White Rose Maths Key Stage 3 Behind the Questions Teacher Guide 3
Ian Davies, Caroline Hamilton and Sahar Shillabeer
00934_P001_144_WRM_TG3.indd 1
01/07/2021 10:20
%# % # ! $ ),11&+$ +! /" !&+$ $/ -%0 / !&"+10 +! &+1"/ "-10 .2 1&,+0 ,# )&+"0 2/1%"/ $/ -%0
# $ ' "& % $ +(+,4+0 ,+ ,+" 0&!" +".2 )&1&"0 4&1% +"$ 1&3" +2* "/0 +(+,4+0 ,+ ,1% 0&!"0 ,)3&+$ -/, )"*0 4&1% ".2 1&,+0 +! &+".2 )&1&"0 " // +$&+$ #,/*2) "
$% %&# $ /,-"/1&"0 ,# +2* "/ ,,(&+$ #,/ 1/21% %" ',2/+"6 1, -/,,# %" ',2/+"6 1, -/,,# " / %&+$ #,/ - 11"/+
# $ $ ! $ +1, 1%/"" !&*"+0&,+0 "10 +! ,1%"/ !& $/ *0 2/# " /" 2/# " /" ,)2*"
$%#& % $ #& ( ,+01/2 1&,+0 0, # / +1/,!2 &+$ ), & "/-"+!& 2) /0 ,/" ), & ,+$/2"+ "
& #$ ,/(&+$ 4&1% +2* "/0 01&* 1&,+ ,)3&+$ -/, )"*0 4&1% +2* "/0 / 1&,+0 1 +! /! #,/*
# % $ "/ "+1 $" 0& 0 "3"/0" -"/ "+1 $"0 ,)3&+$ -"/ "+1 $" -/, )"*0 "-" 1"! -"/ "+1 $" % +$"
% $ ( +1"/-/"1&+$ &))0 +! 01 1"*"+10 +1"/"01 5"0 ,)3&+$ -/, )"*0 4&1% *,+"6
00934_P001_144_WRM_TG3.indd 3
01/07/2021 10:20
"
' & "! -&+$2 1$5($6 ' (-2 .% 1$ 2.-(-& -&+$2 -# +&$!1 $.,$31(" ".-)$"341$2
" "& & "!% ! &$ !% & "!%
7,,$317 .3 3(.- 1 -2+ 3(.-2 -# !$7.-#
" )& "$ %* & "$
.1*(-& 6(3' 1(&'3 -&+$# 31( -&+$2 (-#(-& 4-*-.6- 2(#$2 $7.-# 31( -&+$2
" ! $ !& ! % $ &)
+"4+ 3(-& 6(3' $-+ 1&$,$-3 -+ 1&(-& 2' /$ -+ 1&(-& 2' /$ .1$ 2(,(+ 1(37
" " ( ! $ & " ! #$"#"$& "! #$" %
(1$"3 /1./.13(.- 1$5($6 -5$23(& 3(-& (-5$12$ /1./.13(.- 3(. 1$5(2(3$# $23 !472
" & %
/$$# #(23 -"$ -# 3(,$ $-2(37 -# 4-(32 3$2 -# &1 /'2
" $" &)
1.! !(+(37 .% .-$ $5$-3 .1$ 3' - .-$ $5$-3 1.! !(+(3($2 -# 31$$ #( &1 ,2
" $ $ #$ % !& & "!%
413'$1 &1 /'2 (,4+3 -$.42 $04 3(.-2 1 /'2 .% (-$04 +(3($2
" && ! $ ) "$ ) &
-#+(-& # 3 1$5($6 $04$-"$2 1$5($6 .5(-& .- 6(3' 31(&.-.,$317
00934_P001_144_WRM_TG3.indd 4
01/07/2021 10:20
• 6.*-0# $ !2-01 +3*2'.*#1 ," .0'+#1
