4x + 3 = x + 18
Sometimes, all you need is a little visual assistance to turn algebraic mumble jumble into something understandable. Our help came in the form of Hands on Equations, a program that uses a visual and kinesthetic approach to teaching grade schoolers algebraic concepts. Using only a scale, numbered dice, and colored pawns, students translate equations, like the one above, into one which can be moved and manipulated.
3x + 3 = 18
The key to remember is that the equation rests on a scale. To begin, you eliminate everything on both sides that are equivilents. In this case, one pawn is removed from both sides.
3x = 15
x = 5
Next, subtract 3 from both sides, and solve for x. After some practice, the student begins solving equations through simple illustrations, eliminating the need for the scale and manipulatives.
It's amazing to me that even a 2nd grader can solve these problems, when presented in this way. Boo caught on immediately and was working through the rest of Book One problems on his own. Books Two and Three introduces negative integers, expanding on the same manipulation of pawns and dice. Nevermind that it is all surprisingly easy, but most importantly, the program is fun. Rather than working through dry numbers and letters, you are visualizing and manipulating the components in game-like fashion, to solve for x. Not a bad way to do algebra.
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2 comments:
I am singing Hallelujah. Thanks for sharing this. We aren't anywhere near using it, but none the less, the program will go on my list.
It is not only 2nd graders who find algebraic equations to be "mumble jumble." In one large district in the U.S., 91% of the students failed Algebra 1 last year. For many students algebraic equations make no more sense than would a bunch of Chinese symbols, which accounts for the types of errors students make in working with equations.
The visual aspect of Hands-On Equations demystifies the meaning of the equations. The kinesthetic aspect makes the algebraic properties second nature to the student, e.g., obvious and intuitive. It is this whole-brain approach which accounts for the consistently large pre- to post-test gains that can be found with the use of the program.
In the photo of the examples, the red cubes and blue pawns should be used to reflect how the pieces are used in the program. Wishing you continued success.
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