Word problems with addition and subtraction are easy, right?

Over the course of my 13 years as a grade 5 teacher and now in my third year as a Math Coach, I have witnessed the same situation over and over….a student is presented with a word problem, their brain freezes and they say, “I don’t get it.”  The more I work with the problem types in the CCSS (which are based on Thomas P Carpenter, Elizabeth Fennema, Megan Loef Franke and Linda Levi’s Cognitively Guided Instruction) as well as the modeling of these word problems as found in the word problem generator on Greg Tang’s website, the more I am convinced they are key to helping us with this age-old problem and will even set the foundation for future math learning!  So, so powerful!

For years I thought I was helping my students successfully answer word problems by having them highlight the numbers and the key words that help them decide what operation to do…. I even had the most beautiful key word poster hanging in my classroom!  My students were mostly successful because the vast majority of the word problems they were asked to solve had the result as the unknown.  Now, though, we introduce word problems starting in grade 1 where the unknown could be at any of the places and key words simply will not work anymore.

Here’s an example:

There were 6 birds in a tree.  Some more flew in.  Now there are 9 birds in the tree altogether. How many birds flew in?

More students than we like would see the numbers 6 and 9 and the word “altogether” and think they need to add them together.  They would give the answer of 15 and not look back.

At our school this year, we are dedicating one day of our math intervention time to working on these word problem types and the objective is NOT to find the right numerical answer.  In fact, in my grade 3-5 classrooms I have asked that we only use numbers within 10 to start because I don’t want the cognitive demands of the computation to get in the way of the underlying structure of the word problems.  What I am expecting students to do is:

  • make a model of the word problem with Cuisenaire rods (providing the concrete representation…until they don’t need to see it anymore)
  • draw the model and label it with words from the word problem, the numbers we know, and to put a question mark for the unknown
  • write at least 2 equations that could be used to solve the problem (keeping in mind two important mathematical concepts: the commutative property of addition as well as the understanding that an equal sign means the “same as” and is a relational symbol, not an action symbol)
  • write at least 2 equations that could NOT be used to solve the problem (Opens up the discussion that there is no commutative property of subtraction…if you write 4-9 it will end up in negative numbers. We live in northern NH so our temperature frequently goes below zero which helps my students understand this.)

Here’s are some posters I made to help our staff as we work with our students on this model.

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As you can see, the model will work for any addition or subtraction word problem type the students will come across.  It also perfectly matches the Cuisenaire concrete model when the numbers are kept within 10.  As students progress in their math journey, the numbers will be within 100…within 1,000…and eventually include decimals or fractions…but the basic structure is exactly the same!

If you haven’t checked out Greg Tang’s word problem generator you need to go there right now and check it out at http://www.gregtangmath.com.  Absolutely phenomenal!  You can generate word problems of a specific problem type, specify what you want to be unknown, and determine the number range.  You have the choice of generating one problem or ten that you can then print out.  In addition, when you click on the “hint” it will show you the model which will help you decide how you want to solve the problem.

We have given a pretest to all our kiddos with one question for each problem type with the unknowns at each spot so we can zoom in on exactly the word problem type each student needs to begin working on.  I’m hopeful that it won’t be too long before students see a word problem and say, “I can figure this out!”