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Topic: el fractions etc
Replies: 14   Last Post: Aug 10, 1995 8:05 AM

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 MR GREGORY J KERSHUL Posts: 8 Registered: 12/6/04
el fractions etc
Posted: Aug 8, 1995 11:52 AM

I use a constructivist approach to introducing the many forms of fractions.
Basing the opening activity on prior knowledge of money (decimals and
fractions) and grades (percentages and fractions), I have my fourth and
fifth graders work out decimal equivalents for halves, thirds, fourths,
fifths, sixths, etc. through twentieths (we skip thirteenths and a few
others that are not common). Then students use the decimal fractions to
find fractions which are equivalent and look for and "discover" that the
numerator/denominator relationship is constant for a given group of
equivalent fractions--a pattern! Finally, students extend the pattern they
have found to generate more equivalents to the lists already started (more
that equal 1/2, etc.) and use new ratios to generate new lists 1:50, 1:100 etc.

How can we get from 1/2 to ,50? We think: Money...one dollar (1.00)
divided by 2 is .50. So, could 1/2 be another way of writing 1 divided by
2? It is! ...another algorithm is "discovered"!

Next, students develop a chart showing relationships between:

fraction, division problem, decimal fraction, per cent, and ratio
1/2 = 1 divided by 2 = .50 = 50% = 1:2

We write word problems that show these connections. often ending up with
three forms in the same problem and play with diagrams, circle graphs and
manipulatives to develop number sense in this area. Then we USE this all
figuring decimal then percentage equivalents...what fraction of the class
is in band?...If only 17 students are getting hot lunches and 6 of them are
getting milk in addition to the 4 brown baggers getting milk, what is the
ratio of milk drinkers to non-milk drinkers today--is the percentage of
milk drinkers going up since our nutrition study?.........

Yes, we do use calculators to find decimal fraction equivalents to
fractions. At that point I want students to get excited about the
division/fraction/decimal relationship...excitement with kids means go
fast! Later, many equivalents are memorized (really, internalized) and we
may work the division with paper/pencil or use calculator depending on time
and objectives.
Tonna Kershul
8-11 mixed age class