Foundations of Mathematical Thinking · Junior Infants

Active learning ideas

Simplifying Algebraic Expressions: Combining Like Terms

Active learning works for simplifying algebraic expressions because young learners build mental models by touching, sorting, and grouping objects. When children physically group matching items, they internalize why only like terms combine, turning abstract ideas into concrete understanding. Hands-on experiences create lasting connections that verbal explanations alone cannot match.

• NCCA Curriculum Specifications
• NCCA: Junior Cycle - Strand 3: Algebra - A.1.4

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

Activity 01

• Stations Rotation
• 25 min · Small Groups

Sorting Tray: Matching Fruits

Provide trays with picture cards of fruits like apples, bananas, and oranges. Children sort like items into sections, count each group, and draw simplified totals. Discuss why different fruits stay separate.

Analyse why only 'like terms' can be combined when simplifying an algebraic expression.

Facilitation Tip

During Sorting Tray: Matching Fruits, circulate and ask guiding questions like, 'Why did you put those two apples together?' to reinforce reasoning.

What to look for

Provide students with a collection of mixed manipulatives (e.g., 3 red cubes, 2 blue cubes, 1 red cube). Ask them to sort the items into groups of like terms and then state the total number of red cubes and blue cubes.

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

Activity 02

• Stations Rotation
• 20 min · Pairs

Block Tower Challenge: Color Combines

Give mixed colored blocks representing terms. Pairs build towers by combining like colors first, then stacking different colors. Record expressions before and after simplifying on mats.

Justify the process of combining positive and negative like terms.

Facilitation Tip

For Block Tower Challenge: Color Combines, model how to verbalize the process by saying, 'Two red blocks plus three red blocks equals five red blocks,' to build language habits.

What to look for

Present students with a drawing of 4 apples and 3 bananas. Ask: 'If we wanted to count all the fruit, how could we group them? Why can't we just add all the fruit together to get one big number for all the fruit?'

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

Activity 03

• Stations Rotation
• 30 min · Whole Class

Whole Class Story: Toy Shop Addition

Narrate a shop story with toy pictures on the board. Class chorally identifies and combines like toys as you add them. Children mimic with personal sets, then share simplifications.

Critique common errors made when simplifying expressions with multiple variables.

Facilitation Tip

In Whole Class Story: Toy Shop Addition, pause after each addition to ask children to predict what comes next, keeping them engaged in the narrative.

What to look for

Give each student a card showing a simple expression using pictures, like 2 stars + 3 circles + 1 star. Ask them to draw the simplified expression and write how many stars and how many circles there are.

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

Activity 04

• Stations Rotation
• 15 min · Individual

Individual Mat: Shape Groups

Each child gets shape cutouts on mats with simple expressions. They group and combine like shapes, count, and label new totals. Review by showing one mat to the group.

Analyse why only 'like terms' can be combined when simplifying an algebraic expression.

Facilitation Tip

On Individual Mat: Shape Groups, provide exact quantities of manipulatives so students focus on grouping rather than counting, reducing cognitive load.

What to look for

Provide students with a collection of mixed manipulatives (e.g., 3 red cubes, 2 blue cubes, 1 red cube). Ask them to sort the items into groups of like terms and then state the total number of red cubes and blue cubes.

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

A few notes on teaching this unit

Experienced teachers approach this topic by starting with sensory-rich activities that require no prior knowledge of symbols. Avoid rushing to written expressions; let children explore the concept through touch and movement first. Research shows that when students manipulate objects and describe their actions aloud, they develop stronger algebraic reasoning. Keep the focus on the process of grouping and combining, not just the final answer.

Successful learning looks like students recognizing matching items and grouping them without prompting. You will see children confidently stating simplified groupings and justifying why different items stay separate. Their ability to explain their thinking using the language of 'like terms' shows true understanding.

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Watch Out for These Misconceptions

• During Sorting Tray: Matching Fruits, watch for students who combine all items regardless of type.

  Hand the student a second tray and say, 'Let's try grouping only the matching ones first. Why do you think we put the apples together but not with the bananas?' Let them physically separate and recount to see the totals remain unchanged.

• During Block Tower Challenge: Color Combines, watch for students who believe combining changes the total number of blocks.

  Ask the student to recount the blocks before and after combining, then ask, 'Did the number of blocks change when you grouped them?' Use their recount to show that totals stay the same, just organized differently.

• During Individual Mat: Shape Groups, watch for students who insist order matters for combining.

  Have the student rotate the mat 180 degrees and ask, 'Can you combine the shapes now?' Guide them to see that rearranging doesn’t affect the grouping, reinforcing the commutative property through movement.

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Methods used in this brief

• Stations Rotation