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0000000E 23 5 0 00000533 23 4 0 FF702800 15 84 282 -700 -761 0 yyyyyg 90 -745 Easiteach 11 5 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 divide by 4 16 0 72000 11 39 -10 0 1 0 23 8 0 0000000E 23 5 0 00000533 23 4 0 FF702800 15 84 513 -789 -850 0 yyyyyg 90 -834 Easiteach 25 6 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 divide by original number 16 0 164400 25 39 -10 0 1 0 23 8 0 0000000E 23 5 0 0000052D 23 4 0 FF702800 15 84 688 -879 -940 0 yyyyyg 90 -924 Easiteach 35 7 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 Your number is 5 more than original 16 0 234400 35 39 -10 0 1 0 23 8 0 0000000E 23 5 0 00000591 23 4 0 FF702800 15 960 1017 -346 -407 0 yyyyyf 966 -391 Easiteach 2 8 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 2n 16 0 15600 2 39 -10 0 1 0 23 8 0 0000000E 23 4 0 FF702800 23 5 0 000001E2 15 960 1077 -433 -494 0 yyyyyf 966 -478 Easiteach 6 9 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 2n + 5 16 0 39600 6 39 -10 0 1 0 23 8 0 0000000E 23 4 0 FF702800 23 5 0 000001D6 15 960 1103 -524 -585 0 yyyayf 966 -569 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0000000C 23 9 0 0000005F 23 4 0 FF702800 23 5 0 000000E4 15 960 1085 -710 -771 0 yyyyyc 966 -755 Easiteach 7 16 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 n + 5n 16 0 42800 7 39 -10 0 1 0 23 8 0 0000000E 23 4 0 FF702800 23 5 0 000001E5 15 978 1010 -706 -753 0 yyyyyb 984 -740 Easiteach 1 17 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 2 16 0 5600 1 28 -7 0 1 0 23 8 0 0000000A 23 9 0 0000005F 23 4 0 FF702800 23 5 0 000000E4 15 960 1056 -798 -859 0 yyyyyb 966 -843 Easiteach 5 18 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 n + 5 16 0 31200 5 39 -10 0 1 0 23 8 0 0000000E 23 4 0 FF702800 23 5 0 000001D4 15 960 996 -259 -320 0 yyyaya 966 -304 Easiteach 1 19 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 n 16 0 7200 1 39 -10 0 1 0 23 8 0 0000000E 23 4 0 FF702800 23 5 0 000001A8 15 79 396 -261 -322 0 yyyyya 85 -306 Easiteach 17 20 n 0 nny 0 16777248 0 0 0 0 0 0 256 0 0 Think of a number 16 0 119600 17 39 -10 0 1 0 23 8 0 0000000E 23 5 0 00000591 23 4 0 FF702800 19 80 716 -261 -328 0 yyyyya Outline 21 n 0 n 0 0 0 0 0 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E-ۨXB (@f5ʜ0hc#j21-ꁩIB%(q՝-HHt #ȍD1T24p83h*#@$řd_8iBET] R{@caC#0Cn܆n#l66B u~)Ι(j`F[pb2(0XL&o'{I,Z"(oUm4m<SPܩ"rF sN3—4 fیI=E5pV+t'+ T<#8S$c[n[H`Ȏb) BCʱM\TPJv"pB"$BAX'45رL^zN- Ȃ(- ;#p(ҜdbHn\?+54X"ó#8U1,pOZS)p1Tt5',S'pT)B5 #8l>uy se)dBX @,4,A5H"B F,4CDbJQPn;fB)p$=9B`ɜ8 Maz%& BZs֒@)(Hl#tCK3)m:>P*wew&A&Td)h!:8888Y@; 26 42 469 -68 -381 0 nyyyyg 1 1 n 0 0 0 0 0 0 0 0 nnn 0 y 0 0 26 1032 1374 -50 -352 0 nyyyyf 2 2 n 0 0 0 0 0 0 0 0 nnn 0 y 0 0 15 558 902 -116 -305 0 yyyyyf 564 -262 Easiteach 5 3 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Proof 16 0 130400 5 140 -37 0 1 0 23 4 0 3800A800 23 8 0 00000033 23 5 0 00000497 15 91 1373 -423 -625 0 yyyyyf 97 -484 Easiteach 121 4 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 In courts the burden of proof is with the prosecuter, where they are expect to prove their case beyond reasonable doubt. 16 0 499600 53 55 -15 0 1 0 16 54 467200 48 55 -15 0 0 0 16 103 171200 18 55 -15 0 0 0 23 5 0 00000542 23 18 42 00000079 23 4 96 FF28B800 23 4 120 00000000 15 85 1434 -730 -872 0 yyyyyf 91 -791 Easiteach 71 5 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 In mathematical proof, the luxury of reasonable doubt is not allowed!!! 