Answering via Informal Proof

There is a lot of adversity toward calculating instruments these days. Although there may be some merit to the accusation, I tend to side with the position that calculators have a role in the classroom and when used properly can allow educators to concentrate on the bigger parts of a math problem. Although this is typically not the place for such a discussion, for those interested in my opinion see my writings here

This posting is about limiting the usage of a calculator to a few buttons. The purpose of the exercise is to show the relationships of addition/subtraction or multiplication/division or even exponents/radicals. We do this by asking our students to solve a problem in one format but show its proof via another format.

Example.

Q: What is the product of 5 and 6?

A: 30

Our answer is of course 30. However, instead of accepting this as out answer let's as for an informal proof. Something like this.

Example.

Q: What is the product of 5 and 6?

A: 30; because the quotient of 30 and 6 is 5.

How to use this in the classroom:

Create 5 problems you want your students to be able to solve.

1) 8 - 3

2) 6 x 2

3) 8 / 2

4) etc

5) etc

Create a column for their answer and a column for their informal proof. Base their grade on the informal proof.

Problem Answer Informal Proof

1) 8 – 3      ____5___            ___Because 5 + 3 is 8___

2) 6 x 2      _______              ____________________

3) 8 / 2      _______               ____________________

4) etc         _______                 ____________________

5) etc         _______                 ____________________