The latest article I have been writing for my website deals with combined inequalities(or compound inequalities). One of the difficulties in teaching this topic is helping students understand conceptually the difference between "and" and "or". I try to accomplish this by developing real world examples. For example I give them the statements such as:

"The sky is blue and the grass is green."

"Peyton Manning is a Colt and a running back."

"Barrack Obama is running for president or he is a math teacher."

I then ask them which of the following are true and why. The goal is to get the students to understand that both statements must be true for an "and" inequality to be true. And that at least one must be true for the "or" inequality to be true.

What are other ways to help students understand combined inequalities?

## Tuesday, July 15, 2008

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## 4 comments:

You are going to buy your mom a mother's day present or cook her dinner.

You are going to buy your mom a MD present AND cook her dinner.

--Which do you think your mom will like better?

Also:

Your parents are going to buy you an ipod and pay for college.

Your parents are going to buy you an ipod or pay for college.

--Which do you think will happen, the "and" or the "or" statement?

Those are good examples. I like the different take that you had on it.

I like to work with the concepts of union (or) and intersection (and) visually. I find that if the students can generate a strong visual image in their minds, they are more likely to remember the fundamental meaning.

The intersection of two sets is the set of elements that are in common to both sets (we use AND).

The union of two sets is the set of elements that belong to either set or both sets (we use OR).

Here is the link to a page that demonstrates the visual imagery that I use for these.

I move from these examples to working with sets of numbers, then graphs (see this link).

Excellent Maria!!! Building on your idea, Ven Diagrams could also be utilized.

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