From 195565ee6e2e6b0b5a1ac84ab1ee9329eec2fd5f Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Fri, 4 Sep 2020 13:22:12 +0300 Subject: [PATCH 01/19] updated circumference --- maths-club-pack/content/facilitator/circumference.md | 3 ++- translations/en/facilitator/circumference.md | 3 ++- 2 files changed, 4 insertions(+), 2 deletions(-) diff --git a/maths-club-pack/content/facilitator/circumference.md b/maths-club-pack/content/facilitator/circumference.md index c6db872e..f150ff61 100644 --- a/maths-club-pack/content/facilitator/circumference.md +++ b/maths-club-pack/content/facilitator/circumference.md @@ -38,7 +38,8 @@ Like how this was worked out in question 1, the amount of extra rope needed is t ## Extension -Extension – something to think about, not work out! +**Extension – something to think about, not work out!** + What is even more interesting is what happens when the rope is lifted by a single point. The rope around the bottom of the earth is taut but now there is a large clearance at the top. For an additional 2 metres length of rope, the distance from the earth’s surface to the peak of the rope would be enough to fit **two Statue of Liberty’s underneath it!** ![](../../images/circumference-5.png) diff --git a/translations/en/facilitator/circumference.md b/translations/en/facilitator/circumference.md index b3e19eb7..1ce5d884 100644 --- a/translations/en/facilitator/circumference.md +++ b/translations/en/facilitator/circumference.md @@ -38,7 +38,8 @@ Like how this was worked out in question 1, the amount of extra rope needed is t ## Extension -Extension – something to think about, not work out! +**Extension – something to think about, not work out!** + What is even more interesting is what happens when the rope is lifted by a single point. The rope around the bottom of the earth is taut but now there is a large clearance at the top. For an additional 2 metres length of rope, the distance from the earth’s surface to the peak of the rope would be enough to fit **two Statue of Liberty’s underneath it!** ![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/circumference-5.png?raw=true) From f2114352b7823d3fdb4f11e04246929ca21f7b63 Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Fri, 4 Sep 2020 13:24:01 +0300 Subject: [PATCH 02/19] Made words one, two, three, bold --- maths-club-pack/content/facilitator/coconut-trader.md | 6 +++--- translations/en/facilitator/coconut-trader.md | 6 +++--- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/maths-club-pack/content/facilitator/coconut-trader.md b/maths-club-pack/content/facilitator/coconut-trader.md index 54d304d3..d0fbeb39 100644 --- a/maths-club-pack/content/facilitator/coconut-trader.md +++ b/maths-club-pack/content/facilitator/coconut-trader.md @@ -10,15 +10,15 @@ The key to this question is to realise that you should take all the coconuts fro Emptying the first sack -You currently have three sacks so at each checkpoint you must give three coconuts each time. That means that the sack will be empty after 30 ÷ 3 = 10 checkpoints.You throw away this empty sack. +You currently have three sacks so at each checkpoint you must give **three** coconuts each time. That means that the sack will be empty after 30 ÷ 3 = 10 checkpoints.You throw away this empty sack. Emptying the second sack -You now have two sacks left so at each checkpoint you must give two coconuts each time. That means that the sack will be empty after 30 ÷ 2 = 15 checkpoints. You throw away this empty sack. +You now have two sacks left so at each checkpoint you must give **two** coconuts each time. That means that the sack will be empty after 30 ÷ 2 = 15 checkpoints. You throw away this empty sack. Emptying the third sack -You now have one sack left so at each checkpoint you must give one coconut each time. You have already passed 10 + 5 = 15 checkpoints, which means you have five checkpoints left. That means you must give +You now have one sack left so at each checkpoint you must give **one** coconut each time. You have already passed 10 + 5 = 15 checkpoints, which means you have five checkpoints left. That means you must give out 5 × 1 = 5 coconuts from your final bag. Therefore, you are left with 30 − 5 = 25 coconuts to sell at the market. diff --git a/translations/en/facilitator/coconut-trader.md b/translations/en/facilitator/coconut-trader.md index 54d304d3..d0fbeb39 100644 --- a/translations/en/facilitator/coconut-trader.md +++ b/translations/en/facilitator/coconut-trader.md @@ -10,15 +10,15 @@ The key to this question is to realise that you should take all the coconuts fro Emptying the first sack -You currently have three sacks so at each checkpoint you must give three coconuts each time. That means that the sack will be empty after 30 ÷ 3 = 10 checkpoints.You throw away this empty sack. +You currently have three sacks so at each checkpoint you must give **three** coconuts each time. That means that the sack will be empty after 30 ÷ 3 = 10 checkpoints.You throw away this empty sack. Emptying the second sack -You now have two sacks left so at each checkpoint you must give two coconuts each time. That means that the sack will be empty after 30 ÷ 2 = 15 checkpoints. You throw away this empty sack. +You now have two sacks left so at each checkpoint you must give **two** coconuts each time. That means that the sack will be empty after 30 ÷ 2 = 15 checkpoints. You throw away this empty sack. Emptying the third sack -You now have one sack left so at each checkpoint you must give one coconut each time. You have already passed 10 + 5 = 15 checkpoints, which means you have five checkpoints left. That means you must give +You now have one sack left so at each checkpoint you must give **one** coconut each time. You have already passed 10 + 5 = 15 checkpoints, which means you have five checkpoints left. That means you must give out 5 × 1 = 5 coconuts from your final bag. Therefore, you are left with 30 − 5 = 25 coconuts to sell at the market. From 4c7ba4b2bbd2d8ffa61e247dfd55808da9039769 Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Fri, 4 Sep 2020 13:25:08 +0300 Subject: [PATCH 03/19] Updated Coin-game --- maths-club-pack/content/facilitator/coin-game.md | 6 +++--- translations/en/facilitator/coin-game.md | 6 +++--- 2 files changed, 6 insertions(+), 6 deletions(-) diff --git a/maths-club-pack/content/facilitator/coin-game.md b/maths-club-pack/content/facilitator/coin-game.md index cffbfc1b..805c0a01 100644 --- a/maths-club-pack/content/facilitator/coin-game.md +++ b/maths-club-pack/content/facilitator/coin-game.md @@ -11,7 +11,7 @@ Watch students closely when they start filling in the table to ensure they are o ## Solution -Which of the following scores are impossible in this game and why? 5-2, 7-4, 6-2, +*Which of the following scores are impossible in this game and why? 5-2, 7-4, 6-2,* 5-2 is possible. @@ -19,9 +19,9 @@ Which of the following scores are impossible in this game and why? 5-2, 7-4, 6-2 6-2 is impossible because the game would have stopped before it got to this stage. Player 1 would have already won some time before. -Think of ways the game could end in a tie - Either 5-5, 6-4 or 4-6 +*Think of ways the game could end in a tie* - Either 5-5, 6-4 or 4-6 -What is the chance of winning this game? +*What is the chance of winning this game?* The easiest way to fill in the table is to start in the top left corner, and each square is the sum of the number immediately to the left and immediately above. E.g. The numbers diff --git a/translations/en/facilitator/coin-game.md b/translations/en/facilitator/coin-game.md index 5dc94c5e..1e3989e8 100644 --- a/translations/en/facilitator/coin-game.md +++ b/translations/en/facilitator/coin-game.md @@ -11,7 +11,7 @@ Watch students closely when they start filling in the table to ensure they are o ## Solution -Which of the following scores are impossible in this game and why? 5-2, 7-4, 6-2, +*Which of the following scores are impossible in this game and why? 5-2, 7-4, 6-2,* 5-2 is possible. @@ -19,9 +19,9 @@ Which of the following scores are impossible in this game and why? 5-2, 7-4, 6-2 6-2 is impossible because the game would have stopped before it got to this stage. Player 1 would have already won some time before. -Think of ways the game could end in a tie - Either 5-5, 6-4 or 4-6 +*Think of ways the game could end in a tie* - Either 5-5, 6-4 or 4-6 -What is the chance of winning this game? +*What is the chance of winning this game?* The easiest way to fill in the table is to start in the top left corner, and each square is the sum of the number immediately to the left and immediately above. E.g. The numbers From a9b0c3f777f589cc2993bc6f90fe5d12b2f0d568 Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Fri, 4 Sep 2020 13:26:00 +0300 Subject: [PATCH 04/19] Updated collatz-conjecture --- .../content/facilitator/collatz-conjecture.md | 7 ++++--- maths-club-pack/images/collatz-conjecture-2.png | Bin 6050 -> 0 bytes maths-club-pack/images/collatz-conjecture-3.png | Bin 5303 -> 0 bytes .../en/facilitator/collatz-conjecture.md | 7 ++++--- 4 files changed, 8 insertions(+), 6 deletions(-) delete mode 100644 maths-club-pack/images/collatz-conjecture-2.png delete mode 100644 maths-club-pack/images/collatz-conjecture-3.png diff --git a/maths-club-pack/content/facilitator/collatz-conjecture.md b/maths-club-pack/content/facilitator/collatz-conjecture.md index 12b52cd8..044a5986 100644 --- a/maths-club-pack/content/facilitator/collatz-conjecture.md +++ b/maths-club-pack/content/facilitator/collatz-conjecture.md @@ -19,16 +19,17 @@ finally gets to 1. The number just before, 96, only takes 12 steps! A computer or tablet would be very useful to try and find very long sequences. Here are some instructions for GeoGebra, which you can find online (https://www.geogebra.org/classic/spreadsheet) or it may be installed on the tablet and you do not need the internet. -You will need to use the Mod command: +You will need to use the Mod command: + +Mod[ <Dividend Number> , <Divisor>Number ] -![](../../images/collatz-conjecture-2.png) to check if the number is even. Mod is short for Modulo and gives the remainder when you do a division. e.g. Mod[10,3] would be 1 because there is 1 leftover when you divide 10 by 3. You will also need the If command: -![](../../images/collatz-conjecture-3.png) +If[ <Condition> , <Then> , <Else> ] to choose what to do if it is even and what to do if it is odd. diff --git a/maths-club-pack/images/collatz-conjecture-2.png b/maths-club-pack/images/collatz-conjecture-2.png deleted file mode 100644 index adf40df98d2e8a999432d7e9f5273e4605d67d1e..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 6050 zcmeHLc{r49+rO2qF|vnJ7(Ef0LDpdiqbM`7JW=*#Vk|S3k-h9|wumQ7DnvqrkUdd$ zVq{5(B6~bBwt6qm`+RTDcYMe9M}K^Oe8v#RGiMohC#|k?P zgCK}iM;mJZL3E1XUYMB?yyN;RW5GwbuaODGz}id5)t!8m=u8lz__z{;2;Ri25ad1b zd))AW<}+~Y_us=V^j4tT5419RC9H~+Itety_en)2PS7kwomquL4zgW1eM(kt)9{2V zBJ!m+=7Ojb?Dmu><0SD^vwoJA`DPb8i?aEc%MeM~SXuA|XVLEiMMLE2@d^|Cd!_yw zf$JKZrx3-4x5Xd`Mo$D0nc#HMwqzHiwH?