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Topic: Re:Re:factoring, FOIL,technology
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 Kaidy@aol.com Posts: 7 Registered: 12/6/04
Re:Re:factoring, FOIL,technology
Posted: Jun 15, 1995 9:54 AM
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Sorry for the printout errors in yesterday's posting! Corrected posting
follows.

95-06-13 16:57:42 EDT Lucille L. Peterson wrote:
Fourth graders can explore multiplication by breaking up the factors into
friendly parts.

Here is an exercise we've used successfully with fourth graders:

15 x 12 =
10 + 5
x 10 + 2
--------------
20 + 10
100 + 50
---------------
100 + 70 + 10 = 180

15 x 8 =
10 + 5
x 10 - 2
--------------
- 20 - 10
100 + 50
---------------
100 + 30 - 10 = 120

Problems such as these demonstrate pre-algebra, and the students will no be
so puzzled when they reach middle school and are confronted with
(a+b)x(a+c)=?

In the same posting, mention was made of how younger children enjoy finding
patterns in math. A great game for this sort of activity is Numbers
Challenge. There are 24 different cards, each with four single-digit numbers
on it. Dice are rolled to give a target number of 1 to 24. Players use each
number on a given card and any operations they wish to reach the target
number. Each of the 24 cards has a four-number combination that will reach
all numbers between 1 and 24. It's quite challenging, even for adults! This
is an example using 1, 2, 3 and 4:

3 + 2 - 4 x 1 = 1
4 - 3 + 2 - 1 = 2
4 + 2 - 3 x 1 = 3
4 + 3 - 2 - 1 = 4
4 + 3 - 2 x 1 = 5
4 + 3 - 2 + 1 = 6
(4+3) x (2-1) = 7
4 + 3 + 2 - 1 = 8
4 x 3 - 2 - 1 = 9
4 + 3 + 2 + 1 =10
4 x 2 + 3 x 1 =11
4 x 2 + 3 + 1 =12
4 x 3 + 2 - 1 =13
3 x 4 x 1 + 2 =14
4 x 3 + 2 + 1 =15
4 x 2 x (3-1) =16
(4+1) x 3 + 2 =17
3 x 1 x (2+4) =18
(4+2) x 3 + 1 =19
4 x 1 x (2+3) =20
(4+3) x (2+1) =21
( 4x3-1 ) x 2 =22
4 x 3 x 2 - 1 =23
( 3+2+1 ) x 4 =24

There are many ways to reach each target number. For example:

1 x 3 x (2+4) = 18
2 x 3 x (4-1) = 18
(2+4) x 3 ÷ 1 = 18
(1+3) x 4 + 2 = 18
( 1x2+4 ) x 3 = 18
( 1x4+2 ) x 3 = 18
( 2÷1+4 ) x 3 = 18
( 4÷1+2 ) x 3 = 18

1 x 4 x (3+2) = 20
(2+3) x 4 x 1 = 20
( 1x3+2 ) x 4 = 20
( 1x2+3 ) x 4 = 20
( 2x3-1 ) x 4 = 20
( 3÷1+2 ) x 4 = 20
( 2÷1+3 ) x 4 = 20

Jan Thompson

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