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Re:Re:factoring, FOIL,technology
Posted:
Jun 15, 1995 9:54 AM


Sorry for the printout errors in yesterday's posting! Corrected posting follows.
950613 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 prealgebra, 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 singledigit 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 fournumber 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 (21) = 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 (31) =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 ( 4x31 ) 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 (41) = 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 ( 2x31 ) x 4 = 20 ( 3÷1+2 ) x 4 = 20 ( 2÷1+3 ) x 4 = 20
Jan Thompson



