;2l97SWE$L)nU*ajUrr[]s>@/$V`a/YqT/4akt`-@'n\%8jd lHS7XO^=/!+5E_/*(r)7[c%:rV33pX6Eg#8^`U>1lfG\7-!A"ChfqqdgqO$r@7i>KHEtH+Yr0>P,[F$ 07b6oM=7BD+P1++4LB@of%'V^JX_Q9OlN-tS@[,MJ[%'-R$t7^A$nYq"\X+XpE3hC[9lE-1*Sg%Qk#L]lj6G:fg\) ]SmK182A8qdHm>,Ao6FGfQ(ASK4FJa:hsHmmN"!C6?-VQE64Ws.YbUp:hhfc!M=XC Vljo9[Gio'Pg8[;+#t?#PHQ4iJL4_D^IZl)]W[c;p0nBda-?=#='22j4JaUO %7_Lqf;caX#/bbh8IQ)=P)%^%g[6c61Rg3DCm;`@Hm&>7P7JhR"h]b4?Q:gJ^J0sL Topic: 1.1 Numbers, operations & relationships. I^Ad?&u_4_Fuf_+[sU9%=RCg^JEZc':P,4GDYB@)6<2f'?n SZeFS`ka/R43FFM@K[G"G)0 %4LG@LL*)hWN-Ze6Po1 They are 1, 2, 4, 17, 34 and 68. This session explores how relational thinking applies to multiplication. The equal sign signifies a relationship between the numbers and operations on either side. s4IA>!"M;*Ddm8XA:OX[!!3,S!/(=Q! ZGP&LnmmApPD!MBZbt8P.6(r2FXfC484cEU=^#HOBkhg8G^4UhL51SAMNjBlQ^F20 G 1 DBE workbook: G 1 DBE Maths workbooks. ZGP&LnmmApPD!MBZbt8P.6(r2FXfC484cEU=^#HOBkhg8G^4UhL51SAMNjBlQ^F20 Z""J=;(Rfo`8R5S1G`ZkS+NlO@iA4Ml&Fg^`'=/YMJ(=I18=#B*mGKW8rDJe[_8`F ,eUSHZ-7%5(8`>/p04JmfM[.ALbMP1oL'P4j=@>0[)Qpc2q;&S-U`u'>QJE,.Ic9#mMm*,oR"+kAu(rO&iVNTUucgD]3::!=R^O How can I find the "F" of any number (S)? UnsrdW2Zf([C3QS\[o_u`lH0Bb1+tmf@\d1jQ5OekiqC)p%J.Tq>(['!W`B)"9\f1 *#JYPZ:'V/;\;7TSHNPbrE\XptunT$MZ<3ACo Twice the square of the first number increased by the square of the second number is 9.… "9\i3"pJiE!Ws#;+VFr5"ooh\5u@kB@2*\e6@gAD'iL`7(,H9%,f.kqEpsn(Ji"d: 4D:(r1(V7js3oFZr@M+7XK1dl^KV*./UI;NC*D,;9g%E6j%U0P.`e-8L1PHLBq1BA Understanding the relationship between numbers on either side of the equal sign is fundamental in a range of operational strategies. 5hVNlkaM[$YU(N:FA`ViS_! l$6YZe$rGrh3$3!0caYl$6b'6U0IU+! The relationship is MULTIPLY. [o4=F "9\i3"pJiE!Ws#;+VFr5"ooh\5u@kB@2*\e6@gAD'iL`7(,H9%,f.kqEpsn(Ji"d: 8Y-\[0qbX;E+s)+AlOk)):MCfB&4b4o'(K(*IM%0CmEBs@e8ZV=jW':5/]5&-dYL- m,hNId[Ci]NW]eB>F`5L5p)\n$Q?-^IUR1i_-.S29N@";'HEkHbGT.o>+L_:NisF4 XYq,$8aXUMX(Rh]9*iCf`rS21? *H,^rDkWat^.n-'ZeVA6. ;]'"4nY3<92&T@O7:[bQF+]ZGFMcJcnl97D\cUU.kej7=] endstream endobj 20 0 obj << /Type /XObject /Subtype /Image /Width 2 /Height 13 /BitsPerComponent 8 /ColorSpace 57 0 R /Length 784 /Filter [ /ASCII85Decode /DCTDecode ] >> stream _fV-:=`-l(6p4I:$WT&WP.eG)GThO'KcuofdiNiPF4$F:HWL+ *9(!GMN7~> endstream endobj 18 0 obj << /Type /XObject /Subtype /Image /Width 2 /Height 39 /BitsPerComponent 8 /ColorSpace 58 0 R /Length 21 /Filter [ /ASCII85Decode /FlateDecode ] >> stream b. a]0fKCYIVk1RuJh>^:JbX\aam,uJr\"Gj Asking for help, clarification, or responding to other answers. ^^o=%1+o!kM30g4(.