Identify Number Patterns (In Arithmetic and the Multiplication Table)

Even. I only look at the last digit, 4, which is even.

Odd. I only look at the last digit, 1, which is odd.

Even. Zero in the ones place means that the number is a multiple of 10, so it must be even.

Yes. Even numbers can be shared equally among two people.

No. Odd numbers cannot be shared equally among two people.

Yes! 4 can be put into pairs, and 8 can be put into pairs, so if we put them together, we are just adding pairs.

Yes. All my socks can be put into pairs except one. All your socks can be put into pairs except one. Together, we have several pairs of socks and two unpaired socks. Those unpaired socks become a pair together!

I started with an even number of socks that can be put into pairs. Then I took away an odd number of socks, which means that I take away some pairs and also break up a pair to take one sock. That means that I have an unpaired sock left over, so the amount of leftover socks is an odd number. The rule is: even – odd = odd.

I get an even number! I can think of it as an odd number of groups of even numbers (which can be paired).

I get an odd number. For example, if I have 3 groups that each contain 5 socks, the socks in each group make 2 pairs with 1 sock unpaired. When I combine the groups, there are 3 unpaired socks, which still leaves 1 unpaired.