&'1 1&-02 !& .2#0 .0-4'"#1 0#4'#5 -$ .0'-0 *# 0,',% -32 $ !2-01 +3*2'.*#1 ," .0'+#1 *2&-3%& 2&#1# 2#0+1 0# '+.-02 ,2 ', 2&#'0 -5, 0'%&2 123"#,21 5'** ,##" 2- 0#*7 -, 2&'1 ),-5*#"%# 5&#, 2&#7 #6.*-0# !-,(#!230#1 -32 ,3+ #01 ', 2&# -2&#0 !& .2#01 ', 2&'1 *-!) 0'+# "#!-+.-1'2'-, '1 0#4'1'2#" ," -2& 2&# 8* ""#0 +#2&-"9 ," 2&# 8$ !2-0 20##9 +#2&-" 5&'!& 5 1 31#" ', 2&# # 0*'#0 --)1 0# "#+-,120 2#" 7 2&# #," -$ 2&'1 !& .2#0 123"#,21 1&-3*" # $*3#,2 2 0#!-%,'1',% .0'+# ,3+ #01 #4#, ,3+ #01 +3*2'.*#1 -$ ," -"" ,3+ #01 ,-, +3*2'.*#1 -$ ," 2 '"#,2'$7',% -2&#0 +3*2'.*#1 ," $ !2-01
• -,$31',% 2&# 2#0+1 8$ !2-09 ," 8+3*2'.*#9 +.& 1'1# 2& 2 +3*2'.*# '1 2&# 0#13*2 -$ +3*2'.*'! 2'-,
• 3*2'.*'! 2'-, ," "'4'1'-, 1)'**1 • 1',% 00 71 ," 0 +-"#*1 2- 1-*4# .0- *#+1
• &',)',% 2& 2 '1 .0'+# ,3+ #0 +.& 1'1# 2&# "#$','2'-, -$ 8.0'+#9 1 & 4',% #6 !2*7 25- $ !2-01 0 2&#0 2& , 8! ,,-2 # 1.*'2 3.9
• &# 2#0+1 $ !2-0 ," +3*2'.*# 5'** # +#2 % ', 5&#, ," 0# 0#4'1#" ', *-!)
• 0# 1 -$ 0#!2 ,%*#1
• 00 71 0# 4#07 31#$3* $-0 1&-5',% 2&# $ !2-01 -$ ,3+ #0 ," 2- 3'*" 3. +3*2'.*#1 , 00 7 *')# 2&'1 ! , # 31#" 2- %#,#0 2# 1 + ,7 1#,2#,!#1 1 .-11' *# 31',% 2&# 5-0"1 8$ !2-09 ," 8+3*2'.*#9 2- !&#!) 123"#,21: 3,"#012 ,"',% -3 ! , *1- #6.*-0# 2&# 00 71 $-0+#" 7 .0'+# ,3+ #0 • &# +3*2'.*'! 2'-,1 ," "'4'1'-,1 1&-5, 7 0 +-"#* ! , *1- # 31#" 2- %#,#0 2# 1#,2#,!#1 31',% +3*2'.*#1 ," $ !2-01 -3 ! , *1- 5-0) 2&# -2&#0 5 7 0-3," 7 1)',% 123"#,21 2- 8 0 5 0 +-"#* 00 7 2- 1&-5 2& 2 '1 $ !2-0 +3*2'.*# -$ 9 • !2-0 20##1 0# 2&# + ', 4#&'!*# 31#" $-0 $',"',% .0'+# "#!-+.-1'2'-, 5&'!& 3'*"1 -, 2&# *# 0,',% $0-+ # 0*'#0 --)1 1 !-+. 0'1-, 2&# * ""#0 +#2&-" '1 ',!*3"#" ," '2 +'%&2 # 31#$3* 2- !-+. 0# ," !-,20 12 2&# +#2&-"1 ', !* 11 "'1!311'-, &# 1712#+ 2'! ..0- !& -$ 5-0)',% 2&0-3%& 2&# .0'+#1 ', -0"#0 2& 2 2&# * ""#0 +#2&-" #+.*-71 + 7 # 31#$3* $-0 123"#,21 5&- $'," '2 "'$$'!3*2 2- 1.-2 $ !2-01
