╨╧рб▒с>■  ■                                                                                                                                                                                                                                                                                                                                                                                                                                                   Root Entry        └=nsЄ└@Contents            ъ,SummaryInformation(        бGridInfo    ¤                   ■   ■    ■                                                                    !"#$%&'()2                                345678■                                                                                                                                                                                                                                                                                               Root Entry        └=nsЄ└@Contents        ъ,SummaryInformation(            бGridInfo                    ¤   ■   ■                ■                                                                !"#$%&'()2                                345678■                                                                                                                                                                                                                                                                                               ■   ■   ■                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               GridView                                         GridView                                                 ■   ■   ■                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               ■  рЕЯЄ∙OhлС+'│┘рЕЯЄ∙OhлС+'│┘0qаи┤└╠╪фЁ №    ,8@HPА\dф0@@@@`╝╡╗Г└2`&{9649A0E2-5E50-11d5-A49A-00104BFF5915}Ч, юя  ?        є =8X1╚ РArial1╚ ╝Arial1╚ РArial1╚ ╝Arial1╚ РArial1р╝Arial1рРArial1ЁРArial1╚╝Arial1╚РArial1Ё РArial1Ё ╝Arial"г"#,##0;\-"г"#,##0"г"#,##0;[Red]\-"г"#,##0"г"#,##0.00;\-"г"#,##0.00!"г"#,##0.00;[Red]\-"г"#,##0.00)*&* _-"г"#,##0;* \-"г"#,##0;* _-"г""-";@)* #,##0;* \-#,##0;* "-";@1,.* _-"г"#,##0.00;* \-"г"#,##0.00;* _-"г""-"??;@$+!* #,##0.00;* \-#,##0.00;* "-"??;@\$#,##0_);\(\$#,##0\)\$#,##0_);[Red]\(\$#,##0\)\$#,##0.00_);\(\$#,##0.00\)# \$#,##0.00_);[Red]\(\$#,##0.00\)@ d\ mmmm\ yyyyэьрї  └ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ р └ рї  ╚└ рї  ╚└ р ї  ╚└ р ї  ╚└ р ї  ╚└ рЁ H└ р А└ р └и р  └ р А└ р  шк А@р  шк ВА р  шк Ар "°к Ар  шк БА@р  шк БАА р "°к БАр "°к БАА р  шк @р #°к А р "°к @р #°к БАА р шл AАIА@ р шл AАЙА@ р шл БАIА@ р шл БАЙА@ р  И└ р ╚л р  ╚л р  И└ р ╚й р шй БАА@р шй БА@р"°К БАВА р"°К БАА р ╚К р └и р"╪и р ╚и р"╪и Е Title PageЕ ActivityЕRecording Sheet   d№йё╥MbP?_*+%МБ┴&APage &PГД&ш?'ш?(Ё?)Ё?б" dXр?р?2ўС ь   └└└  ?Є  Ў ╨};} :@@@@@@@@@ Б@ +@ Б@ Б@ Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@ Б@!Б@"Б@#Б@$Б@%Б@&Б@'Б@(Б@)Б@*Б@+Б@,Б@-Б@.Б@/Б@0Б@1Б@╛4444 5Zoom╛&44444444444U6MZoom is an investigative activity which looks at converging number sequences.╛,44444444444444S6KThe sequences 'zoom in' on a particular number according to the rules being╛,44444444444444"6used to make the sequence.