`pfb@281))Naiki2pwXG9@B4k6bCz3FT z<(dYB5YY~UFqXqf;aoKd4n%EVcY>iW-pJP1$yUh@p{5E`@kRp&E(D6TkhhC7$ph_; zLHy+x4es}TMj?d$8bWcxAWU!2(@OcDF}KD=8_Vq-0PsGLm3~q=yfQV(l$S@(|f`@oyhkf`_d; z(Un3ZlZ5tsTHBC4DHsF-*oFRfzK8yQypufs1_8i<+Owdfky5CC4yO>W{x8G#EI)?t zO-5fNdJ~*YutXOE$peIdL7bMB`ODc4>*ar1Pyc1ybA;A$v9>1|6YVGtKW6;h_{sq@BxPA(OpBntD zyMDp-QwaRj;9uSK{|heI4{1jr0X^phgj*zB0uDqUy@!U55i_{_ne8GW2wtg!RX6e; zS)$FFOoJcwbH!4YduV z>npgdgEPyi?c}=^Y8`Y|*C0`yy|84zIA5x{)#a3c>o<17z0B6l*I%TV%&evQb+4(` z_N-xMe0u!4gAZY`R#JR7ZwRxP!1&;d60UH@kS3TwNRw5`zE{9f*eLzqe`bhlvXU|h zvX$b4Uzz}>5FSM^L&`76P>g$aX{mL3I;T5k+Fj{+O^tM_rR`CE{w6~`Ojx=C+1;h3 zrKO~-ETpaubH&s&c3nwco-qo$FA5u6U$2@eJuoo9w_uqiX({jtn{^{hgYJ=00kzoR zk@sj94vVFa6IAY1uT4x?!QpVL&DD=pejCM;40vQ}b59SO@e_-d*dq$% zNX39HSu-;;D_h%;FJIis#;d}@7*0t_vOa6@T0X`NV}Pvu{RJi`Cxs9<*!2w&CSjA4h}Lx zihk>-kmk>Gc+TnTC#DqLcPlS17m}0X*7!#} z64TP6A3i)`F^%ULn$OD=eTyR0fj8({SW`_0Hf`va@06#c(#&K%|{ z1ULZ5*DOhJM8Qri(;-n=i< z9UUE-1VU~~k+55ave!XjVc~=}JCiC`VH+D8*}DtX)zy15Lp6l$Wcc6v%p4633*%qN zVnb+v?Dz7XfBR&-1-J57gt|jU(=YWzrV`0g&{hy763BLVH%;Kp%bIz zhL(7>Z;>DcSp@|rT2X%f86zWZ;2D2cB`P6-o%D|HR=j!5HDPIKj-sNX*}1tFbJWNB z`uag5BUikAeZeuPe^xS(NeOQx&J!FQe9_dDMO0KY`Sxu$vgX#OsN#%23TjllaMS?# zE?nQ($cS%u+Wh%jj36ZLqepSJwzhWm_UA#e9jzqy+s0$gYH4Z7N=vI>NJZwBm&+D6l4ynV*A{TR)gh5chn18;BM*;^+|sx|vBN-5-~0MCGY3b&#+VmsxOtIg69E_(CnrrZ8D()}*R!~5c$mKjvmtPuHpxWs z^t|8DAefk#Xm*1_Dc299{rS27b$k1Zn&tYK7+w@YN~(8-FcJtX zN9c^D<#@&#<jh^->|C6{WJS7a%D1U_HCb_YCnpJc@_RVI7HZ78@vUw6u-|JdCnuIf?a<2izAT%Y zo6IaMAz4|1SVUjpwo!9)Gi@S-t%T5V$i&2CWdsnj5TFVwl}cOfK)KBgoU~95a64uC z3=WmJjLOq9Fz`!;E3GDHX0npWFd!h{qWEnwF|o$3bOjDxUM8Rq3NM#2f`t$E zhSnm}N_Kw!M;=05tsh!q+-NJ-+Q&KfNRn!7NmZ;%`^IT+YI;OmLV|;x9RjkTvr{)y z6|{FLvH!%va2XRME5EyZ&Qbsn$54s&ek_8+t3XypCiqGHR{Oo7&O}iK1%=w(_0e~a z2X+guRKP6#zc4Jls}3nHMq;(J?&LJ-?j^Rm>MnNseC@`2KcJn?>gwKX+oXL=wOj#c ziin9Zb4Jng^YdTXzYD5$*57}pRzS4j+m-~_c&n)Ivg1{OUb*LWx0AvA`S<>`bTk{h z@7*beZoqw0eh#Ijr6r}MP3w!J)-EnZ{l(?w+@LpIJw3x>V_D+_l!Di0dTd*wd7!{s zw>ZI$-PqJbS6^SRt*iU;P40!*t?tp?q2Xa+5t02M3ZSK+z~3&UOsszFSXo_tktXNl zx-y|28WE9QTFMa@7l&Rx3Oyr@MaRV*1Wn@_rjjVcN%oD=Op+3=D)0#gw{#JfE~m2T5Ei48$VTFI_scu(;?mReybVt5CF+ z%{>FizS{K>r#;1)oh<_NRzgC8Rj*3lR}UQ3JnPfLe{-h-)}t)rL4lFD!6T!?E?it( zIhP(+jL^V(5{bfU0K~2YBqb#cP^nr|Q&Y97SCzHoM9=3MNE|~vC@qyPx~6Ix;Kt4o z8y9C_Z!hZQD4X7JM?RdEg+n0_6<2UzYVBK~ODx92-;H)=t~Y!zpQ1{Gs<9<>>2+ zZf|cd@!KGQP5sp6r}XevUDd5wk>u3W?B~zZew$K@HWJq&5Pn--T}{Zy=qyTzMcdKx ze7>~ss$=;MAC~DLvQLe-ZGD~R;NWQD{33YO(GjMpsX0_?%Op>Fm)}paDB9EY%^4*P mOyC6YKcv3Zj}ySn?M*>Lu~&E+nkR4Xk8B++JhoWFD)?U=FGywp diff --git a/maths-club-pack/images/collatz-conjecture-3.png b/maths-club-pack/images/collatz-conjecture-3.png deleted file mode 100644 index ae124f75752cefd6c4b4af49929ff9984397947b..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 5303 zcmeHLX*iT^8-A$lOP047VHzn3gQjHOPz(*m@-f*;#xllW5K|aSULwWViWG&&k|oL# zUNpkc6phd#5^o`U%1+-seI0M_pYKOMz8~Ll^c*wu%-q*?pU-`t*LhvfHP1y$^JBsS zFaZdHgpIKnD{vkFZ&^Mb@TsOkE(50vG`t1`Z)2t1a9yGN@zHz+G&&>zJ>e1_y^dXBrNusUeu%W zTuG4EXy)Mz4T;h^ji=e~cL4qV&l6SpUe< z<9=a$u}V2#@B$rz1U8ewlI+ZIXjfl~nzNg)3sEhI;s@3WL5KB%{G46Ah*Y=>kwo^< zLCn-QA>d>;9fa)xGj%gR1EL2ROYjURtI=lFuq3R$Izz+Wo&Y}Nrbf19lBmg>)91BuIO&$49cPiQazqoTOKioN! z(U#;OqPHD}OdWX4nhNg`MZPrNkXuVJIz!6Y9*9dOLNI!Tp#iR? 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The number just before, 96, only takes 12 steps! A computer or tablet would be very useful to try and find very long sequences. Here are some instructions for GeoGebra, which you can find online (https://www.geogebra.org/classic/spreadsheet) or it may be installed on the tablet and you do not need the internet. -You will need to use the Mod command: +You will need to use the Mod command: + +Mod[ <Dividend Number> , <Divisor>Number ] -![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/collatz-conjecture-2.png?raw=true) to check if the number is even. Mod is short for Modulo and gives the remainder when you do a division. e.g. Mod[10,3] would be 1 because there is 1 leftover when you divide 10 by 3. You will also need the If command: -![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/collatz-conjecture-3.png?raw=true) +If[ <Condition> , <Then> , <Else> ] to choose what to do if it is even and what to do if it is odd. 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Learners may wish to first try with an example using numbers for the length and width of the field, however this is not necessary to solve the problem. +## Solution +This is a question about perimeter. The key to a quick and easy +solution here is to understand that the edges of the fence parallel +to the edges of the field will always be the same WHATEVER THE +SIZE OF THE FIELD. -## Solution +The extra fence is only needed at the corners (shown in the +diagram). -![](../../images/fence-around-a-field-3.png) +In total there will be 8 extra pieces, all measuring the same +length, perhaps called *w*. +![](../../images/fence-around-a-field-3.png) +We know that the extra length of fence is 1 metre which is the total length of the 8 pieces. Therefore if 8w = 1m, **w = 12.5 centimetres**. The path is too narrow for a tractor but a mouse could easily run along it. +## Extension +This problem sets up nicely for another called the *belt around the earth*, +which goes as follows: +Imagine a piece of rope is tied the entire way around the earth, along the +equator, so that it fits perfectly. 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zX-XW}K{*JZg&8-h*OSH*HCdZ48yi8ME5Js^z^4qNA!pwf?vHo`buSVa%pw>Cp-Yz}xX^zNRy%%G-cFD>~MnuQG}iw0rXv zqmie-oj#j)c1avSVp|C$U`88e?Ue9~s+iv{0_yIV(P)*)T%goj+rB93`?Yu&nqKA+>WTP=`%5=FGuY{QyV&b`K0>Lxc4wIc zZt+uaznLeOB7J>}H^nLeP4=g~Im(w?C1fa`KxuHAt$rB#C Date: Tue, 8 Sep 2020 10:26:05 +0300 Subject: [PATCH 07/19] made top-left-number-bold --- maths-club-pack/content/facilitator/magic-cards.md | 5 +++-- translations/en/facilitator/magic-cards.md | 5 +++-- 2 files changed, 6 insertions(+), 4 deletions(-) diff --git a/maths-club-pack/content/facilitator/magic-cards.md b/maths-club-pack/content/facilitator/magic-cards.md index 64c99f61..74937868 100644 --- a/maths-club-pack/content/facilitator/magic-cards.md +++ b/maths-club-pack/content/facilitator/magic-cards.md @@ -1,11 +1,12 @@ # Magic Cards -## Introduction +## Introduction + Place the cards randomly on the desk and ask a student to find all the cards with their birth date on (e.g. they might be born on the 12th of November 2005 so they would be looking for all the cards with a 12 on it). Ask them to tell you the colour of all the cards that their number is on. -Then all you need to do is add together the top left number of each of those cards and it will instantly tell you what date they were born on. +Then all you need to do is add together the **top left number** of each of those cards and it will instantly tell you what date they were born on. Do this a few times with the students. They can pick any new number for you to guess. Then ask them to work out how you are doing it so quickly. diff --git a/translations/en/facilitator/magic-cards.md b/translations/en/facilitator/magic-cards.md index 64c99f61..74937868 100644 --- a/translations/en/facilitator/magic-cards.md +++ b/translations/en/facilitator/magic-cards.md @@ -1,11 +1,12 @@ # Magic Cards -## Introduction +## Introduction + Place the cards randomly on the desk and ask a student to find all the cards with their birth date on (e.g. they might be born on the 12th of November 2005 so they would be looking for all the cards with a 12 on it). Ask them to tell you the colour of all the cards that their number is on. -Then all you need to do is add together the top left number of each of those cards and it will instantly tell you what date they were born on. +Then all you need to do is add together the **top left number** of each of those cards and it will instantly tell you what date they were born on. Do this a few times with the students. They can pick any new number for you to guess. Then ask them to work out how you are doing it so quickly. From a28a80fb1a7b361e82f5f9db490c7728e8b7a49b Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Tue, 8 Sep 2020 10:39:49 +0300 Subject: [PATCH 08/19] removed "." on the introduction of making-squares --- .../content/facilitator/making-squares.md | 2 +- maths-club-pack/images/making-squares-2.png | Bin 24422 -> 57359 bytes translations/en/facilitator/making-squares.md | 2 +- 3 files changed, 2 insertions(+), 2 deletions(-) diff --git a/maths-club-pack/content/facilitator/making-squares.md b/maths-club-pack/content/facilitator/making-squares.md index e1d4799f..67a325d2 100644 --- a/maths-club-pack/content/facilitator/making-squares.md +++ b/maths-club-pack/content/facilitator/making-squares.md @@ -1,6 +1,6 @@ # Making squares -## Introduction. +## Introduction This game is a great way to practice using coordinates and develop geometrical reasoning (understanding of shapes). It might be a good idea to play the game once altogether, splitting the class into two teams. Each team takes it in turns to mark a point on the game grid until one team can join four of their own points together and make a square. 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It might be a good idea to play the game once altogether, splitting the class into two teams. Each team takes it in turns to mark a point on the game grid until one team can join four of their own points together and make a square. A typical game on a smaller grid might look like: From 7e35a55c591fcbed59dbe641270af33f33988939 Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Tue, 8 Sep 2020 11:58:30 +0300 Subject: [PATCH 09/19] added missed line ; number-challange-1 --- .../content/facilitator/number-challenge-1.md | 13 +++++-------- translations/en/facilitator/number-challenge-1.md | 13 +++++-------- 2 files changed, 10 insertions(+), 16 deletions(-) diff --git a/maths-club-pack/content/facilitator/number-challenge-1.md b/maths-club-pack/content/facilitator/number-challenge-1.md index eb06ccde..dedb5701 100644 --- a/maths-club-pack/content/facilitator/number-challenge-1.md +++ b/maths-club-pack/content/facilitator/number-challenge-1.md @@ -12,13 +12,11 @@ The solutions are **not important**, it is about the thinking process learners g 1. The first two numbers add up to 11 so we can try different pairs. If they were 5 and 6 then the other number would have to be 12 or 13 but then none of the pairs add up to 22, so it's wrong. If we keep trying values we see that the first numbers can only be 3 and 8 and the other number will be 14 which works with all the information. However, if the numbers were bigger this would take much longer. - A better way is to use **algebra** and **simultaneous equations.** Let the three numbers be x, y and z , and . If the first pair is x and y , then we know that x + y =13. If the second pair is x and z then, x + z = 17 and the last pair must be y and z so y + z = 22. This gives us three simultaneous equations: - x + y = 11 ; x + z = 17 ; y + z = 22 + A better way is to use **algebra** and **simultaneous equations.