Discuss and Choose

7449 /www/nrich/html/content/id/7449/ 1 2011-03-18T16:13:58 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> This activity challenges you to decide on the 'best' number to use in each of the following statements. You may like to talk to someone else about what you're thinking. You may need to do some estimating, some calculating and some research. Please send us your solutions and don't forget to explain how you arrived at your conclusions. <mdo:image alt="catA" height="122" src="catA.jpg" width="175"></mdo:image> 1) There are roughly 10 million/500 million/1000 million domestic cats in the world. 2) On average cats weigh 1.5/4.5/8 kg. 3) Domestic cats sleep on average 8-9/13-14/18-19 hours a day. <mdo:image alt="DogA" height="122" src="DogA.jpg" width="175"></mdo:image> 4) There are roughly 400 million/600 million/800 million domestic dogs in the world. 5) The average life of a dog is 10-14/14-18/18-20 years. <mdo:image alt="DolphinA" height="122" src="DolphinA.jpg" width="175"></mdo:image> 6) Dolphins live in groups called pods or schools of up to 12/20/30 individuals. <mdo:image alt="ElephantA" height="122" src="ElephantA.jpg" width="175"></mdo:image> 7) Adult elephants need to drink about 100/200/400 litres of water a day. <mdo:image alt="GiraffeA" height="122" src="GiraffeA.jpg" width="175"></mdo:image> 8) A giraffe's neck is about 120/170/220 cm long. 9) A giraffe's tail hair is 2/5/10 times as thick as the average human hair. <mdo:image alt="LionA" height="122" src="LionA.jpg" width="175"></mdo:image> 10) An average male lion weighs 180/250/330 kg. 11) A lion's roar can be heard 8/12/16 kms away. 12) Lions rest for 10/15/20 hours a day on average.</mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Some good suggestions came to us from pupils from many different countries. The answers I used were from a Nature Statistics web site. Mya from Ricards Lodge High School, UK sent in the following ideas for number $7$. She showed a good use of animal knowledge and of mathematical skills. I think that I might have a solution for number $7$. The question is ... Adult elephants need to drink about $100$/$200$/$400$ litres of water a day. I think that it is ... $100$l. An average adult human should drink about $2$ litres of water a day (coffee and tea don't count). An average ADULT human weights about between $65$/$80$ kg. So the median of the two numbers is $78$, so it should be approximately $1$l per $39$ kg ($39$ is half $78$), for a human. So bearing that in mind if an average adult elephant however weights $4.6$ tons, so converting that into kg that would be $4600$kg.($1$ ton is equal to $1000$kg.) So that is more than $70$ times more than an average human weight ... because $65x70$ would give you $4550$kg - only $50$kg short of $4600$kg. So if you multiply that by $70$ then multiply the amount of water (litres) by $70$ ... so you would get $140$. Rounding it to the nearest hundred you get $100$l !! I think that is right. Ella, from the same school, sent in these answers: $1) 500$ million $2) 4.5$kg $3) 13-14$ hours $4) 400$ million $5) 10-14$ years $6) 20$ individuals $7) 100$ litres $8) 170$cm $9) 5$ times as thick $10) 180$kg $11) 8$km $12) 20$ hours Aadil from Riverside Primary School, UK sent in these good suggestions as answers, many of which were correct: $1$. $500$ million $2$. $4.5$kg $3$. $18-19$ hours a day $4$. $600$ million $5$. $10-14$ years $6$. $30$ individuals $7$. $200$ litres $8$. $170$ cm $9$. $5$x $10$. $250$kg $11$. $16$km Betina, Luiza and Katrina from the British School in Barra, Brazil sent in these solutions, written here in the same order as their names: $1$ $500, 500, 500$ $2$ $4.5, 4.5, 4.5$ $3$ $13-14, 13-14, 13-14$ $4$ $600, 400, 400$ $5$ $18-20, 10-14, 10-14$ $6$ $12, 12, 12$ $7$ $400, 200, 200$ $8$ $220, 170, 170$ $9$ $5, 10, 10$ $10$ $330, 250, 250$ $11$ $8, 8, 8$ $12$ $15, 20, 20$ <div style="margin-left: 40px;"> </div> We also had answers from Germain, Mount Zion School, U.S.A., Julia from TromsØ School in Norway and Harry and Fin from Jebel Ali School in U.A.E. The answers that I used to set the challenge were: $1) 500 $ $2) 4$ to $5$ $3) 13$ to $14 $ $4) 400$ $5) 10$ to $14$ $6) 12$ $7) 200$ $8) 170$ $9) 10$x $10) 180$ $11) 8$ $12) 20$ </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>Discuss and Choose</h2> This activity challenges you to decide on the 'best' number to use in each of the following statements. You may like to talk to someone else about what you're thinking. You may need to do some estimating, some calculating and some research. Please send us your solutions and don't forget to explain how you arrived at your conclusions. <mdo:image alt="catA" height="122" src="catA.jpg" width="175"></mdo:image> 1) There are roughly 10 million/500 million/1000 million domestic cats in the world. 