3#12'-, '1 4#07 1'+.*# /3#12'-, 2- .0-+-2# "'1!311'-, -$ +3*2'.*#1 ," . 22#0,1 5'2&', 2&#+ 3#12'-, *--)1 2 2&# !03!' * ,##" 2- 0#!-%,'1# #4#, ," 2&#0#$-0# -"" ,3+ #01 ," /3#12'-, .0-4'"#1 1-+# +3*2'.*'! 2'-, $*3#,!7 .0 !2'!# $ 123"#,21 0# ,-2 !-,$'"#,2 5'2& 2&# 2'+#1 2 *#1 2&#7 !-3*" !!#11 2&# !-,2#,2 -$ 2&# !& .2#0 31',% ! *!3* 2-0 1- 2& 2 2&#7 12'** ..0#!' 2# 2&# *# 0,',% .-',21
23"#,21 ! , "0 5 2&# 00 71 $-0 13..-02 '$ ,##"#" ,!-30 %# 2&#+ 2- + )# 1#,2#,!#1 31',% 2&# 5-0"1 8$ !2-09 ," 8+3*2'.*#9 1 5#** 1 2- 50'2# "-5, 2&# +3*2'.*'! 2'-, ," "'4'1'-, $ !21 % ', 123"#,21 ! , # !& **#,%#" 2- 31# 2&# 5-0" 8+3*2'.*#9 1 5#** 1 2&# 5-0" 8$ !2-09 -3 !-3*" *1- 0#.0#1#,2 2&# 00 71 1 0#!2 ,%*#1 -$ 1+ ** 1/3 0#1 ," + )# 2&# *',) 2- 0# 23"#,21 1&-3*" # *# 2- ,15#0 2&'1 /3#12'-, 31',% 2&#'0 ),-5*#"%# -$ 2'+#1 2 *#1 -3 !-3*" 31# 2&'1 1 2&# 1'1 $-0 "'1!311'-, -32 &-5 2- 0#!-%,'1# +3*2'.*#1 -$ ,3+ #01 ," ',!*3"# $-0 #6 +.*# 31',% 0#.# 2#" "'4'1'-, 7 2- '"#,2'$7 +3*2'.*# -$
00934_P001_144_WRM_TG3.indd 28
01/07/2021 10:20
% ,0". .+,".0&"/ +# *1) ". *! !"2"(+, 0%" &!" / +# 0%" % ,0". *! $+ +* 0+ ."2&/" 0%" +* ",0 +# ,.&)" *1) ". 3%& % * " &((1/0. 0"! 1/&*$ * .. 5 3&0% /&*$(" .+3 +. +(1)* +*(5 ."2&/"/ 0%" 1/" +# # 0+. 0.""/ 0+ #&*! 0%" ,.&)" !" +),+/&0&+* +# *1) ". / +2"."! &* ++' ++' +10 #+. /01!"*0/ &* (1!&*$ 1**" "// .5 / *! /,(&00&*$ 5 !!&0&+* . 0%". 0% * )1(0&,(& 0&+*
(++'/ 0 ("// +))+* # 0+.&/ 0&+*/ +# *1) "./ 0% 0 % 2" "4 0(5 03+ ,.&)" # 0+./ (("! /")& ,.&)" 01!"*0/ +1(! &*2"/0&$ 0" *1) "./ +# 0%&/ #+.) #1.0%". &# !"/&."! #+. "4 ),("
&/ /"0 +# 0%."" +*/" 10&2" /")& ,.&)"/ "4,(+."/ 1/&*$ +*" ,.&)" # 0+.&/ 0&+* 0+ #&*! 0% 0 +# ."( 0"! *1) ". $ &* 0%&/ +1(! " "40"*!"!
