Simplifying Algebraic Expressions: Like Terms

Active learning works for this topic because students need to physically and visually experience the balance of equations before moving to abstract symbols. The process of combining terms and solving equations relies on spatial reasoning and logical sequencing, which are strengthened through hands-on methods.

• Year 8
• Mathematics
• 3 activities
• 20 min–40 min

Learning Objectives

1. Identify like terms within algebraic expressions containing variables and exponents.
2. Combine like terms using addition and subtraction to simplify algebraic expressions.
3. Explain the distributive property as a method for combining like terms.
4. Analyze the effect of simplifying an expression on its value for given variable substitutions.
5. Justify the rule for combining like terms based on the properties of operations.

Simulation Game

⏱ 30 min·Whole Class

Simulation Game: The Human Balance Scale

Two students represent the sides of an equation, holding 'weights' (numbers) and 'mystery boxes' (variables). To find the value of the box, the class must direct them to remove or add weights from both sides simultaneously to keep the 'scale' level.

Prepare & details

Justify the rule for combining like terms in an algebraic expression.

Facilitation Tip: During The Human Balance Scale, have students physically step onto marked spots on the floor to represent each side of the equation, reinforcing the concept of balance.

Setup: Flexible space for group stations

Materials: Role cards with goals/resources, Game currency or tokens, Round tracker

• Apply
• Analyze
• Evaluate
• Create
• Social Awareness
• Decision-Making

Inquiry Circle

⏱ 40 min·Pairs

Inquiry Circle: Equation Backtracking

Students work in pairs to create 'flowcharts' for complex equations. They start with 'x', show the operations applied to it, and then work backward using inverse operations to find the starting value.

Prepare & details

Differentiate between terms that can be combined and those that cannot.

Facilitation Tip: For Equation Backtracking, provide colored pencils and have students annotate each step of their backtracking process in a different color to visualize the sequence.

Setup: Groups at tables with access to source materials

Materials: Source material collection, Inquiry cycle worksheet, Question generation protocol, Findings presentation template

• Analyze
• Evaluate
• Create
• Self-Management
• Self-Awareness

Think-Pair-Share

⏱ 20 min·Pairs

Think-Pair-Share: Error Analysis

The teacher displays a solved equation with a common mistake (e.g., only subtracting from one side). Students identify the error individually, discuss why it breaks the 'balance' with a partner, and present the correct method.

Prepare & details

Analyze the impact of simplifying an expression on its overall value.

Facilitation Tip: In Error Analysis, assign each pair a unique error card so they can focus on one type of mistake at a time, making the discussion more targeted and productive.

Setup: Standard classroom seating; students turn to a neighbor

Materials: Discussion prompt (projected or printed), Optional: recording sheet for pairs

• Understand
• Apply
• Analyze
• Self-Awareness
• Relationship Skills

Teaching This Topic

Experienced teachers approach this topic by grounding instruction in the concrete before moving to the abstract, using analogies like 'reverse BEDMAS' (SAMDEB) to help students understand the order of operations when solving equations. Avoid rushing to procedural steps; instead, build fluency through repeated exposure to balanced equations. Research suggests that students who struggle often benefit from kinesthetic activities first, as they help internalize the concept of balance before symbolic manipulation.

What to Expect

By the end of these activities, students will confidently identify like terms, combine them correctly, and solve two-step equations while maintaining the balance of the equation. They will also articulate why certain terms cannot be combined and explain the steps they took to simplify or solve.

Watch Out for These Misconceptions

Common Misconception

During The Human Balance Scale, watch for students who adjust only one side of the scale to 'balance' it, indicating they are not applying inverse operations to both sides.

What to Teach Instead

Pause the activity and ask students to describe what happens when only one side of a real balance scale is adjusted. Have them physically demonstrate the correction by adding or removing the same amount from both sides.

Common Misconception

During Equation Backtracking, watch for students who incorrectly identify the first operation to undo, leading to an incorrect sequence of steps.

What to Teach Instead

Have students use the SAMDEB (reverse BEDMAS) analogy to identify the last operation performed. Provide a visual or written reminder of the 'socks and shoes' metaphor to guide their process.

Assessment Ideas

Quick Check

After The Human Balance Scale, present students with a list of terms, such as 3x, 5y, -2x, 7, 4y, -1. Ask them to circle all terms that are 'like terms' with 3x. Then, have them write down the simplified expression by combining all like terms on the list.

Exit Ticket

During Error Analysis, give each student a card with an algebraic expression, for example, '4a + 7b - 2a + 3'. Ask them to write down the simplified expression. On the back, have them explain in one sentence why '4a' and '7b' cannot be combined.

Discussion Prompt

After Equation Backtracking, pose the expression '3x + 5y'. Ask students: 'Can this expression be simplified further? Why or why not?' Facilitate a brief class discussion, prompting students to use the term 'like terms' in their explanations.

Extensions & Scaffolding

• Challenge: Provide students with an expression like '2(3x + 4) - 5(x - 2)' and ask them to simplify it completely. Have them create their own similar problem for a partner to solve.
• Scaffolding: For students who find combining terms difficult, provide a scaffolded worksheet with all like terms grouped and color-coded, asking them to combine only the terms with the same color.
• Deeper exploration: Introduce multi-step equations with fractions, such as '3/4x + 2 = 5/6'. Ask students to solve these and explain each step, focusing on why common denominators are not always necessary.

Key Vocabulary

Term	A term is a single number or variable, or numbers and variables multiplied together. Terms are separated by addition or subtraction signs.
Like Terms	Like terms are terms that have the exact same variable(s) raised to the exact same power(s). The coefficients can be different.
Coefficient	The numerical factor of a term that contains a variable. For example, in the term 5x, the coefficient is 5.
Variable	A symbol, usually a letter, that represents an unknown quantity or a quantity that can change.
Algebraic Expression	A mathematical phrase that can contain ordinary numbers, variables, and operation signs, but no equal sign.