16 0 532400 56 55 -15 0 1 0 16 57 118800 14 55 -15 0 0 0 23 5 0 0000053F 19 0 0 2000 2000 0 yyyyye Outline 6 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 13 0 -1150 1488 0 H:\Lesson_plans\Year_11\11R1\Algebra\Proof\Algebraic_proof.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 4 0 0 -1 -1 -1 0 65536  0 0 0 0 8 0 1557 0 0 0 0 0 9 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 15 71 1368 -65 -207 0 yyyyyg 77 -126 Easiteach 72 1 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Prove that if you multiply 2 odd numbers together you get an odd number. 16 0 505600 53 55 -15 0 1 0 16 54 177600 18 55 -15 0 0 0 23 5 0 00000518 15 84 245 -285 -367 0 yyyyyg 90 -346 Easiteach 6 2 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Proof: 16 0 57200 6 55 -15 0 1 0 23 5 0 00000549 15 578 1072 -283 -365 0 yyyyyf 584 -344 Easiteach 20 3 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 m and n are integers 16 0 190400 20 55 -15 0 1 0 23 4 0 FF28B800 23 5 0 0000036C 23 4 1 FFFFFFFF 23 4 6 FF28B800 23 4 7 FFFFFFFF 15 85 1321 -418 -560 0 yyyyyf 91 -479 Easiteach 66 4 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 in order for the numbers to be odd, they can't be a multiple of 2. 16 0 481200 51 55 -15 0 1 0 16 52 124400 14 55 -15 0 0 0 23 5 0 0000053F 15 83 1061 -585 -667 0 yyyyyf 89 -646 Easiteach 40 5 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2m represents a number in 2 times table. 16 0 384000 40 55 -15 0 1 0 23 4 0 FF28B800 23 5 0 0000053E 23 4 2 FFFFFFFF 15 84 846 -683 -765 0 yyyyyf 90 -744 Easiteach 32 6 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2m + 1 can't be in 2 times table 16 0 297600 32 55 -15 0 1 0 23 4 0 FF28B800 23 5 0 0000053F 23 4 7 FFFFFFFF 15 86 1318 -809 -891 0 yyyyyf 92 -870 Easiteach 50 7 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 We can use the following to represent odd numbers. 16 0 485600 50 55 -15 0 1 0 23 5 0 0000053D 15 209 521 -917 -1061 0 yyyyyf 215 -1028 Easiteach 6 8 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2m + 1 16 0 117600 6 105 -27 0 1 0 23 8 0 00000026 23 4 0 3800A800 23 5 0 000004D4 15 786 1050 -922 -1056 0 yyyyyf 792 -1024 Easiteach 6 9 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2n + 1 16 0 98400 6 96 -26 0 1 0 23 8 0 00000023 23 4 0 3800A800 23 5 0 0000028F 19 568 1121 -285 -371 0 yyyyye Outline 10 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 78 1347 -423 -558 0 yyyyye Outline 11 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 75 1086 -585 -669 0 yyyyye Outline 12 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 77 1019 -688 -765 0 yyyyye Outline 13 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 75 1368 -798 -1082 0 yyyyye Outline 14 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 13 0 -1150 1488 0 H:\Lesson_plans\Year_11\11R1\Algebra\Proof\Algebraic_proof.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 5 0 0 -1 -1 -1 0 65536  0 0 0 0 7 0 1557 0 0 0 0 0 10 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 15 103 1400 -74 -216 0 yyyyyg 109 -135 Easiteach 72 1 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Prove that if you multiply 2 odd numbers together you get an odd number. 