Words to Expressions

Overview

In lesson 17 of 26, students translate verbal phrases and linear pattern rules into algebraic expressions. The lesson builds on prior work with variables, constants, coefficients, and pattern rules, using concrete language, visual models, and repeated oral rehearsal before independent practice.

Learning intentions

Students will:

• translate verbal phrases into algebraic expressions;
• distinguish accurately between “more than,” “less than,” “times,” and “sum”;
• connect a pattern rule written in words to an expression;
• explain what one operation in an expression means.

Success criteria

• I can identify the variable and operation words in a phrase.
• I can write an algebraic expression that matches a verbal phrase.
• I can explain why “5 less than x” is written as (x - 5), not (5 - x).
• I can check that my expression makes sense using a value or pattern.

Curriculum links

• Patterns and Relations — oral and written patterns and their corresponding relations.
• Patterns and Relations — tables of values, relations, and graphs.
• Algebraic expressions — evaluating and representing expressions in multiple ways.
• Mathematical processes — communication, connections, mental mathematics and estimation, problem solving, reasoning, and visualization.

Lesson structure (50 minutes)

1. 0–5 min · Attention hook and retrieval. Teacher displays the opening question in the hook and retrieval slides: “A number increases by 4 each time. How could we describe this rule?” and briefly revisits variable, constant, coefficient, and operation. Students silently choose a possible rule, then explain it to a partner using a sentence frame: “The rule means ___ each time.”

2. 5–15 min · Explicit teaching. Teacher uses the phrase-to-expression teaching slides and guided notes to model a translation routine: underline the variable, circle operation words, identify the order of the language, and write the expression. Model:

• “the sum of (x) and 6” → (x + 6);
• “6 more than (x)” → (x + 6);
• “3 times (x)” → (3x);
• “5 less than (x)” → (x - 5). Students copy one phrase per line, use hand gestures for addition, subtraction, and multiplication, and chorally read each expression. Emphasise that “less than” reverses the order of the spoken numbers.

3. 15–25 min · Concrete phrase-card investigation. Teacher displays a phrase at a time on the phrase-card investigation slides and gives each student a small set of paper counters or algebra tiles. For “4 more than (n),” students build one unknown group and four extra units; for “2 times (n),” they build two equal unknown groups. Students record the matching expression and justify it with the frame: “I wrote ___ because the phrase says ___.” Teacher deliberately includes one incorrect expression for students to correct.

4. 25–35 min · Guided Mathology practice. Teacher distributes the guided translation worksheet and completes the first four items with the class, pausing after each phrase to ask, “What operation word did you notice?” and “Which quantity comes first?” Students complete the next items independently, then compare answers with a partner. Teacher provides read-aloud support, points to a visual operation cue, and checks one student at a time to prevent distractible students from taking over.

5. 35–44 min · Independent practice and pattern connection. Teacher directs students to the independent section of the guided translation worksheet and then assigns a short, differentiated set in Mathletics. Students translate phrases such as “7 more than (p),” “(y) less than 12,” “4 times (m),” and “the sum of (a) and 9.” They also write an expression for a pattern rule such as “start at (n) and add 3.” Students may substitute a simple value to check whether their expression produces the expected result.

6. 44–50 min · Evidence checkpoint and closure. Teacher displays the checkpoint instructions in the checkpoint and closure slides. Each student completes four translations: “the sum of (x) and 8,” “6 more than (t),” “3 times (q),” and “4 less than (r),” then explains the meaning of one operation in words or a labelled drawing. Students share one common error and one strategy that helped.

Resources

• the complete phrase-to-expression slide deck
• the guided translation worksheet
• Guided notes with one phrase per line
• Paper counters or algebra tiles
• Operation gesture cue cards: add, subtract, multiply
• Mathology translation activity
• Mathletics assignment
• Whiteboards and markers

Assessment

• Knowledge and Understanding: During modelling and guided practice, record whether each student identifies variables, constants, coefficients, and operation words, and translates phrases accurately. Progress is shown by moving from prompted examples to independent translations.
• Mental Mathematics: Ask students to mentally predict the effect of adding, subtracting, or multiplying by a small number before writing. Progress is shown when students use operation language and estimate whether an expression is reasonable.
• Problem Solving: Use the pattern-rule task and checkpoint explanation to assess whether students connect words, expressions, and pattern changes. Progress is shown when students justify the order of terms rather than relying only on memorised keywords.
• Collect the four-item checkpoint and note errors in “more than,” “less than,” and multiplication for follow-up practice.

Differentiation

• Provide a colour-coded routine: variable in blue, operation word in red, number in green; use arrows to show the order for “less than.”
• Offer sentence frames, gesture cues, oral rehearsal, read-aloud support, and dyslexia-friendly formatting with a clear sans-serif font, generous spacing, and one phrase per line.
• For students on modified programmes or with a mathematics disability, reduce the number range, use counters or tiles, provide a word bank, and work with one phrase at a time before combining tasks.
• For students ready for challenge, ask them to write two different phrases for the same expression and explain why “(x - 5)” and “5 less than (x)” are equivalent.