Types of Problems

Separate Problems

"Action" (elements are removed from a given set) Separate Result Unknown: Typical subtraction problem (7-3=___) Sam had 7 pennies. She gave John 3. Now how many pennies does Sam have? Separate Change Unknown: Subtraction problem with the unknown being the amount subtracted (7 - __ = 4) Separate Start Unknown: Subtraction problem with the first quantity unknown ( ___ - 3 = 4)

Types of problems:

Part Part Whole, Joint, Separate, Compare

Joint Problems

"Action" Joint Result Unknown: Typical addition problem ( 3 + 4 = _ ) Sam had 3 pennies. John gave her 4 more. How many does she have now? Join Change Unknown: Addition problem with the unknown being the amount added (3 + __ = 7) Sam had 3 pennies. John gave her some more. Now she has 7. How many did John give her? Join Start Unknown: Addition problem with the first quantity unknown (__ + 4 = 7 ) Sam had some pennies...John gave her 4 more. Now she has 7. How many did she start with?

Compare Problems

"NO Action" (Involves comparisons between 2 disjoint sets) Compare with the Difference Unknown: Comparisons of 2 discrete sets or amounts --a "more than" question (There are 5 yellow and 3 green. How many more yellow than green are there?) Compare with the Larger Unknown: There are 3 green. There are 2 more yellow than green. How many are yellow? 2 + 3 = ___ Compare with the Smaller Unknown: There are 5 yellow. There are 2 more yellow than green. How many green are there? 5 - 2 = ___

Part Part Whole

"NO action" (involves a relationship between a set and its two subsets) Part Part Whole with Whole Unknown: An addition problem with no joining action. (3 + 4 = ___) Sam has 3 pennies and 4 nickels. How many coins does he have total? Part Part Whole with Part Unknown: No joining addition problem with one of the parts unknown (3 + ___ = 7) Sam has 7 cookies. 3 are chocolate and the rest are sugar. How many sugar are there?