I just started observing a junior high class and was pleasantly surprised when the teacher pulled out Manipulatives to help the students visualize balancing algebraic expressions. I had never seen or experienced their use in learning algebra, and it gave me wonderful new ideas of how to use them in my future teaching.
The Manipulatives are used to represent the x terms and the integers and differentiate positive and negative terms. In this way students need to follow logical rules of keeping the equation balanced by literally taking away or adding the same thing to both sides. The long bars represent 1x and each small square represents 1. Furthermore, both bars and squares are positive when green/yellow, and negative when red. I think it's a quite brilliant way of physically representing a potentially abstract concept for learners. I definitely plans on utilizing this type of manipulative strategy in my future classrooms.
Below is an example of an equation being represented by the manipulatives. 3x-5 is represented by 3 green bars and 5 red squares while x-3 is represented by 1 green bar and 3 yellow squares. To solve for x, students would first remove a green bar from both sides and rewrite the equation to be 2x-5=3 with the visual matching. They would next add five yellow tiles to each side which would cancel out the red squares on the one side while adding with 3 to be 8 on the other side. The equation would then be written as 2x=8. The final move of the Manipulatives would be to divide the positive eight squares evenly with the two remaining green bars(x's). This would mean there would be 4 squares per bar, meaning x=4. I wish I had pictures for each step, but I don't at the moment. I'll try to update when I get a chance to take pictures of other examples.
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