I Like ...

6962 /www/nrich/html/content/id/6962/ 1 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Mr Gilderdale was using this interactivity with his class: <mdo:flash height="400" width="550"><param value="/content/id/6962/like25.swf" name="movie" ></param><param value="7" name="flashplayerversion" ></param></mdo:flash> He had thought of a number rule and he asked the class to choose numbers to test. If the number they chose fitted his rule, he put it under 'I like these numbers'. If the number they chose didn't fit his rule, he put it under 'I don't like these numbers'. Here is a picture of the game after the class had chosen four numbers: <mdo:image height="288" width="400" src="ILike1.gif" alt="I like 5 and 15. I don't like 18 and 22."></mdo:image> What could Mr Gilderdale's rule be? If you were in Mr Gilderdale's class, which number would you choose next to test your idea? How could you find out Mr Gilderdale's rule in the smallest number of guesses? </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Milo thought that We would have to test all 25 numbers to be sure what his rule was. Do you agree? Helen of Lea Valley Primary school had a good idea: For the "I like these numbers" I put $\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24\}$ because they are even and for "I don't like" I put $\{1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25\}$ because they are odd. Kate of Bilton Junior School exclaimed: It is the five times table, well it has to be! What do you think? Rischabh of the European School of Varese was unsure and wants more information: It is either odd numbers, or the five times table. I would like to try number $7$. If it goes on the left, it means it's the odd numbers, and if it goes on the right, it's the five times table. I will also try $10$ to be sure. What if the number $7$ and the number $10$ went into the "I don't like" section. Are there any other possibilities? Simran said: The rule might be to select the numbers with units of $5$. On the other hand what might the rule be if we tried $7$ and $10$ and both numbers went into the "I like" section? </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><div class="embed"> <h2>I Like ...</h2> Mr Gilderdale was using this interactivity with his class: <mdo:flash height="400" id="/content/id/6962/like25.swf" width="550"><param name="allowfullscreen" value="true"></param><param name="allowfullscreen" value="true"></param> <param name="movie" value="/content/id/6962/like25.swf"></param> <param name="flashplayerversion" value="7"></param> </mdo:flash> He had thought of a number rule and he asked the class to choose numbers to test. If the number they chose fitted his rule, he put it under 'I like these numbers'. If the number they chose didn't fit his rule, he put it under 'I don't like these numbers'. Here is a picture of the game after the class had chosen four numbers: <mdo:image alt="I like 5 and 15. I don't like 18 and 22." height="288" src="ILike1.gif" width="400"></mdo:image> What could Mr Gilderdale's rule be? If you were in Mr Gilderdale's class, which number would you choose next to test your idea? How could you find out Mr Gilderdale's rule in the smallest number of guesses? </div> <h3>Why do this problem?</h3> <div><a href="http://nrich.maths.org/6962&part=">This problem</a> challenges children to make sense of information by applying their knowledge of number properties. They are required to make and test hypotheses, and this will encourage them to work in a systematic way.</div> <h3>Possible approach</h3> <div>You could introduce this problem by demonstrating <a href="/content/id/6962/like25.swf">the interactivity</a> yourself. Choose a rule and invite children to offer numbers. If the number fits your rule, drag it to the 'I like ...' side of the screen. If the number doesn't fit your rule, drag it to the other side. Try to remain silent during the activity so the only feedback the children get is the position of their chosen numbers. You might insist that the children must all agree on the rule before someone is allowed to check it with you. You could challenge them to find the rule by choosing, for example, fewer than ten numbers.</div> <div>Once they are familiar with the way the game works, show them the picture of Mr Gilderdale's class's game and set them off on the problem itself, perhaps working in pairs. You may need to bring them together for a 'mini plenary' at some stage, so they can share how they are getting on so far.</div> <div>In a plenary, you could use the interactivity to work through their suggested solutions, encouraging them to justify their ideas.</div> <div>Of course this game can be played without the interactivity at all, which means that the choice of numbers is completely unrestricted. You could start off a game on the board, which could continue over several days. In this way, learners can form a hypothesis for your rule, but you will not confirm their hypothesis, you will only place numbers in the appropriate column.</div> <h3>Key questions</h3> <div>What do the numbers Mr Gilderdale likes have in common? What is the same about them?</div> <div>What do the numbers Mr Gilderdale doesn't like have in common?</div> <div>What number could you choose to test your idea?</div> <h3>Possible extension</h3> <div>Some children might like creating their own 'snapshots' of an imaginary game, so that the rule is ambigous.</div> <h3>Possible support</h3> <div>Having a <a href="/content/id/6962/1-100_NumberGrid.pdf">hundred square</a> to mark the 'I like' numbers on might help some children see, and understand, a pattern.</div> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">What do the numbers Mr Gilderdale likes have in common? What is the same about them? What do the numbers Mr Gilderdale doesn't like have in common? </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> Rule could be: odd multiples of 5 5 as the units digit less than 16 less than 17 </mdoxml> 2 3 1 0 0 0 0 I Like ... Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea? Using, Applying and Reasoning about Mathematics Making and testing hypotheses Numbers and the Number System Properties of numbers Numbers and the Number System Comparing and Ordering numbers Numbers and the Number System Odd and even numbers Numbers and the Number System Factors and multiples Information and Communications Technology Interactivities Admin Lower primary mapping document