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| | == Turtle Art/Tutorials/Fractions == |
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| This is the outline that will be fleshed out in Turtle Art.
| | Read at https://help.sugarlabs.org/turtleart_tutorials/fractions.html |
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| * Cut a pie in pieces, and color some of the pieces, as Tony did. That
| | The source file has been moved to [https://github.com/godiard/help-activity/blob/master/source/turtleart_tutorials/fractions.rst GitHub] |
| gives the basic idea of a fraction. Point out that when you cut a pie in,
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| say, 8 pieces, you are doing 1 divided by 1/8.
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| * Cut more than one pie in the same number of pieces each. This lets us
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| talk about "improper" fractions and mixed fractions (integer plus
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| fraction), and converting between them. We can also introduce rational
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| numbers at some stage of child development.
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| * Cut a pie in pieces, and cut the pieces into smaller pieces
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| (multiplication of the simplest fractions, such as 1/2 times 1/3). Some
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| fractions can be described using the bigger pieces, and some require the
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| smaller pieces. Talk about reducing fractions to lowest terms. (You will
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| need other materials in order to talk about Greatest Common Divisors. I'll
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| do something on that.) Take some time on multiplying fractions. Then
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| notice that, for example, if you divide a pie into sixths, three of the
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| pieces make a half. 3 times 1/6 is 1/2, so 1/2 divided by 3 is 1/6, and
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| 1/2 (= 3/6) divided by 1/6 is 3. (Assuming prior understanding that if the
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| product of, say, 2 and 3 is 6, then 6/3 = 2 and 6/2 = 3.)
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| * Cut several pies. For example, cut two pies into three pieces each, and
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| then color pairs of pieces. How many groups of two pieces make two pies?
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| Congratulations, you have just divided 2 by 2/3.
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| * Work other examples, dividing whole numbers by fractions, then fractions
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| by other fractions, choosing cases that come out even to start with.
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| * Now look at examples where one fraction does not go evenly into the
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| other. What do you have to do to make sense of the remainder? Say you have
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| a pizza cut into 8 pieces, and you have hungry pizza eaters who want three
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| slices each. How many can you accommodate? Well, two, with two slices left
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| over. Two slices is 2/3 of three slices, so that comes to 2 2/3 portions.
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| None of this requires Turtle Art. You can cut pies or cakes, or pieces of
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| construction paper to do all of this. Oh, yes. How many pieces do the
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| local pizza parlors cut pizzas into? What fractions can you make from
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| those pieces? Can you find pictures of pizzas from directly above, so that
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| they appear as circles? (Yes.) What else? Craters on the moon? The whole
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| moon? Circular swimming pools, fountains, ponds?
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| It remains an open question whether the children will discover the
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| invert-and-multiply rule for dividing fractions by themselves, whether
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| they will need broad hints, or whether they will have to be told. It would
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| be interesting to me to hear how they would explain these ideas to each
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| other. I will be interested to hear your results.
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