E. Joseph Kocinski
Edison Middle School
Field Mentor: Shelley Schmidt
How to Handle A Broken Calculator
-Adapted from James P. Dildine’s "The Island of Broken Calculators"
You sit down to take your algebra test when you suddenly realize that your calculator is malfunctioning. Some keys will not work at certain times. What are you going to do?
This experience sounds like quite a nightmare! Fortunately, numbers are very powerful tools that can be used in a variety of ways.
The purpose of this lesson is to explore just what series of calculator keys could be pushed if a particular key(s) was not working. The goal is for students to experiment with each problem by playing with the problems to see how many solutions they can find. Remember that the mathematical answer is not important here, but how the students arrive at the answer is the focus of this lesson.
For this lesson, students will be divided into eight groups of similar ability. We will start by showing students a few examples on the overhead.
We will start with an easy problem and then progress onto more difficult ones.
Possible solutions: 3+3+1, 3+2+2, 3+(8/2)
Possible solutions: 6*(3+2), 6*(4+1), 6*(10/2)
Possible solutions: 44/4, 4+4+(4/4)+(4/4)+(4/4), (4/4)+(4/4)+…+(4/4) 11 times
We will then pass out two notecards with problems on them to each group. Every group will get problem 1, two groups will get problem 2, two will get problem 3, and so on. We will give the students around 10 minutes to work as a group and to come up with as many solutions as they can.
Next we will solve problem 1 as a class using the overhead projector. One group will give a solution and then all other groups are invited to contribute additional solutions. We will follow this same process for the remaining three problems.
1) Calculate 60/4 with no 4 key.
Possible solutions: 30/2, 60/(2+2), 120/8, 60*0.25
Possible solutions: 7*(3*4), 7*(6+6), 7*(5+7), 7*(4+8), etc.
Possible solutions: ((4+4)+9)*(1+1), ((4*2)+9)*(1+1), ((7+1)+9)*(6/3)
Possible solutions: (25*4)*(25*4), (25*4)^2, (50*2)*(50*2), (20*5)*(20*5)
Possible solutions: (4+4)/4, (4/4)+(4/4), (4*4)/(4+4)
If time permits, we will then have the students work in their group and try to come up with problems and solutions on their own. If time still remains, we will have some groups come up and present their problem on the overhead.
No formal assessment is necessary for this lesson. It is an exercise to get students thinking about numbers. They will hopefully experiment with many combinations of numbers and operations. We hope that they will see possibilities that they did not originally consider, and we hope that they can present solutions to us that we did not consider.