# Problem Solving

## Teaching Word Problems

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## PickANumber

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Example
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Pick a whole number bigger than two. Multiply it by three. Subtract five from that answer. Circle that answer. Take your number again, and multiply it by eight, and add six. Add the new answer to the circled answer. (Algebraically 3x5 + 8x + 6 = 11x + 1)

Then the teacher asks for the result and gives the first number. Students should be asked for suggestions on how this is done. Suggestions the teacher should be ready for are ones such as “You have them all worked out ahead of time.” So be prepared to make up new examples. This activity will allow for arithmetic practice. Some numbers offered as results by students will be incorrect and the teacher will ask them to check their work.

Before the students become frustrated it is time to show how variables are used to solve the problem. I hear a dialogue such as this. “Problem says pick a number. We don’t know what it is so let us use a letter in its place. (That is the variable concept.) Let x be the number. Next we are to multiply the number by 3 that gives 3x. Then we are to subtract 5 which we indicate by 3x5. We were told to circle it so its underlined. Now take the number again and multiply by 8 getting 8x. Next add 6 for a result of 8x+6. Finally, add the result to the circled answer. 3x5+8x+6= 11x+1. (Here is a use of a manipulative skill.) So what does all this mean? Well, if we took your original number multiplied it by eleven and then added one, we would get the same result as all those other operations give. So to get your number all that needs to be done is to reverse the last two steps: subtract one from your answer and divide by eleven.”

I see this shown in two columns the words on one side the algebra on the other. Since one less than the student’s result should be divisible by eleven, this is an opportunity to practice arithmetic.