╛,4444444444444╛04644444444444444S6KCan you spot the connection between the rules being used and the number the╛,444444444444446sequence zooms in on?╛,444444444444446╛,44444444444444B6:For more free resources like this, make a regular visit to╛,4444444444444╛0 444444444444444╛ 4444 7www.numeracysoftware.com╛& 4444444444╛0 444444444444444╛0 444444444444444╛0 444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0╛0╛0╛0╛0╛0╛0╛0 ╛0!╛0"╛0#╛0$╛0%╛0&╛0'╛0(╛0)╛0*╛0+╛0,╛0-╛0.╛0/╛00╛01111> ╢аddЩ   d№йё╥MbP?_*+%МБ┴&APage &PГД&ш?'ш?(Ё?)Ё?б" dXр?р? ўС ь   └└└  ?Є  Ў ╨}д}}t}Т}W}ь}▌}д}  Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ *www.numeracysoftware.com╛********* **+" Look down this column of numbers.╛,,,,,-~3Y@ **>+6 Each number is the number above divided by 5, plus 1.╛,,,,,-$.5@D└D D **1+) e.g. 100 ў 5 = 20 and 20 + 1 = 21╛,,,,,-$.═╠╠╠╠╠@D└D D **G+? e.g. 21 ў 5 = 4.2 and 4.2 + 1 = 5.2 and so on Е.╛,,,,,-$.R╕ЕыQ@D└D D **'+ This sequence zooms in on 1.25╛,,,,,-$.║I +ЗЎ?D└D D *╛*+,,,,,-$.М█hoБЇ?D└D D **K+C Change the number in the top red `&{9649A0E2-5E50-11d5-A49A-00104BFF5915}Ч, юя  ?        є =8X1╚ РArial1╚ ╝Arial1╚ РArial1╚ ╝Arial1╚ РArial1р╝Arial1рРArial1ЁРArial1╚╝Arial1╚РArial1Ё РArial1Ё ╝Arial"г"#,##0;\-"г"#,##0"г"#,##0;[Red]\-"г"#,##0"г"#,##0.00;\-"г"#,##0.00!"г"#,##0.00;[Red]\-"г"#,##0.00)*&* _-"г"#,##0;* \-"г"#,##0;* _-"г""-";@)* #,##0;* \-#,##0;* "-";@1,.* _-"г"#,##0.00;* \-"г"#,##0.00;* _-"г""-"??;@$+!* #,##0.00;* \-#,##0.00;* "-"??;@\$#,##0_);\(\$#,##0\)\$#,##0_);[Red]\(\$#,##0\)\$#,##0.00_);\(\$#,##0.00\)# \$#,##0.00_);[Red]\(\$#,##0.00\)@ d\ mmmm\ yyyyэьрї  └ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ рї  ─└ р └ рї  ╚└ рї  ╚└ р ї  ╚└ р ї  ╚└ р ї  ╚└ рЁ H└ р А└ р └и р  └ р А└ р  шк А@р  шк ВА р  шк Ар "°к Ар  шк БА@р  шк БАА р "°к БАр "°к БАА р  шк @р #°к А р "°к @р #°к БАА р шл AАIА@ р шл AАЙА@ р шл БАIА@ р шл БАЙА@ р  И└ р ╚л р  ╚л р  И└ р ╚й р шй БАА@р шй БА@р"°К БАВА р"°К БАА р ╚К р └и р"╪и р ╚и р"╪и Е Title PageЕ ActivityЕRecording Sheet   d№йё╥MbP?_*+%МБ┴&APage &PГД&ш?'ш?(Ё?)Ё?б" dXр?р?2ўС ь   └└└  ?Є  Ў ╨};} :@@@@@@@@@ Б@ +@ Б@ Б@ Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@ Б@!Б@"Б@#Б@$Б@%Б@&Б@'Б@(Б@)Б@*Б@+Б@,Б@-Б@.Б@/Б@0Б@1Б@╛4444 5Zoom╛&44444444444U6MZoom is an investigative activity which looks at converging number sequences.╛,44444444444444S6KThe sequences 'zoom in' on a particular number according to the rules being╛,44444444444444"6used to make the sequence.╛,4444444444444╛04644444444444444S6KCan you spot the connection between the rules being used and the number the╛,444444444444446sequence zooms in on?╛,444444444444446╛,44444444444444B6:For more free resources like this, make a regular visit to╛,4444444444444╛0 444444444444444╛ 4444 7www.numeracysoftware.com╛& 4444444444╛0 444444444444444╛0 444444444444444╛0 444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0444444444444444╛0╛0╛0╛0╛0╛0╛0╛0 ╛0!╛0"╛0#╛0$╛0%╛0&╛0'╛0(╛0)╛0*╛0+╛0,╛0-╛0.╛0/╛00╛01111> ╢аddЩ   d№йё╥MbP?_*+%МБ┴&APage &PГД&ш?'ш?(Ё?)Ё?б" dXр?р? ўС ь   └└└  ?Є  Ў ╨}д}}t}Т}W}ь}▌}д}  Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ Б@ *www.numeracysoftware.com╛********* **+" Look down this column of numbers.╛,,,,,-~3Y@ **>+6 Each number is the number above divided by 5, plus 1.╛,,,,,-$.5@D└D D **1+) e.g. 100 ў 5 = 20 and 20 + 1 = 21╛,,,,,-$.═╠╠╠╠╠@D└D D **G+? e.g. 21 ў 5 = 4.2 and 4.2 + 1 = 5.2 and so on Е.╛,,,,,-$.R╕ЕыQ@D└D D **'+ This sequence zooms in on 1.25╛,,,,,-$.║I +ЗЎ?D└D D *╛*+,,,,,-$.М█hoБЇ?D└D D **K+C Change the number in the top red cell to something other than 100.╛,,,,,-$.╢°уЇ?D└D D **F+> Try lots of different starting numbers. What do you notice?╛,,,,,-$.$Шjf-Ї?D└D D *╛ *+,,,,,-$ .╕{ Ї?D└D D * *N +F By changing the numbers in the red cells below you can change the way╛ ,,,,,-$ .h╛5Ї?D └D D * *4 +, the numbers in the sequence arecell to something other than 100.╛,,,,,-$.╢°уЇ?D└D D **F+> Try lots of different starting numbers. What do you notice?╛,,,,,-$.$Шjf-Ї?D└D D *╛ *+,,,,,-$ .╕{ Ї?D└D D * *N +F By changing the numbers in the red cells below you can change the way╛ ,,,,,-$ .h╛5Ї?D └D D * *4 +, the numbers in the sequence are worked out.╛ ,,,,,-$ .HYkЪ Ї?D └D D *╛ *+,,,,,-$ .EтЇ?D └D D *╛ *+, / Divide by~ 1@╛ ,,-$ .iзУlЇ?D └D D *╛ *+, 0 Add~2Ё?╛ ,,-$.|!╖Ї?D └D D *╛*+,,,,,-$.╙WЇ?D└D D **N+F Change the 'Add' number to 2. What does the sequence zoom in on now?╛,,,,,-$.А]▐Ї?D└D D *╛*+,,,,,-$.y,Ї?D└D D **O+G Try dividing by and adding different numbers and see what the sequence╛,,,,,-$.хЇ?D└D D **M+E zooms in on each time. Record your findings on the Recording Sheet.╛,,,,,-$.h╟Ї?D└D D *╛********** > ╢аddЩ   d№йё╥MbP?_*+%МБ┴&APage &PГД&ш?'ш?(Ё?)Ё?б" dXр?р?ўС ь   └└└  ?Є■ Ў ╨};}8}gБ@Б@Б@Б@@@@@@ @ @ @ @ @@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@+#Record your findings on this sheet.╛ >6Type in the number the sequence zooms in on each time.╛ IAe.g. when you divide by 5 and add 1 the sequence zooms in on 1.25╛ ╛" ╛ Divide by╛ ╛ ╜0 @ @ @ @ @ @! @ ╛  ╛ " #- 4╛&&&&&&' ╛ " #- 3╛ &&&╛&&&' ╛ " #- 2╛&&&&&&'   $Add #- 1╛ &&&&&&'   $or~ #╛ &&&&&&'   $Subtract #+ 1╛ &&&~ &Ї?╛ &&' ╛ " #+ 2╛ &&&&&&' ╛ " #+ 3╛ &&&&&&' ╛  %+ 4╛(((((() ╛" ;3Can you spot any patterns in your table of results?╛ [SCould you predict which number the sequence would zoom in on for other combinations╛ not shown on the table?╛ ╛" ╛" ╛" ╛" ╛" ╛"   > ╢аddЩ   worked out.╛ ,,,,,-$ .HYkЪ Ї?D └D D *╛ *+,,,,,-$ .EтЇ?D └D D *╛ *+, / Divide by~ 1@╛ ,,-$ .iзУlЇ?D └D D *╛ *+, 0 Add~2Ё?╛ ,,-$.|!╖Ї?D └D D *╛*+,,,,,-$.╙WЇ?D└D D **N+F Change the 'Add' number to 2. What does the sequence zoom in on now?╛,,,,,-$.А]▐Ї?D└D D *╛*+,,,,,-$.y,Ї?D└D D **O+G Try dividing by and adding different numbers and see what the sequence╛,,,,,-$.хЇ?D└D D **M+E zooms in on each time. Record your findings on the Recording Sheet.╛,,,,,-$.h╟Ї?D└D D *╛********** > ╢аddЩ   d№йё╥MbP?_*+%МБ┴&APage &PГД&ш?'ш?(Ё?)Ё?б" dXр?р?ўС ь   └└└  ?Є■ Ў ╨};}8}gБ@Б@Б@Б@@@@@@ @ @ @ @ @@Б@Б@Б@Б@Б@Б@Б@Б@Б@Б@+#Record your findings on this sheet.╛ >6Type in the number the sequence zooms in on each time.╛ IAe.g. when you divide by 5 and add 1 the sequence zooms in on 1.25╛ ╛" ╛ Divide by╛ ╛ ╜0 @ @ @ @ @ @! @ ╛  ╛ " #- 4╛&&&&&&' ╛ " #- 3╛ &&&╛&&&' ╛ " #- 2╛&&&&&&'   $Add #- 1╛ &&&&&&'   $or~ #╛ &&&&&&'   $Subtract #+ 1╛ &&&~ &Ї?╛ &&' ╛ " #+ 2╛ &&&&&&' ╛ " #+ 3╛ &&&&&&' ╛  %+ 4╛(((((() ╛" ;3Can you spot any patterns in your table of results?╛ [SCould you predict which number the sequence would zoom in on for other combinations╛ not shown on the table?╛ ╛" ╛" ╛" ╛" ╛" ╛"   > ╢аddЩ