The document introduces variables and expressions using letters like p, x, and y to represent unknown numbers in algebraic expressions. It provides examples of writing expressions to represent changes to unknown quantities, such as subtracting, adding, multiplying, or dividing the variable by a number. The key use of variables is to stand in for unknown values that can help represent and solve problems algebraically.

1. We forgot to take the register for 7 Bruno on Tuesday! Oh no! 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒑 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 7 𝐵𝑟𝑢𝑛𝑜 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 𝐵𝑟𝑢𝑛𝑜 =𝒑 𝒑=𝟑𝟎 If everyone was here then 𝒑=𝟏𝟓 If there was only ½ the class then 𝒑= TODAY …..

2. 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒑 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 7 𝐵𝑟𝑢𝑛𝑜 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 𝐵𝑟𝑢𝑛𝑜 =𝒑 𝑯𝒆𝒓𝒆 𝒘𝒆 𝒂𝒓𝒆 𝒖𝒔𝒊𝒏𝒈 𝒑 𝒕𝒐 𝒓𝒆𝒑𝒓𝒆𝒔𝒆𝒏𝒕 𝑼𝑵𝑲𝑶𝑾𝑵 𝑽𝑨𝑳𝑼𝑬 (𝒏𝒖𝒎𝒃𝒆𝒓). However, tomorrow some pupils may be absent so ‘𝒑’ can VARY (i.e. change) We call ‘𝒑’ a VARIABLE.

3. The number of FISH in a shoal is an UNKNOWN VALUE and can VARY. 𝐿𝑒𝑡 𝒇 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑖𝑠h The number of text books in school Is an UNKNOWN VALUE and can VARY. 𝐿𝑒𝑡 𝒕 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑥𝑡 𝑏𝑜𝑜𝑘𝑠. The numbers for this SUM are UNKNOWN VALUES and can VARY. 𝐿𝑒𝑡 𝒙 𝑎𝑛𝑑 𝒚 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑖𝑛 𝑡h𝑒 𝑠𝑢𝑚. 𝒙+𝒚=𝟏𝟎𝟎

4. In algebra, we use letter symbols to stand for numbers. These letters are called unknowns or variables. Sometimes we can work out the value of the letters and sometimes we can’t. We can use algebra to help us solve problems by making up algebraic expressions and equations using the letters to represent the unknown value or variable.

5. FOR EXAMPLE, 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 𝐵𝑟𝑢𝑛𝑜 =𝒑 What would happen if I sent 2 pupils outside? How can I write the total number of pupils in Bruno NOW? There were 𝒑 pupils now 2 pupils have gone. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 𝐵𝑟𝑢𝑛𝑜 𝑖𝑠 𝒑−𝟐

6. FOR EXAMPLE, 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 𝐵𝑟𝑢𝑛𝑜 =𝒑 What would happen if I sent 10 pupils outside? How can I write the total number of pupils in Bruno NOW? There were 𝒑 pupils now 10 pupils have gone. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 𝐵𝑟𝑢𝑛𝑜 𝑖𝑠 𝒑−10

7. FOR EXAMPLE, 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 𝐵𝑟𝑢𝑛𝑜 =𝒑 What would happen if 5 pupils joined our class? How can I write the total number of pupils in Bruno NOW? There were 𝒑 pupils and now there are 5 MORE. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑢𝑝𝑖𝑙𝑠 𝑖𝑛 𝐵𝑟𝑢𝑛𝑜 𝑖𝑠 𝒑+𝟓

8. WRITING AN ALGEBRAIC EXPRESSION… Suppose Simone has a packet of biscuits and she doesn’t know how many biscuits it contains. 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒃 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑏𝑖𝑠𝑐𝑢𝑖𝑡𝑠 𝑖𝑛 𝑎 𝑓𝑢𝑙𝑙 𝑝𝑎𝑐𝑘𝑒𝑡 𝑇𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝐵𝑖𝑠𝑐𝑢𝑖𝑡𝑠=𝒃 At break Simone opens the packet and eats 4 biscuits, she can write an expression for the number of biscuits left: b – 4

