Mathematics · Year 7

Active learning ideas

Creating Algebraic Expressions

Active learning works for creating algebraic expressions because students need repeated practice translating between language and symbols. Moving word phrases into expressions helps them see math as a way to model real situations, not just symbols on a page.

• ACARA Content Descriptions
• AC9M7A01

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

Activity 01

• RAFT Writing
• 25 min · Pairs

Card Sort: Phrase-Expression Matches

Prepare cards with word phrases on one set and algebraic expressions on another. Pairs sort and match them, then write justifications for each pair. Regroup to share and verify matches with the class.

Construct an algebraic expression to represent a real-world scenario.

Facilitation Tip

During Card Sort: Phrase-Expression Matches, circulate and listen for students explaining their matches aloud, this verbal reasoning builds clarity.

What to look for

Present students with a list of word phrases (e.g., 'twice a number plus seven', 'ten less than a third of a quantity'). Ask them to write the corresponding algebraic expression for each phrase on mini whiteboards. Observe for correct use of variables and operations.

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

Activity 02

• RAFT Writing
• 35 min · Small Groups

Group Challenge: Scenario Translators

Provide small groups with real-world scenarios, like 'total cost for n shirts at $20 each plus $5 tax.' Groups write expressions, test with numbers, and present to justify. Vote on clearest expressions.

Differentiate between an expression and an equation.

Facilitation Tip

In Group Challenge: Scenario Translators, assign each group a different real-world scenario so they experience multiple contexts before regrouping to share strategies.

What to look for

Provide students with a simple real-world scenario, such as 'Sarah earns $15 per hour babysitting.' Ask them to: 1. Write an algebraic expression to represent her total earnings after 'h' hours. 2. Write one sentence explaining what the variable 'h' represents.

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

Activity 03

• RAFT Writing
• 20 min · Whole Class

Relay Build: Expression Relay

Divide class into teams. One student per team runs to board, hears a phrase from teacher, writes expression, tags next teammate. First team with all correct wins; review errors together.

Explain how variables allow us to represent unknown quantities in a concise way.

Facilitation Tip

For Relay Build: Expression Relay, set a strict 2-minute timer per station to keep energy high and prevent overthinking.

What to look for

Pose the question: 'What is the difference between '5x' and '5x = 25'?'. Facilitate a class discussion where students explain that '5x' is an expression and '5x = 25' is an equation, highlighting the role of the equals sign in an equation.

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

Activity 04

• RAFT Writing
• 30 min · Individual

Individual: Expression Journals

Students create personal journals with daily scenarios, like 'time to travel d km at 60 km/h.' They translate to expressions, substitute values, and reflect on variable use. Share select entries.

Construct an algebraic expression to represent a real-world scenario.

What to look for

Present students with a list of word phrases (e.g., 'twice a number plus seven', 'ten less than a third of a quantity'). Ask them to write the corresponding algebraic expression for each phrase on mini whiteboards. Observe for correct use of variables and operations.

• Apply
• Analyze
• Create
• Social Awareness
• Self-Awareness

A few notes on teaching this unit

Teach this topic by focusing on the structure of language first, then symbols. Avoid rushing to algebra rules; instead, emphasize parsing phrases step by step. Research shows that students benefit from collaborative translation before independent work, so build in partner talk before writing.

Students will confidently translate word phrases to algebraic expressions and justify their choices. They will explain the meaning of variables and distinguish expressions from equations in context.

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Watch Out for These Misconceptions

• During Card Sort: Phrase-Expression Matches, watch for students treating variables as fixed numbers like n=5.

  Have students substitute three different values into their matched expressions during the sort and observe that the same expression can yield different results, reinforcing variables as placeholders.

• During Group Challenge: Scenario Translators, watch for students confusing expressions with equations.

  Ask groups to explicitly label each part of their translated scenario as 'expression' or 'equation' before sharing, using the equals sign as a clear divider.

• During Card Sort: Phrase-Expression Matches, watch for students writing '5n' for 'a number more than five'.

  Provide feedback cards with correct examples of commutative phrasing (e.g., 'n + 5') and have students re-sort to correct their errors.

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Methods used in this brief

• RAFT Writing