World of Tan 23 - Transform this...into...that

1513 /www/nrich/html/content/01/10/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=1512&part=index">World of Tan 22 - An Appealing Stroll</a> . It is Saturday morning. There is no school today and Little Ming and Little Fung are deep in slumber. Granma T has already been up hours - naturally! The smell of fresh bread is the first thing the youngsters are aware of. The warm sunlight and a quiet yard below gradually seeps into their drowsiness. GT: Come on you two! There is much to be done. [Only groans can be heard as the children argue about who gets to the bathroom first...] GT: It is no good filling us with stories about 'transformations' or whatever it was you did at school. The yard has to be transformed. So .... LM: Breakfast first, please [Little Fung pleads similarly!] LM: Why, oh why, can't we just laze around like other children? LF: There is no school today - so why do we have to be up with birds? Is there no justice? LM: Why did you have to go on so about the transformations we did in school? Granma T seems to have found a perfect excuse to get us doing chores... LF: Again! Surprise, surprise... LM: Race you down - can you smell that lovely bread? LF: Yes, it does make mornings more bearable GT: You are missing the best part of the day... LF: Why do grown ups always say that? LM: Especially when YOU are tired and still sleepy. GT: Come on now, no more moaning. Get your breakfast then out into the yard. Let us put theory into practice. LM: Ugh! GT: Yes, I was most taken with what you had to say about transforming one thing into another... my mind has been racing with things that transform... from one state into another... and into another. LF: Oh yes? [ Still not fully awake!] GT: Flour, water and yeast transformed into bread. Bread eaten and transformed into energy. Children full of energy go out into the yard and tidying up...PERFECT example. LM: What was that about being full of energy? LF: Granma, you appear to have got the idea about transformations. LM: But WE were only talking about mathematical transformations and the things that stay the same after some change has taken place.... GT: Pardon me! Does that make sense? LF: Yes! We could go into the yard and do nothing! GT: Oh no, into the yard doing the chores transforms into pocket money and going to the market this afternoon. LM: Granma! You certainly have grasped the idea of transformations ...but why does the yard always need doing? Are there no other transformations we could do for you? LF: How about a transformation that changes me from being drowsy and back to being asleep? GT: Come on it is seven o' clock. The yard must be tidy before the others appear and they begin to transform our closed removal firm back into life. LM: (Stifling a yawn) Having everyone around soon changes the atmosphere here - no more peace and tranquillity but hustle, bustle and clatter. LF: What have you written here Granma? ...Metamorph.. Oh I can't say this word! GT: Meta MOR Phosis! You had better ask Mai Ling about that once the yard has been done....All that starts with caterpillars and butterflies... LM: I am beginning to get confused... Little Fung let's just get on with the yard.... In the meantime, transform this: <mdo:flash height="380" id="/content/01/10/tan1/1513-1.swf" width="600"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/01/10/tan1/1513-1.swf"></param> <param name="flashplayerversion" value="7"></param> <param name="height" value="380"></param> <param name="width" value="600"></param> </mdo:flash> into that! <mdo:flash height="380" id="/content/01/10/tan1/1513-2.swf" width="600"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/01/10/tan1/1513-2.swf"></param> <param name="flashplayerversion" value="7"></param> <param name="height" value="380"></param> <param name="width" value="600"></param> </mdo:flash> There are more activities in the <a href="http://nrich.maths.org/public/viewer.php?obj_id=1513&part=note">notes</a> . The story continues in <a href="http://nrich.maths.org/public/viewer.php?obj_id=1514&part=index">World of Tan 24 - Clocks</a> . </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"> <mdo:image width="247" height="215" alt="First solution" src="1513a.gif"></mdo:image><mdo:image width="263" height="225" src="1513b.gif" alt="Second solution"></mdo:image> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Children you might like to: <ul> <li>List some of the transformations that take place as you get ready for school.</li> <li>Sort these transformations into different categories of change.</li> <li>Find different words that mean the same as transform or transformation.</li> <li>Discuss things that transform more than once - going from one state to another then another...then another. What is the most transformations you can think of?</li> </ul> <div>Parents you might like to...</div> <ul> <li>Talk through the idea of things that change gradually/ quickly.</li> <li>Work through some examples of a physical transformation e.g. tidying up iii. Consider things that change with time. With heat? Things that chemically change.</li> <li>Investigate those things that DO NOT change.</li> <li>Explore other words that mean transformation.</li> </ul> <div>Teachers you might like to...</div> <ul> <li>Consider some of the (many) different mathematical transformations -e.g. reflections, rotations,.....multiplying by three and adding one, squaring,...</li> <li>Illustrate the idea of transformation using Lewis Carroll's idea of "Doublets", whereby one word is gradually changed into another word by altering one letter at a time...e.g. pig, wig, wag, way, say, sty.</li> <li>Discuss and classify the different types of transformations that we can have.</li> <li>Consider multiple transformations.</li> <li>List and develop the different words associated with transformations.</li> <li>In the above - look for aspects that do NOT change within the transformation. </li> </ul> </mdoxml> 2 4 0 0 0 0 0 World of Tan 23 - Transform this...into...that Can you fit the tangram pieces into these outlines? 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