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Tuesday, January 7, 2014

Multiplication and Division Word Problems and the Common Core

If you walk into any third or fourth grade classroom during math time, there is a good chance they are going to be working on multiplication or division.  One of the things I see third and fourth graders struggle with the most is the application of multiplication and division in story problems.  I also think that teaching multiplication and division in the context of story problems makes it comes alive for students.

What are the Common Core standards for multiplication and division in grade 3 and 4?  Check them out:

  • CCSS.Math.Content.3.OA.A.3 Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
  • CCSS.Math.Content.4.OA.A.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem, distinguishing multiplicative comparison from additive comparison.1
See that little 1 at the end?  That refers you to a footnote that asks you to check out Table 2 in the glossary.  Many third and fourth grade teachers have not yet had an opportunity to do this.  Especially if you are accessing the standards online, it can be tricky to find.  

Here is a look:

A look at Table 2 from the Common Core glossary.  It shows the 9 problem types third and fourth graders are responsible for under the Common Core.  Take not that grade 3 needs to master the problem types in the first two rows and grade 4 is responsible for all 9 problem types.  

 When I first took a look at this table, I noticed that most of the questions in my curriculum, most of the questions I write or ask my students and most of the questions my students write only represent 4 of these problem types.  I immediately printed this table and placed it on a wall in each classroom and area that I work with third and fourth graders in.  I immediately started trying out other problem types on my students.  At first they were challenging.  I had to choose numbers that were friendlier or easier to see the relationship between in order for them to access the problems.  Now that I am more aware of the different problem types, I do a much better job at making sure they are all represented in my curriculum and daily teaching practices.

Even though the compare problems (third row) are not assessed until grade 4, I have made sure my third graders get exposure to these types of problems.  Especially by starting out with friendly numbers in the known fact range for these kids, I have helped them access these problems.  I wouldn't want them to come across a new problem type in fourth grade with challenging numbers.

If you also teach multi-digit addition and subtraction you may want to read up on the 12 different problem types in addition and subtraction that your students should be familiar with.

Because I have been more aware of these different problem types, we have spent quite a bit of time working on them over the past week months in grades 3 and 4 during whole group instruction and partner work time.  I wanted to see what students would be able to do on their own.  I created a set of task cards to use with my students in grades 3 and 4.

I spread the cards out around the perimeter of the gym.  Each kid got a clipboard, pencil and record sheet.  Then they went around from card to card solving problems and recording answers on their record sheet.  It was great to see how engaged they were and I was quite impressed with the work they did.

Check out these great action shots:
A student works on card 17.  Notice the * by the card number?   I put a small * on each card that had a compare problem on it.  This helped me remember which cards third graders are assessed on versus which ones they are being exposed to.  When I did this with my grade 3 kids, I had a few kids who struggle a bit that had a more challenging time with these cards.  Several students were told to do the ones with out * and then I met with a small group near the end to do the ones with * together.  
Contemplating a story problem 

I loved seeing how some students represented the "division" questions with division equations and others chose to set it up as a missing factor problem.  This is something I spent a few minutes talking about in the wrap-up discussion.  I put up several papers that had different equations but equivalent answers and we had a great discussion about the relationship between multiplication and division
As students finished, I had them have a "math talk" with another student who was also finished.  This consists of them comparing answers and going out to find any cards they disagree on.  If they can't come to an agreement they ask an adult for help.  It works great! 
As kids finish their math talk, I like to have some blank task cards for the early finishers to write their own problems on.  This gives me another measure of their level of understanding and gives other kids who are finished a chance to solve some more problems.  The early finishers often like to make a problem that is slightly more challenging than others and it is a great way for the speedy kids to challenge each other.  It also gives kids who need more time the opportunity to finish the problem set without being disrupted by their speedy peers.  
Want to give this a try with your students?
You can grab all 20 cards for one low price or grab a sample set of 4 for free!  
Which problem types do your students see the most of?  Is there a problem type (or a few problem types) that your students need more practice with?  Please respond in the comments below!


  1. I like your task cards. I need to try something like this with my ones.

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    1. Addition and subtraction has 12 problem types for grade 1. I have a post coming up later this week about how I address all these problem types with first graders.