--- title: "Words into expressions" subtitle: "Algebra Foundations · Expressions · Lesson 4" --- # Words into expressions **Name:** {{field-24}} **Date:** {{field-15}} **Class:** {{field-15}} > **Key question:** "Twice as many", "5 less than", "shared between 4": every maths sentence about a number can be written with a letter. :::teacher-note **In one sentence:** 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). **Students should be able to say:** 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. **Width:** the unmarked parts are the floor every student does (predict, run, investigate and make). Typical adds the modify practice; wider adds the real-world contexts. They add contexts, not difficulty. Students work in the online tutorial alongside this sheet. ::: ## Predict Try it with a real number: what is 5 less than 12? Which expression gives that? :::keep-together **$n$ is a number. Which expression means "5 less than $n$"?** ☐ $5 - n$ ☐ $\frac{n}{5}$ ☐ $5n$ ☐ $n - 5$ My prediction, and why: {{lines-3}} ::: :::teacher-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. ::: ## Run Try it on the board in the tutorial. Was your prediction right? What was different? {{lines-2}} ## From words to an expression :::keep-together ### Three more than twice n Here is how to turn words into an expression, one step at a time. 1. $\text{3 more than twice } n$ — Break the words into the parts they name. 2. $\text{twice } n$ — Start with the part said first: twice a number is $2 \times n$. 3. $2n$ — A number next to a letter means multiply, so write $2n$. 4. $\text{3 more than } 2n$ — "More than" means add 3 to that. 5. $2n + 3$ — The expression. 6. $n = 4: \; 2 \times 4 + 3 = 11$ — Check with a number: twice 4 is 8, and 3 more is 11. **Write an expression for "3 more than $x$".** Answer: {{field-15}} ::: :::teacher-note **Answer:** x + 3 x + 3. Check with x = 10: 3 more than 10 is 13, and 10 + 3 = 13. ::: :::keep-together ### Find the mistake **A number $n$ is divided by 4. Which expression is that?** ☐ $\frac{n}{4}$ ☐ $\frac{4}{n}$ ☐ $4n$ ::: :::teacher-note **Answer:** $\frac{n}{4}$ n ÷ 4 puts n on top: n/4. Check with n = 20: 20 ÷ 4 = 5. 4/n would be 4 ÷ 20. ::: :::keep-together ### 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. ``` Line: {{field-15}} Why is it wrong? {{lines-2}} ::: :::teacher-note **Answer:** 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. ::: :::typical ## 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.** Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ::: ## Say it, then write it :::keep-together ### Older **Ben is $n$ years old. His sister is 6 years older. Write an expression for his sister's age.** Answer: {{field-15}} ::: :::teacher-note **Answer:** n + 6 n + 6. If Ben is 10, his sister is 16. ::: :::keep-together ### Eggs **Eggs come in boxes of 12. Write an expression for the number of eggs in $b$ boxes.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 12b 12b: 12 eggs in each of b boxes. Check with b = 2: 24 eggs. ::: :::keep-together ### Pizza **A pizza has 8 slices. $n$ slices are eaten. Write an expression for the slices left.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 8 - n 8 − n: you start with 8 and take n away. Here 8 comes first, unlike "8 less than n". ::: :::keep-together ### Review **Review: find $3n + 5$ when $n = 4$.** Answer: {{field-15}} ::: :::teacher-note **Answer:** 17 3 × 4 + 5 = 12 + 5 = 17. ::: ## 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. Work in the tutorial. Plan first: what will you change, and how will you test it? {{box-4}} ## Exit ticket :::keep-together **Write an expression for: (a) 4 less than n; (b) 2 more than 5 times n; (c) n shared between 3.** {{lines-3}} ::: :::teacher-note **Answer:** (a) n − 4. (b) 5n + 2. (c) n/3. :::