Exploring word problems further

In a recent post (here), I mentioned my affinity for word problems. And studying Children’s Mathematics (Carpenter et al, 2014) as a graduate student makes me like them even more.

I enjoy solving them, but I also like writing them for my daughter Rosie. Indeed, I find it quite rewarding to design a word problem involving her favorite animals, toys, etc, and see her have fun strengthening her logical skills.

Maybe you would like to give it a try too ? Need some examples?

Let’s start with addition. When I write an addition problem for Rosie, I try to keep in mind these 3 formats (Carpenter et al., 2014):

  • Problem 1: Rosie had 3 beads. She found 5 more beads. How many beads does Rosie have altogether?
  • Problem 2: Rosie had 3 beads. She found some more. Then, she had 8 beads. How many beads did Rosie find ?
  • Problem 3: Rosie had some beads. She found 5 more beads. Then, she had 8 beads. How many beads did Rosie have at the beginning?

They can all be seen as addition problems (3 + 5 = 8).  Still, they are all different as the Unknown Part varies. In Problem 1, the Unknown Part is the Result (3 + 5 = X), in Problem 2, it is the Change (3 + X = 8), in Problem 3, it is the Start (X + 5 = 8), making these problems more or less arduous to solve. And providing several ways for Rosie to deeply explore addition.

A similar strategy of varying the Unknown part can be used with subtraction problem (e.g. “Rosie had 5 beads. She gave 2 beads away. How many beads does Rosie have left?” vs “Rosie had 5 beads. She gave some beads away. Now she has 3 beads left. How many beads did Rosie give away?”)

And because there is more, much more than addition and subtraction problems, I thought this table (here) would be quite helpful for you to see examples of different types of word problems.

One more thing that I discovered recently to explore word problems further, and that Rosie enjoys a lot: provide her with an equation, and have her come up with a story that would match it (e.g. “The answer is 3 + 2 = 5. What could be the problem?” or see post Pit Stop #4). It was a little tricky at first, but Rosie now loves creating her own story, based on her own interests (after all, it is all about motivation, right?). Your child may like it too ?

Have fun  !



  • Carpenter, T., Fennema, E., Franke, M., L. Levi, and Empson, S. (2014) Children’s Mathematics. Portsmouth, NH: Heinemann, 2nd Ed. ISBN-10: 0325052875

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