** Let the three numbers be x, y and z , and . If the first pair is x and y , then we know that x + y =13. If the second pair is x and z then, x + z = 17 and the last pair must be y and z so y + z = 22. This gives us three simultaneous equations: + + x + y = 11; x + z = 17; y + z = 22 - Equation 2 - Equation 1 gives: z - y = 6 . Now add this to Equation 3 to get 2z = 28. -Which means z = 14 . Using the original equations we can then work out that x = 3 - - and y = 8. + Equation 2 - Equation 1 gives: z - y = 6 . Now add this to Equation 3 to get 2z = 28.Which means z = 14 . Using the original equations we can then work out that x = 3 and y = 8. Now try the question if the totals were 73, 140 and 109. Which method is faster now? @@ -34,8 +32,7 @@ Which means z = 14 . Using the original equations we can then work out that x = Do the same and you will see it's not possible to have a 2 or a 4 between the 1s. You can solve it from there. -3. 99 + $\frac{9}{9}$ = 99 +1 = 100 or even $\frac{99}{99}$ = 100. - This question requires some creativity! +3. 99 + $\frac{9}{9}$ = 99 +1 = 100 or even $\frac{99}{99}$ = 100. This question requires some creativity! diff --git a/translations/en/facilitator/number-challenge-1.md b/translations/en/facilitator/number-challenge-1.md index 768cd7e6..b6421299 100644 --- a/translations/en/facilitator/number-challenge-1.md +++ b/translations/en/facilitator/number-challenge-1.md @@ -12,13 +12,11 @@ The solutions are **not important**, it is about the thinking process learners g 1. The first two numbers add up to 11 so we can try different pairs. If they were 5 and 6 then the other number would have to be 12 or 13 but then none of the pairs add up to 22, so it's wrong. If we keep trying values we see that the first numbers can only be 3 and 8 and the other number will be 14 which works with all the information. However, if the numbers were bigger this would take much longer. - A better way is to use **algebra** and **simultaneous equations.** Let the three numbers be x, y and z , and . If the first pair is x and y , then we know that x + y =13. If the second pair is x and z then, x + z = 17 and the last pair must be y and z so y + z = 22. This gives us three simultaneous equations: - x + y = 11 ; x + z = 17 ; y + z = 22 + A better way is to use **algebra** and **simultaneous equations.** Let the three numbers be x, y and z , and . If the first pair is x and y , then we know that x + y =13. If the second pair is x and z then, x + z = 17 and the last pair must be y and z so y + z = 22. This gives us three simultaneous equations: + + x + y = 11; x + z = 17; y + z = 22 - Equation 2 - Equation 1 gives: z - y = 6 . Now add this to Equation 3 to get 2z = 28. -Which means z = 14 . Using the original equations we can then work out that x = 3 - - and y = 8. + Equation 2 - Equation 1 gives: z - y = 6 . Now add this to Equation 3 to get 2z = 28.Which means z = 14 . Using the original equations we can then work out that x = 3 and y = 8. Now try the question if the totals were 73, 140 and 109. Which method is faster now? @@ -34,8 +32,7 @@ Which means z = 14 . Using the original equations we can then work out that x = Do the same and you will see it's not possible to have a 2 or a 4 between the 1s. You can solve it from there. -3. 99 + $\frac{9}{9}$ = 99 +1 = 100 or even $\frac{99}{99}$ = 100. - This question requires some creativity! +3. 99 + $\frac{9}{9}$ = 99 +1 = 100 or even $\frac{99}{99}$ = 100. This question requires some creativity! From 52bbcc815c6bd99860cc12d18dd9b352e81f549e Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Tue, 8 Sep 2020 12:49:18 +0300 Subject: [PATCH 10/19] added hyper-link on base 2; russian-multiplication --- maths-club-pack/content/facilitator/russian-multiplication.md | 4 ++-- translations/en/facilitator/russian-multiplication.md | 4 ++-- 2 files changed, 4 insertions(+), 4 deletions(-) diff --git a/maths-club-pack/content/facilitator/russian-multiplication.md b/maths-club-pack/content/facilitator/russian-multiplication.md index f2e5f52e..32bfe6c1 100644 --- a/maths-club-pack/content/facilitator/russian-multiplication.md +++ b/maths-club-pack/content/facilitator/russian-multiplication.md @@ -19,7 +19,7 @@ It will work for any two numbers. An insight into why it always works can be giv (taken from http://mathforum.org/dr.math/faq/faq.peasant.html) -Binary numbers are numbers written in base two instead of base ten. This means that place value depends on powers of two instead of powers of ten: instead of ones, tens, and hundreds places, base two has a ones place, a twos place, a fours place, and so on. For example, fourteen in base two is 1110: +Binary numbers are numbers written in [base two](https://mathforum.org/dr.math/faq/faq.bases.html) instead of base ten. This means that place value depends on powers of two instead of powers of ten: instead of ones, tens, and hundreds places, base two has a ones place, a twos place, a fours place, and so on. For example, fourteen in base two is 1110: 1110 (base 2) @@ -77,7 +77,7 @@ We are trying to multiply 12 by 13. One way to do this would be to use long mult -Notice that we are adding 2*13 and 10*13 to get our final answer. This works because of the distributive property: +Notice that we are adding 2*13 and 10*13 to get our final answer. This works because of the [distributive property](): 12 * 13 diff --git a/translations/en/facilitator/russian-multiplication.md b/translations/en/facilitator/russian-multiplication.md index 79fca08b..f0b2ab24 100644 --- a/translations/en/facilitator/russian-multiplication.md +++ b/translations/en/facilitator/russian-multiplication.md @@ -19,7 +19,7 @@ It will work for any two numbers. An insight into why it always works can be giv (taken from http://mathforum.org/dr.math/faq/faq.peasant.html) -Binary numbers are numbers written in base two instead of base ten. This means that place value depends on powers of two instead of powers of ten: instead of ones, tens, and hundreds places, base two has a ones place, a twos place, a fours place, and so on. For example, fourteen in base two is 1110: +Binary numbers are numbers written in [base two](https://mathforum.org/dr.math/faq/faq.bases.html) instead of base ten. This means that place value depends on powers of two instead of powers of ten: instead of ones, tens, and hundreds places, base two has a ones place, a twos place, a fours place, and so on. For example, fourteen in base two is 1110: 1110 (base 2) @@ -77,7 +77,7 @@ We are trying to multiply 12 by 13. One way to do this would be to use long mult -Notice that we are adding 2*13 and 10*13 to get our final answer. This works because of the distributive property: +Notice that we are adding 2*13 and 10*13 to get our final answer. This works because of the [distributive property](): 12 * 13 From b9c4cc03b4fccdce99b7c8320f1a8e3a763a0773 Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Tue, 8 Sep 2020 12:59:46 +0300 Subject: [PATCH 11/19] added line between true and consider; treaure-hunt --- maths-club-pack/content/facilitator/treasure-hunt.md | 6 ++++-- translations/en/facilitator/treasure-hunt.md | 6 ++++-- 2 files changed, 8 insertions(+), 4 deletions(-) diff --git a/maths-club-pack/content/facilitator/treasure-hunt.md b/maths-club-pack/content/facilitator/treasure-hunt.md index 14d65aed..fa35676b 100644 --- a/maths-club-pack/content/facilitator/treasure-hunt.md +++ b/maths-club-pack/content/facilitator/treasure-hunt.md @@ -4,9 +4,11 @@ There are two different approaches to this puzzle. You can assume that: -•Each chest contains the treasure, or that +* Each chest contains the treasure, or that -•Each statement is true and consider the four cases that arise. +* Each statement is true + +and consider the four cases that arise. The way a student structures their answer will play a big part in how easy they find the answer. diff --git a/translations/en/facilitator/treasure-hunt.md b/translations/en/facilitator/treasure-hunt.md index 70f65205..f0555e58 100644 --- a/translations/en/facilitator/treasure-hunt.md +++ b/translations/en/facilitator/treasure-hunt.md @@ -4,9 +4,11 @@ There are two different approaches to this puzzle. You can assume that: -•Each chest contains the treasure, or that +* Each chest contains the treasure, or that -•Each statement is true and consider the four cases that arise. +* Each statement is true + +and consider the four cases that arise. The way a student structures their answer will play a big part in how easy they find the answer. From 19a7c4633b7edf17d23691a1979da7bb31e3b8ee Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Thu, 10 Sep 2020 05:03:53 +0300 Subject: [PATCH 12/19] added two-eggs --- .../content/facilitator/two-eggs.md | 90 ++++++++++++++++++ maths-club-pack/content/student/two-eggs.md | 15 +++ maths-club-pack/cover_images/two-eggs.svg | 1 + maths-club-pack/images/two-eggs-1.png | Bin 0 -> 48364 bytes maths-club-pack/images/two-eggs-2.png | Bin 0 -> 12421 bytes maths-club-pack/images/two-eggs-3.png | Bin 0 -> 12490 bytes maths-club-pack/images/two-eggs-4.png | Bin 0 -> 13616 bytes maths-club-pack/images/two-eggs-5.png | Bin 0 -> 14251 bytes maths-club-pack/images/two-eggs-6.png | Bin 0 -> 44664 bytes translations/en/facilitator/two-eggs.md | 90 ++++++++++++++++++ translations/en/student/two-eggs.md | 9 ++ 11 files changed, 205 insertions(+) create mode 100644 maths-club-pack/content/facilitator/two-eggs.md create mode 100644 maths-club-pack/content/student/two-eggs.md create mode 100644 maths-club-pack/cover_images/two-eggs.svg create mode 100644 maths-club-pack/images/two-eggs-1.png create mode 100644 maths-club-pack/images/two-eggs-2.png create mode 100644 maths-club-pack/images/two-eggs-3.png create mode 100644 maths-club-pack/images/two-eggs-4.png create mode 100644 maths-club-pack/images/two-eggs-5.png create mode 100644 maths-club-pack/images/two-eggs-6.png create mode 100644 translations/en/facilitator/two-eggs.md create mode 100644 translations/en/student/two-eggs.md diff --git a/maths-club-pack/content/facilitator/two-eggs.md b/maths-club-pack/content/facilitator/two-eggs.md new file mode 100644 index 00000000..f0610e06 --- /dev/null +++ b/maths-club-pack/content/facilitator/two-eggs.md @@ -0,0 +1,90 @@ +# Two Eggs + +## Introduction + +This mind-teaser is an interesting one because there are so many different approaches that will allow you to find out the answer, but there is only one optimal approach! Students will develop their critical thinking skills by using trial and error and thinking about how to improve their method each time. + +There are no tricks involved with this puzzle. There is no need to consider terminal velocity, potential energy or wind resistance. Both eggs are identical. + +Get students to think about the puzzle themselves before reading on. + +## Solution + +Approach A - worst case 100 + +The first logical approach would be to test every floor from the bottom floor to the top floor. So, we could start from the 1st floor and drop the egg from there. If it survives we can move up to try again from the 2nd floor, then the 3rd floor and so on. We keep moving a floor up each time until the egg breaks, and we get +the solution. For example, if the egg breaks on the 67th floor, we know that the highest floor than an egg +can withstand a drop is from the 66th floor. In this case, we would have dropped a single egg 67 times! + +There is also a chance that the egg will not break from the 100th floor and by using this approach we would have dropped the egg 100 times in total to find this out! + +This approach is clearly not optimal. + +Approach B - worst case 50 + +Can we can halve the number of egg drops? What if we start by dropping the first egg from the 50 th floor? + +**What happens if the egg breaks from the 50th floor?