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# Algebraic conventions

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### Algebraic conventions

1. 1. motiv8<br />maths.co.uk<br />
2. 2. Algebra<br />16/06/2011<br />Objective<br />Algebraic <br />conventions<br />Keywords<br />Algebra<br />Convention<br />Squared<br />
3. 3. Bronze Medal<br />GOOD<br />Silver Medal<br />GREAT<br />Gold Medal<br />HERO<br />Achievements<br />Know that a letter can be any number<br />Know how to multiply using letters with<br />numbers<br />Know how to divide using letters with <br />numbers<br />
4. 4. Introduction<br />
5. 5. Bored Ben!<br />Ben’s teacher tells him to think of a number…<br />What could it be?<br />My number <br />is…….?<br />1 <br />53<br />½<br />5.6<br />-2¼<br />-2.8<br />
6. 6. Ben’s number!<br />What IS the number then?<br />I’m not<br />saying!<br />What can we use<br />for Ben’s number?<br /> Letters!!<br />
7. 7. All about algebra!<br />What letters can we use?<br />a b c d e f g h I j k l<br />m n o p q r s t u v w x<br />y z<br />A B C D E F G H I J K L<br />M N O P Q R S T U V W X<br />Y Z<br />
8. 8. All about algebra!<br />So…a letter in <br />maths means…..<br />A<br />number!!<br />I get it!!!!<br />We just don’t know<br />what the number is!<br />
9. 9. Match up!<br />Match up two numbers that are the same!<br />Find the odd ones out!<br />c<br />Y<br />N<br />b<br />Y<br />c<br />n<br />y<br />C<br />X<br />C<br />d<br />y<br />N<br />X<br />n<br />Click letters in yellow box to show matching pair<br />Click on odd ones out to reveal.<br />
10. 10. Multiplying<br />(Letters & numbers)<br />
11. 11. Ben’s number<br />n<br />n<br />Ben’s number is……<br />..I think I’ll<br />double it!<br />What<br />happened?<br />in algebra this is……<br />n<br />x<br />2<br />2<br />..got rid of..<br />Put the<br />number first!<br />
12. 12. Gurdeep’s number<br />Gurdeep’s number is different to Ben’s..<br />f<br />..I want<br />to times it<br />by 6!<br />f x 6<br />6f<br />
13. 13. The rules!<br />x<br />In algebra…<br />When a letter is…<br />A number…<br />PUT THE NUMBER<br />FIRST!<br />
14. 14. Ben says!<br />Number is<br />“y”<br />I’m thinking of a number.<br />7y<br />1<br />Times it by 7?<br />What’s the answer if I….<br />12y<br />2<br />Multiply it by 12?<br />3y<br />3<br />Treble it?<br />4y<br />4<br />Have 4 lots of it?<br />1.8y<br />5<br />Multiply it by 1.8?<br />¼y<br />6<br />Times it by ¼?<br />
15. 15. Multiplying algebra<br />Worksheet 1<br />Complete these questions.<br />6f<br />7a<br />11<br />f x 6<br />1<br />a times 7<br />23k<br />8e<br />12<br />23 x k<br />2<br />8 multiplied by e<br />13<br />6y<br />y x 6<br />3<br />Double x<br />2x<br />14<br />15m<br />m x 15<br />4<br />Multiply h by 5<br />5h<br />1.4d<br />5k<br />15<br />1.4 x d<br />5<br />5 lots of k<br />3.7d<br />16<br />g x 3.7<br />6<br />6v<br />6 times v<br />0.5n<br />9p<br />17<br />0.5 x n<br />7<br />p multiplied by 9<br />½c<br />3d<br />18<br />½ x c<br />8<br />Treble d<br />¾h<br />8w<br />19<br />h x ¾<br />9<br />Multiply 8 by w<br />1¼a<br />20<br />1¼ x a<br />10<br />14x<br />x lots of 14<br />
16. 16. When letters aren't numbers!<br />The great pyramid at Giza, Egypt<br />The m means<br />metres! It<br />isn’t a number!<br />140m!<br />..is about 140 <br />metres tall!<br />
17. 17. Multiplying<br />(Letters & letters)<br />
18. 18. Ben and Gurdeep<br />…want to multiply their numbers together<br />n<br />x<br />f<br />n<br />f<br />What<br />happened?<br />Letters in <br />alphabetical<br />order!<br />abcdefghijklmnopqrstuvwxyz<br />
19. 19. All by itself!<br />Who is right?<br />If I times my<br />number by itself<br />I get…..<br />n²<br />n x n<br />nn<br />If I times my<br />number by itself<br />I get…..<br />f x f<br />2f<br />f²<br />