2) On average cats weigh 1.5/4.5/8 kg. 3) Domestic cats sleep on average 8-9/13-14/18-19 hours a day. <mdo:image alt="DogA" height="122" src="DogA.jpg" width="175"></mdo:image> 4) There are roughly 400 million/600 million/800 million domestic dogs in the world. 5) The average life of a dog is 10-14/14-18/18-20 years. <mdo:image alt="DolphinA" height="122" src="DolphinA.jpg" width="175"></mdo:image> 6) Dolphins live in groups called pods or schools of up to 12/20/30 individuals. <mdo:image alt="ElephantA" height="122" src="ElephantA.jpg" width="175"></mdo:image> 7) Adult elephants need to drink about 100/200/400 litres of water a day. <mdo:image alt="GiraffeA" height="122" src="GiraffeA.jpg" width="175"></mdo:image> 8) A giraffe's neck is about 120/170/220 cm long. 9) A giraffe's tail hair is 2/5/10 times as thick as the average human hair. <mdo:image alt="LionA" height="122" src="LionA.jpg" width="175"></mdo:image> 10) An average male lion weighs 180/250/330 kg. 11) A lion's roar can be heard 8/12/16 kms away. 12) Lions rest for 10/15/20 hours a day on average. </div> <h3>Why do this problem?</h3> <div>This <a href="http://nrich.maths.org/7449&part=">activity</a> gives an opportunity to discuss the quantities involved in the statements and may involve estimation, calculation and/or research. Children will rely not only on what they have learnt from school but also information they have picked up from elsewhere. The discussion may well reveal some surprises, particularly in terms of their understanding of different units of measurement. </div> <h3>Possible approach</h3> <div>The activity could be suitable for small group or whole class discussions, depending on the experiences of the children involved. You might find it helpful to print off copies of <a href="/content/id/7449/DiscussChoose.pdf">this sheet</a> which has all the statements on it. The statements could be cut up so that each is on a separate card. </div> <div> </div> <div>The role of the adult in this kind of situation is to enable discussion to take place effectively. It may be that after an initial discussion about each statement, you assign a pair or small group of children a few statements each and invite them to come up with evidence to support their suggested answer. If possible, encourage them to record as they go along so that they have a reminder of what they did.</div> <h3>Key questions</h3> <div>So, what do "you" think about what "they" have just said?</div> <div>Tell us your thoughts about ...</div> <div>So, what do you all think?</div> <div>Do some of you agree with ...?</div> <div>If so, why? Or why not?</div> <div>How could we be more sure?</div> <h3>Possible extension</h3> <div>Youngsters could create their own challenges in a similar way for others to discuss.</div> <h3>Possible support</h3> <div>Try to help by listening, sharing and offering thoughts where appropriate. </div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Could you make an estimation? What extra information might you need to find out? </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">1/ There are 500 Million cats 2/ Cats weigh 4 to 5 kg 3/ Cats sleep for 13 to 14 hours 4/ There are 400 million dogs 5/ Dogs on average live 10 to 14 years 6/ Dolphins live in schools of 12 7/ Elephants need 200 litres 8/ Giraffe's neck is 170 cm 9 Giraffe tail hair is 10 times thicker 10/ Lion weighs 180 kg 11/ Lion's roar heard 8 kilometres away 12 Lions rest for 20hours a day </mdoxml> 5 3 1 1 0 0 0 Discuss and Choose This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research. Using, Applying and Reasoning about Mathematics Selecting and using information Using, Applying and Reasoning about Mathematics Real world Calculations and Numerical Methods Estimating and approximating Admin Upper primary mapping document