World of Tan 19 - Working Men

1509 /www/nrich/html/content/01/05/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=1508&part=index">World of Tan 18 - Soup</a> . <mdo:flash height="420" id="/content/01/05/tan1/1509-1.swf" width="600"><param name="allowfullscreen" value="true"></param><param name="movie" value="/content/01/05/tan1/1509-1.swf"></param> <param name="flashplayerversion" value="7"></param> <param name="height" value="420"></param> <param name="width" value="600"></param> </mdo:flash> It was almost the end of the tea-break. Things were being cleared away and the chairs stacked neatly into the corner, when Wah Ming posed his question - as is his wont! Wah Ming: How do you find the centre of a circle? After some to-ing and fro-ing it was generally agreed that all you had to do was fold it in half and then in half again. Where the folds crossed was the centre! Chi Wing: Yes, that's alright for a circle of paper, or table cloth or even a small rug? Wei Ping: Umm each of those can be done! WM: But what if its a large circle of concrete? Or an enormous flower bed? WP: Umm, can't fold them so easily! CW: Or that wooden stage we have to lift and move next week! WM: Let's ask Granma T - I've heard she was always good at geometry at school. The workmen went back to the tasks for the afternoon - a note was left for Granma T explaining the predicament and could she help? The next day the workmen were back in the yard and busy with the task of moving some furniture into storage when across from the house is heard: Scholars! Did you learn nothing at school? All gathered round. An explanation was about to begin: GT: Imagine you can walk round the edge of circle - any size, large or small. All seemed at ease with this instruction. GT: Now imagine that Mai Ling is standing stock still on the edge and she is feeding out some rope attached to your waist. So as you walk around the circle -the rope is kept tight at all times. CW: And the rope will lengthen as I walk further around. WM: Yes, until you get to that point when the rope starts to slacken. GT: That is when you have gone as far out as possible and you are about to begin the journey back to where you started. WM/ WP/ CW: Agreed GT: Now, where is the point when the rope slackens? WP: At the end of the longest line across the circle - the diameter! GT: Your problem about the centre should be easy now. Good morning! And off she went leaving the workmen scratching their heads and looking round somewhat sheepishly. Undaunted the foreman breaks the tension. CW: Of course that's how to do it, now lets get back to the furniture moving. We can resolve this at tea break. ....in the meantime, complete the silhouette. How would you describe the shape? There are some more activities in the <a href="http://nrich.maths.org/public/viewer.php?obj_id=1509&part=note">notes</a> , and the story continues in <a href="http://nrich.maths.org/public/viewer.php?obj_id=1510&part=index">World of Tan 20 - Fractions</a> . </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image width="363" height="189" src="1509a.gif" alt="Solution"></mdo:image> </mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Children you might like to: <ul> <li>List all the words to do with circles or being being circular.</li> <li>Discuss with your friends how to finish Grandma T's method of finding the centre of a circle</li> <li>Write an acrostic about circles.</li> <li>Find out all you can about pi, using the internet.</li> </ul> <div>Parents you might like to:</div> <ul> <li>Explore the house and garden for things circular or cylindrical.</li> <li>Help find out more about pi. What exactly is this 'mysterious' number?</li> <li>Explain what you learnt about circles when you were at school.</li> <li>Discuss the phrase 'as is his wont'. What does this mean? Are there similar phrases?</li> <li>Explain the words annulus and annular.</li> </ul> <div>Teachers you might like to:</div> <ul> <li>Explore the relationship between the distance around different circular objects e.g. tins, and the distance directly across them. also help find out more about the (transcendental) number pi. What about the different values that are used in school books? And why?</li> <li>Encourage youngsters to write mnemonics to remember pi for some of its many places of decimals. - e.g. May I have a large container of coffee (i.e the value of pi to 7 decimal places 3.1415926) n.b. to 30 decimal places pi's value is 3.141 592 653 897 543 238 452 643 383 279.</li> <li>Explore shapes that are circular but can appear elliptical - try a teacup full of liquid when viewed from the side . Or, try viewing something elliptical - is it possible to see circles from particular points of view?</li> <li>consider the different ways circles can be packed or the different ways cylinders can be (safely) stacked.</li> </ul> </mdoxml> 2 4 0 1 0 0 0 World of Tan 19 - Working Men Can you fit the tangram pieces into the outline of this shape. How would you describe it? Information and Communications Technology Interactivities Mathematics Tools Tangram Transformations and their Properties Compound transformations Using, Applying and Reasoning about Mathematics Practical Activity Using, Applying and Reasoning about Mathematics Visualising