** + +If the egg breaks from being dropped from the 50th floor, then it would break from every floor above this. +We would then only have 1 egg remaining to check all the floors below in a similar method to Approach A +(one floor at a time, starting from the 1st floor to the 49th floor). As a worst case, we would have to check 50 floors. + +**What happens if the egg does not break from the 50th floor?** + +If the egg did not break from being dropped from the 50th floor, then it would not break from any floor +below this. So again, we would only have 1 egg remaining to check all the floors above in a similar method to Approach A (one floor at a time, starting from the 51st floor to the 100th floor). As a worst case, we would have to check 50 floors in total. + +This is still not optimal. + +Approach C - worst case 19 + +What would happen if we started off dropping our first egg at intervals of 10 floors? (for example, 10th +floor, 20th floor, 30th floor etc.). + +We would start by dropping the egg from the 10th floor. If the egg does not break, then it would not break from any floor below this and we can try again from the 20th floor. If the egg still does not break, we can try from the 30th floor, then the 40th floor and so on. Once the egg breaks from being dropped, we know that the solution is somewhere in the 9 floors below. + +For example, the egg did not break from the 90th floor but it did break from the 100th floor, so we know that the egg must break on one of the floors between 90 and 100. We test the 91st floor first then the 92nd floor and so on until the egg breaks and we have the solution. + +The worst case would be if the egg breaks from the 99th floor because this would take us 19 egg drops in total. + +![](../../images/two-eggs-2.png) + +Why are these not the best approaches? How can you make them optimal in their worst case? + +The optimal solution - worst case 14 + +We should start by dropping an egg from the 14th floor. Can you think about why before reading on? + +**What happens if the egg breaks from the 14 th floor?** + +If the egg breaks from being dropped from the 14th floor, then it would break from every floor above this. We should then check the 1st floor, then the 2nd floor, all the way up to the 13th floor (13 floors). In the worst-case scenario, we would have to check 14 floors in total: 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. + +![](../../images/two-eggs-3.png) + +**What happens if the egg does not break from the 14 th floor?** + +If the egg did not break from being dropped from the 14th floor, then it would not break from any floor +below this. Then we would check the 27 th floor next. This is because if it breaks at the 27th floor, we would only have to check all the floors from the 15th to the 26th one (12 floors). Start by checking the 15th floor,then the 16th floor, all the way up to the 26th floor. In the worst-case scenario, we would again have to check 14 floors in total: 14, 27, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26. + +![](../../images/two-eggs-4.png) + +**What happens if the egg still does not break?** + +If the egg did not break from the 27th floor, then you would have to check from the 39th floor. And if it breaks from being dropped from the 39th floor, you would only have to check the floors from the 28th to the 38th one (11 floors). Meaning that in the worst-case scenario, we would still only have to the check 14 floors in total: 14, 27, 39, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38. + +![](../../images/two-eggs-5.png) + +Can you spot the pattern yet? + +Using the same logic, you should then move up to check the 50th floor and repeat the process. Then the +60th floor, the 69th floor, the 77th floor, the 84th floor, the 90th floor, the 99 th floor and finally the 100th floor. + +Putting this all together gives us: + +![](../../images/two-eggs-6.png) + +Using this strategy, you would be able to cover all the floors and the number of attempts would never be bigger than 14! + + + diff --git a/maths-club-pack/content/student/two-eggs.md b/maths-club-pack/content/student/two-eggs.md new file mode 100644 index 00000000..fedd760a --- /dev/null +++ b/maths-club-pack/content/student/two-eggs.md @@ -0,0 +1,15 @@ +--- +title: Two Eggs +type: problem +order: 35 +--- + +# Two Eggs + +You are given **two eggs** and access to a 100-storey building. + +If an egg is dropped and does not break, it can be dropped again. Once the egg breaks, it cannot be used again. If an egg breaks when dropped from floor n, then it would also have broken from any floor above that. If an egg survives a fall,then it will survive any fall shorter than that. + +How would you find out what the highest floor is from which an egg will **not** break when dropped out of the window? 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zsY>$5VIws}q8Y^l>Q#Qo8_2-ysEtH-1n!d+au00u^)#22nAn<L2k49{f}laW7BXL{<$`!M zoR{sy{(n+1iI;v90@vfdApproach A - worst case 100 + +The first logical approach would be to test every floor from the bottom floor to the top floor. So, we could start from the 1st floor and drop the egg from there. If it survives we can move up to try again from the 2nd floor, then the 3rd floor and so on. We keep moving a floor up each time until the egg breaks, and we get +the solution. For example, if the egg breaks on the 67th floor, we know that the highest floor than an egg +can withstand a drop is from the 66th floor. In this case, we would have dropped a single egg 67 times! + +There is also a chance that the egg will not break from the 100th floor and by using this approach we would have dropped the egg 100 times in total to find this out! + +This approach is clearly not optimal. + +Approach B - worst case 50 + +Can we can halve the number of egg drops? What if we start by dropping the first egg from the 50 th floor? + +**What happens if the egg breaks from the 50th floor?** + +If the egg breaks from being dropped from the 50th floor, then it would break from every floor above this. +We would then only have 1 egg remaining to check all the floors below in a similar method to Approach A +(one floor at a time, starting from the 1st floor to the 49th floor). As a worst case, we would have to check 50 floors. + +**What happens if the egg does not break from the 50th floor?** + +If the egg did not break from being dropped from the 50th floor, then it would not break from any floor +below this. So again, we would only have 1 egg remaining to check all the floors above in a similar method to Approach A (one floor at a time, starting from the 51st floor to the 100th floor). As a worst case, we would have to check 50 floors in total. + +This is still not optimal. + +Approach C - worst case 19 + +What would happen if we started off dropping our first egg at intervals of 10 floors? (for example, 10th +floor, 20th floor, 30th floor etc.). + +We would start by dropping the egg from the 10th floor. If the egg does not break, then it would not break from any floor below this and we can try again from the 20th floor. If the egg still does not break, we can try from the 30th floor, then the 40th floor and so on. Once the egg breaks from being dropped, we know that the solution is somewhere in the 9 floors below. + +For example, the egg did not break from the 90th floor but it did break from the 100th floor, so we know that the egg must break on one of the floors between 90 and 100. We test the 91st floor first then the 92nd floor and so on until the egg breaks and we have the solution. + +The worst case would be if the egg breaks from the 99th floor because this would take us 19 egg drops in total. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/two-eggs-2.png?raw=true) + +Why are these not the best approaches? How can you make them optimal in their worst case? + +The optimal solution - worst case 14 + +We should start by dropping an egg from the 14th floor. Can you think about why before reading on? + +**What happens if the egg breaks from the 14 th floor?** + +If the egg breaks from being dropped from the 14th floor, then it would break from every floor above this. We should then check the 1st floor, then the 2nd floor, all the way up to the 13th floor (13 floors). In the worst-case scenario, we would have to check 14 floors in total: 14, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/two-eggs-3.png?raw=true) + +**What happens if the egg does not break from the 14 th floor?** + +If the egg did not break from being dropped from the 14th floor, then it would not break from any floor +below this. Then we would check the 27 th floor next. This is because if it breaks at the 27th floor, we would only have to check all the floors from the 15th to the 26th one (12 floors). Start by checking the 15th floor,then the 16th floor, all the way up to the 26th floor. In the worst-case scenario, we would again have to check 14 floors in total: 14, 27, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/two-eggs-4.png?raw=true) + +**What happens if the egg still does not break?