20. 20. Micah says!<br />Number is<br />“e”<br />I’m thinking of a number.<br />em<br />1<br />Times it by m?<br />What’s the answer if I….<br />ae<br />2<br />Multiply it by a?<br />ey<br />3<br />Have y lots of it?<br />beh<br />Times it by b, then<br />by h?<br />4<br />e²<br />5<br />Times it by e?<br />e²k<br />Times it by itself<br />then by k?<br />6<br />
21. 21. Multiplying algebra<br />Worksheet 2<br />Complete these questions.<br />ch<br />ad<br />11<br />h x c<br />1<br />a times d<br />dk<br />fh<br />12<br />d x k<br />2<br />h multiplied by f<br />13<br />hk<br />Multiply n by d<br />h x k<br />dn<br />3<br />14<br />am<br />m x a<br />4<br />gt<br />g lots of t<br />abc<br />15<br />vw<br />w times v<br />a x b x c<br />5<br />adk<br />PH<br />16<br />d x a x k<br />6<br />P multiplied by H<br />u²<br />17<br />u x u<br />7<br />Multiply n by m<br />mn<br />m²<br />18<br />m x m<br />dn<br />8<br />d lots of n<br />K times by E then<br />by H<br />g²<br />19<br />g x g x f<br />EHK<br />9<br />Multiply D by C and U<br />CDU<br />ab²<br />20<br />b x a x b<br />10<br />
22. 22. When letters aren't numbers!<br />Meet Pythagoras. A very famous greek mathematician.<br />I weigh<br />84 <br />kilograms!<br />The kg means<br />kilograms NOT<br />84 x k x g<br />84kg<br />
23. 23. Georges <br />homework<br />
24. 24. George’s Homework<br />Worksheet 3<br />Mark George’s homework. (For each mistake take one mark)<br />George’s<br />answer<br />Right<br />answer<br />Right or<br />wrong<br />1<br />3 times T<br />3t<br />3T<br />2<br />h multiplied by 4<br />4h<br />Double k<br />3<br />k2<br />2k<br />George’s<br />mark<br />4<br />5.2y<br />5.2 lots of y<br />What mark<br />would George<br />get out of<br />10?<br />5<br /> ½n<br />2n<br />n times by ½<br />5<br />6<br />f x b<br />bf<br />df<br />10<br />7<br />e x p<br />ep<br />d x k x a<br />8<br />adk<br />g²<br />9<br />gg<br />g x g<br />kw²<br />w x k x w <br />10<br />
25. 25. Dividing<br />
26. 26. Dividing numbers<br />What happens when we divide numbers?<br />a<br />b<br />a<br />b<br />
27. 27. Dividing numbers<br />What happens when we divide numbers?<br />b<br />a<br />b<br />a<br />
28. 28. What’s going on?<br />So what IS happening when we divide numbers?<br />H<br />K<br />H<br />K<br />This number…<br />This number…<br />Goes on the<br />bottom<br />Goes on top<br />
29. 29. Dividing numbers<br />What happens when we divide numbers?<br />2<br />m<br />2<br />m<br />
30. 30. Dividing numbers<br />What happens when we divide numbers?<br />y²<br />4<br />y²<br />4<br />
31. 31. Chelsea says!<br />Number is<br />“u”<br />I’m thinking of a number.<br />1<br />Divide it by n?<br />What’s the answer if I….<br />2<br />Divide g by it?<br />g<br />u<br />u<br />u<br />u<br />u<br />n<br />u<br />y<br />u<br />3<br />f<br />k²<br />Share it with y people?<br />4<br />Split it into f lots?<br />5<br />Divide it by k²?<br />1<br />6<br />Divide it by itself<br />
32. 32. h<br />c<br />c<br />3<br />y<br />h<br />n<br />3<br />m<br />m<br />m²<br />h<br />g<br />7<br />g<br />a<br />w²<br />d<br />b²<br />8<br />d²<br />14<br />a²<br />k<br />b<br />1<br />c<br />a²<br />1<br />1<br />k²<br />2g<br />k<br />d<br />2h<br />4c<br />f<br />Dividing algebra<br />Worksheet 4<br />Complete these questions.<br />11<br />h ÷ c<br />1<br />g divided by d<br />12<br />c ÷ h<br />2<br />3 divided by y<br />13<br />Divide n by m<br />3 ÷ m<br />3<br />14<br />m² ÷ 7<br />4<br />Split h into g lots<br />15<br />Divide w² by 8<br />a ÷ b²<br />5<br />16<br />d ² ÷ a²<br />6<br />Share 14 with k people<br />17<br />u ÷ u<br />7<br />Divide b into c lots<br />18<br />m ÷ m<br />8<br />a² divided by k²<br />19<br />y divided by itself<br />2g ÷ k<br />9<br />20<br />d ÷ 4c<br />10<br />2 lots of h divided by f<br />
33. 33. Pupil<br />worksheets<br />