16 0 505600 53 55 -15 0 1 0 16 54 177600 18 55 -15 0 0 0 23 5 0 00000518 15 116 277 -294 -376 0 yyyyyg 122 -355 Easiteach 6 2 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Proof: 16 0 57200 6 55 -15 0 1 0 23 5 0 00000549 15 610 1104 -292 -374 0 yyyyyf 616 -353 Easiteach 20 3 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 m and n are integers 16 0 190400 20 55 -15 0 1 0 23 4 0 FF28B800 23 5 0 0000036C 23 4 1 FFFFFFFF 23 4 6 FF28B800 23 4 7 FFFFFFFF 15 107 509 -434 -516 0 yyyyyf 113 -495 Easiteach 17 4 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 (2m + 1) (2n + 1) 16 0 153600 17 55 -15 0 1 0 23 4 0 3800A800 23 5 0 00000532 15 111 545 -559 -641 0 yyyyyf 117 -620 Easiteach 17 5 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 4mn + 2m + 2n + 1 16 0 166400 17 55 -15 0 1 0 23 4 0 3800A800 23 5 0 00000526 23 18 1 00000079 15 121 560 -674 -756 0 yyyyyf 127 -735 Easiteach 18 6 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2(2mn + m + n) + 1 16 0 168400 18 55 -15 0 1 0 23 4 0 3800A800 23 5 0 00000522 23 18 3 00000079 15 101 1417 -837 -979 0 yyyyyf 107 -898 Easiteach 61 7 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 As 1 is being added to an even number, the result must be odd 16 0 513200 54 55 -15 0 1 0 16 55 62400 6 55 -15 0 0 0 23 5 0 0000052D 19 102 551 -432 -517 0 yyyyye Outline 8 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 105 549 -547 -639 0 yyyyye Outline 9 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 104 555 -667 -758 0 yyyyye Outline 10 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 93 1405 -829 -978 0 yyyyye Outline 11 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 13 0 -1150 1488 0 H:\Lesson_plans\Year_11\11R1\Algebra\Proof\Algebraic_proof.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 6 0 0 -1 -1 -1 0 65536  0 0 0 0 6 0 1557 0 0 0 0 0 11 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 15 88 1445 -89 -231 0 yyyyyg 94 -150 Easiteach 71 1 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Prove that the sum of any 2 consecutive odd numbers is a multiple of 4. 16 0 535600 56 55 -15 0 1 0 16 57 124400 14 55 -15 0 0 0 23 5 0 00000545 15 95 255 -289 -371 0 yyyyyg 101 -350 Easiteach 6 2 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2n + 1 16 0 56800 6 55 -15 0 1 0 23 5 0 00000542 15 816 976 -293 -375 0 yyyyyg 822 -354 Easiteach 6 3 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2n + 3 16 0 56800 6 55 -15 0 1 0 23 5 0 000003FE 15 103 459 -423 -505 0 yyyyyg 109 -484 Easiteach 15 4 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2n + 1 + 2n + 3 16 0 135200 15 55 -15 0 1 0 23 5 0 00000536 15 101 261 -568 -650 0 yyyyyg 107 -629 Easiteach 6 5 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 4n + 4 16 0 56800 6 55 -15 0 1 0 23 5 0 00000538 15 106 302 -694 -776 0 yyyyyg 112 -755 Easiteach 8 6 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 4(n + 1) 16 0 71200 8 55 -15 0 1 0 23 5 0 00000533 15 98 783 -892 -974 0 yyyyyg 104 -953 Easiteach 28 7 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Sum must be a multiple of 4. 16 0 266800 28 55 -15 0 1 0 23 5 0 0000052D 19 93 261 -287 -364 0 yyyyyf Outline 8 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 811 993 -287 -371 0 yyyyyf Outline 9 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 95 474 -417 -499 0 yyyyyf Outline 10 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 86 308 -575 -651 0 yyyyyf Outline 11 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 86 333 -693 -773 0 yyyyyf Outline 12 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 19 94 779 -888 -991 0 yyyyyf Outline 13 n 0 n 0 0 0 0 0 0 0 0 0 0 24 5 00000005 24 2 00000079 24 1 ffffd700 24 0 0000ff00 13 0 -1150 1488 0 H:\Lesson_plans\Year_11\11R1\Algebra\Proof\Algebraic_proof.