Fourteen types of Story Problems
Story problems will be taught throughout this unit in all sections but this is the section that they will learn about the each type and how it relates to other types of problems (inverse operations) but will not be learning the names of each type of problem.
The taxonomy of the Common Core1 distinguishes three main types of problem: change problems, which involve a quantity changing over time; comparison problems, in which one quantity is described as being larger or smaller, greater or less, than another quantity; and part-part-whole problems, in which a large collection is made up of two sub-collections. There are six types of change problems, (three involving increase of a quantity, and three involving decrease), six types of compare problems, and two types of part, part, whole problems. This is just the one step problems! These problems will not be taught in isolation but instead be taught with attention to inverse operations and to the commutative property just as in the other sections. Students need to be able to make connections with these problems to truly internalize what they are learning. It is also important to keep the story scenario the same so that students can concentrate on the numbers and not the reading. This means that when we are doing apple problems, all of the problems will have the same colors of apples and not suddenly change to truck problems (for example).
I will teach all of the change problems together. We will have lots of discussions on what the story is asking us, is there an action happening in the story, who is the action happening to, what type of problem it is, how do we know what type it is, and how can we restate the problem to make it an inverse operation.
I will have a chart to which we will add each type of problem to as we learn them so we can refer back to it when we are not sure what our problem is asking us. (Is it asking us to add or subtract?) Students will also have this information in the math notebook.
Change plus/final unknown is an addition problem with the total unknown.
Example: There were three apples in the basket at breakfast and Sam added seven apples to the basket at lunch. How many apples are in the basket?
Change plus / change unknown just means it is an addition problem and what is being added is unknown.
Example: There were three apples in the basket at breakfast, Sam added more apples at lunch. Now there are ten apples in the basket. How many apples did Sam put in the basket?
Change plus/ Initial unknown just means it is an addition problem because something is being added together but the first number is unknown. This is the hardest type of change plus problem, therefore, it will be taught last.
Example: Some apples were in the basket at breakfast. Sam put seven apples in the basket at lunch, now there are ten apples in the basket. How many apples were in the basket at breakfast?
Change minus/ final unknown is a subtraction problem with the difference unknown. Example: There were ten apples in the basket before lunch and four apples were eaten at lunch. How many apples are still in the basket?
Change minus/ change unknown is a subtraction problem where what is being subtracted is unknown.
Example: There were eight apples in the basket at breakfast and some were eaten at lunch, now there are three apples in the basket. How many apples were eaten at lunch?
Change minus/ Initial unknown just means it is a subtraction problem since something is being removed but we do not know the initial number.
Example: There were some apples in the basket before breakfast and four apples were eaten during breakfast. Now there are six apples in the basket. How many apples were in the basket before breakfast?
Part, part, whole/ whole unknown is an addition problem that is adding similar items (red and yellow apples or blue and green cars) with the total unknown.
Example: There are seven apples and two oranges in the basket. How many pieces of fruit are in the basket?
Part, part, whole/ part unknown could be an addition or subtraction problem depending on how you set the problem up.
Example: There were nine pieces of fruit in a basket on the table. The basket had four apples and the rest were oranges. How many oranges were in the basket? I would set this problem up as a subtraction problem.
Compare greater / smaller unknown is a problem that compares quantities of two things and someone has more of a quantity than someone else, and the smaller quantity is unknown.
Example: Tim has two more apples than Joe. If Tim has six apples, how many apples does Joe have?
Compare less/ smaller unknown is a problem that compares quantities of two things and someone has less of a quantity than someone else, with the smaller number unknown.
Example: Tim has six fewer apples than Joe. If Joe has nine apples, how many apples does Tim have?
Compare greater / greater unknown is a problem that compares quantities of two things and someone has more of a quantity than someone else, and the larger number is unknown.
Example: Tim has six more apples than Joe. Joe has two apples. How many apples does Tim have?
Compare less / greater unknown is a problem that compares quantities of two things and someone has less of a quantity than someone else, and the larger number is unknown. Example: Tim has one less apple than Joe. If Tim has seven apples, how many apples does Joe have?
Compare greater / difference unknown is a problem that compares quantities of two objects and one of the amounts is larger than the other one, and difference in the amounts is unknown.
Example: Tim has six apples and Joe has four apples. How many more apples does Tim have than Joe?
Compare less / difference unknown is a problem that compares two quantities and one of the amounts is smaller than the other one but the difference in the amounts is unknown.
Example: Tim has six apples and Joe has four apples. How many fewer apples does Joe have than Tim?
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