We moved into a new unit of study today.... ssshhh... basics of algebra! Since algebra can be so abstract, I wanted to give the kids a good foundation to build upon. I found a program called Hands-On Equations that has been around for many years. This program has all kinds of data supporting its success. Basically, the concept behind Hands-On- Equations is to begin working with algebra concretely (with manipulatives), move to pictoral (draw pictures), and end at the abstract level (equation).
Today we worked concretely, with manipulatives (see above)! We began by noting that since we are working with a scale, both sides of the scale must be equal for the scale to balance. I explained that this whole idea is what math is all about.... both sides of an = sign, should EQUAL (balance)!
- We practiced working with the idea of placing a number cube on the right side of the scale and a pawn on the left. We discovered that the pawn's value was = to the number on the cube.
- Then we moved to placing a number cube on the right side of the scale and having two pawns on the left. This time the pawns' value, which was equal, added TOGETHER would equal the value of the number cube.
- Then we moved to having pawns on both sides of the equation. This meant that a little more trial and error was involved as we worked to determine the value of "x".
Finally, we worked through a series of equations. Students set up their math equation using the scale, pawns (our variable: x), and the number cubes (our constant). For example:
Working together, and using trial and error, students were successful in determining the value of x. For example, to solve the shown equation:
- x = 1 so 1+8 = 1 x 3 NO
- x = 2 so 2 + 8 = 2 x 3 NO
- x = 3 so 3 + 8 = 3 x 3 NO
- x = 4 so 4 + 8 = 4 x 3 YES
The value of x (each blue pawn) is 4!
I know that a class was a success when students want to do more... we were VERY successful today!
HOMEWORK: xtramath.org and Word Problems