Words into expressions

Classroom resources

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Students will be able to

• I can say what operation each word in a sentence about a number means.
• I can write an expression from words, with the operations in the right order.
• I can check my expression by trying a number I can work out in words.

Timing

Predict and Run 8 min · Investigate 15 min · Modify 12 min · Practise and Make 10 min

Before class

Do the Run and Modify boards yourself first. They hide the formula on purpose: the board does what the words say and shows the result, so students check their expression against it.

The new move is turning each word into an operation. The most common error is "less than" (Ana's mistake): the numbers are written in the order they are spoken, 7 − n, when the number you start from comes first, n − 7. Always check with a real number: 7 less than 10 is 3.

The pizza question in Practise is the opposite on purpose: "n slices are eaten from 8" starts from 8, so 8 − n is correct. Ask students what is being taken away from what.

Running the lesson

1. Predict: take a show of hands. Ask a student who chose 5 − n to work out 5 less than 12, then try 5 − 12.
2. Run: ask students to say what the board is doing to n before they write anything.
3. Investigate: model the worked example live. Say the words in steps and write each step as you say it.
4. Modify: at each task, ask 'what is the first thing the words do to n?' before writing.
5. Make: ask for the expression in words as well as in symbols.

When students get stuck

Answers to the checks

1. 5 less than n: $n$ is a number. Which expression means "5 less than $n$"?
   n − 5. 5 less than 12 is 7, which is 12 − 5. The thing you start from (n) comes first in the subtraction, even though 5 is said first.
2. what do the words give?: Set $n = 12$. The board gives "5 less than $n$". What does it show? Does that match your prediction?
   
3. Three more than twice n: Write an expression for "3 more than $x$".
   x + 3
   x + 3. Check with x = 10: 3 more than 10 is 13, and 10 + 3 = 13.
4. Find the mistake: A number $n$ is divided by 4. Which expression is that?
   $\frac{n}{4}$
   n ÷ 4 puts n on top: n/4. Check with n = 20: 20 ÷ 4 = 5. 4/n would be 4 ÷ 20.
5. Your turn: Ana writes "7 less than $n$". Click the line where she goes wrong.
   line 3
   Line 3: "7 less than n" means take 7 away from n, so n − 7. Check with n = 10: 7 less than 10 is 3, but 7 − 10 is −3.
6. Half: Write an expression for "half of $n$".
   n/2
   n/2 (or n ÷ 2). Check: half of 6 is 3, and 6 ÷ 2 = 3.
7. More than: Write an expression for "5 more than 3 times $n$".
   3n + 5
   3n + 5: 3 times n, then 5 more. Check with n = 4: 3 × 4 + 5 = 17.
8. Less than: Write an expression for "2 less than 4 times $n$".
   4n - 2
   4n − 2. Check with n = 3: 4 × 3 = 12, and 2 less than that is 10.
9. Two letters: Write an expression for "the product of $a$ and $b$".
   ab
   ab means a × b. Check with a = 3 and b = 4: 3 × 4 = 12.
10. Older: Ben is $n$ years old. His sister is 6 years older. Write an expression for his sister's age.
    n + 6
    n + 6. If Ben is 10, his sister is 16.
11. Eggs: Eggs come in boxes of 12. Write an expression for the number of eggs in $b$ boxes.
    12b
    12b: 12 eggs in each of b boxes. Check with b = 2: 24 eggs.
12. Pizza: A pizza has 8 slices. $n$ slices are eaten. Write an expression for the slices left.
    8 - n
    8 − n: you start with 8 and take n away. Here 8 comes first, unlike "8 less than n".
13. Review: Review: find $3n + 5$ when $n = 4$.
    17
    3 × 4 + 5 = 12 + 5 = 17.
14. find the rule: The mystery board follows a rule in $n$. Move $n$ and watch $T$. Write an expression for $T$.
    4n - 1
    T = 4n − 1: 4 times n, then 1 less. In words: "1 less than 4 times n".

Solutions

One possible solution for each task. Other correct programs are fine.

other words › Half

Open task: any program that does what the step asks.

other words › More than

Open task: any program that does what the step asks.

other words › Less than

Open task: any program that does what the step asks.

other words › Two letters

Open task: any program that does what the step asks.

find the rule

Open task: any program that does what the step asks.

Stretch and support

Stretch: Write expressions for: 'the next whole number after n', '3 less than half of n', 'the cost of n pens at 2 dollars each and one ruler at 5 dollars'.

Support: Give a table of words and their operation (more than: +, less than: −, times, twice, half, divided by) to use as a key.

Coach prompt (optional)

For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.

You are a patient maths coach for a Year 7 student in Australia. Help me understand ONE idea only, from the lesson "Words into expressions".

The idea: Translating words to algebraic expressions: I can Students translate verbal descriptions of mathematical relationships into algebraic expressions using constants, variables and operations.

What understanding looks like:
- Correctly translates a verbal description into an algebraic expression.
- Correctly translates an algebraic expression into a verbal description.
- Does not confuse 'n less than 5' (5 − n) with 'n minus 5' (n − 5).

Mistakes students often make here:
- A student writes 7 − n for '7 less than n' (Ana's mistake).
- A student writes 5n for '5 more than n'.

How to coach me (rules from the Waypoints Kit coach):
- Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question.
- Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit).
- If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go.
- Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back.
- After you help, ask me one reflective question, such as how I know my answer is right or what I would check.
- Praise my effort and method, not my ability.
- You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so.
- Use simple words.
- Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Words into expressions".

Exit ticket

Write an expression for: (a) 4 less than n; (b) 2 more than 5 times n; (c) n shared between 3.

(a) n − 4. (b) 5n + 2. (c) n/3.

What each step is for

• 5 less than n: Committing to an expression for 'less than' exposes writing the numbers in the order they are spoken: 5 − n.
• what do the words give?: Comparing the board's numbers with the words fixes the meaning of 'less than' before any expression is written.
• from words to an expression: Each word names an operation; an expression is those operations written in the order the words say them, and a number check catches a swapped order.
• other words: One change at a time: dividing, adding after multiplying, subtracting after multiplying, and two letters.
• say it, then write it: Turning everyday sentences into expressions, where the order of a subtraction depends on the story; the review is substituting.
• find the rule: Reading an expression off a mystery board reverses the lesson: from numbers back to words and an expression.

Where it leads

Next: when brackets are needed. 'Add 3 to n, then double it' is not 2n + 3. After that, expressions describe whole situations, which leads into Linear relations (y = mx + c) and into Equations.