Problem Types
Addition and Subtraction: Problem Structures
One goal for problem solving should be that students read and understand a problem and have a strategy that they can use to solve the problem.
Did you know that there are 11 different story structures that students might see when looking at addition and subtraction word problems? As teachers, we need to make sure that we are using a variety of these structures when we create problems for our students to solve. I find myself tending to use the same structures time and again in my problems.
The following chart helps me check myself. The chart is adapted from: Children’s Mathematics, Cognitively Guided Instruction. Carpenter, Fennema, Franke, Levi, and Empson. 1999. Heinemann.
 Although the math in each is simple and the numbers are the same, pull out some unifix cubes and try each problem. Think about what a student would need to think about in order to solve each problem. Are there multiple ways the problems could be approached? (What would the bar models look like for each of these problems? (Check out: http://www.thinkingblocks.com for some bar model examples that fall into each category.)
Problem Type




Join

(Result Unknown)
Tim has 3 apples. His mom gives him 5 more apples. How many apples does Tim have altogether?

(Change Unknown)
Tim has 3 apples. How many apples does his mom need to give him so that he has 8 apples altogether?

(Start Unknown)
Tim has some apples. His mom gives him 5 more apples. Now he has 8 apples. How many apples did Tim have to start?

Separate

(Result Unknown)
Tim had 8 apples. He gave 3 to Sue. How many apples does he have left?

(Change Unknown)
Tim had 8 apples. He gave some to Sue. Now he has 5 apples left. How many did he give to Sue?

(Start Unknown)
Tim had some apples. He gave 3 to Sue. Now he has 5 left. How many apples did he start with?

PartPart Whole

(Whole Unknown)
Tim has 3 red apples and 5 green apples. How many apples does he have?

(Part Unknown)
Tim has 8 apples. 3 are red, the rest are green. How many green apples does Tim have?

Compare

(Difference Unknown)
Tim has 8 apples. Sue has 3 apples. How many more apples does Tim have than Sue?

(Compare Quantity Unknown)
Sue has 3 apples. Tim has 5 more than Sue. How many apples does Tim have?

(Referent Unknown)
Tim has 8 apples. He has 5 more than Sue. How many apples does Sue have?

If you would like ideas or help creating story problems, please let me know. Which do you think we use most frequently? Which do you think we do not expose students to often enough?

none
Great Sites for Word Problem Ideas
Greg Tang Math  This site allows you to change the problem type as well as which variable is the unknown. It also allows you to adjust the range of the numbers included in the problems so that it can be used for a wide range of students.
Thinking Blocks  Has a variety of problems and uses bar models to show solution ideas. This site include all four operations as well as fractions, ratios and proportions, and a junior site with smaller numbers.