Understanding Multiplication and Division in Word Problems

So, the fun and games of learning how to make arrays, skip counting on number lines and using models to solve multiplication problems has lead to the equally exciting task of solving division problems. Everyone seems to be making great progress and making meaning of multiplication and division in real world problems, UNTIL … wait for it … wait for it … We mix the two together!   And here the real “fun” begins … A few students usually have an intuition about the structure of the problems and just “get it” with out much help, but the majority of students need direct, systematic instruction paired with hands on or pictorial examples to really, truly, deeply, understand the difference between multiplication and division in word problems.  But where can we start?

Start with The Same Story!

I like to take the same story and write 3 word problems that use the same story, but ask 3 different questions.  This really helps my students to see how multiplication and division can be the same and different in a word problem and help them to see to importance of analyzing the question.   How many times have you had a student choose multiplication to solve a division problem because they “saw the word each”?  Solving similar problems and then discussing the problems in relation to each other can really get students thinking deeper about problem solving.

For example, my 3 word problems might be:

  1. Jeff had 4 plates of cookies to take to his neighbors.  He put 6 cookies on each plate.  How many cookies was Jeff giving his neighbors?
  2. Jeff had 4 plates of cookies to take to his neighbors. He had 24 cookies and put an equal number of cookies on each plate.  How many cookies did he put on each plate?
  3. Jeff had 24 cookies to take to his neighbors.  He put the cookies on plates. Each plate had 6 cookies.  How many plates did he use?

The three problems have the same story, but different clues are given and different questions are asked for each problem.  (Get this FREEBIE here)

As we work through the problems, I ask my students these questions:

  1. What is the question asking me to find?
  2. Does the story tell me the total?
  3. Does the story tell me the number in each group?
  4. Does the story tell me the number of groups?

Draw pictures or make diagrams!

We write down the question and clues. Then draw a picture …

multiplication and division word problems.png

After discussing how we made our picture we make our number sentence.

Write a number sentence and label the answers.

multiplication word problem.png

Compare and Reflect!



Continue to have meaningful discussion as you practice!

As you continue working guided problems with students ask them to explain why they are choosing to multiplication or division. Encourage students to question each other when working in small groups or with partners.  Have them write their own examples of word problems using the same story, but different questions.

And, of course, practice, practice, practice!




Top 5 Tips for Decomposing Fractions

As I have mentioned in previous posts about fractions, starting with hands on and pictorial activities is vital for helping primary intermediate level students understand fractions. Today I would like to share my top 5 tips for decomposing fractions. These are mainly focused on 3rd – 5th grade, but may be helpful for some older and younger students as well.


1.)  I love using my pizza game for hands on fractions!  If you don’t have a pizza game, you can use plastic fraction circles or make pizza fractions from paper plates. Show your students a fraction of a pizza such as 5/6. After guided them to name the fraction, show them one way to decompose it by giving 2/6 to one student and 3/6 to another student. Point out that 2/6 + 3/6 is a way to decompose 5/6 and ask if they can name any other ways.  Act out other representations such as 2/6 + 1/6 + 2/6 by giving those slices to other students.  Try this with several different students.


2.)  Give students color tiles or unifix cubes. Give specific directions such as make a rectangle with 3 red, 2 blue and 7 yellow.  What fraction of your tiles are not yellow? (5/12)  Move the red and blue apart a little to show how 5/12 can also be represented as 3/12 + 2/12.  Do this with a few other fractions as well.



3.) Give students pictures of fractions and have them cut them up to show ways to decompose the fraction.


4.) Coloring Practice – Give students pictures of fractions with nothing shaded.  Give them directions on what color to color different parts.  Then guide them to write number sentences to decompose the fractions.


5.) Play Games!  Make your own games to practice decomposing fractions or try one of the games I have available on my TpT page.




Multiplication With Partial Products and Box Method

There are so many great ways to teach multi digit multiplication now!  I remember being in school “way back when” and we learned one way, the only way, the standard algorithm.  Now there are many other models for kids to work with, and most of them help build an understanding of mathematical relationships between numbers.  Two methods I find to be helpful are the “Box Method” and the “Partial Products Method.”  Eventually students move on to the standard algorithm (“old school”) and the partial products/box methods help them to understand the steps! Continue reading

Mastering Multiplication

Knowing multiplication facts help students see the patterns and relationships between numbers that are needed to be successful in other areas of math!   Division, renaming fractions, and balancing equations are just a few examples where being able to recall facts quickly and correctly are extremely helpful!

So what do you do as a teacher or a parent of  upper elementary or older students who have not mastered the multiplication facts? Continue reading

Halloween Freebie!

Now that it is finally starting to feel like Fall I have done a little Halloween decorating and made a few new Halloween Math Games!  The first one I would like to share is a FREEBIE!


To download the Halloween Addition Bingo Game for FREE, just click the photo above!