Mathematics · Secondary 2

Active learning ideas

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.

• MOE Syllabus Outcomes
• MOE: Algebraic Expansion and Factorisation - S2

• 20–35 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Hundred Languages
• 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.

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 ______'.

What to look for

Present students with a list of algebraic items (e.g., 3x, 5y, 2x + 4, 7 = 10, 9). Ask them to identify and label each as a 'term', 'expression', or 'equation'. Follow up by asking them to circle all 'like terms' within a given expression.

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Hundred Languages
• 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.

Differentiate between terms, expressions, and equations.

What to look for

Give each student a card with a simple algebraic expression involving the distributive law, such as 4(x + 2). Ask them to write two sentences explaining the steps they would take to simplify it and then show the simplified result.

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Hundred Languages
• 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.

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

What to look for

Pose the question: 'Why can we combine 5 apples and 3 apples to get 8 apples, but we cannot combine 5 apples and 3 oranges to get 8 apple-oranges?' Guide students to connect this analogy to why only like terms can be combined in algebra.

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Hundred Languages
• 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.

Explain the importance of order of operations in algebraic expressions.

What to look for

Present students with a list of algebraic items (e.g., 3x, 5y, 2x + 4, 7 = 10, 9). Ask them to identify and label each as a 'term', 'expression', or 'equation'. Follow up by asking them to circle all 'like terms' within a given expression.

• Understand
• Apply
• Create
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

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.

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.

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Watch Out for These Misconceptions

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

  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.

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Methods used in this brief

• Hundred Languages