Problem Solving

I am currently Teaching two Extended Algebra 1 classes. Because we have extended time I covered the necessary material and we are using the next 4 weeks to review for the Algebra 1 Core 40 Exam. I have been revisiting old activities and using the "High Achiever" website on the doe.

The address is ..... http://dualmus.doe.state.in.us/hiach/login.asp?Valid=1

All the questions are multiple choice and students take the exercises on the computer. I am able to create any length of exercise and pick questions from a bank of questions that meet the Algebra 1 standards. We generally have a review day/activity and then complete an exercise on High Achiever. My hope is that this will help the students feel more comfortable when they take the Core 40 via the computer..... Ok enough about that.
Because we had been reviewing all week I decided to use Friday as a day for problem solving and at the end of class a we went over yesterdays High Achiever exercise.

I gave my students the following problems.
Half of the room received this problem the March Issue of the Mathematics Teacher.

The other half of the room worked on the following problems from Menu Collection Problems Book.

4.5 Nails and Pails
A pail containing 40 nails weighs 175 grams. The same pail with 20 nails weighs 95 grams. How much does the pail weigh? How much does each nail weigh?

4.2 Leading by a Head
A six foot tall person walks around the earth. How much further does the person's head travel than the person's feet?


If students finished early they were to work on the other problems. I really enjoyed working with the students on all 3 problems. When we finished the students posted their answers on the board and we discussed different solution methods to the problems. The students struggled the most with the Mowing the Lawn problem and found the Nail problem to be pretty easy. However, we had multiple solutions methods to the Nail problem. Between my two classes we saw at least 5 different solutions methods, including one that involved drawing pictures, one that involved systems of equation, and one that used system of equations thinking but wasn't presented in that manner. As a result of the variety of solution methods I knew that it was a good problem. Students were engaged during the solution process and as we discussed the different solution methods. I know the problem might seem elementary, but it was the thinking and problem solving process that I was evaluating. We were also able to reviewthe elimination method for solving systems of equations and about how we could or couldn't use a proportion to solve the problem.

The mowing problem also had varied solutions, but what held up the students was knowing where to start and what to find first. After some hints the students were able to arrive at an answer and present a solution. The various methods for this problem after arriving at the areas involved, proportions, the d=rt formula, and unit rates.

Just wanted to share my experiences.