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# Words into expressions

Algebra Foundations · Expressions

<!-- Speaker note: Students turn words such as more than, less than, twice and divided by into expressions, writing the operations in the order the words say them and checking with a number (AC9M7A02, node 1). About 45 minutes (Predict and Run 8 min · Investigate 15 min · Modify 12 min · Practise and Make 10 min). -->

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## Today

**We are learning to** words such as "more than", "less than", "twice" and "divided by" each mean an operation. Write the operations in the order the words say them, then check with a number.

- 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.

<!-- Speaker note: 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. -->

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## Why it matters

> "Twice as many", "5 less than", "shared between 4": every maths sentence about a number can be written with a letter.

<!-- Speaker note: A letter can stand for any number, so a sentence about "a number" can be written as an **expression**. Each word that tells you what to do to the number, such as *more than*, *less than*, *twice* or *divided by*, becomes an operation. The skill is writing the operations in the order the words give them. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Predict

**$n$ is a number. Which expression means "5 less than $n$"?**

- $5 - n$
- $\frac{n}{5}$
- $5n$
- $n - 5$

<!-- Speaker note: What happens: 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. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: take a show of hands. Ask a student who chose 5 − n to work out 5 less than 12, then try 5 − 12. -->

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## Try it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Falgebra%2Fwords-to-expressions%2Fstep-2&code=widget%3A+formula%0Aformula%3A+T+%3D+n+-+5%0Ahide%3A+formula%0Aslider+n%3A+0%2C+20%2C+3%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/algebra/words-to-expressions/?full=step-2#step-2)

<!-- Speaker note: The board does what the words say to $n$, and shows the result $T$. Try other values of $n$. Is $5 - n$ ever the same as what the board shows? -->

<!-- Speaker note: Teacher: ask students to say what the board is doing to n before they write anything. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What happened?

* 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.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Three more than twice n

Here is how to turn words into an expression, one step at a time.

$$\text{3 more than twice } n$$

1) $\text{twice } n$ — Start with the part said first: twice a number is $2 \times n$.
2) $2n$ — A number next to a letter means multiply, so write $2n$.
3) $\text{3 more than } 2n$ — "More than" means add 3 to that.
4) $2n + 3$ — The expression.
5) $n = 4: \; 2 \times 4 + 3 = 11$ — Check with a number: twice 4 is 8, and 3 more is 11.

<!-- Speaker note: Model this live on the board before revealing anything: write each line and say why, pausing to ask the class what comes next. Then click to reveal the lines and compare. Script. Start: write 3 more than twice n and say "Break the words into the parts they name." Line 1: write twice n and say "Start with the part said first: twice a number is 2 × n." Line 2: write 2n and say "A number next to a letter means multiply, so write 2n." Line 3: write 3 more than 2n and say ""More than" means add 3 to that." Line 4: write 2n + 3 and say "The expression." Line 5: write n = 4: 2 × 4 + 3 = 11 and say "Check with a number: twice 4 is 8, and 3 more is 11." -->

<!-- Speaker note: Teacher: model the worked example live. Say the words in steps and write each step as you say it. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Three more than twice n

**Write an expression for "3 more than $x$".**

* Answer: x + 3

<!-- Speaker note: x + 3. Check with x = 10: 3 more than 10 is 13, and 10 + 3 = 13. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Find the mistake

**A number $n$ is divided by 4. Which expression is that?**

- $\frac{n}{4}$
- $\frac{4}{n}$
- $4n$

* Answer: $\frac{n}{4}$

<!-- Speaker note: n ÷ 4 puts n on top: n/4. Check with n = 20: 20 ÷ 4 = 5. 4/n would be 4 ÷ 20. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Your turn

**Ana writes "7 less than $n$". Click the line where she goes wrong.**

```
 1  Write "7 less than n" as an expression.
 2  "Less than" means subtract, so I use −.
 3  7 less than n is 7 − n.
 4  So the expression is 7 − n.
```

* Answer: line 3

<!-- Speaker note: 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. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Other words



- **Half:** The board does what the words say, and shows the answer. Write your expression, then check it with a number.
- **More than:** 
- **Less than:** 
- **Two letters:** 

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/algebra/words-to-expressions/?full=step-4#step-4)

<!-- Speaker note: What this step is for: One change at a time: dividing, adding after multiplying, subtracting after multiplying, and two letters. For students who need more support: Give a table of words and their operation (more than: +, less than: −, times, twice, half, divided by) to use as a key. For early finishers: 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'. When students get stuck: A student writes 7 − n for '7 less than n' (Ana's mistake). Ask: What is 7 less than 10? What does 7 − 10 give? Fix: 'Less than' takes the amount away from the number: start from n, then subtract: n − 7. / A student writes 5n for '5 more than n'. Ask: If n is 10, what is 5 more than n? What is 5n? Fix: 'More than' means add. Multiply is for 'times' or 'lots of'. -->

<!-- Speaker note: Teacher: at each task, ask 'what is the first thing the words do to n?' before writing. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Older

**Ben is $n$ years old. His sister is 6 years older. Write an expression for his sister's age.**

* Answer: n + 6

<!-- Speaker note: n + 6. If Ben is 10, his sister is 16. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Eggs

**Eggs come in boxes of 12. Write an expression for the number of eggs in $b$ boxes.**

* Answer: 12b

<!-- Speaker note: 12b: 12 eggs in each of b boxes. Check with b = 2: 24 eggs. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Pizza

**A pizza has 8 slices. $n$ slices are eaten. Write an expression for the slices left.**

* Answer: 8 - n

<!-- Speaker note: 8 − n: you start with 8 and take n away. Here 8 comes first, unlike "8 less than n". -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Review

**Review: find $3n + 5$ when $n = 4$.**

* Answer: 17

<!-- Speaker note: 3 × 4 + 5 = 12 + 5 = 17. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Make: find the rule

Say your expression in words, the way you did in this lesson.

Stretch: write a story that your expression could describe.

[Open this step](https://studio.learningwaypoints.com/tutorials/maths/algebra/words-to-expressions/?full=step-6#step-6)

<!-- Speaker note: What this step is for: Reading an expression off a mystery board reverses the lesson: from numbers back to words and an expression. Hints, in order: Try n = 0 and n = 1. How much does T go up each time n goes up by 1? / At n = 0 the board shows −1. -->

<!-- Speaker note: Teacher: ask for the expression in words as well as in symbols. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## 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.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this 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. -->