Numberless Math Story Problems

Cover for post Numberless Math Story Problems with sample math problem and drawing of tree and birds that corresponds with math problem.

In Teaching Math With Story Problems, we talked about why math word problems are such a powerful teaching tool and why we should think of them as story problems instead.  But, what if your child still struggles with understanding how the numbers in the problem relate to each other?

Then, it is time to remove the numbers and start with a numberless word  problem!  I know it might sound like we are not even talking about math any more if there are no numbers! But read on and it will all start to make sense.

Pinnable cover for blog post Numberless Math Story Problems showing a problem and a drawing depicting the problem.

What are Numberless Word Problems?

A numberless word or story problem is a math problem where the numbers are replaced with the word “some” at first.  This way children can start to form the story in their heads without worrying about the numbers.  They can even start to draw out or use manipulatives to model what is happening.  Then, once they have the idea, you slowly start to add the numbers into the problem.

For example, you would start with a problem like “The dog had some treats and then the boy gave it some more treats.”

How to Present Numberless Word Problems

When presenting a numberless word problem, you present the information one step at a time.

Step One:  Take the problem you want to work on, replace the numbers with ‘some’ and remove the question.  For example, let’s say your original problem is: “Damian has 6 cars and then his mom gives him 4 more.  How many cars does Damain have then?”

You will change it to “Damian has some cars and then his mom gives him some more.”  Then, encourage your child to explain what is going on.  Or have them use some manipulatives or a drawing to show what the story is about.

If your child has trouble conceptualizing the problem, go ahead and draw or show him what is going on in the story.

Two piles of matchbox cars on a white surface.
You can use actual cars to model the problem or any kind of math manipulative.

Step Two: Once your child understands the story, add the first number to the story: “Damian has 6 cars and then his mom gives him some more.”  Check with your child that she understands what is going on.  You could ask her to tell or show you what she knows.

Six matchbox cars lined up on the left and a pile of matchbox cars on the right.
We now have one amount that we can model exactly and the other amount is still unknown and can just be left in a pile.

Step Three: Now, add the second number to the problem: “Damian has 6 cars and then his mom gives him 4 more.”  Again, check in with your child and make sure he is still understanding the story.

Matchbox cars lined up in a group of six and a group of four.
Both amounts can now be modeled.

Step Four: This is where you add in the question: “Damian has 6 cars and then his mom gives him 4 more.  How many cars does Damian have then?”  You can use your drawing or model you created to answer.  Or you could encourage your child to use manipulatives like an abacus to answer the question.  If you use a drawing, it does not need to look like actual cars.  Your child could just make a dot for each one.

Write the Related Equation

Once your child has determined the correct answer, write out the appropriate equation. Talk about why you are putting each number where it goes as you write it.

Matchbox cars lined up in a group of six and a group of four with the equation 6+4=10 written on a whiteboard in pink.

For the above problem, 6 + 4 = 10 is the obvious equation.  But some problems may have more than one appropriate equation.  For example, consider the following problem:  “Gina had 15 markers.  She bought some more markers.  Then, she had 50 markers.  How many markers did Gina buy?”  You may see this problem as 50 – 15 = 35.  But, your child may see it as 15 + ? = 50.

By observing your child solving the problem, you should have an idea of which equation will make more sense to them.  Model writing that equation while talking through where the numbers go and why.

So for the above problem, you might say: “Gina had 15 markers so we will write that number first.  Then, she buys some more markers so we know we are adding. We figured out using our resources, that she bought 35 more markers so that is our next number.  And then, we know that altogether, she has 50 markers so that is our sum.”

You could also follow-up by placing the numbers in part-part-whole circles, especially if you are not sure your child is understanding how the numbers relate to each other well.

Part-part-whole circles drawn on whiteboard in pink and filled in with the numbers 50, 15, and 35.

As your children become more familiar with working with math story problems, you may find that you do not need to go through all the steps above.  However, keep in mind that if you present a new Type of Math Story Problem, you may need to go back to these steps until they feel comfortable with the new type.

Other Math Story Problem Resources

Pinnable cover for blog post Teaching Math With Story Problems showing printed math word problems. Pinnable cover for blog post 14 Types of Math Story Problems showing printable math story problem templates.

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