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 9 0 0 -1 -1 -1 0 65536  0 0 0 0 5 0 1557 0 0 0 0 0 13 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 15 108 499 -41 -123 0 yyyyyg 114 -102 Easiteach 16 1 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Exam question... 16 0 149200 16 55 -15 0 1 0 23 5 0 00000518 15 927 963 -163 -220 0 yyyyyg 933 -205 Easiteach 1 2 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 7200 1 36 -9 0 1 0 23 9 0 00000061 23 8 0 0000000D 23 5 0 00000222 23 4 0 3800A800 15 537 944 -171 -253 0 yyyyyg 543 -232 Easiteach 21 3 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 (n - a ) - (n - a) 16 0 155600 21 55 -15 0 1 0 23 5 0 0000032A 23 4 0 3800A800 15 582 618 -171 -228 0 yyyyyg 588 -213 Easiteach 1 4 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 7200 1 36 -9 0 1 0 23 9 0 00000061 23 8 0 0000000D 23 5 0 0000022D 23 4 0 3800A800 15 115 505 -172 -254 0 yyyyyg 121 -233 Easiteach 17 5 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Factorise fully: 16 0 148800 17 55 -15 0 1 0 23 5 0 00000512 15 688 724 -175 -232 0 yyyyyg 694 -217 Easiteach 1 6 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 7200 1 36 -9 0 1 0 23 9 0 00000061 23 8 0 0000000D 23 5 0 000001BB 23 4 0 3800A800 15 126 607 -587 -669 0 yyyyyg 132 -648 Easiteach 20 7 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 n and a are integers 16 0 185200 20 55 -15 0 1 0 23 5 0 00000513 15 807 843 -671 -728 0 yyyyyg 813 -713 Easiteach 1 8 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 7200 1 36 -9 0 1 0 23 9 0 00000061 23 8 0 0000000D 23 5 0 00000222 15 417 824 -679 -761 0 yyyyyg 423 -740 Easiteach 21 9 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 (n - a ) - (n - a) 16 0 155600 21 55 -15 0 1 0 23 5 0 0000032A 15 462 498 -679 -736 0 yyyyyg 468 -721 Easiteach 1 10 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 7200 1 36 -9 0 1 0 23 9 0 00000061 23 8 0 0000000D 23 5 0 0000022D 15 860 1451 -681 -763 0 yyyyyg 866 -742 Easiteach 25 11 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 is always an even integer 16 0 229200 25 55 -15 0 1 0 23 5 0 00000307 15 113 433 -683 -765 0 yyyyyg 119 -744 Easiteach 13 12 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Explain why 16 0 120800 13 55 -15 0 1 0 23 5 0 0000050E 15 568 604 -683 -740 0 yyyyyg 574 -725 Easiteach 1 13 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 7200 1 36 -9 0 1 0 23 9 0 00000061 23 8 0 0000000D 23 5 0 000001BB 15 1227 1467 -993 -1075 0 yyyyyg 1233 -1054 Easiteach 9 14 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 (4 marks) 16 0 88800 9 55 -15 0 1 0 23 5 0 00000186 15 116 1382 -272 -354 0 yyyyyf 122 -333 Easiteach 39 15 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 _______________________________________ 16 0 499200 39 55 -15 0 1 0 23 5 0 00000524 15 116 1382 -348 -430 0 yyyyyf 122 -409 Easiteach 39 16 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 _______________________________________ 16 0 499200 39 55 -15 0 1 0 23 5 0 00000524 15 116 1382 -424 -506 0 yyyyyf 122 -485 Easiteach 39 17 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 _______________________________________ 16 0 499200 39 55 -15 0 1 0 23 5 0 00000524 15 116 1382 -501 -583 0 yyyyyf 122 -562 Easiteach 39 18 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 _______________________________________ 16 0 499200 39 55 -15 0 1 0 23 5 0 00000524 15 110 1376 -795 -877 0 yyyyyf 116 -856 Easiteach 39 19 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 _______________________________________ 16 0 499200 39 55 -15 0 1 0 23 5 0 00000524 15 110 1376 -871 -953 0 yyyyyf 116 -932 Easiteach 39 20 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 _______________________________________ 16 0 499200 39 55 -15 0 1 0 23 5 0 00000524 60 66 0 0 61 8 61 9 61 10 61 13 60 67 0 0 61 2 61 6 61 4 61 3 13 0 -1150 1488 0 H:\Lesson_plans\Year_11\11R1\Algebra\Proof\Algebraic_proof.