9. I think of a number….. Let the letter 𝑘 represent my unknown number. I then ADD 5 to my number. As an expression…. +𝟓 𝒌

10. I think of the number 12. Let the letter 𝒙 represent a unknown number. I then my unknown number 𝒙 to 12. As an expression…. + 𝒙 𝟏𝟐

11. I think of the number 50. Let the letter 𝒂 represent a unknown number. I then MINUS 𝒂 from 50. As an expression…. − 𝒂 𝟓𝟎

12. 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒚 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑐𝑒 𝑐𝑟𝑒𝑎𝑚𝑠 𝑖𝑛 𝑚𝑦 𝑓𝑟𝑒𝑒𝑧𝑒𝑟. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑖𝑐𝑒 𝑐𝑟𝑒𝑎𝑚𝑠=𝒚 I go to the supermarket and buy a pack of 5 ice creams and put them in my freezer. Write an EXPRESSION for number of ice creams. 𝒚+𝟓

13. 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒔 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑤𝑒𝑒𝑡𝑠 𝑖𝑛 𝑎 𝑠h𝑜𝑝. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑤𝑒𝑒𝑡𝑠=𝒔 The shopkeeper buys a box of 100 sweets. Write an EXPRESSION for number of sweets. 𝒔+𝟏𝟎𝟎

14. 𝑇h𝑒 𝑠h𝑜𝑝𝑘𝑒𝑒𝑝𝑒𝑟 h𝑎𝑠 400 𝑝𝑒𝑛𝑛𝑦 𝑠𝑤𝑒𝑒𝑡𝑠 𝑖𝑛 𝑎 h𝑒𝑟 𝑠h𝑜𝑝. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑤𝑒𝑒𝑡𝑠=𝟒𝟎𝟎 The shopkeeper sells 𝒔 penny sweets in a day. Write an EXPRESSION for number of sweets. 𝟒𝟎𝟎 −𝒔

15. 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒋 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑖𝑟𝑠 𝑜𝑓 𝑗𝑒𝑎𝑛𝑠 𝑁𝑒𝑤 𝐿𝑜𝑜𝑘 h𝑎𝑣𝑒 𝑖𝑛 𝑖𝑡𝑠 𝑓𝑙𝑎𝑔 𝑠h𝑖𝑝 𝑆𝑡𝑜𝑟𝑒. 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑖𝑟𝑠 𝑜𝑓 𝑗𝑒𝑎𝑛𝑠=𝒋 In one day New Look sold 89 pairs of jeans. Write an EXPRESSION for number of pairs of jeans. 𝒋−𝟖𝟗

16. 𝑁𝑒𝑤 𝐿𝑜𝑜𝑘 h𝑎𝑣𝑒 𝟐𝟓𝟎 𝑝𝑎𝑖𝑟𝑠 𝑜𝑓 𝑗𝑒𝑎𝑛𝑠 𝑖𝑛 𝑡𝑜𝑡𝑎𝑙 𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑎𝑖𝑟𝑠 𝑜𝑓 𝑗𝑒𝑎𝑛𝑠=250 On Monday New Look had a delivery of 𝒋 pairs of jeans. Write an EXPRESSION for number of pairs of jeans. 𝟐𝟓𝟎+𝒋

17. I think of a number….. Let the letter 𝒚 represent my unknown number. I then MULTIPLY my number by 2. As an expression…. 𝒚 ×𝟐 =𝟐𝒚

18. I think of a number….. Let the letter 𝒑 represent my unknown number. I then MULTIPLY my number by 11 As an expression…. 𝒑 ×𝟏𝟏 =𝟏𝟏𝒑

19. Kerrie is on a game show and has won £𝑥 ! 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒙 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡h𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑚𝑜𝑛𝑒𝑦 𝑠h𝑒 h𝑎𝑠 𝑤𝑜𝑛. She then takes a chance and DOUBLES her money ! As an expression how much money has she won? 𝟐 ×𝒙 =𝟐𝒙

