--- marp: true theme: default html: true --- # When brackets are needed Algebra Foundations · Expressions --- ## Today **We are learning to** brackets keep a part together so it is worked out first. If a sentence says to do something to a whole result, such as "add 3, then double it", the expression needs brackets. - I can say which step is done first, and what is then done to its whole result. - I can put brackets around the part that is done first, and leave them out when they are not needed. - I can show with a number that 2(n + 3) and 2n + 3 are different. --- ## Why it matters > "Add 4, then double it" and "double it, then add 4" sound alike. They give different answers, and different expressions. --- 💬 Discussion ## Predict **Dan has $n$ stickers. He gets 3 more, then doubles the lot. Which expression is the number he ends with?** - $n + 6$ - $2n + 3$ - $5n$ - $2(n + 3)$ --- ✍️ Activity ## Try it {{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fmaths%2Falgebra%2Fbrackets%2Fstep-2&code=widget%3A+formula%0Aformula%3A+T+%3D+2%28n+%2B+3%29%0Ahide%3A+formula%0Aslider+n%3A+0%2C+10%2C+1%0A&fresh=1}} [Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/maths/algebra/brackets/?full=step-2#step-2) --- ✅ Check ## What happened? * 2(n + 3). He adds 3 first (n + 3), then doubles all of it. 2n + 3 would double only his own stickers and add 3 afterwards. --- 💬 Discussion ## Add 3, then double Here is how to decide where the brackets go. $$\text{add 3 to } n, \text{ then double the result}$$ 1) $n + 3$ — The first step: add 3 to $n$. 2) $\text{double the result}$ — "The result" is the whole of $n + 3$, not just $n$. 3) $2(n + 3)$ — Brackets keep $n + 3$ together, so it is worked out first and then doubled. 4) $n = 4: \; 2(4 + 3) = 2 \times 7 = 14$ — Check: add 3 to 4 to get 7, then double it. 5) $2n + 3$ — Compare: this doubles $n$ only and then adds 3. For $n = 4$ it gives 11, not 14. --- ✅ Check ## Add 3, then double **Write an expression for "add 4 to $n$, then multiply the result by 5".** * Answer: 5(n + 4) --- ✅ Check ## Find the mistake **Which expression means "subtract 3 from $n$, then divide the result by 2"?** - $\frac{n}{2} - 3$ - $\frac{n - 3}{2}$ - $n - \frac{3}{2}$ * Answer: $\frac{n - 3}{2}$ --- ✅ Check ## Your turn **Jo writes "add 2 to $x$, then multiply by 6". Click the line where she goes wrong.** ``` 1 Write "add 2 to x, then multiply by 6" as an expression. 2 Add 2 to x is x + 2. 3 Then multiply by 6, so I write 6x + 2. 4 So the expression is 6x + 2. ``` * Answer: line 3 --- ✍️ Activity ## New sentences - **Subtract, then multiply:** The board does what the words say. Write your expression, then check it with a number. - **No brackets:** - **Two letters:** - **Halving:** [Open this step](https://studio.learningwaypoints.com/tutorials/maths/algebra/brackets/?full=step-4#step-4) --- ✅ Check ## Books **Books cost 8 dollars each. Write an expression for the cost of $n$ books after taking 5 dollars off the total.** * Answer: 8n - 5 --- ✅ Check ## A group **A group of $n$ adults and 3 children each pay 6 dollars. Write an expression for the total.** * Answer: 6(n + 3) --- ✅ Check ## Which is bigger? **When $n = 5$, which is bigger, $2(n + 3)$ or $2n + 3$?** - $2n + 3$, which is 13 - They are the same - $2(n + 3)$, which is 16 * Answer: $2(n + 3)$, which is 16 --- ✅ Check ## Review **Review: find $4(n - 1)$ when $n = 6$.** * Answer: 20 --- ✍️ Activity ## Make: find the rule Say the steps in words: what does the rule do first, and what next? Stretch: write a rule of your own with brackets and ask a partner to find it from the board. [Open this step](https://studio.learningwaypoints.com/tutorials/maths/algebra/brackets/?full=step-6#step-6) --- ✅ Check ## Exit ticket **Write an expression for: (a) add 6 to n, then multiply by 3; (b) multiply n by 3, then add 6. Which one gives 15 when n = 3?** * (a) 3(n + 6); (b) 3n + 6. (b): 3 × 3 + 6 = 15; (a) gives 27.