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 1 0 0 -1 -1 -1 0 65536  0 0 0 0 4 0 1557 0 0 0 2318 0 14 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 15 309 1095 -243 -380 0 yyyyyg 315 -348 Easiteach 17 1 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Lesson Objectives 16 0 307200 17 99 -26 0 1 0 23 8 0 00000024 23 9 0 00000065 23 5 0 00000508 15 126 1357 -548 -640 0 yyyyyg 132 -617 Easiteach 46 2 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 To be able to use algebraic proof confidently. 16 0 485200 46 63 -17 0 1 0 23 8 0 00000017 23 4 0 3800A800 23 5 0 00000515 3 nnn 155 0 41 82 2359 1871 0 0 0 0 nnnnnnnnn 2400 1920 0 0 0 0 1 98 0000FF00 0000FF00 1 1 1 MultimediaBank AAmine C:\Program Files\Research Machines\Easiteach\Skins\graphic.xml1280,1024011897199121141210711001629116912516591169101301311331150851116910211031105110911111105881929207110617109213071251108936402106111411071115111055781912211231124112613000266525300113002130031300413005130061300713008130091301213014130131310026662531021310313104131051310613107131081310911111320026642532011320513206132071320813209132101330026682533021330313304133051330713308133091331013400661125340213409150006131202151006441202110130131133135002667258500733625850319300733525105006601202110600690120211013013113315800738108985031 13 0 -1150 1488 0 H:\Lesson_plans\Year_11\11R1\Algebra\Proof\Algebraic_proof.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 8 0 0 -1 -1 -1 0 65536  0 0 0 0 3 0 1557 0 0 0 0 0 15 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 15 41 1333 -179 -261 0 yyyyyg 47 -240 Easiteach 56 1 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 The mean of five consecutive integers 1, 2, 3, 4, 5 is 3 16 0 509600 56 55 -15 0 1 0 23 5 0 00000518 15 48 729 -313 -395 0 yyyyyg 54 -374 Easiteach 28 2 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 The square of this mean is 9 16 0 265200 28 55 -15 0 1 0 23 5 0 00000573 15 53 1399 -460 -542 0 yyyyyg 59 -521 Easiteach 55 3 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 The mean of the squares of those 5 consecutive integers 16 0 531200 55 55 -15 0 1 0 23 4 0 3800A800 23 5 0 00000563 15 61 630 -577 -659 0 yyyyyg 67 -638 Easiteach 29 4 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1 , 2 , 3 , 4 , 5 is 11 16 0 220400 29 55 -15 0 1 0 23 4 0 3800A800 23 5 0 0000055B 15 83 118 -575 -629 0 yyyayf 89 -614 Easiteach 1 5 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 6800 1 33 -9 0 1 0 23 8 0 0000000C 23 9 0 0000005F 23 4 0 3800A800 23 5 0 000004F2 15 168 203 -574 -628 0 yyyaye 174 -613 Easiteach 1 6 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 6800 1 33 -9 0 1 0 23 8 0 0000000C 23 9 0 0000005F 23 4 0 3800A800 23 5 0 0000047A 15 243 278 -576 -630 0 yyyaye 249 -615 Easiteach 1 7 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 6800 1 33 -9 0 1 0 23 8 0 0000000C 23 9 0 0000005F 23 4 0 3800A800 23 5 0 00000405 15 318 353 -574 -628 0 yyyayd 324 -613 Easiteach 1 8 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 6800 1 33 -9 0 1 0 23 8 0 0000000C 23 9 0 0000005F 23 4 0 3800A800 23 5 0 000003CB 15 396 431 -574 -628 0 yyyayd 402 -613 Easiteach 1 9 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 6800 1 33 -9 0 1 0 23 8 0 0000000C 23 9 0 0000005F 23 4 0 3800A800 23 5 0 00000366 15 69 1370 -715 -917 0 yyyyyd 75 -776 Easiteach 134 10 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Prove algebraicly that the mean of any 5 consecutive integers squared is always 2 less than the mean of the squares of those integers. 