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
"." )+." #(1"* 5 ,. 0& " &/ ,.+2&!"! 1"/0&+* "4,(& &0(5 (++'/ 0 0%" ." )+!"( / * (0".* 0&2" 0+ 0%" .. 5
* +1. $" /01!"*0/ 0+ "4,(+." +!! *! "2"* *1) "./ ,.&)"/ "0 %&/ ,.&)" $"*". 0+. #+. 0+ /%+1(! ,.+2+'" &*0"."/0&*$ !&/ 1//&+* (++'/ %" ! 0+ $"*". (&/&*$ 0%" *1) ". +# ,.&)" # 0+./ +# *1) ". $&2"* &0/ ,.&)" # 0+.&/ 0&+* * +1. $" /01!"*0/ 0+ "4,(+." 0%" !&2&/& &(&05 +# "4,+*"*0/ 0+ ..&2" 0 0%" $"*". (&/ 0&+*
+1 +1(! !&/ 1// /01!"*0/9 ,."#".."! )"0%+!/ #+. # 0+.&/&*$ ( .$" *1) "./ / &0 0%" / )" +. !&##"."*0 #.+) %+3 0%"5 3+1(! 0 '(" /) ((". *1) "./
00934_P001_144_WRM_TG3.indd 29
01/07/2021 10:20
• ' -+ ' "+, & *'% ('"&, • ' -+ ' "+, & *'% +,* " !, $"& +! (
& ,!"+ ! (, * +,- &,+ '&+" * ,! % &"& ' ,! /'* 2$' -+3 + + , ' ('"&,+ ,! , + ,"+ 1 ". & *-$ ! +- +, ((*' ! "+ ,' -+ '"&+ & '-&, *+ ,' ! $( ,' +-(('*, ,! "* ."+- $"+ ,"'& ' ,! ( ,!+ & ,! & ,' '&+,*- , ,! + -* , $1 -+"& '% ,*" $ )-"(% &, , "+ /'*,! "&. +,"& +- " " &, ,"% "& ,! *$1 +, + '* +,- &,+ ,' '% %"$" * /",! ,! , *% + ", "+ $"# $1 ,' & / '' %','* +#"$$+ * & ,' '&+,*- , $' " -* , $1 "% +( &, '&+,*- ,"& ( ,, *&+ -+"& '* 0 %($ '. *$ (("& "* $ + "+ '' / 1 ' ! $("& +,- &,+ ,' . $'( ,! + +#"$$+
• " " -$,1 /",! ,! -& %"$" * $ & - ' ! $( • ! +#"$$+ ' ! (, * * -"$, -('& ',! "& +,- &,+ ,' * % % * ", ( *+"+, /",! ,! -+ ' ,! -+ ' ( "*+ ' '%( ++ + & '* * /"& (* "+ % ,! % ," $ $ & - ,!*'- !'-, ,! " * %+ ,' +"%($ + $ ! (, * & ,*1 ,' "&,*' - ,! '& (, ' $' -+ • '&+,*- ,"'& ' + &', "&, *$ . +"$1 "&,' ',! * /! & +,- 1"& ',! * $' #+ * + ' ,! -**" -$-% +' ", %" !, /'*,! • " " -$,1 -+"& ( "*+ ' '%( ++ + ,- &,+ % 1 + ,,"& +" +( " " ,"% + ,' (* ,"+ ,!"+ '* & ,' * %"& ,' !'$ ,! '%( ++ + , ,! 0 %($ "& +, *, * ,"."," + 1 , *%+ +- ! + ,'( * ,! * ,! & , ,! *% 2$' -+3 & * "& '* "& ,! + % / 1 • $-&, ( & "$+ % # " * %+ * $ ++ -* , +' 1'- % 1 & $ * +-(($1 ' +! *( & *+ & * + *+ • '"&+ & '-&, *+ * -+ -$ '* ',! & * ,"& ,! +! ( + ' ,! $' " +,- " "& ,!"+ ! (, * & ,' "$$-+,* , ,! & '* ,! -+ ' '% ,*" $ )-"(% &, ,' (*' - -* , * ,! * ,! & ((*'0"% , + ,+ ' ('"&,+ - +, ,"."," + * (*'." "& ,! 0 * "+ + & 1'- & . *1 ,! "+, & + & $' " + * )-"* • 2 -% & '% ,*13 "+ -& $, *& ,". ,! , & -+ "& $ * *''% '* ,! ($ 1 *'-& ,- &,+ & (*'." /",! % ,* +," #+ '* , ( % +-* + & +# ,' +, & *, "& "+, & % *'% ('"&, '* / $$ + )- +,"'& ' * ,"
- +,"'& (*'." + (*' " " & 1 (* ," , -+"& ( "* ' '%( ++ + & )- +,"'& ! #+ ,! , +,- &,+ * % % * ,! " * & ,/ & ,! * "-+ & " % , * ' "* $ - +,"'& (*'." + %'* (* ," , -+"& ( "* ' '%( ++ + '- '-$ "&.", +,- &,+ ,' * , ,! "* '/& +" &+ '* ,' + !'/ +% $$ ,! 1 & -* , $1 (*' - ,! '& ". & ,' (*'%', ,! . $'(% &, ' ,! "* %','* +#"$$+ & -* 1
