Teacher2Teacher 
Q&A #9409 
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From: Nancy To: Teacher2Teacher Public Discussion Date: 2003020420:30:10 Subject: Use manipulatives (cups and objects) I have taught students this method because many find solving equations too abstract to 'see' what is happening. It takes some prep time to set up. Use 10 pairs of paper cups,pennies, and other easytofind objects (Qtips, plastic spoons, washers, bolts, paper clips, etc.) This works great for equations involving only positive numbers  where I start them. For negative numbers, I use something different. 1. Mark 2 cups on the outside with the same number (1  10)and the equation that represents its contents. Pennies stand for constants and the objects represent variables. For example, if you are trying to teach them to solve 3B + 1 = 2B + 5, put 3 Bolts + 1 penny in one cup and write 3B + 1 on the outside. In the other cup put 2 bolts and 5 pennies. 2. The student knows that the goal is to get one bolt (variable) in one of the cups and only pennies (constants) in the other. To keep it balanced, you have to remove the same amount of items from each cup. The students usually dump the contents out into two piles and begin taking away the same from each pile. I have them write down what they are doing with the equation as they are doing it. 3. After replacing the contents correctly back into their cups, they take another pair of cups and repeat until 67 are done. By the time this is over, they really have a grasp on equations. 4. For negative numbers, I draw a little scale with objects on them where negative numbers are represented with "balloons" making that side lighter than the other. It is still a visual way for students to picture what is happening. Hope this helps!
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