16 0 493200 52 55 -15 0 1 0 16 53 513200 54 55 -15 0 0 0 16 108 244000 26 55 -15 0 0 0 23 5 0 00000553 23 18 6 00000079 23 4 35 0000FF00 23 4 38 FFFFFFFF 23 4 73 0000FF00 23 4 79 FFFFFFFF 15 95 601 -7 -175 0 yyyyyc 101 -136 Easiteach 9 11 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Have a go 16 0 195200 9 123 -33 0 1 0 23 5 0 000001FA 23 8 0 0000002D 23 9 0 00000063 23 4 0 0000FF00 15 584 671 -28 -168 0 yyyyyc 590 -135 Easiteach 3 12 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 ... 16 0 27600 3 101 -27 0 1 0 23 8 0 00000025 23 9 0 00000062 23 4 0 0000FF00 23 5 0 00000345 13 0 -1150 1488 0 H:\Lesson_plans\Year_11\11R1\Algebra\Proof\Algebraic_proof.et nnyn 45 0 1 1 0 1 0 0 n 0 0 FFFFFF00 n 0 65536 0 0 00000000 0 0 0 0 0 UK_English 7 0 0 -1 -1 -1 0 65536  0 0 0 0 1 0 1557 0 0 0 2318 0 64 0 1 8 0 0 20 Voting Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCell Comic_Sans_MS 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 VotingCross Wingdings 100 14 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 0 0 0 nn 20 Bullet_list Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 -15 n 15 25 25 yn 20 Chart_text Arial 100 10 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Easiteach Comic_Sans_MS 100 20 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yy 20 Heading Arial 100 16 00000000 FFFFFF00 0 120 70859 lynny 120 0 n 20 0 0 yn 20 Hypertext Arial 100 12 FF770000 0000FF00 0 120 1098 lnnyy 120 0 n 0 0 0 nn 20 Junior Arial 100 28 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 20 25 25 yn 20 MyEasiteach Copperplate_Gothic_Bold 100 20 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Paragraph Times_New_Roman 100 12 00000000 FFFFFF00 0 120 70859 lnnyy 120 0 n 15 25 25 yn 20 Question_text Comic_Sans_MS 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 15 25 25 yn 20 Spreadsheet_buttons Arial 100 12 00000000 FFFFFF00 0 120 70859 lnnny 120 0 n 20 25 25 yn 20 Text_selection Arial 100 12 FFFFFF00 A0A0A000 0 120 1098 lynyy 120 0 n 0 0 0 nn 21 VotingInner 0 2 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 VotingOuter 0 5 FFE0D200 FFE0D200 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Algebra_card 0 2 00000000 F0F0F000 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Answer_box 0 2 00000000 EFC2C200 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart 0 2 00000000 EFEFEF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Chart_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Entry_field 0 2 00000000 FFFFFF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 ETRotate 0 0 FF000000 00FF0000 nyn 00 0 yn 0 n nn n 00000000 00000000 0 0 n 21 Filled 0 2 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Group_selection 1 2 C0C0C000 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Markup 0 10 00000000 FFFFFF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Outline 0 2 00000000 FFFFFF00 nyy 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Printer_limits 0 0 A0A0A000 A0A0A000 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Question_box 0 2 00000000 F5C4F700 ynn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Rotation_tag 0 0 00FF0000 00FF0000 yyn 