Adding and Subtracting Algebraic Expressions

Students often confuse combining like terms and handling signs when adding or subtracting algebraic expressions. Active learning works here because it lets them physically group, flip, and combine terms, which makes abstract rules concrete. When students see ‘3x + 2x = 5x’ in action, the concept sticks better than when they just watch a teacher write it on the board.

• Class 7
• Mathematics
• 4 activities
• 15 min–25 min

Learning Objectives

1. Calculate the sum of two or more algebraic expressions by combining like terms.
2. Calculate the difference between two algebraic expressions by correctly distributing the negative sign and combining like terms.
3. Compare the process of adding algebraic expressions to adding integers, identifying similarities and differences in sign handling.
4. Construct an algebraic expression where subtracting a parenthesized expression requires distributing a negative sign to all terms within the parentheses.
5. Analyze the impact of parentheses and subtraction signs on the simplification of algebraic expressions.

Collaborative Problem-Solving

⏱ 15 min·Pairs

Like Terms Matching

Students match cards with algebraic terms to combine like terms correctly. They discuss signs before grouping. This reinforces identification of like terms.

Prepare & details

Analyze the impact of parentheses and subtraction signs on combining algebraic expressions.

Facilitation Tip: During Like Terms Matching, ask students to verbalise why certain terms belong together before combining them.

Setup: Flexible seating that allows clusters of 5-6 students; desks can be grouped in rows of three facing each other if fixed furniture limits rearrangement. Wall or board space for displaying group norm charts and the session agenda is helpful.

Materials: Printed problem brief cards (one per group), Role cards: Facilitator, Questioner, Recorder, Devil's Advocate, Communicator, Group norm chart (printable poster format), Individual reflection sheet and exit ticket, Timer visible to the class (board countdown or projected timer)

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 20 min·Pairs

Sign Flip Challenge

Provide expressions with parentheses; students subtract by flipping signs and simplify. Pairs check each other's work. It highlights subtraction pitfalls.

Prepare & details

Compare the process of adding expressions to adding integers.

Facilitation Tip: During Sign Flip Challenge, remind students to flip the sign of every term inside the parentheses when subtracting.

Setup: Flexible seating that allows clusters of 5-6 students; desks can be grouped in rows of three facing each other if fixed furniture limits rearrangement. Wall or board space for displaying group norm charts and the session agenda is helpful.

Materials: Printed problem brief cards (one per group), Role cards: Facilitator, Questioner, Recorder, Devil's Advocate, Communicator, Group norm chart (printable poster format), Individual reflection sheet and exit ticket, Timer visible to the class (board countdown or projected timer)

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 25 min·Small Groups

Expression Builder

In small groups, students build and simplify expressions from word problems. They present one to the class. Connects to real contexts.

Prepare & details

Construct an example where subtracting an expression requires distributing the negative sign.

Facilitation Tip: During Expression Builder, circulate and ask groups to justify why their simplified expressions are equivalent to the original.

Setup: Flexible seating that allows clusters of 5-6 students; desks can be grouped in rows of three facing each other if fixed furniture limits rearrangement. Wall or board space for displaying group norm charts and the session agenda is helpful.

Materials: Printed problem brief cards (one per group), Role cards: Facilitator, Questioner, Recorder, Devil's Advocate, Communicator, Group norm chart (printable poster format), Individual reflection sheet and exit ticket, Timer visible to the class (board countdown or projected timer)

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Collaborative Problem-Solving

⏱ 15 min·Whole Class

Quick Combine Relay

Whole class divides into teams; relay race to add/subtract expressions on board. Builds speed and accuracy.

Prepare & details

Analyze the impact of parentheses and subtraction signs on combining algebraic expressions.

Facilitation Tip: During Quick Combine Relay, ensure students write each step clearly, especially when distributing negative signs.

Setup: Flexible seating that allows clusters of 5-6 students; desks can be grouped in rows of three facing each other if fixed furniture limits rearrangement. Wall or board space for displaying group norm charts and the session agenda is helpful.

Materials: Printed problem brief cards (one per group), Role cards: Facilitator, Questioner, Recorder, Devil's Advocate, Communicator, Group norm chart (printable poster format), Individual reflection sheet and exit ticket, Timer visible to the class (board countdown or projected timer)

• Apply
• Analyze
• Evaluate
• Create
• Relationship Skills
• Decision-Making
• Self-Management

Teaching This Topic

Teachers should avoid rushing to the rule ‘add like terms’ without first building the concept of ‘like’ through grouping. Use concrete examples before moving to abstract terms. Research shows that students learn better when they see algebra as an extension of arithmetic, so connect each step to familiar number operations. Avoid teaching tricks like ‘change the sign and add’ without the conceptual foundation of distributing -1.

What to Expect

By the end of these activities, students should add or subtract algebraic expressions correctly, handling like terms and signs with confidence. They should also explain why terms like 3x and 5x combine but 3x and 2y do not. Clear articulation of steps and sign rules is the marker of successful learning.

Watch Out for These Misconceptions

Common Misconception

During Like Terms Matching, watch for students grouping terms with different variables as if they were the same.

What to Teach Instead

Ask them to read the matched pairs aloud, e.g., ‘3x and 5x are like terms because they both have the variable x with the same power.’

Common Misconception

During Sign Flip Challenge, watch for students ignoring the negative sign when removing parentheses.

What to Teach Instead

Have them highlight the negative sign in red and physically flip the sign of each term inside the parentheses before combining.

Common Misconception

During Expression Builder, watch for students failing to distribute signs inside parentheses before combining terms.

What to Teach Instead

Ask them to rewrite the expression without parentheses first, showing each step clearly on paper.

Assessment Ideas

Quick Check

After Like Terms Matching, write two expressions on the board, e.g., (4m + 3n) and (2m - n). Ask students to write the sum and difference on mini whiteboards. Observe their grouping and sign handling.

Exit Ticket

After Sign Flip Challenge, give students a card with a problem like: Simplify (7p - 2q) - (3p + 5q). Ask them to show all steps, especially the sign flip. Collect cards to assess distribution and combining.

Discussion Prompt

After Expression Builder, pose the question: ‘How is adding integers like 6 + (-4) similar to adding algebraic expressions like 6x + (-4x)?’ Then ask: ‘How is subtracting integers like 6 - 4 different from subtracting algebraic expressions like (6x) - (4x + y)?’ Facilitate a discussion on sign rules and distribution.

Extensions & Scaffolding

• Challenge: Ask students to create two expressions with three terms each, where the sum and difference both simplify to zero. They must explain their choices.
• Scaffolding: Provide a partially completed expression with blanks for coefficients and signs. Ask students to fill in missing terms to make the sum or difference correct.
• Deeper exploration: Introduce expressions with exponents, such as (3x^2 + 2x) - (x^2 - 4x), to extend understanding to higher-degree terms.

Key Vocabulary

Algebraic Expression	A mathematical phrase that contains variables, numbers, and operation signs. For example, 3x + 5y - 7.
Term	A single number or variable, or numbers and variables multiplied together. Terms are separated by addition or subtraction signs. For example, in 3x + 5y - 7, the terms are 3x, 5y, and -7.
Like Terms	Terms that have the same variables raised to the same powers. For example, 4x and -2x are like terms, but 4x and 4x² are not.
Coefficient	The numerical factor of a term. For example, in the term 5y, the coefficient is 5.
Constant	A term that does not contain any variables. For example, in the expression 2x + 9, the constant is 9.