Thursday, April 8, 2010

Balancing Apples

As part of the Florida Algebra standards for second grade, students are required to “describe and apply equality to solve problems, such as in balancing situations” to a high level of cognitive complexity. In other words, students must be able to look at a situation and determine the unknown by using what they know about the problem. What great critical thinking for our second graders! (They think of these problems as puzzles and love them!)

Let’s take a look at a basic example:

Alyssa made two identical apples balance with two different two gram weights. How much does each apple weigh?

Most students can easily see that there are two identical apples and two identical amounts of weight. Each apple must be worth two grams. 1apple = 2g or 2g = 1 apple. These problems are not all this simple. Here is another example:

This time, Alyssa made five identical apples balance with fifteen grams. How much does each apple weigh?

Students usually begin by skip counting by a number smaller than the overall weight (fifteen grams). They know that each apple weighs exactly the same amount, and solve these problems by repeated addition using a “guess and check” method. In the beginning, they may try each apple weighing 1 gram.

At this point, students usually quickly notice that the apples do not weigh enough to balance the scale. Students would then use a larger number to try to balance the scale. (As students become more familiar with multiplication and division concepts, they begin to look at these problems differently. In second grade, we are building their thinking and number sense to this point.) Students would finally solve the problem as: 1 apple = 3 g or 3 g = 1 apple.

Of course these problems get much more complex as time goes on. Look for more of these exciting balance problems coming home soon! In the mean time, check out some of the links below:

(Easy, Medium, and Difficult) Math Mammoth
(Easy, Medium, and Difficult) Illuminations and Student Sheet
(Difficult) Math Playground

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