** + +If the egg did not break from the 27th floor, then you would have to check from the 39th floor. And if it breaks from being dropped from the 39th floor, you would only have to check the floors from the 28th to the 38th one (11 floors). Meaning that in the worst-case scenario, we would still only have to the check 14 floors in total: 14, 27, 39, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/two-eggs-5.png?raw=true) + +Can you spot the pattern yet? + +Using the same logic, you should then move up to check the 50th floor and repeat the process. Then the +60th floor, the 69th floor, the 77th floor, the 84th floor, the 90th floor, the 99 th floor and finally the 100th floor. + +Putting this all together gives us: + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/two-eggs-6.png?raw=true) + +Using this strategy, you would be able to cover all the floors and the number of attempts would never be bigger than 14! + + + diff --git a/translations/en/student/two-eggs.md b/translations/en/student/two-eggs.md new file mode 100644 index 00000000..116ff520 --- /dev/null +++ b/translations/en/student/two-eggs.md @@ -0,0 +1,9 @@ +# Two Eggs + +You are given **two eggs** and access to a 100-storey building. + +If an egg is dropped and does not break, it can be dropped again. Once the egg breaks, it cannot be used again. If an egg breaks when dropped from floor n, then it would also have broken from any floor above that. If an egg survives a fall,then it will survive any fall shorter than that. + +How would you find out what the highest floor is from which an egg will **not** break when dropped out of the window? How would you minimise the number of egg drops it takes to find this out? + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/two-eggs-1.png?raw=true) \ No newline at end of file From fd682409882565b40bcef1025181d405d0a5dde2 Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Thu, 10 Sep 2020 09:58:41 +0300 Subject: [PATCH 13/19] added frog-party --- .../content/facilitator/frog-party.md | 32 ++++++++++++++++++ maths-club-pack/content/student/frog-party.md | 21 ++++++++++++ maths-club-pack/cover_images/frog-party.svg | 1 + maths-club-pack/images/frog-party-1.png | Bin 0 -> 44465 bytes maths-club-pack/images/frog-party-2.png | Bin 0 -> 78865 bytes maths-club-pack/images/frog-party-3.png | Bin 0 -> 131939 bytes maths-club-pack/images/frog-party-4.png | Bin 0 -> 4308 bytes maths-club-pack/images/frog-party-5.png | Bin 0 -> 9232 bytes maths-club-pack/images/frog-party-6.png | Bin 0 -> 8468 bytes translations/en/facilitator/frog-party.md | 32 ++++++++++++++++++ translations/en/student/frog-party.md | 15 ++++++++ 11 files changed, 101 insertions(+) create mode 100644 maths-club-pack/content/facilitator/frog-party.md create mode 100644 maths-club-pack/content/student/frog-party.md create mode 100644 maths-club-pack/cover_images/frog-party.svg create mode 100644 maths-club-pack/images/frog-party-1.png create mode 100644 maths-club-pack/images/frog-party-2.png create mode 100644 maths-club-pack/images/frog-party-3.png create mode 100644 maths-club-pack/images/frog-party-4.png create mode 100644 maths-club-pack/images/frog-party-5.png create mode 100644 maths-club-pack/images/frog-party-6.png create mode 100644 translations/en/facilitator/frog-party.md create mode 100644 translations/en/student/frog-party.md diff --git a/maths-club-pack/content/facilitator/frog-party.md b/maths-club-pack/content/facilitator/frog-party.md new file mode 100644 index 00000000..146a2c24 --- /dev/null +++ b/maths-club-pack/content/facilitator/frog-party.md @@ -0,0 +1,32 @@ +# Frog Party + +## Introduction + +This is a really fun problem, and can be used to build many much harder problems. It is important when starting to problem to make sure the rules are clear. You might want to do this by showing examples of moves which are and are not allowed, using coins on top of pieces of paper or similar. + +## Solution + +There are many ways to solve this, and it is possible to have a party on every single lily pad. Two examples are given below, however you should ask students to also share their solutions + +![](../../images/frog-party-3.png) + +## Extension + +There are lots of ways you can make this problem more challenging and interesting, +which include: + + - Add more lily pads, is it still possible with 6, 10 or N? + + ![](../../images/frog-party-4.png) + +- Choose one of the frogs to be the Queen frog, who must be at the top of the +party + + ![](../../images/frog-party-5.png) + +- Swap one of the frogs for a lazy toad, who refuses to move. Is it still possible? + + ![](../../images/frog-party-6.png) + +Note, the strategy used in the second solution of working from the inside out also works +for any number of lily pads! \ No newline at end of file diff --git a/maths-club-pack/content/student/frog-party.md b/maths-club-pack/content/student/frog-party.md new file mode 100644 index 00000000..a59361e4 --- /dev/null +++ b/maths-club-pack/content/student/frog-party.md @@ -0,0 +1,21 @@ +--- +title: Frog Party +type: problem +order: 37 +--- + +# Frog Party + +5 frogs want to have a party. To do this they must all be on the same lily pad. + +![](../../images/frog-party-1.png) + +Frogs can jump left and right however there are a couple of rules: + +![](../../images/frog-party-2.png) + +Can you find a way to move the frogs so they can have a party together on the same lily pad? + +Is it possible to have a party on every lily pad? + + diff --git a/maths-club-pack/cover_images/frog-party.svg b/maths-club-pack/cover_images/frog-party.svg new file mode 100644 index 00000000..f7d167ae --- /dev/null +++ b/maths-club-pack/cover_images/frog-party.svg @@ -0,0 +1 @@ + \ No newline at end of file diff --git a/maths-club-pack/images/frog-party-1.png b/maths-club-pack/images/frog-party-1.png new file mode 100644 index 0000000000000000000000000000000000000000..42df9867202f4b28cc54b3fa7c202689361c9f1a GIT binary patch literal 44465 zcmeFZRa9J2v@Hk(w?GBgqHrtRLxA8GG`I$L*Wm8%8VZNt?n!VD?j%@n2@)LoaNm9J zc7OE8{pgP#<1$7_!QN+`eb!lf*_@k5cn0iuH;ERpL}V5ybu*KD}Wn 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It is important when starting to problem to make sure the rules are clear. You might want to do this by showing examples of moves which are and are not allowed, using coins on top of pieces of paper or similar. + +## Solution + +There are many ways to solve this, and it is possible to have a party on every single lily pad. Two examples are given below, however you should ask students to also share their solutions + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/frog-party-3.png?raw=true) + +## Extension + +There are lots of ways you can make this problem more challenging and interesting, +which include: + + - Add more lily pads, is it still possible with 6, 10 or N? + + ![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/frog-party-4.png?raw=true) + +- Choose one of the frogs to be the Queen frog, who must be at the top of the +party + + ![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/frog-party-5.png?raw=true) + +- Swap one of the frogs for a lazy toad, who refuses to move. Is it still possible? + + ![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/frog-party-6.png?raw=true) + +Note, the strategy used in the second solution of working from the inside out also works +for any number of lily pads! \ No newline at end of file diff --git a/translations/en/student/frog-party.md b/translations/en/student/frog-party.md new file mode 100644 index 00000000..bcd2e041 --- /dev/null +++ b/translations/en/student/frog-party.md @@ -0,0 +1,15 @@ +# Frog Party + +5 frogs want to have a party. To do this they must all be on the same lily pad. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/frog-party-1.png?raw=true) + +Frogs can jump left and right however there are a couple of rules: + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/frog-party-2.png?raw=true) + +Can you find a way to move the frogs so they can have a party together on the same lily pad? + +Is it possible to have a party on every lily pad? + + From 03f8cf1006081e10768cb391312ad443aa737505 Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Thu, 10 Sep 2020 10:07:43 +0300 Subject: [PATCH 14/19] added counting-chickens --- .../content/facilitator/counting-chickens.md | 27 ++++++++++++++++++ .../content/student/counting-chickens.md | 20 +++++++++++++ .../cover_images/counting-chickens.svg | 1 + .../images/counting-chickens-1.png | Bin 0 -> 59323 bytes .../images/counting-chickens-2.png | Bin 0 -> 152753 bytes .../images/counting-chickens-3.png | Bin 0 -> 10701 bytes .../images/counting-chickens-4.png | Bin 0 -> 73627 bytes .../en/facilitator/counting-chickens.md | 27 ++++++++++++++++++ translations/en/student/counting-chickens.md | 14 +++++++++ 9 files changed, 89 insertions(+) create mode 100644 maths-club-pack/content/facilitator/counting-chickens.md create mode 100644 maths-club-pack/content/student/counting-chickens.md create mode 100644 maths-club-pack/cover_images/counting-chickens.svg create mode 100644 maths-club-pack/images/counting-chickens-1.png create mode 100644 maths-club-pack/images/counting-chickens-2.png create mode 100644 maths-club-pack/images/counting-chickens-3.png create mode 100644 maths-club-pack/images/counting-chickens-4.png create mode 100644 translations/en/facilitator/counting-chickens.md create mode 100644 translations/en/student/counting-chickens.md diff --git a/maths-club-pack/content/facilitator/counting-chickens.md b/maths-club-pack/content/facilitator/counting-chickens.md new file mode 100644 index 00000000..f0560d5c --- /dev/null +++ b/maths-club-pack/content/facilitator/counting-chickens.md @@ -0,0 +1,27 @@ +# Counting Chickens + +## Introduction + +This activity looks at the interesting concept of having a circle with n points on its perimeter and what happens when you joint those points up. + +Three examples are given on the question sheet so students can see how to visualize the problems. The activity questions rely on students being able to develop on these primary examples to solve more complicated cases. The extension looks at spotting a pattern and developing a rule. + +It is advisable that students try drawing out each case. It should be noted that the use of colours can be a +way for students to picture the different regions more easily. + +## Solution + +![](../../images/counting-chickens-2.png) + +## Extension + +Is there a pattern between the number of fence posts and the maximum number of chickens that can be kept? + +Hint: Fill out this table (some of it has been filled out for you) + +![](../../images/counting-chickens-3.png) + +Using Pascal’s triangle, what will happen if you add the numbers to the left of the line in each row? Can +you spot the pattern now? Can you explain this strange pattern? + +![](../../images/counting-chickens-4.png) \ No newline at end of file diff --git a/maths-club-pack/content/student/counting-chickens.md b/maths-club-pack/content/student/counting-chickens.md new file mode 100644 index 00000000..56bf9605 --- /dev/null +++ b/maths-club-pack/content/student/counting-chickens.md @@ -0,0 +1,20 @@ +--- +title: Counting Chickens +type: problem +order: 36 +--- + +# Counting Chickens +A farmer keeps his chickens in circular fields,separated by fence posts and straight fencing. + +![](../../images/counting-chickens-1.png) + +Can you work out how many chickens the +farmer can keep if he has: + +1\)     4 fence posts + +2\)     5 fence posts + +3\)     6 fence posts + diff --git a/maths-club-pack/cover_images/counting-chickens.svg b/maths-club-pack/cover_images/counting-chickens.svg new file mode 100644 index 00000000..731d0959 --- /dev/null +++ b/maths-club-pack/cover_images/counting-chickens.svg @@ -0,0 +1 @@ + \ No 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++++++++++++++++++ translations/en/student/monkey-business.md | 18 +++++++ 6 files changed, 143 insertions(+) create mode 100644 maths-club-pack/content/facilitator/monkey-business.md create mode 100644 maths-club-pack/content/student/monkey-business.md create mode 100644 maths-club-pack/cover_images/monkey-business.svg create mode 100644 maths-club-pack/images/monkey-business-1.png create mode 100644 translations/en/facilitator/monkey-business.md create mode 100644 translations/en/student/monkey-business.md diff --git