Before doing word problems the student must appreciate the variable concept. One strategy to show students a use of the variable concept is the pick a number game. The class has writing materials, the teacher tells them to pick a number and then dictates some operations for the class to perform on their numbers. When the students are finished, the teacher asks each one for a result and quickly tells the value of the original number. Interest will be aroused by the difference in time taken by the students to get the second number and the speed at which the teacher gets all the original numbers. Students will want to know the trick, “How was it done?” If the teacher wants to avoid mental arithmetic the operations can be selected to give a common result for any initial number.
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.