Review of Algebraic Basics

Active learning strengthens students' grasp of algebraic basics by engaging them in physical and collaborative tasks. Moving beyond worksheets, these activities let students see, touch, and discuss why operations work the way they do, reducing rote memorization and building lasting understanding.

• Secondary 2
• Mathematics
• 4 activities
• 20 min–35 min

Learning Objectives

1. Calculate the simplified form of algebraic expressions by combining like terms.
2. Explain the distributive law using examples involving multiplication of a constant or variable by a binomial.
3. Differentiate between algebraic terms, expressions, and equations, providing examples of each.
4. Justify the process of combining like terms based on the definition of a term and variable properties.
5. Apply the order of operations (BODMAS/PEMDAS) to evaluate algebraic expressions accurately.

Chalk Talk

⏱ 25 min·Pairs

Pairs Sort: Like Terms Matching

Provide cards with algebraic terms like 3x, 2x, 5y, 4. Pairs sort into like-term piles, combine where possible, and write simplified expressions. Pairs justify one grouping to the class, noting why unlike terms stay separate.

Prepare & details

Explain the importance of order of operations in algebraic expressions.

Facilitation Tip: During Expression Builder, provide sentence stems for students who struggle to articulate their simplifications, such as 'I combined ______ because they both have ______'.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

Chalk Talk

⏱ 30 min·Small Groups

Small Groups: Distributive Relay

Divide class into groups of four. Write an expression like 2(3x + 4) on board. First student distributes over first term, passes note to next for second term, then simplify. Fastest accurate group wins.

Prepare & details

Differentiate between terms, expressions, and equations.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

Chalk Talk

⏱ 35 min·Whole Class

Whole Class: BODMAS Challenge

Display expressions on board or screen, like 2 + 3 × 4. Students solve individually on mini-whiteboards, hold up answers. Discuss order step-by-step, vote on common errors.

Prepare & details

Justify why only like terms can be combined in an algebraic expression.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

Chalk Talk

⏱ 20 min·Individual

Individual: Expression Builder

Students receive jumbled terms and operations, rearrange into correct order using BODMAS, simplify. Swap with partner for checking, then share revisions.

Prepare & details

Explain the importance of order of operations in algebraic expressions.

Setup: Large papers on tables or walls, space to circulate

Materials: Large paper with central prompt, Markers (one per student), Quiet music (optional)

• Understand
• Analyze
• Evaluate
• Self-Awareness
• Self-Management

Teaching This Topic

Start with concrete examples before abstract symbols. Use visuals like algebra tiles to anchor the distributive law, as research shows hands-on tools help students connect operations to real quantities. Avoid rushing through the order of operations; instead, have students verbalize each step to reinforce precision. Watch for students who mechanically follow BODMAS without understanding why multiplication comes before addition.

What to Expect

By the end of these activities, students should confidently identify like terms, apply the distributive law correctly, and follow the order of operations without hesitation. They will justify their steps verbally or in writing, showing clear reasoning for combining terms or expanding expressions.

Watch Out for These Misconceptions

Common Misconception

During BODMAS Challenge, watch for students who perform operations strictly left-to-right, ignoring the hierarchy of operations.

What to Teach Instead

Have students compare their step-by-step work on mini-whiteboards with a peer, asking them to justify why multiplication must occur before addition in expressions like 5 + 2 × 3.

Assessment Ideas

Discussion Prompt

During BODMAS Challenge, pose the prompt: 'If you have 10 + 2 × 4, does it make sense to add 10 and 2 first? Why or why not?' Guide students to connect the discussion to the necessity of following the order of operations in algebra.

Extensions & Scaffolding

• Challenge students to create their own expressions using like terms and non-like terms, then swap with a peer to identify and simplify each other's work.
• For students who struggle, provide a bank of like terms already grouped by color or shape to help them visually separate matching and non-matching terms.
• Deeper exploration: Ask students to design a real-world scenario where combining unlike terms would lead to an incorrect or illogical result, such as mixing different units of measurement.

Key Vocabulary

Term	A single number, a single variable, or numbers and variables multiplied together. Terms are separated by addition or subtraction signs.
Like Terms	Terms that have the exact same variable(s) raised to the exact same power(s). Only like terms can be combined.
Expression	A combination of terms, numbers, and operation symbols that represents a mathematical relationship but does not contain an equals sign.
Equation	A mathematical statement that two expressions are equal, indicated by an equals sign (=).
Distributive Law	A rule stating that multiplying a sum by a number is the same as multiplying each addend by the number and adding the products. For example, a(b + c) = ab + ac.