a/maths-club-pack/content/facilitator/monkey-business.md b/maths-club-pack/content/facilitator/monkey-business.md new file mode 100644 index 00000000..49b9d1f7 --- /dev/null +++ b/maths-club-pack/content/facilitator/monkey-business.md @@ -0,0 +1,50 @@ +# Monkey Business + +## Introduction + +This is another problem where the solution seems impossible because there are too many things to consider (1000 monkeys!), but again becomes achievable once simplified and able to see patterns. To start the problem you should ensure students understand the rules, perhaps imitating with 4 students and the same number of coins or cards that can be flipped to face up or down. + +The first student flip all cards up (u):                         [u, u, u, u] + +The second student flip the evens down (d):            [u, d, u, d] + +The third student would flip card 3:                           [u, d, d, d] + +The fourth student would flip card 4:                         [u, d, d, u] + + + + +## Solution + +1.For the first part of the problem you only need to consider 10 monkeys (as the 11th monkey and later will not press any of the first 10 switches). So which monkeys will press switch number 10? Well, as 10 is divisible by 1, 2, 5 and 10 there are exactly 4 monkeys which will press the switch + +* Monkey 1 turns it on + +* Monkey 2 turns it off + +* Monkey 5 turns it back on + +* Monkey 10 turns it back off + +So switch 10 will be **off**. + +2.The next part is more challenging, but again relies of thinking about how many monkeys will press each switch. + +Switch 10 was off because every time one monkey turned it on another turned it off. We were able to split the number 10 into factor pairs (1x10, 2x5), which will always result in the light being turned off. + +Most numbers will be pressed by an even number of monkeys, e.g. 24 has factors (1x24, 2x12, 3x8, 4x6), so monkeys 1, 2, 3, 4, 6, 8, 12, 24 will press the switch, and as this is an even number the light will be off. + +Square numbers are the only ones which do not, e.g. 16 has factors (1x16, 2x8, **4x4**). Monkeys 1, 2, **4**, 8, 16 will press the switch, and as this is an odd number the light will stay on (monkey 4 won’t press it twice!). + +**So we just need to work out how many square numbers there are between 1 and 1000?** + +If we think about the larges square number less than 1000, **30x30=900, 31x31=961, 32x32=1024** + +So there will be **31 switches left on**! (switch numbers 1, 4, 9, 16, 25, 36, ... , 900, 961) + +## Extension + +How many lights would stay on if only the even numbered monkeys decided to take their turn pressing the switches? + + \ No newline at end of file diff --git a/maths-club-pack/content/student/monkey-business.md b/maths-club-pack/content/student/monkey-business.md new file mode 100644 index 00000000..1821bb19 --- /dev/null +++ b/maths-club-pack/content/student/monkey-business.md @@ -0,0 +1,24 @@ +--- +title: Monkey Business +type: problem +order: 38 +--- + +# Monkey Business + +A large room has 1000 lightbulbs in it, all are switched off, but each has its own switch to turn on + +1000 monkeys enter the room and decide to press the light switches in a very particular way. + +![](../../images/monkey-business-1.png) + +The 1st monkey presses every multiple of 1. +The 2nd monkey presses every multiple of 2. +The 3rd monkey presses every multiple of 3. +Etc., until the 1000th monkey. + +After all the monkeys have finished pressing switches: +1. Will light number 10 be on or off? + +2. 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To start the problem you should ensure students understand the rules, perhaps imitating with 4 students and the same number of coins or cards that can be flipped to face up or down. + +The first student flip all cards up (u):                         [u, u, u, u] + +The second student flip the evens down (d):            [u, d, u, d] + +The third student would flip card 3:                           [u, d, d, d] + +The fourth student would flip card 4:                         [u, d, d, u] + + + + +## Solution + +1.For the first part of the problem you only need to consider 10 monkeys (as the 11th monkey and later will not press any of the first 10 switches). So which monkeys will press switch number 10? Well, as 10 is divisible by 1, 2, 5 and 10 there are exactly 4 monkeys which will press the switch + +* Monkey 1 turns it on + +* Monkey 2 turns it off + +* Monkey 5 turns it back on + +* Monkey 10 turns it back off + +So switch 10 will be **off**. + +2.The next part is more challenging, but again relies of thinking about how many monkeys will press each switch. + +Switch 10 was off because every time one monkey turned it on another turned it off. We were able to split the number 10 into factor pairs (1x10, 2x5), which will always result in the light being turned off. + +Most numbers will be pressed by an even number of monkeys, e.g. 24 has factors (1x24, 2x12, 3x8, 4x6), so monkeys 1, 2, 3, 4, 6, 8, 12, 24 will press the switch, and as this is an even number the light will be off. + +Square numbers are the only ones which do not, e.g. 16 has factors (1x16, 2x8, **4x4**). Monkeys 1, 2, **4**, 8, 16 will press the switch, and as this is an odd number the light will stay on (monkey 4 won’t press it twice!). + +**So we just need to work out how many square numbers there are between 1 and 1000?** + +If we think about the larges square number less than 1000, **30x30=900, 31x31=961, 32x32=1024** + +So there will be **31 switches left on**! (switch numbers 1, 4, 9, 16, 25, 36, ... , 900, 961) + +## Extension + +How many lights would stay on if only the even numbered monkeys decided to take their turn pressing the switches? + + \ No newline at end of file diff --git a/translations/en/student/monkey-business.md b/translations/en/student/monkey-business.md new file mode 100644 index 00000000..c97fe670 --- /dev/null +++ b/translations/en/student/monkey-business.md @@ -0,0 +1,18 @@ +# Monkey Business + +A large room has 1000 lightbulbs in it, all are switched off, but each has its own switch to turn on + +1000 monkeys enter the room and decide to press the light switches in a very particular way. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/monkey-business-1.png?raw=true) + +The 1st monkey presses every multiple of 1. +The 2nd monkey presses every multiple of 2. +The 3rd monkey presses every multiple of 3. +Etc., until the 1000th monkey. + +After all the monkeys have finished pressing switches: +1. Will light number 10 be on or off? + +2. How many lights in total will be on? + From aa665ff906421e6adb5739ff48e257b53e36ce8f Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Thu, 10 Sep 2020 12:13:04 +0300 Subject: [PATCH 16/19] added locks-and-keys --- .../content/facilitator/locks-and-keys.md | 37 ++++++++++ .../content/student/locks-and-keys.md | 17 +++++ .../cover_images/locks-and-keys.svg | 68 ++++++++++++++++++ maths-club-pack/images/locks-and-keys-1.png | Bin 0 -> 28857 bytes translations/en/facilitator/locks-and-keys.md | 37 ++++++++++ translations/en/student/locks-and-keys.md | 11 +++ 6 files changed, 170 insertions(+) create mode 100644 maths-club-pack/content/facilitator/locks-and-keys.md create mode 100644 maths-club-pack/content/student/locks-and-keys.md create mode 100644 maths-club-pack/cover_images/locks-and-keys.svg create mode 100644 maths-club-pack/images/locks-and-keys-1.png create mode 100644 translations/en/facilitator/locks-and-keys.md create mode 100644 translations/en/student/locks-and-keys.md diff --git a/maths-club-pack/content/facilitator/locks-and-keys.md b/maths-club-pack/content/facilitator/locks-and-keys.md new file mode 100644 index 00000000..b3d6cf1b --- /dev/null +++ b/maths-club-pack/content/facilitator/locks-and-keys.md @@ -0,0 +1,37 @@ +# Locks and Keys + +## Introduction + +This problem is not specified very precisely, and in this case it is intentional. The aim of this problem is to work with assumptions. The problem has different solutions under different assumptions, and it might be +easy or even impossible depending on the assumptions. For example, if we assume that the messenger can break the box or the lock, then the problem is impossible (and somewhat pointless). + +There is no right or wrong solution because there is no right or wrong set of assumptions. However, if we specify our assumptions clearly, then for the given set of assumptions any solution is either right or wrong. +The facilitator should encourage students to decide on what should be allowed or not so that the problem is not solved too easily or made impossible. + +This activity involves lots of discussion between groups. It could help to have paper cutouts of locks, keys and boxes so students can demonstrate rather than only explain. You should encourage students to demonstrate their solutions, and to challenge each other to see if they can find a way to intercept. + +## Solution + +There’s are lots of different strategies that could be tested and argued, here we will only outline a few possibilities, it is up to the students and facilitator to decide if their own solutions work or not. + +We will start with a few assumptions: + +         1. The messenger cannot break the box or the lock. + +         2. The messenger cannot make copies of keys. + +**Case 1:** Alice locks the box and sends it to Bob. Bob sends the messenger back to Alice. Alice now gives the messenger the key to send it to Bob. The messenger gives the key to Bob and Bob unlocks the box. + +**Intercept:** The messenger only pretends to deliver the box to Bob, but instead keeps it. He then returns it back to Alice and obtains the key to unlock the box and read the message. + +**Case 2:** Alice sends the key using a different messenger than for the box. + +**Intercept:** The messengers collaborate. You would need to decide in the rules whether this would be possible. + +**Case 3:** Alice locks the box with her lock and sends it to Bob. Bob attaches his own lock and sends it back.Alice takes her lock off the box and sends it back again. Finally, Bob takes his own lock off to read the message. + +**Intercept:** In this case there would be no way to intercept the message without breaking the box or copying keys! + +## Extension + +Bob opens the box and see it is instructions to play a game. To start the game Alice and Bob will flip a coin to decide who goes first, however they will still need the messenger to communicate the outcome. Who should flip the coin? Who should choose heads or tails? How can they communicate in a way so that neither person can cheat? diff --git a/maths-club-pack/content/student/locks-and-keys.md b/maths-club-pack/content/student/locks-and-keys.md new file mode 100644 index 00000000..bb4f693d --- /dev/null +++ b/maths-club-pack/content/student/locks-and-keys.md @@ -0,0 +1,17 @@ +--- +title: Locks and Keys +type: problem +order: 39 +--- + +# Locks and Keys + +Alice has a secret message that she wants to +send to Bob, who lives far away. She has a box and a lock and one key. Bob also has a lock with one key. + +![](../../images/locks-and-keys-1.png) + +To send things between each other Alice and +Bob have a messenger, who can travel multiple times between them. 