World of Tan 27

1518 /www/nrich/html/content/02/03/tan1/ 5 2011-02-01T00:00:01 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> This activity follows on from <a href="http://nrich.maths.org/public/viewer.php?obj_id=1517&part=index">World of Tan 26 - Old Chestnut</a> . <mdo:flash height="660" id="/content/02/03/tan1/1518.swf" width="600"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/02/03/tan1/1518.swf"></param> <param name="flashplayerversion" value="7"></param> <param name="height" value="660"></param> <param name="width" value="600"></param> </mdo:flash> As usual the Little Fung and Little Ming are arguing - but unusually for them it is about schoolwork. Very strange... LF: I tell you, it is about numbers! LM: No, it is about sharing things out! LF: Numbers! LM: Sharing! LF: NUMBERS! LM: It is about having equal amounts. LF: My teacher showed us it was all about numbers. On what she calls a number line. LM: But we have been shown that it is about sharing things out fairly. LF: NUMBERS, NUMBERS, dear brother LM: Oh, this is hopeless .I am going into the yard to find someone sensible to talk to. LF: That is, if you can find them! They are ALL in a meeting to talk about getting a bigger van and the alterations needed in the yard to allow the van in. LM: Oh yes, but they will know all about fractions. Didn't they help us once before? LF: Yes, we could settle this nonsense once and for all. Where you get your ideas from is a mystery to me. LM: I am not as bad as you..anyway they could confuse us further. The children enter the office and find everyone - Granma T, Mai Ling, Chi Wing, Wai Ping and Wah Mung sitting round the table enjoying cups of tea. The business appears to have finished and what better time to interrupt! LF: Can you settle an argument? CW: Umm, that will make a change LM: No we can't agree about fractions. WM: Fractions! - but don't you do those at school? LF: Yes. So what do you remember from school? GT: That might not be so easy for us older ones - Little Fung LM: Oh stop teasing. you must remember what you learnt at school! LF: And anyway you all must use them here when working.. so what are fractions? WP: Never use them! Never needed to. Cannot help you. CW: Let me ask both of you a question. What do you multiply 6 by to get 2? A short pause and everyone looking blank except one LF: A third - one over three. CW: Now that is a fraction! LM: But surely that is like sharing six crackers out between 3 people and everybody getting two apiece! WM: To take a third of something is the same as dividing by 3! GT: But a fraction is also a ratio! What is the ratio of males to females here in this room? LM (counting): 3 females; 4 men. GT: The fraction ¾ expresses a relationship between those two quantities LF: NOOOOOOO LF: Three sevenths of us are female and four sevenths are male.. WM: I do remember at school having to turn things upside down to multiply - now what is all that to do with fractions? WP: Eh, remember that riddle? Half of a half of a half of a half of a half is what? ML: Almost nothing. Now let us get back to the business in hand - out you children go .... GT: Yes out you go we have to decide what are the implications of having a van that is half as big again.... In the meantime, complete the silhouette of Little Fung at the table asking about fractions. There are more activities in the <a href="http://nrich.maths.org/public/viewer.php?obj_id=1518&part=note">notes</a> . The story continues in <a href="http://nrich.maths.org/public/viewer.php?obj_id=1519&part=index"></a> <a href="http://nrich.maths.org/public/viewer.php?obj_id=1520&part=index">World of Tan 28 - Concentrating on Coordinates</a> . </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image width="505" height="303" src="1518.gif" alt="Solution to person at table"></mdo:image> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Children you might like to: <ul> <li>List all the different instances when you use fractions.</li> <li>Think about how you met fractions in school and what you have been taught. What can you remember?</li> <li>Convince someone that a quarter is bigger than a fifth. (hint: think of sweets)</li> <li>Take a line make it half as big again. Draw a shape on dotty paper - now make that half as big again.</li> </ul> <div>Parents you might like to:</div> <ul> <li>Explain in what contexts you use fractions at work and in the home.</li> <li>Investigate the fractional parts of a pound before the decimalisation of our currency in 1972.</li> <li>Convince someone a quarter is bigger than a fifth.</li> <li>Investigate the idea of ratio when mixing water and squash or when sharing out meals/ sweets etc.</li> <li>Explore the use of fractions within the context of time.</li> </ul> <div>Teachers you might like to:</div> <ul> <li>Explore the Tangram to explain and illustrate the 'sixteenths' family of fractions.</li> <li>Consider the differing ways of re' presenting fractional quantities.</li> <li>Explain why "we turn one fraction upside down and multiply out"</li> <li>Investigate mixing liquids/ sharing sweets in differing ratios.</li> <li>Develop the vocabulary of fractions and illustrate the different members of the fraction family - vulgar fractions, improper fractions, decimal fractions, etc.</li> <li>Halve a square in as many different ways as possible.</li> </ul> </mdoxml> 2 4 0 1 0 0 0 World of Tan 27 - Sharing Can you fit the tangram pieces into the outline of Little Fung at the table? Mathematics Tools Tangram Transformations and their Properties Compound transformations Using, Applying and Reasoning about Mathematics Practical Activity Using, Applying and Reasoning about Mathematics Visualising Information and Communications Technology Interactivities