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.

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

Learning Objectives

1. Identify like terms in simple algebraic expressions using concrete manipulatives.
2. Combine like terms to simplify algebraic expressions, representing the process with drawings.
3. Explain why terms must be alike to be combined using examples with objects.
4. Demonstrate the simplification of expressions involving positive like terms through sorting and counting.

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.

Prepare & details

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.

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·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.

Prepare & details

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.

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

⏱ 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.

Prepare & details

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.

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 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.

Prepare & details

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.

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

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.

What to Expect

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.

Watch Out for These Misconceptions

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Common Misconception

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

What to Teach Instead

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.

Assessment Ideas

Quick Check

After Sorting Tray: Matching Fruits, provide students with a mix of two types of manipulatives (e.g., 4 green triangles and 3 yellow triangles). Ask them to sort the items and state the total for each group, noting who groups correctly and explains why.

Discussion Prompt

During Whole Class Story: Toy Shop Addition, pause after adding groups of toys and ask, 'If we have 5 cars and 2 dolls, can we add them together to get one big number? Why or why not?' Listen for responses that reference matching types and separate totals.

Exit Ticket

After Individual Mat: Shape Groups, give each student a card with a simple picture-based expression like 2 hearts + 3 stars + 1 heart. Ask them to draw the simplified groups and write the total for hearts and stars, collecting these to check for accuracy and reasoning.

Extensions & Scaffolding

• Challenge: Provide students with a mix of three types of items (e.g., 3 red circles, 2 blue circles, 4 red squares). Ask them to simplify the expression and explain why the squares cannot be combined with the circles.
• Scaffolding: For students struggling during Sorting Tray: Matching Fruits, reduce the number of items to two types and provide a visual reference card showing the matching pairs.
• Deeper: After Block Tower Challenge: Color Combines, introduce a simple written expression like '2R + 3R + 1B' and ask students to match it to their tower groups.

Key Vocabulary

Term	A single number or variable, or numbers and variables multiplied together. In this topic, terms are represented by objects or pictures.
Like Terms	Terms that have the same variable or object. For example, 'red blocks' and 'red blocks' are like terms, but 'red blocks' and 'blue blocks' are not.
Combine	To put together or add like terms. When we combine like terms, we find the total number of those specific items.
Expression	A mathematical phrase that can contain numbers, variables, and operation signs. It does not have an equals sign.