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corrected posting re patterns
Posted:
Jun 15, 1995 1:11 PM


Sorry for the errors in my posting. I don't know what I was doing wrong, but have retyped the entire message, which 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 not 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
Jan Thompson



