Pick A Box
Task 91 ... Years 4 - 10
SummaryA collection of decorated boxes is sorted into 3 groups according to several criteria, the mathematical ones of which relate to consecutive numbers and finding their sum. There are actually several solutions to the problem, but students will often reach what they think is a solution, only to find that on a second or third check there is a condition not satisfied. Once the one solution has been found, the challenge becomes:
IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.
Due to the multiple conditions that need to be satisfied, it may be necessary to read the 'frustration level' for some students and decide to intervene.
Students at East Devonport Primary.
Their teacher has organised Mathematician Teams.
The third clue is one entry point for providing assistance. Adding numbers in the three groups counts each of the fifteen numbers once. Therefore the total of these totals must be the same as the total of the numbers 1 through 15, which is 120. Then we need three consecutive numbers adding to 120 and they must be 39, 40 and 41.
Finding the total of numbers from 1 to 15 will be a challenge for some students and great opportunity for the teacher to ask Can you check this another way?.
To extend the problem ask the students to consider the possibility of another solution. To date we know of these:
Given there are multiple solutions, a further challenge would be to add a clue so that the problem has a unique solution. And of course, students could be challenged to create their own similar problem with the equipment or a subset of the equipment such as just the boxes numbered from 1 to 8.
More SolutionsFintona Girls' School
Year 5, Vanessa Stockley
Vanessa's class found lots of new solutions. What a great problem! Every group can be successful. And with so many solutions available, the new challenge of adding just one clue so that the problem has a unique solution is a great extension.
Whole Class InvestigationTasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.
Each pair (or perhaps group of 4) will need a set of 'boxes' before the lesson can become a whole class investigation. Cut rectangles of white card, provide markers and ask the students to design their own using these rules:
For more ideas and discussion about this investigation, open a new browser tab (or page) and visit Maths300 Lesson 70, Pick A Box.
Is it in Maths With Attitude?Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.
The Pick A Box task is an integral part of:
The Pick A Box lesson is not part of any Maths With Attitude kit, but it could be used to enhance:
A Pick Box Task 91 (Mwaka 4 - 10): Mkusanyiko wa masanduku yaliyopambwa umegawanywa katika vikundi vitatu kulingana na vigezo kadhaa, ambavyo vya hisabati vinahusiana na nambari mfululizo na kupata jumla yao. Kuna suluhisho kadhaa kwa tatizo, lakini mara nyingi wanafunzi hufikia kile wanachofikiri ni suluhisho, tu kupata kwamba katika ukaguzi wa pili au wa tatu kuna hali haijatimizwa. Mara moja suluhisho moja imepatikana, changamoto inakuwa: Iceberg Kazi ni ncha ya kujifunza iceberg. Sikuzote kuna mambo mengi zaidi ya yale yaliyoandikwa kwenye kadi. Kwa sababu ya hali nyingi ambazo zinahitaji kutoshelezwa, inaweza kuwa muhimu kusoma 'kiwango cha kukata tamaa' kwa wanafunzi fulani na kuamua kuingilia kati. Wanafunzi katika East Devonport Primary. Mwalimu wao amepanga Timu za Wanahisabati. Kidokezo cha tatu ni njia moja ya kutoa msaada. Kuongeza namba katika makundi matatu huhesabu kila moja ya namba kumi na tano mara moja. Kwa hiyo jumla ya jumla hizi lazima ziwe sawa na jumla ya namba 1 hadi 15, ambayo ni 120. Kwa mfano, tunahitaji kuongeza namba tatu mfululizo ambazo zinaongeza 120, 39, 40, na 41. Kupata jumla ya namba kutoka 1 hadi 15 itakuwa changamoto kwa baadhi ya wanafunzi na fursa kubwa kwa mwalimu kuuliza Je, unaweza kuangalia hii njia nyingine? Ili kupanua tatizo waulize wanafunzi kuzingatia uwezekano wa suluhisho jingine. Kwa sasa tunajua haya: Kwa kuwa kuna suluhisho nyingi, changamoto nyingine itakuwa kuongeza kiashiria ili tatizo hilo liwe na suluhisho la kipekee. Wanafunzi wanaweza pia kupewa changamoto ya kuunda tatizo lao wenyewe la mfano na vifaa au sehemu ya vifaa kama vile masanduku yaliyoorodheshwa kutoka 1 hadi 8. "Kama ilivyoelezwa katika kitabu cha ""Fintona Girls' School: Year 5 Vanessa Stockley's Class Found Many New Solutions"" (Fintona Girls' School: Mwaka wa Tano Vanessa Stockley's Class Found Many New Solutions)." Ni tatizo kubwa kama nini! Kila kikundi kinaweza kufanikiwa. Na kwa sababu ya suluhisho nyingi zinazopatikana, changamoto mpya ya kuongeza kiashiria kimoja tu ili tatizo hilo liwe na suluhisho la kipekee ni upanuzi mkubwa. Kazi za Uchunguzi wa Darasa Lote ni mwaliko kwa wanafunzi wawili kufanya kazi kama mwanahisabati. Kazi pia inaweza kubadilishwa kuwa uchunguzi wa darasa nzima ambayo mfano jinsi mwanahisabati kazi. Kila jozi (au labda kikundi cha 4) itahitaji seti ya'masanduku' kabla ya somo kuwa uchunguzi wa darasa nzima. Kuchukua kadi nyeupe, kutoa alama na kuuliza wanafunzi kubuni yao wenyewe kwa kutumia sheria hizi: Kwa mawazo zaidi na majadiliano kuhusu uchunguzi huu, kufungua tab mpya browser (au ukurasa) na kutembelea Maths300 somo 70, Pick Box. Maths With Attitude ni seti ya vifaa vya kujifunza vya mikono kutoka miaka ya 3 hadi 10 ambayo huunda matumizi ya kazi na uchunguzi wa darasa nzima katika mpangaji wa wiki kwa wiki. Pick A Box ni sehemu muhimu ya masomo ya Maths With Attitude.