Hi Liz and Samantha,
If I have a bag of lollipops and I want to divide them all between the two of you than I can organize the lollipops in two rows, one for Liz and the other for Samantha. If I can do it so that you each gets the same number of lollipops then the number I had in the bag must have been even. If I can't organize them into a 2row array with the same number in each row then the number of lollipops must have been odd.
Penny
Liz and Samantha wrote back.
I am in 5th grade & was not sure about this...
If you call the numbers that cannot be arranged into 2row arrays, Odd Numbers, would you call the numbers that can be arranged into 2row
arrays, Even Numbers?
Would I have been wrong if I called them "Products"?
This was the third question in our homework. The one before it was a group of numbers, we had to take out the ones that could be put into 2row arrays.
The question before that was multiplication questions that you had to put the answers into the 2row arrays They were all the even numbers...
Therefore, Samantha said that they were "Products", when the teacher may not have been connecting all of the questions & just was looking for "Even Numbers"...
What do you think...
Thanks so much.
Liz & Samantha
Hi again,
You are correct when you say "the numbers that can be arranged into 2row
arrays are even numbers". To call them products however is erroneous. the number 15 is a product, 15 = 3 5 but 15 is odd not even. In fact
 the product of two even number is even
 the product of an even number and an odd number is even
 the product of an odd number and an even number is even, but
 the product of two odd numbers is odd.
What you can say is that a number is even if it can be written of the product of two numbers, one of which is 2. Thus, for example
 6 is even since 6 = 2 3
 4 is even since 4 = 2 2
 2 is even since 2 = 2 1
but 9 is not even since you can't write 9 as 2 times another integer.
Penny