20. Anjelica is on a game show and has won £𝑚 ! 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒎 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡h𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑚𝑜𝑛𝑒𝑦 𝑠h𝑒 h𝑎𝑠 𝑤𝑜𝑛. She then takes a chance and TRIPLES her money ! As an expression how much money has she won? 𝟑×𝒎 =𝟑𝒎

21. Nicole is on a game show and has won £𝑑 ! 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒅 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡𝑠 𝑡h𝑒 𝑎𝑚𝑜𝑢𝑛𝑡 𝑜𝑓 𝑚𝑜𝑛𝑒𝑦 𝑠h𝑒 h𝑎𝑠 𝑤𝑜𝑛. Unfortunately she takes a chance but loses so HALVES her money! As an expression how much money has she won? =𝒅𝟐 𝒅÷𝟐

22. 𝑀𝑎𝑟𝑦 h𝑎𝑠 𝑙𝑜𝑡𝑠 𝑜𝑓 𝑝𝑒𝑛𝑠 𝑖𝑛 h𝑒𝑟 𝑝𝑒𝑛𝑐𝑖𝑙 𝑐𝑎𝑠𝑒. What letter could we use to represent the number of pens Mary has? 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒑 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑛𝑠 𝑀𝑎𝑟𝑦 h𝑎𝑠 𝑖𝑛 h𝑒𝑟 𝑝𝑒𝑛𝑐𝑖𝑙 𝑐𝑎𝑠𝑒. Maia then gives Mary her pens so Mary has DOUBLE the number of pens. As an expression how pens does Mary have now? 𝟐 ×𝒑 =𝟐𝒑

23. 𝐿𝑒𝑡 𝑡h𝑒 𝑙𝑒𝑡𝑡𝑒𝑟 𝒘 𝑟𝑒𝑝𝑟𝑒𝑠𝑒𝑛𝑡 𝑡h𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑛𝑠 𝑀𝑎𝑟𝑦 h𝑎𝑠 𝑖𝑛 h𝑒𝑟 𝑝𝑒𝑛𝑐𝑖𝑙 𝑐𝑎𝑠𝑒. Mary lends HALF her pens to Sian. As an expression how pens does Mary have now? =𝒘𝟐 𝒘÷𝟐

24. Akokor built a tower 𝐳 metres high. She then decides to TRIPLE the height of her tower! As an expression how high is Akokor’s tower? 𝟑×𝒛 =𝟑𝒛

25. Dabby has £𝑥 in her wallet. Ciara has 5 TIMES as much money in her wallet. As an expression how much money does Ciara have? 𝟓×𝒙 =𝟓𝒙

26. Chimezie has 𝐡 pairs of socks. Penny has 4 TIMES as many pairs of socks. As an expression how many socks does Penny have? =𝟒𝒉 𝟒×𝒉 Niamh has HALF as many pairs of socks as Chemizie? As an expression how many socks does Niamh have? =𝒉𝟐 𝒉÷𝟐

29. Georgia went Strawberry picking one summer. 𝑆h𝑒 𝑝𝑖𝑐𝑘𝑒𝑑 𝒎 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑖𝑒𝑠 She ate 10 strawberries at Lunch. How many strawberries does she have now? 𝒎 - 10 Sian also went Strawberry picking with Georgia. 𝑆𝑖𝑎𝑛 𝑝𝑖𝑐𝑘𝑒𝑑 𝒏 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑖𝑒𝑠 Sian then picked 20 more strawberries. How many strawberries does she have now? 𝒏 + 20

30. Sonya and Madalena went Strawberry picking too 𝑆𝑜𝑛𝑦𝑎 𝑝𝑖𝑐𝑘𝑒𝑑 𝒎 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑖𝑒𝑠 𝑀𝑎𝑑𝑎𝑙𝑒𝑛𝑎 𝑝𝑖𝑐𝑘𝑒𝑑 𝒏 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑖𝑒𝑠 How many strawberries does do they have altogether? + = 𝒎+𝒏 + 𝒎 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑖𝑒𝑠 𝒏 𝑠𝑡𝑟𝑎𝑤𝑏𝑒𝑟𝑟𝑖𝑒𝑠