Tables

Each child gets a worksheet with □ × 2 and blank table. They stamp numbers 1-4 into the box, draw or stamp the product, and colour the pattern.

Prepare & details

Analyse how changing the value of a variable impacts the result of an algebraic expression.

Facilitation Tip: For Stamp Tables, model how to fill in the table row by row, pointing to the expression and the substituted value each time.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

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

Teaching This Topic

Teachers should start with hands-on manipulatives to make variables tangible, then move to semi-concrete representations like tables. Avoid rushing to abstract symbols without grounding in concrete experiences. Research suggests that young learners benefit from repeated exposure to substitution in varied contexts before formalizing rules.

What to Expect

Successful learning looks like children substituting values correctly, following the order of operations, and explaining how changing the variable affects the result. They should participate in discussions about patterns and use tables to represent their work clearly.

Watch Out for These Misconceptions

Common Misconception

During Manipulative Play: Box Substitution, watch for children adding before multiplying because they rely on natural counting order.

What to Teach Instead

Guide them to model 3 × □ with three groups of cubes first, count the total, then add any remaining values to reinforce the correct order.

Common Misconception

During Station Rotation: Order Stations, watch for children treating the box symbol as a fixed placeholder for one number.

What to Teach Instead

Have students rotate through stations with different values for the box, filling in tables to see how the result changes with each substitution.

Common Misconception

During Pattern Parade, watch for children assuming the variable’s value doesn’t affect the outcome.

What to Teach Instead

Use the class-generated pattern tables to ask, 'What happens when we make the box bigger?' and have students predict and verify the impact together.

Assessment Ideas

Quick Check

After Manipulative Play: Box Substitution, present the expression '□ + 4' and ask students to show with cubes how the answer changes when □ is 3 and then when □ is 5. Observe if they correctly substitute and add each time.

Exit Ticket

During Station Rotation: Order Stations, collect each student’s completed table showing steps for '2 × □ + 1' with □ = 3. Check that they follow multiplication before addition and write the correct final answer.

Discussion Prompt

After Whole Class: Pattern Parade, ask, 'If we have the expression □ + 5, what happens to the answer if we make □ bigger? What if we make □ smaller?' Encourage students to reference their tables and explain the pattern using the word 'variable'.

Extensions & Scaffolding

• Challenge students who finish early by asking them to create their own expressions using the box symbol and write a short story about how the variable changes the outcome.
• For students who struggle, provide sticky notes with pre-written values to place in the box, reducing cognitive load while they focus on computation.
• Use extra time to introduce a second variable, such as □ + △, and explore how two variables interact in simple patterns.

Key Vocabulary

variable	A symbol, usually a shape like a square or a letter, that stands for a number we don't know yet or that can change.
expression	A mathematical phrase that can contain numbers, variables, and operation signs, like '□ + 3' or '2 × □'.
substitute	To replace a variable with a specific number when solving an expression.
evaluate	To find the numerical answer of a mathematical expression by doing the calculations.
order of operations	The specific steps to follow when calculating an expression, such as doing multiplication before addition.