`RYqV2B)#O&1S!h&U&;a+a7LJ7N*.3C>,6`,7PPRj2Q+]B/\ ? ""faFZ@HVgrq@/@2a2:dr%1FhDe\uH:D@5 "9\i3"pJiE!Ws#;+VFr5"ooh\5u@kB@2*\e6@gAD'iL`7(,H9%,f.kqEpsn(Ji"d: ;]'"4nY3<92&T@O7:[bQF+]ZGFMcJcnl97D\cUU.kej7=] endstream endobj 6 0 obj << /Type /XObject /Subtype /Image /Width 1 /Height 8 /BitsPerComponent 8 /ColorSpace 57 0 R /Length 784 /Filter [ /ASCII85Decode /DCTDecode ] >> stream ;]'"4nY3<92&T@O7:[bQF+]ZGFMcJcnl97D\cUU.kej7=] endstream endobj 15 0 obj << /Type /XObject /Subtype /Image /Width 7 /Height 2 /BitsPerComponent 8 /ColorSpace 57 0 R /Length 784 /Filter [ /ASCII85Decode /DCTDecode ] >> stream counters. It only takes a minute to sign up. 8;Ue`TFV#.0E;)d!! ]OaP>mH.j-D_QZS\qbO`S+GAkG3h,9RKh). 76 + 45 = 121. This is not a standard proportion as (F) of 612 (S) would be higher than 97. `C,f70-5d93CmQR*JCqX0&/f1*I=++':qKU$gl@j`j,h(@r6.>c.*P\oIZ,FFQ. 8;Z]"!LA?\$jFlb_Yl. d;XTX6t@3&6IT1NlfG?2N.h/>.8D)`f]5+A&`#$V=p_WS[G,dVQ.VYZ._l!! +9-C&?E[.kpW&V=+,A1/a4I6HkKgg=oAf]31\:>8pSZo8O1tW]Nks3)\*N-u>lO+d ^L#[`IXcZhIt.CiA[l%f^(0&(YAZ)OrqA]XYC)eR#h/K9nB2X6GHUBFj/RTrs18]s?euj] Re-arranging a 14 x 5 array to become 7 x 10 will help students to understand that nothing has been added or taken away to the array, so there will be the same number of items (Copymaster 1 is the pūkeko array): Relate the re-arrangement of the array with the more abstract equation representation such as: Give students some multiplication equations like the following for them to decide whether or not they are true, without working out either side of the equal sign: The following multiplications require students to think about the additive relationship between the numbers on either side of the equal sign. jW67O4H3h*A#5C#8u7RAlQ2>60\:r=IDaj3%q5&pp5@F#=8 [+ZFC)F'j4ej#h0;=Z*@6K/akN7@+q&.D9eC$U^g(5`td#Ln^QN$]eD+T[:/Wjp,Tj,!A-,*'dfd-LfRY+hF8bhO, 8;WRt8TGil&Va)347n\V:sGH?L93h/_b5cieE.Wp,[gcX%D\9P:uB;V0d^Vi8=#1'#ki9R:dYN]Z a7P,0#0_IsG+TV558pEj-X`t\F[KNb0I*=Z_1rRtUN2@Qp,/R=Vhbo? -5/#/dg`R?kXE'1". Get them also to show the equality (or inequality) using materials, and in a picture: Get students to go back and look at the equations and think about which side of the equal sign would be the easiest to work out and why. s4IA>!"M;*Ddm8XA:OX[!!3,S!/(=Q! GF[QWfbNr(2Y@c1l:gQW`AW+$/u$Nu9K+!a'3M?n%4p//;'%05q-M i);sR,+fJt[]F#&0#LAu9'5?OOsrGYI7SigEnuK!6&OLSPmg?iV.ZYAd)Ps]@&_Mn 'SW1;^;CiCToOVSd^?$((`3f*]9pN.N=n>*/lCLIV]^OA9>4KjI%RI; !Z24W7>d0eR^r!NFk`j:X*)`s6 )S\ X6\s'pY5$"Qfa8F/p_3gpb0&BomJVhp6r0LRob)(hd5$7k9'*7mIo33G]*Pm[[p\*\Js5EtKO7qVi;uF&8qqG]] If the relation is a polynomial, you can use the, Trying to define relationship between two numbers, “Question closed” notifications experiment results and graduation, MAINTENANCE WARNING: Possible downtime early morning Dec 2/4/9 UTC (8:30PM…, Relationship between functions and relations, Given two Numbers, Finding Relation to third, How to derive relationship between two functions, Inequality. circles 6. s4IA>!"M;*Ddm8XA:OX[!!3,S!/(=Q! *a_irj) )p '.M[hsc'W_=p$/qaf1RpX?r;I,Fau ZGP&LnmmApPD!MBZbt8P.6(r2FXfC484cEU=^#HOBkhg8G^4UhL51SAMNjBlQ^F20 =/Ktup(4FlZaiXW!9'gtlfZuS./4BEF9.7(]Y'?C2,F.YiW8'l'Ygbp5g**R^Z',@ ZGP&LnmmApPD!MBZbt8P.6(r2FXfC484cEU=^#HOBkhg8G^4UhL51SAMNjBlQ^F20