Activities/Turtle Art/Tutorials/Fractions - Revision history

Rdrsadhu: Migrate to GitHub

2018-07-28T13:31:10Z

Migrate to GitHub

@@ Line 1: / Line 1: @@
-{{stub}}
+== Turtle Art/Tutorials/Fractions ==
-This is the outline that will be fleshed out in Turtle Art.
+Read at https://help.sugarlabs.org/turtleart_tutorials/fractions.html
-* Cut a pie in pieces, and color some of the pieces, as Tony did. That gives the basic idea of a fraction. Point out that when you cut a pie in, say, 5 pieces, you are doing 1 divided by 1/5.
+The source file has been moved to [https://github.com/godiard/help-activity/blob/master/source/turtleart_tutorials/fractions.rst GitHub]

FGrose: moved Activities/TurtleArt/Tutorials/Fractions to Activities/Turtle Art/Tutorials/Fractions: deCamelCase

2012-07-23T15:37:24Z

moved Activities/TurtleArt/Tutorials/Fractions to Activities/Turtle Art/Tutorials/Fractions: deCamelCase

← Older revision		Revision as of 11:37, 23 July 2012
(No difference)

Mokurai: Add illustration

2011-07-20T02:37:09Z

Add illustration

← Older revision		Revision as of 22:37, 19 July 2011
Line 5:		Line 5:
	* Cut a pie in pieces, and color some of the pieces, as Tony did. That gives the basic idea of a fraction. Point out that when you cut a pie in, say, 5 pieces, you are doing 1 divided by 1/5.		* Cut a pie in pieces, and color some of the pieces, as Tony did. That gives the basic idea of a fraction. Point out that when you cut a pie in, say, 5 pieces, you are doing 1 divided by 1/5.

	[[File:~~TAFivePieSlices~~.png]]		[[File:Five_pie_slices_image.png]]

	* Cut more than one pie in the same number of pieces each. This lets us talk about "improper" fractions and mixed fractions (integer plus fraction), and converting between them. We can also introduce rational numbers at some stage of child development.		* Cut more than one pie in the same number of pieces each. This lets us talk about "improper" fractions and mixed fractions (integer plus fraction), and converting between them. We can also introduce rational numbers at some stage of child development.

Mokurai: Add Turtle Art images

2011-07-20T01:46:54Z

Add Turtle Art images

← Older revision		Revision as of 21:46, 19 July 2011
Line 3:		Line 3:
	This is the outline that will be fleshed out in Turtle Art.		This is the outline that will be fleshed out in Turtle Art.

	* Cut a pie in pieces, and color some of the pieces, as Tony did. That gives the basic idea of a fraction. Point out that when you cut a pie in, say, 8 pieces, you are doing 1 divided by 1/8.		* Cut a pie in pieces, and color some of the pieces, as Tony did. That gives the basic idea of a fraction. Point out that when you cut a pie in, say, 5 pieces, you are doing 1 divided by 1/5.

			[[File:TAFivePieSlices.png]]

	* Cut more than one pie in the same number of pieces each. This lets us talk about "improper" fractions and mixed fractions (integer plus fraction), and converting between them. We can also introduce rational numbers at some stage of child development.		* Cut more than one pie in the same number of pieces each. This lets us talk about "improper" fractions and mixed fractions (integer plus fraction), and converting between them. We can also introduce rational numbers at some stage of child development.

Mokurai: Line breaks, minor edits

2011-07-15T23:52:42Z

Line breaks, minor edits

← Older revision		Revision as of 19:52, 15 July 2011
Line 3:		Line 3:
	This is the outline that will be fleshed out in Turtle Art.		This is the outline that will be fleshed out in Turtle Art.

	* Cut a pie in pieces, and color some of the pieces, as Tony did. That		* Cut a pie in pieces, and color some of the pieces, as Tony did. That gives the basic idea of a fraction. Point out that when you cut a pie in, say, 8 pieces, you are doing 1 divided by 1/8.
	gives the basic idea of a fraction. Point out that when you cut a pie in,
	say, 8 pieces, you are doing 1 divided by 1/8.

	* Cut more than one pie in the same number of pieces each. This lets us		* Cut more than one pie in the same number of pieces each. This lets us talk about "improper" fractions and mixed fractions (integer plus fraction), and converting between them. We can also introduce rational numbers at some stage of child development.
	talk about "improper" fractions and mixed fractions (integer plus
	fraction), and converting between them. We can also introduce rational
	numbers at some stage of child development.

	* Cut a pie in pieces, and cut the pieces into smaller pieces		* Cut a pie in pieces, and cut the pieces into smaller pieces (multiplication of the simplest fractions, such as 1/2 times 1/3). Some fractions can be described using the bigger pieces, and some require the smaller pieces. Talk about reducing fractions to lowest terms. (You will need other materials in order to talk about Greatest Common Divisors. I'll do something on that.) Take some time on multiplying fractions. Then notice that, for example, if you divide a pie into sixths, three of the pieces make a half. 3 times 1/6 is 1/2, so 1/2 divided by 3 is 1/6, and 1/2 (= 3/6) divided by 1/6 is 3. (Assuming prior understanding that if the product of, say, 2 and 3 is 6, then 6/3 = 2 and 6/2 = 3.)
	(multiplication of the simplest fractions, such as 1/2 times 1/3). Some
	fractions can be described using the bigger pieces, and some require the
	smaller pieces. Talk about reducing fractions to lowest terms. (You will
	need other materials in order to talk about Greatest Common Divisors. I'll
	do something on that.) Take some time on multiplying fractions. Then
	notice that, for example, if you divide a pie into sixths, three of the
	pieces make a half. 3 times 1/6 is 1/2, so 1/2 divided by 3 is 1/6, and
	1/2 (= 3/6) divided by 1/6 is 3. (Assuming prior understanding that if the
	product of, say, 2 and 3 is 6, then 6/3 = 2 and 6/2 = 3.)

