Hands-on Equations

Today we started a new program which we will be using throughout the year. It's called "Hands-on Equations" and its a nifty program designed to help students master algebraic concepts by using objects that students can touch and move about. In this program, students use small game pieces to represent variables like x or y and number cubes to represent the numbers. The pieces are placed on a board which looks like a balance with the center column of the balance representing the equal sign. This way the students can manipulate equations by adding or subtracting pieces.

For example, suppose they are solving the equation 2x + 6 = x + 8. The students place two game pieces on the left side of the balance along with a cube with the number 6. On the right side they place one game piece and a number 8 cube. Now to solve the problem first they take away one game piece from each side. Although they do not write it down, they have actually simplified the equation to x + 6 = 8. They further simplify the problem by subtracting 6 from each side. On the left side, the number cube just disappears, and on the right side the 8 cube is replaced by a 2 cube. Now they have the answer: x = 2. They then return to the original equation to test whether x = 2 is correct. They calculate (2 x 2) + 6 = 2 + 8. Since 10=10 they know that the answer is correct.

Now this may seem complicated when I write it down step by step. But, think about it, can you imagine how complicated washing the dishes would seem if we read a written description of how to do it? It's the same with Hands-on Equations. It's easy and fun just to play with the pieces and get the answer.

At first some bright students can be frustrated because they are able to solve the problem using mental math and a "guess-and-check" strategy. But, as the program progresses, the problems become harder and harder, and the only way to solve them is to use the pieces. So we make an issue of actually using the pieces even if they already know the answer. Really, today's problems were pretty easy and we mostly concentrated on learning to set up the pieces instead of solving the problems.

Homework: Just a little math review here. Do page H35 in the back of the math book. This reviews the lessons for chapter 4.