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Cardinality
Children will learn how to count before they understand that the last count word indicates the amount of the set or the cardinality of the set. Children who have made this connection are said to have the cardinality principle, which is a refinement of their early ideas about quantity.

Number Sense
a good intuition about umbers and their relationships. It develops gradually as a result of exploring numbers, visualizing them in a variety of contexts, and relating them in ways that are not limited by traditional algorithms

Commutative Property
In addition, it means that it makes no difference in which order two numbers are added.

Associative property
For addition, when adding three or more numbers, it does not matter whether the first pair are added first or if you start with any other pair of addends.

Comparing Problems
Involves the comparison of 2 quantities. The third amount is the difference between the two. Ex. George has 12 knuts ad Fred has 8 Knuts. How many more pennies does George have than Fred?

Part Part Whole
two parts are combined into one whole. George has 4 galleons and Fred has 8 galleons. They put their Galleons together. How many do they have now?

Join
3 quantities are involved: an initial or starting amount, a change amount, and the resulting amount. Dobby has 3 socks. Harry gave him 4 more. How many socks does Dobby have all together?

Separate
initial amount is the whole or the largest amount, whereas in the "join" problems the result is whole. Here, the change is that an amount is being removed from the initial value. Ex. Ginny has 7 puffskiens. She gave 2 to Lua. How many puffskiens does Ginny have now?

Equal groups: Whole uknown
 Harry has 4 bags of chocolate frogs. There are six chocolate frogs in each bag. How many chocolate frogs does Harry have altogether?
 If licorice wands cost 5 knuts each, how much did Sirius pay for 7 licorice wands?

Equal Groups: Size of groups unknown
 (Partition division)
 James has 24 fizzing whizbees. He wants to share them equally among his four friends. How many fizzing whizbees will each friend recieve?

Equal groups, number of groups unknown
 measurement division
 Hagrid has 24 dragon eggs (God help us). He puts them into bags containing 6 eggs each. How many bags did Hagrid use?

comparison: product uknown
Winky drank 6 bottles of butterbeer. Professor Trelawny had 4 times as many drinks as Winky. How many drinks did Trelawny have?

Comaprison: set size uknown.
 partition division
 Ron caught 24 quaffles. He caught 4 times as many as McClaggen did. How may quaffles did McClaggen save?

Comparison: Multiplier unknown.
Snape made 24 potions while James only made 6. How many times as many potions did Snape have?

Combination
Mrs. Weasley baught 4 pairs of pants and 3 jackets and they all can be worn together. How many different outfits consisting of a pair of pants and a jacket does Mrs. Wealsey have?