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The aim of this problem is to work with assumptions. The problem has different solutions under different assumptions, and it might be +easy or even impossible depending on the assumptions. For example, if we assume that the messenger can break the box or the lock, then the problem is impossible (and somewhat pointless). + +There is no right or wrong solution because there is no right or wrong set of assumptions. However, if we specify our assumptions clearly, then for the given set of assumptions any solution is either right or wrong. +The facilitator should encourage students to decide on what should be allowed or not so that the problem is not solved too easily or made impossible. + +This activity involves lots of discussion between groups. It could help to have paper cutouts of locks, keys and boxes so students can demonstrate rather than only explain. You should encourage students to demonstrate their solutions, and to challenge each other to see if they can find a way to intercept. + +## Solution + +There’s are lots of different strategies that could be tested and argued, here we will only outline a few possibilities, it is up to the students and facilitator to decide if their own solutions work or not. + +We will start with a few assumptions: + +         1. The messenger cannot break the box or the lock. + +         2. The messenger cannot make copies of keys. + +**Case 1:** Alice locks the box and sends it to Bob. Bob sends the messenger back to Alice. Alice now gives the messenger the key to send it to Bob. The messenger gives the key to Bob and Bob unlocks the box. + +**Intercept:** The messenger only pretends to deliver the box to Bob, but instead keeps it. He then returns it back to Alice and obtains the key to unlock the box and read the message. + +**Case 2:** Alice sends the key using a different messenger than for the box. + +**Intercept:** The messengers collaborate. You would need to decide in the rules whether this would be possible. + +**Case 3:** Alice locks the box with her lock and sends it to Bob. Bob attaches his own lock and sends it back.Alice takes her lock off the box and sends it back again. Finally, Bob takes his own lock off to read the message. + +**Intercept:** In this case there would be no way to intercept the message without breaking the box or copying keys! + +## Extension + +Bob opens the box and see it is instructions to play a game. To start the game Alice and Bob will flip a coin to decide who goes first, however they will still need the messenger to communicate the outcome. Who should flip the coin? Who should choose heads or tails? How can they communicate in a way so that neither person can cheat? diff --git a/translations/en/student/locks-and-keys.md b/translations/en/student/locks-and-keys.md new file mode 100644 index 00000000..c23321b0 --- /dev/null +++ b/translations/en/student/locks-and-keys.md @@ -0,0 +1,11 @@ +# Locks and Keys + +Alice has a secret message that she wants to +send to Bob, who lives far away. She has a box and a lock and one key. Bob also has a lock with one key. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/locks-and-keys-1.png?raw=true) + +To send things between each other Alice and +Bob have a messenger, who can travel multiple times between them. But they don’t trust him, and don’t want him to read the message. + +How can Alice send her message to Bob without the messenger reading it? From ea91e95578dc5849e768696c8fe8084be1b93ea2 Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Thu, 10 Sep 2020 13:18:27 +0300 Subject: [PATCH 17/19] added scales-and-weights --- .../content/facilitator/scales-and-weights.md | 38 ++++++++++++++++++ .../content/student/scales-and-weights.md | 23 +++++++++++ .../cover_images/scales-and-weights.svg | 1 + .../images/scales-and-weights-1.png | Bin 0 -> 29101 bytes .../images/scales-and-weights-2.png | Bin 0 -> 19311 bytes .../images/scales-and-weights-3.png | Bin 0 -> 17819 bytes .../en/facilitator/scales-and-weights.md | 38 ++++++++++++++++++ translations/en/student/scales-and-weights.md | 17 ++++++++ 8 files changed, 117 insertions(+) create mode 100644 maths-club-pack/content/facilitator/scales-and-weights.md create mode 100644 maths-club-pack/content/student/scales-and-weights.md create mode 100644 maths-club-pack/cover_images/scales-and-weights.svg create mode 100644 maths-club-pack/images/scales-and-weights-1.png create mode 100644 maths-club-pack/images/scales-and-weights-2.png create mode 100644 maths-club-pack/images/scales-and-weights-3.png create mode 100644 translations/en/facilitator/scales-and-weights.md create mode 100644 translations/en/student/scales-and-weights.md diff --git a/maths-club-pack/content/facilitator/scales-and-weights.md b/maths-club-pack/content/facilitator/scales-and-weights.md new file mode 100644 index 00000000..8130a749 --- /dev/null +++ b/maths-club-pack/content/facilitator/scales-and-weights.md @@ -0,0 +1,38 @@ +# Scales and Weights + +## Introduction + +The statement is not 100% precise, so: You want to put all the flour in one bag and weigh it, not splitting it into smaller bags for weighing. The weights to measure are whole numbers only. + +## Solution + +This problem has two different versions depending on the assumptions you're using. Both are interesting, +and it is worth **encouraging students to try both.** + +- The first version is probably slightly easier, and assumes that you can only put weighing stones on the side of the scale. + +- In the second version, you can put weighing stones on either side, giving more options. + +**Encourage students to try for much smaller numbers than 40 first.** For example, if we only want to measure weights up to 7kg, then weighing stones of 1 kg and 2 kg and 4kg are sufficient (check that you can measure 1,2,3,4,5,6,7kg with these!). + +If we could put weights on both sides we could come up with more interesting solutions, for example if we had 1kg, 3kg and 6kg weights we could weight 1,2,3,4,5,6,7,8,9, and 10! + +E.g. If we have 8kg of flour, we could add the 1kg weight to it and it would balance against the 6kg and 3kg. See if you can make all the other numbers! + +![](../../images/scales-and-weights-3.png) + +The best strategy for the first problem is to start from 1kg, and every time there is a number you can’t +make add another stone. Quickly you see that if you have **1kg, 2kg, 4kg, 8kg, 16kg,** you can measure every +number up to 31kg. You will therefore need a 5th stone to reach 40kg. You could make this a 9kg stone, +however it would be better if you added a **32kg** stone and now can measure everything up to 63kg. + +For the second problem you not only want to consider the total when stones are added together, but the difference when they are subtracted (because you can have stones on either side). You want to give as many different numbers as possible using as few stones as possible. + +To start we will either need a 1kg stone, or 2 stones with a 1kg difference. In the example above we started +with a 1kg stone but what if we started with **1kg** and **3kg**? We can now measure 1,2,3,4.To get 5kg we can pick the largest number which will balance against the 5kg flour + 1kg + 3kg stones, so we should pick **9kg**. This now lets us make every number up to 9+3+1 = 13kg. To get 14kg we simply add a **27kg** stone, because 27kg – 9kg – 3kg – 1kg = 14. With the 27kg stone we can now measure everything up to 40Kg, so **it is possible with only these 4 stones!** + + +## Extension + +Continue this process to see which stones you would use up to 1000kg. Is there a formula you could use to +calculate? diff --git a/maths-club-pack/content/student/scales-and-weights.md b/maths-club-pack/content/student/scales-and-weights.md new file mode 100644 index 00000000..88b8f61f --- /dev/null +++ b/maths-club-pack/content/student/scales-and-weights.md @@ -0,0 +1,23 @@ +--- +title: Scales and Weights +type: problem +order: 40 +--- + +# Scales and Weights + +You have a shop selling maize flour by weight. +Your customers may want to buy any amount +between 1 and 40 kg of flour. + +![](../../images/scales-and-weights-1.png) + +You also have a balancing scale and want to +buy weighing stones to use with it. + +![](../../images/scales-and-weights-2.png) + +Which weighing stones should you buy so you +can measure any weight between 1 and 40 +kg? 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zLBat0W3<#-e%AQ`LcdT~MF08GfeSTO5vnNYTqa)fknh2A6n840TTx!VA3z@E!OiBq z^v46h4GU{)_h{c(oS#QmqtkNI?l3?Epg$=ZNDvnhsaY2>R8!xuy6v(BYz>D$n<@bp zkO(A2d5H~L@)jIKCvwg(E)P=D(kMT%BtqrnInDH;})q>Q&y=c+K)t^OuhY?1h&gQ@Wz(h_;S+Y*t HB<%kH4%`OD literal 0 HcmV?d00001 diff --git a/translations/en/facilitator/scales-and-weights.md b/translations/en/facilitator/scales-and-weights.md new file mode 100644 index 00000000..8de229f7 --- /dev/null +++ b/translations/en/facilitator/scales-and-weights.md @@ -0,0 +1,38 @@ +# Scales and Weights + +## Introduction + +The statement is not 100% precise, so: You want to put all the flour in one bag and weigh it, not splitting it into smaller bags for weighing. The weights to measure are whole numbers only. + +## Solution + +This problem has two different versions depending on the assumptions you're using. Both are interesting, +and it is worth **encouraging students to try both.** + +- The first version is probably slightly easier, and assumes that you can only put weighing stones on the side of the scale. + +- In the second version, you can put weighing stones on either side, giving more options. + +**Encourage students to try for much smaller numbers than 40 first.** For example, if we only want to measure weights up to 7kg, then weighing stones of 1 kg and 2 kg and 4kg are sufficient (check that you can measure 1,2,3,4,5,6,7kg with these!). + +If we could put weights on both sides we could come up with more interesting solutions, for example if we had 1kg, 3kg and 6kg weights we could weight 1,2,3,4,5,6,7,8,9, and 10! + +E.g. If we have 8kg of flour, we could add the 1kg weight to it and it would balance against the 6kg and 3kg. See if you can make all the other numbers! + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/scales-and-weights-3.png?raw=true) + +The best strategy for the first problem is to start from 1kg, and every time there is a number you can’t +make add another stone. Quickly you see that if you have **1kg, 2kg, 4kg, 8kg, 16kg,** you can measure every +number up to 31kg. You will therefore need a 5th stone to reach 40kg. You could make this a 9kg stone, +however it would be better if you added a **32kg** stone and now can measure everything up to 63kg. + +For the second problem you not only want to consider the total when stones are added together, but the difference when they are subtracted (because you can have stones on either side). You want to give as many different numbers as possible using as few stones as possible. + +To start we will either need a 1kg stone, or 2 stones with a 1kg difference. In the example above we started +with a 1kg stone but what if we started with **1kg** and **3kg**? We can now measure 1,2,3,4.To get 5kg we can pick the largest number which will balance against the 5kg flour + 1kg + 3kg stones, so we should pick **9kg**. This now lets us make every number up to 9+3+1 = 13kg. To get 14kg we simply add a **27kg** stone, because 27kg – 9kg – 3kg – 1kg = 14. With the 27kg stone we can now measure everything up to 40Kg, so **it is possible with only these 4 stones!