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Sue Lampkin - Mountain View, California - Kenneth E. Slater Elementary School
What first grade math teachers need to know

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Case Development:
The Carnegie Foundation for the Advancement of Teaching

The essential elements of
problem solving:
Question
Data
Plan
Answer
Check

A few years ago, I taught math to first through fourth graders every day in a lab situation.  During those five years, their classroom teachers and I found plenty of opportunities to discuss the children’s understandings of math. We discovered that, no matter what their age, the children had a difficult time pulling out the essential pieces of information in story problems and then solving them with understanding.  They didn’t know how to organize their data or how to organize their thinking.  Oh, how I wish I had known about the QDPA√ strategy then!

Does this method remind you of Hungarian mathematician George Polya? I thought it might!
The Five Steps

#1 Question - What it is that we want to
find out

• What is the question in the problem? 

• What does the problem ask? 

• What is it that we are trying to find out? 

• What do we need to find out?

 student work sample
#2 Data - The information (often numbers) provided in the problem

• What data do we have in the problem?  What information is provided?  What numbers do we see in the problem?  Where do  the numbers come from?

•  Do the numbers alone explain our data to someone else reading this problem?  Should we label our data?  Are there important words that we need to write beside the numbers?  (e.g. more or less)  

• Will the data enable us to answer the stated question, or do we need to know something else before we answer it? 

• Is there a missing piece of data? How can we find the missing data?  Is there another question that will help us find it, a question that’s not there? (2-step problem)  What is the hidden question that we must answer first, before we can answer the stated question? 
#3 Plan - What we need to do with the data to solve

• How can we find out what the problem is asking?  What do we need to do with the data to solve the problem?  How do we get the answer to the question?     

• Can we draw a picture plan to help us solve the problem?  What do we need to put in the picture?  How will we label the parts of our picture?

• Would it help to use real things (beans, cubes, etc.) ?

• How do we want to organize our data?

• Is there an equation that will help us solve the problem? 
#4 Answer - The outcome of the plan

• What is the solution to the word problem?

• What is the answer to our question?

• Do we need to label our answer?

• Do the units in our answer relate directly to the question?

• Can we write a sentence stating what the answer is?

• Do we need to include the units in our sentence in order for it to make sense?

#5 Check - Looking carefully to see if the answer is correct

• Re-read the word problem.

• Look carefully at all the steps to determine whether the answer is correct or not.

• Re-examine our drawings, computation, etc.

• Did we find what we were looking for?

• Did we answer the question?

• Does our answer make sense?

• Is there an equation that would help us check our answer?

• Can we work backwards to check  our computation?