# Properties & Operations

Monday 8/22/11 Practice – Evens page 11 / Tuesday 8/23/11 Practice Odds page 11

More help with Properties;

Glossary of Properties from the Math Forum

Students also have a basic list of the properites on page 10 of their resource book.

Closure is a concept that is sometimes hard for 9th graders to grasp.  I like this explanation of the giraffe cage at the zoo…Ask Dr. Math for examples of closure.

Example for Closure we used from Questions 30-33.

T is the set of odd whole numbers.  So I ask students to list some of the numbers in this set…

T = {1, 3, 5, 7, 9, 11, 13…}

We check for closure under Addition, Subtraction, Multiplication & Division.

1 + 3 = 4  Is 4 in the set T? no, so T is not closed under Addition.

11 – 5 = 6  Is 6 in the set T?  no, so T is not closued under Subtraction

3 * 13 = 39 Is 39 in the set T? yes
5 * 11 = 55 Is 55 in the set T? yes
All students multiplied an odd * odd and ALL students got a result that was odd!
So… T is closed under multiplication.

9 / 3 = 3 works, but if we can find at least one CounterExample
13 / 5 =  2.6, since 2.6 is not an odd whole number, T is not closed under Division.