** + + +## Extension + +Continue this process to see which stones you would use up to 1000kg. Is there a formula you could use to +calculate? diff --git a/translations/en/student/scales-and-weights.md b/translations/en/student/scales-and-weights.md new file mode 100644 index 00000000..3979a096 --- /dev/null +++ b/translations/en/student/scales-and-weights.md @@ -0,0 +1,17 @@ +# Scales and Weights + +You have a shop selling maize flour by weight. +Your customers may want to buy any amount +between 1 and 40 kg of flour. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/scales-and-weights-1.png?raw=true) + +You also have a balancing scale and want to +buy weighing stones to use with it. + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/scales-and-weights-2.png?raw=true) + +Which weighing stones should you buy so you +can measure any weight between 1 and 40 +kg? (You want to buy as few as possible) + From 6146c3d4df62a0f005e355a19c1a07292795375c Mon Sep 17 00:00:00 2001 From: Grace Kebirungi Date: Thu, 10 Sep 2020 15:45:03 +0300 Subject: [PATCH 18/19] added picture-puzzles-1 --- .../content/facilitator/picture-puzzles-1.md | 13 +++++++++++++ .../content/student/picture-puzzles-1.md | 15 +++++++++++++++ .../cover_images/picture-puzzles-1.svg | 1 + maths-club-pack/images/picture-puzzles-1-1.png | Bin 0 -> 156009 bytes maths-club-pack/images/picture-puzzles-1-2.png | Bin 0 -> 199142 bytes .../en/facilitator/picture-puzzles-1.md | 13 +++++++++++++ translations/en/student/picture-puzzles-1.md | 9 +++++++++ 7 files changed, 51 insertions(+) create mode 100644 maths-club-pack/content/facilitator/picture-puzzles-1.md create mode 100644 maths-club-pack/content/student/picture-puzzles-1.md create mode 100644 maths-club-pack/cover_images/picture-puzzles-1.svg create mode 100644 maths-club-pack/images/picture-puzzles-1-1.png create mode 100644 maths-club-pack/images/picture-puzzles-1-2.png create mode 100644 translations/en/facilitator/picture-puzzles-1.md create mode 100644 translations/en/student/picture-puzzles-1.md diff --git a/maths-club-pack/content/facilitator/picture-puzzles-1.md b/maths-club-pack/content/facilitator/picture-puzzles-1.md new file mode 100644 index 00000000..0f1f4662 --- /dev/null +++ b/maths-club-pack/content/facilitator/picture-puzzles-1.md @@ -0,0 +1,13 @@ +# Picture Puzzles 1 + +## Introduction + +These problems can all be solved in different ways, but it is recommended you encourage students to use logic and reasoning skills instead of guessing numbers. Usually each line gives you a piece of information that you can use in the next, so you should think carefully about each piece of information before moving onto the next. The problems also get harder as you go, so encourage students to start with the top-left puzzle first. + +## Solution + +![](../../images/picture-puzzles-1-2.png) + +## Extension + +Ask students to try and make their own picture puzzles! \ No newline at end of file diff --git a/maths-club-pack/content/student/picture-puzzles-1.md b/maths-club-pack/content/student/picture-puzzles-1.md new file mode 100644 index 00000000..c27e7742 --- /dev/null +++ b/maths-club-pack/content/student/picture-puzzles-1.md @@ -0,0 +1,15 @@ +--- +title: Picture Puzzles 1 +type: problem +order: 41 +--- + +# Picture Puzzles 1 + +The following 4 problems all have pictures to +represent numbers. 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maths-club-pack/images/special-numbers-1.png | Bin 0 -> 37220 bytes .../en/facilitator/special-numbers.md | 37 ++++++++++++++++++ translations/en/student/special-numbers.md | 16 ++++++++ 6 files changed, 113 insertions(+) create mode 100644 maths-club-pack/content/facilitator/special-numbers.md create mode 100644 maths-club-pack/content/student/special-numbers.md create mode 100644 maths-club-pack/cover_images/special-numbers.svg create mode 100644 maths-club-pack/images/special-numbers-1.png create mode 100644 translations/en/facilitator/special-numbers.md create mode 100644 translations/en/student/special-numbers.md diff --git a/maths-club-pack/content/facilitator/special-numbers.md b/maths-club-pack/content/facilitator/special-numbers.md new file mode 100644 index 00000000..ba85aa3c --- /dev/null +++ b/maths-club-pack/content/facilitator/special-numbers.md @@ -0,0 +1,37 @@ +# Special Numbers + +## Introduction + +This problem comes from the Nrich website with additional notes: http://nrich.maths.org/2129 + +The problem allows students to explore properties of numbers and start learning how to make *conjectures* (rules that they think might exist). + +Give the class some time to look for special numbers - once a few have been found, more will quickly follow. Once there is a consensus that a group of special numbers has been found, bring the class together and share what they think is going on. Ask them "Are you sure you've found all the special numbers? How could we be certain?" For this we need algebra. + +## Solution + +Introduce the class to the algebraic representation of the problem. + +Ask them, "If the first digit of the number is *a* and the second digit is *b*, what are expressions for the sum +and product of the digits?" Students should work out it is *a* + *b* for the **sum** and *ab* or *axb* for the **product.** +If they don't see this, show them with some examples with numbers in place of *a* and *b*. + +Next, how can we write the number as an algebraic expression? This is harder, you will probably need to show students that the number can be written as 10*a* + *b*. For example, 35 can be written as 3 × 10 + 5, because 3 is the tens digit and 5 is the units digit. + +Now we have an equation: 10*a* + *b* = (*a* + *b*) + (*a* × *b*)        (number = sum + product) + +Subtract *b* from both sides and subtract *a* from both sides to get 9*a* = *a* × *b*. Divide by *a* because *a* is not zero and we get *b* = 9. This means any number with unit digit 9 will work. Try all 9 possibilities 19, 29, ..., +99 to check that it works. + +If some students are not familiar with algebraic expressions, show them the extension questions. + +## Extension + +Then present the suggestions for other types of special numbers: +* I add twice the tens digit to the units digit, then add this to the product of the digits. I get back to my original number. +* I add three times the tens digit to the units digit, then add this to the product of the digits. I get back to my original number. +* I add four times... or five times... or... + +Can you work out which number are special using these definitions? + +Can you use algebra to help you to find these special numbers? diff --git a/maths-club-pack/content/student/special-numbers.md b/maths-club-pack/content/student/special-numbers.md new file mode 100644 index 00000000..47779b1b --- /dev/null +++ b/maths-club-pack/content/student/special-numbers.md @@ -0,0 +1,22 @@ +--- +title: Special Numbers +type: problem +order: 41 +--- + +# Special Numbers + +Can you guess my special two digit number? + +My number is special because if I add the **sum** of its digits to the **product** of its digits, it gives my original number! + +What could my number be? + +![](../../images/special-numbers-1.png) + +         1.       Can you find a special number? + +         2.       Can you find more than one? + +         3.       Can you find them all? + diff --git 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additional notes: http://nrich.maths.org/2129 + +The problem allows students to explore properties of numbers and start learning how to make *conjectures* (rules that they think might exist). + +Give the class some time to look for special numbers - once a few have been found, more will quickly follow. Once there is a consensus that a group of special numbers has been found, bring the class together and share what they think is going on. Ask them "Are you sure you've found all the special numbers? How could we be certain?" For this we need algebra. + +## Solution + +Introduce the class to the algebraic representation of the problem. + +Ask them, "If the first digit of the number is *a* and the second digit is *b*, what are expressions for the sum +and product of the digits?" Students should work out it is *a* + *b* for the **sum** and *ab* or *axb* for the **product.** +If they don't see this, show them with some examples with numbers in place of *a* and *b*. + +Next, how can we write the number as an algebraic expression? This is harder, you will probably need to show students that the number can be written as 10*a* + *b*. For example, 35 can be written as 3 × 10 + 5, because 3 is the tens digit and 5 is the units digit. + +Now we have an equation: 10*a* + *b* = (*a* + *b*) + (*a* × *b*)        (number = sum + product) + +Subtract *b* from both sides and subtract *a* from both sides to get 9*a* = *a* × *b*. Divide by *a* because *a* is not zero and we get *b* = 9. This means any number with unit digit 9 will work. Try all 9 possibilities 19, 29, ..., +99 to check that it works. + +If some students are not familiar with algebraic expressions, show them the extension questions. + +## Extension + +Then present the suggestions for other types of special numbers: +* I add twice the tens digit to the units digit, then add this to the product of the digits. I get back to my original number. +* I add three times the tens digit to the units digit, then add this to the product of the digits. I get back to my original number. +* I add four times... or five times... or... + +Can you work out which number are special using these definitions? + +Can you use algebra to help you to find these special numbers? diff --git a/translations/en/student/special-numbers.md b/translations/en/student/special-numbers.md new file mode 100644 index 00000000..c6ad8ced --- /dev/null +++ b/translations/en/student/special-numbers.md @@ -0,0 +1,16 @@ +# Special Numbers + +Can you guess my special two digit number? + +My number is special because if I add the **sum** of its digits to the **product** of its digits, it gives my original number! + +What could my number be? + +![](https://github.com/supportingami/sami-maths-club/blob/master/maths-club-pack/images/special-numbers-1.png?raw=true) + +         1.       Can you find a special number? + +         2.       Can you find more than one? + +         3.       Can you find them all? +

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