	* Cut several pies. For example, cut two pies into three pieces each, and		* Cut several pies. For example, cut two pies into three pieces each, and then color pairs of pieces. How many groups of two pieces make two pies? Congratulations, you have just divided 2 by 2/3.
	then color pairs of pieces. How many groups of two pieces make two pies?
	Congratulations, you have just divided 2 by 2/3.

	* Work other examples, dividing whole numbers by fractions, then fractions		* Work other examples, dividing whole numbers by fractions, then fractions by other fractions, choosing cases that come out even to start with.
	by other fractions, choosing cases that come out even to start with.

	* Now look at examples where one fraction does not go evenly into the		* Now look at examples where one fraction does not go evenly into the other. What do you have to do to make sense of the remainder? Say you have a pizza cut into 8 pieces, and you have hungry pizza eaters who want three slices each. How many can you accommodate? Well, two, with two slices left over. Two slices is 2/3 of three slices, so that comes to 2 2/3 portions.
	other. What do you have to do to make sense of the remainder? Say you have
	a pizza cut into 8 pieces, and you have hungry pizza eaters who want three
	slices each. How many can you accommodate? Well, two, with two slices left
	over. Two slices is 2/3 of three slices, so that comes to 2 2/3 portions.

	None of this requires Turtle Art. You can cut pies or cakes, or pieces of		None of this requires Turtle Art. People have been learning fractions for thousands of years. You can cut pies or cakes or plots of land or the floor of the classroom or a tabletop or pieces of construction paper to do all of this. Oh, yes. How many pieces do the local pizza parlors cut pizzas of various sizes into? What fractions can you make from those pieces? Can you find pictures of pizzas from directly above, so that they appear as circles and you can print them and cut them up? (Yes.) What else? Craters on the moon? The whole moon? Circular swimming pools, fountains, ponds, coins, cups?
	construction paper to do all of this. Oh, yes. How many pieces do the
	local pizza parlors cut pizzas into? What fractions can you make from
	those pieces? Can you find pictures of pizzas from directly above, so that
	they appear as circles? (Yes.) What else? Craters on the moon? The whole
	moon? Circular swimming pools, fountains, ponds?

	It remains an open question whether the children ~~will~~ discover the		It remains an open question whether the children can discover the invert-and-multiply rule for dividing fractions by themselves in a sufficently rich environment, whether they will need broad hints, or whether they will have to be told. It would be interesting to me to hear how they would explain these ideas to each other. I will be interested to hear your results.
	invert-and-multiply rule for dividing fractions by themselves, whether
	they will need broad hints, or whether they will have to be told. It would
	be interesting to me to hear how they would explain these ideas to each
	other. I will be interested to hear your results.

Mokurai: Outline of new page

2011-07-15T23:45:06Z

Outline of new page

New page

{{stub}}

This is the outline that will be fleshed out in Turtle Art.

* Cut a pie in pieces, and color some of the pieces, as Tony did. That
gives the basic idea of a fraction. Point out that when you cut a pie in,
say, 8 pieces, you are doing 1 divided by 1/8.

* Cut more than one pie in the same number of pieces each. This lets us
talk about "improper" fractions and mixed fractions (integer plus
fraction), and converting between them. We can also introduce rational
numbers at some stage of child development.

* Cut a pie in pieces, and cut the pieces into smaller pieces
(multiplication of the simplest fractions, such as 1/2 times 1/3). Some
fractions can be described using the bigger pieces, and some require the
smaller pieces. Talk about reducing fractions to lowest terms. (You will
need other materials in order to talk about Greatest Common Divisors. I'll
do something on that.) Take some time on multiplying fractions. Then
notice that, for example, if you divide a pie into sixths, three of the
pieces make a half. 3 times 1/6 is 1/2, so 1/2 divided by 3 is 1/6, and
1/2 (= 3/6) divided by 1/6 is 3. (Assuming prior understanding that if the
product of, say, 2 and 3 is 6, then 6/3 = 2 and 6/2 = 3.)

* Cut several pies. For example, cut two pies into three pieces each, and
then color pairs of pieces. How many groups of two pieces make two pies?
Congratulations, you have just divided 2 by 2/3.

* Work other examples, dividing whole numbers by fractions, then fractions
by other fractions, choosing cases that come out even to start with.

* Now look at examples where one fraction does not go evenly into the
other. What do you have to do to make sense of the remainder? Say you have
a pizza cut into 8 pieces, and you have hungry pizza eaters who want three
slices each. How many can you accommodate? Well, two, with two slices left
over. Two slices is 2/3 of three slices, so that comes to 2 2/3 portions.

None of this requires Turtle Art. You can cut pies or cakes, or pieces of
construction paper to do all of this. Oh, yes. How many pieces do the
local pizza parlors cut pizzas into? What fractions can you make from
those pieces? Can you find pictures of pizzas from directly above, so that
they appear as circles? (Yes.) What else? Craters on the moon? The whole
moon? Circular swimming pools, fountains, ponds?

It remains an open question whether the children will discover the
invert-and-multiply rule for dividing fractions by themselves, whether
they will need broad hints, or whether they will have to be told. It would
be interesting to me to hear how they would explain these ideas to each
other. I will be interested to hear your results.