,- &,+ & -+ " * &, "+, & + ,' * ! ,! & * $ * +-$, ,! , ,! $' -+ ' ('"&,+ , *, "& "+, & *'% "0 ('"&, "+ "* $ '- '-$ $+' "+ -++ -+"& ,! '*& * ' +# ,' (*' - )- * &, ". + (* ," , "&, *(* ,"& ,! '*% $$1 (!* + * )- +, '* $' -+ ,! , "+ "* $ /", ( *, "&,*' - "& ,! + , ' ('"&,+ "&+" ,! "* $ "+ -++ ,! & '* (* "+ $ & - /! & + *" "& $' " . $'(+ ,! " + *'% )- +,"'& ,' $''# , $' " "& 1 %'* ,! & '& + , ' * )-"* % &,+ '- '-$ 0, & ,!"+ 1 +! "& +'% * "'&+ & +#"& +,- &,+ ,' + *" ,! %
00934_P001_144_WRM_TG3.indd 50
01/07/2021 10:20
'+ ) %+)& , % #& % - #&' + * %+)& , % (, *+ &% # %"* +& + &%*+), + &% & +) % # * % + ') - &,* '+ ) + #*& # %"* &). ) * +& 0+ &) *3 + &) $ % #& " #&&"* + ) *+) + % + &$ % & + #& . + % * ' # *+ ' )+ ##&.* *+, %+* +& ) + - 0 $ " % ,' + ) &.% #& , *+ &% ')&- * &%+ /+ &) ,* % #& +& % ) &%* % /'#&) * . 0 ) &% %* * ' $ + $&) ) # - %+ &) ') + # + % &% &,+* - %+ * % * - %+ * & + ) ,# ) ) &%* ) /'#&) % (, *+ &% . ')&- * '# %+0 & &''&)+,% + * &) *" ##* ') + % + * %- *+ + - &%+ /+
$ ))&)* (, *+ &% & ) + ,+ %&. #&&"* + + #& ,* & '& %+* + )+ % *+ % )&$ # % ) + ) + % / '& %+ $ + + * *+ * +& % % ) ,% )*+ % % ) + ) + % +& ) &) ) *,#+* * + - +0 . + + %,$ )* *, + #0 !,*+ &,# )) &,+ ') + ##0 &) %*. ) % + (, *+ &% *' ##&.* & )&$ &+ '& %+ % # % ) &- ) % #, % + ) &%* + 0 ')& , * . ## * + ' + * + "# * &$$&% $ * &% '+ &% **& + . + ) . % + #& ,* & '& %+* + + ) / *+ % )&$ # % * * .&)+ # ** * ,** &% + * *0 +& ')&- + + + )*+ #+ )% + - * .)&% 0 $ *,) % +, %+* $ 0 %+ ) *+ +& # )% + + + #& ,* % ## 1*+ ,$2 # %" + * +& + * ' & ),%% % +) " &) 1 * & ) + % # 2 - #&'* + * +& + #& ,* &,+* * ' +, %+* * &,# &%* ) + # % * $ %+* % - )+ * * ' ) + #0 ) ' +* (, *+ &% % + &%+ /+ & +) % # &, &,# % #, &+ ) +) % # * +& % &,) ,)+ ) ') + #&&"* + ) &%* % + * + $ %* * ' * +.& (, *+ &%* ')&- &''&)+,% + * &) /'#&) + &% & + + - + * &- ) % + '+ ) * % ) % 0 % #, % &+ ) & *+ # * *, * '&*+* % . ##* + + .&,# ) *+) + + & 3* $&- $ %+
* *" ##* ') + / ) * &,# * - % ,* &) ) - * &% # + ) % + 0 ) '')&') +
% &)$ % &' % % %- *+ + &% + + /+ % * + * & + '+ ) * $ # ) * +& &%* ) + #& + &% & * ,) +0 $ ) * %* &,+* , # % * $ )&$ - ) &,* ) + # % ) * ' * % &,) *+, %+* +& ,* ' ) & &$' ** * +& &%* ) + ' + & * + &/ )&+ + * * &,# /+ % 0 #&&" % + ) + % # * % ) %+ % + # &) %+ + &%* % 0 ,* % &+ ) * ' *
* ) # + &% &$' ) * % &%+) *+* + #& $ + % + * '+ )
00934_P001_144_WRM_TG3.indd 51
01/07/2021 10:20