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection 1 0 0000DD00 DDDDDD00 nyy 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Selection_tag 0 0 0000DD00 0000DD00 yny 00 0 nn 0 n nn n 00000000 00000000 0 0 n 21 Shadow 0 2 BBBBBB00 80808000 yny 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Snipping_cross 0 0 00000000 DDDDDD00 nyy 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Table_frame 0 5 00000000 FFFFFF00 yyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Table_grid 0 2 00000000 EFEFEF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Text_flows 0 5 88888800 88888800 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Tree_lines 0 10 FF000000 0000FF00 nyn 00 5 yn 0 n nn n 00000000 00000000 0 0 n 21 Word_builder 0 5 C0C0C000 E8E8E800 yyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 21 Writing_Frame 0 5 FFFF0000 0096FF00 nyn 00 5 nn 0 n nn n 00000000 00000000 0 0 n 85 Round l Wingdings -2147483648 100 85 Roman I TimesNewRoman 0 100 85 Number 1. TimesNewRoman 0 100 85 Letter (a) CourierNew 0 80 85 Diamond t Wingdings 0 100 85 Star Wingdings 0 100 85 Flower | Wingdings 65280 100 85 Hand F Wingdings -2147483648 100 85 Note ! Wingdings -2147483648 100 15 48 326 -38 -120 0 yyyyyg 54 -99 Easiteach 11 5 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 Prove that: 16 0 104000 11 55 -15 0 1 0 23 4 0 3800A800 23 5 0 0000056D 15 53 1198 -113 -195 0 yyyayg 59 -174 Easiteach 44 6 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 1. Sum of 2 consecutive numbers must be odd. 16 0 450919 44 55 -15 0 1 0 23 4 0 3800A800 23 5 0 00000568 15 53 1317 -201 -283 0 yyyayg 59 -262 Easiteach 49 8 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2. Sum of 2 consecutive odd numbers must be even. 16 0 498519 49 55 -15 0 1 0 23 4 0 FF702800 23 5 0 00000568 15 54 1343 -298 -440 0 yyyayg 60 -359 Easiteach 66 11 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 3. Product of 2 consecutive even numbers must be a multiple of 4. 16 0 508519 50 55 -15 0 1 0 16 51 166919 15 55 -15 0 0 0 23 4 0 3800A800 23 5 0 00000568 15 53 1452 -445 -587 0 yyyayg 59 -506 Easiteach 98 15 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 4. If you multiply 2 consecutive odd numbers and then add 1, the result will be a multiple of 4. 16 0 552747 54 55 -15 0 1 0 16 55 411719 43 55 -15 0 0 0 23 4 0 FF702800 23 5 0 00000568 15 53 1415 -590 -732 0 yyyayg 59 -651 Easiteach 82 19 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 5. If you add 3 consecutive numbers and then subtract 2, you get a multiple of 3. 16 0 537719 53 55 -15 0 1 0 16 54 281719 28 55 -15 0 0 0 23 4 0 3800A800 23 5 0 00000568 15 55 1410 -739 -941 0 yyyayg 61 -800 Easiteach 136 22 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 6. For any 4 consecutive numbers, the product of the middle 2 numbers is always 2 more than the product of the first and last numbers. 16 0 521719 52 55 -15 0 1 0 16 53 534919 51 55 -15 0 0 0 16 105 321319 31 55 -15 0 0 0 23 4 0 FF702800 23 5 0 00000568 15 53 1318 -941 -1083 0 yyyayg 59 -1002 Easiteach 75 23 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 7. There is only 1 prime number of the form k - 1 where k is an integer. 16 0 498919 51 55 -15 0 1 0 16 52 242519 23 55 -15 0 0 0 23 4 0 0000FF00 23 5 0 00000553 15 1179 1213 -942 -992 0 yyyyyg 1185 -978 Easiteach 1 24 n 0 nny 0 16777248 0 0 0 0 0 0 0 0 0 2 16 0 6400 1 30 -8 0 1 0 23 5 0 0000005A 23 8 0 0000000B 23 9 0 00000061 23 4 0 3800A800 26 1247 1434 -37 -174 0 nyyyyf 1 33 n 0 0 0 0 0 0 0 0 nnn 0 y 0 0 60 68 0 0 61 24 61 23