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Math Games & Activities, Vol. 1

Math Balance Worksheets (pp. 130, 131, 132)

Non-verbal directives for use with a math balance in teaching arithmetic to elementary school students. (See BALANCE BEAM CUTOUT.)

The convention for the worksheets is as follows:

A triangle between weights represents the balance point of a math balance.

A triangle without a slash means the math balance is balanced.

A triangle with a slash means the math balance is tilted.

Weights next to one another represent weights on different (but not necessarily adjacent) pegs.

Overlapping weights represent weights on the same peg.

Weights with numbers on them represent weights on pegs bearing the numbers.

On page 130, problem b can be used to introduce even numbers, problem c, odd numbers, and problem e, the distributive property—that a(b+c) = ab+ac for all numbers a, b, and c. On page 131, problem c can be used to introduce less than and greater than, but perhaps a better way to introduce them is as “greedy” mouths: mouths that always eat the bigger number. And on page 132, problems a and b can be presented in an exhaustive sense: How many solutions? The answer: Only the number indicated.

Regarding the problems for which there are only the indicated number of solutions, an assertion to that effect is easily verified by putting all the number of solutions indicated on a math balance and noting the pattern they exhibit. They show that the “next” solution, if there were one, would extend beyond the limits of the math balance.

The answers for the worksheets will vary, but they will be something like the following on the next page: