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The old "Sum and Difference" game is a simple trick that even very young children can play to amaze and frustrate playmates or (better yet) adults (even teachers) whose algebra skills have atrophied. It's a great way to introduce "unknown" numbers to beginning algebra students. --- Instructions: Pick any two numbers. Add them (first number plus second number), and report the total. Then subtract them IN THE SAME ORDER (i.e. first number minus second number), and report the total. You can determine the two numbers using simple algebra: 1st number = x (perhaps: 7). 2nd number = y (perhaps: 12). Let: a = x + y, and let: b = x – y. The player will report to you the values of "a" and "b," the sum and difference of the two numbers (in our example, these numbers are 19 and -5). Add these results in your head (in this case, the sum is 14), and what you have will always be twice one of these numbers [since a + b = (x + y) + (x – y) = 2x.]...

The old "Sum and Difference" game is a simple trick that even very young children can play to amaze and frustrate playmates or (better yet) adults (even teachers) whose algebra skills have atrophied. It's a great way to introduce "unknown" numbers to beginning algebra students. --- Instructions: Pick any two numbers. Add them (first number plus second number), and report the total. Then subtract them IN THE SAME ORDER (i.e. first number minus second number), and report the total. You can determine the two numbers using simple algebra: 1st number = x (perhaps: 7). 2nd number = y (perhaps: 12). Let: a = x + y, and let: b = x – y. The player will report to you the values of "a" and "b," the sum and difference of the two numbers (in our example, these numbers are 19 and -5). Add these results in your head (in this case, the sum is 14), and what you have will always be twice one of these numbers [since a + b = (x + y) + (x – y) = 2x.]...

The old "Sum and Difference" game is a simple trick that even very young children can play to amaze and frustrate playmates or (better yet) adults (even teachers) whose algebra skills have atrophied. It's a great way to introduce "unknown" numbers to beginning algebra students. --- Instructions: Pick any two numbers. Add them (first number plus second number), and report the total. Then subtract them IN THE SAME ORDER (i.e. first number minus second number), and report the total. You can determine the two numbers using simple algebra: 1st number = x (perhaps: 7). 2nd number = y (perhaps: 12). Let: a = x + y, and let: b = x – y. The player will report to you the values of "a" and "b," the sum and difference of the two numbers (in our example, these numbers are 19 and -5). Add these results in your head (in this case, the sum is 14), and what you have will always be twice one of these numbers [since a + b = (x + y) + (x – y) = 2x.]...