When you think of teaching your students how to solve math word problems with the unknown in ALL positions, do you panic just a bit?
Or maybe a lot?
I know my first reaction is, “Oh, pleeeeeease give me a cup of coffee, or a frappuccino for a sugar boost, this is going to be one loooong day!
It’s true, solving math word problems can be very challenging for students because they are expected to identify the type of word problem it is (join, separate, compare, etc.), determine what unknown they must solve for, AND select strategies to solve it.
Even though our little darlings try to make it easy by absentmindedly adding numbers together to get the sum or subtracting one number from another to get the difference, it’s not that simple. Students must truly understand the problem scenario before they can solve it.
What a huge task this is for our little guys and gals, huh?
If only we had a way to help them truly process the problem and understand what they were being asked to solve.
Are you ready for some good news?
There IS a way to significantly help your students better understand and solve story problems. Really! It’s true!
It’s a strategy called, Numberless Word Problems…and it’s so easy to implement.
What Are Numberless Word Problems?
When I initially heard of numberless math word problems my first thoughts were, “No way! Impossible! How can math word problems be numberless? The terms totally contradict one another, right?”
Well, there’s a lot more to numberless word problems than what I initially thought. In fact, a numberless word problem isn’t entirely numberless, it just starts out that way.
All numbers are removed temporarily while students process what the situation is and determine what information is needed to solve the problem. As students ask for specific information, snippets of data are revealed until a solution is reached. Sounds intriguing, huh?
Well, I decided to give this new approach a try because, honestly, there was nothing to lose. My students found it VERY confusing to solve just about any word problem.
Let’s just say they randomly guessed at what to do. Oh! My! Goodness! It was not pretty!
So, I said a little prayer for good luck and jumped right in to using numberless word problems with my first graders. The results weren’t immediate, but with repeated exposure and practice students began to identify the parts of the problem and see the relationships between them.
They became more flexible in their thinking and more confidently solved for the unknown regardless of its position. Their progress and positive attitudes warmed my heart! It was truly awesome!
Just in case you are excited to give it a try but need a place to start, at the end of this post you will find a link to Free Numberless Word Problem Samples for first grade and a Lesson Outline.
Steps to Introduce Numberless Word Problems
Choose a word problem and remove the numbers and question.
Select a word problem from your math curriculum or write one yourself. Just remove the numbers and the question and read it aloud to students. (If desired, you can purchase numberless word problems online.)
Ask students what they notice about the problem and have them look closely for any math they see. It may be challenging for them at first but, with a little patience, you will be pleasantly surprised.
Creating a chart like the one below is helpful, especially when you first introduce this strategy.
Brainstorm what the question could be & reveal it.
Ask students, “What question might be asked?”
This encourages your students to think about what “could be” asked, which helps them identify and process important aspects of the problem.
The first time you have students do this, don’t be surprised if they respond with silence and blank stares. They may not understand what to do since the question is typically given at the end of a problem.
Don’t worry though, it gets much easier as they are exposed to additional numberless problems. They start thinking they are awesome “question detectives.”
After questions are brainstormed, REVEAL the actual question and have students restate it.
Identify what information needs to be given to enable students to solve the problem. Reveal those amounts.
Ask students if they can answer the question now. Hopefully, they will shout out that they need numbers.
Ask students what information (numbers) they need you to tell them in order for them to solve the problem. Since this can be a little tricky for students, it helps to have them partner share before sharing aloud. As numbers are given, write them right into the problem and reread it.
After you give the first snippet of information, be ready for some excited students to shout out the amount given and act as though they knew it all along.
Your students now have almost all the information they need. All they have to do is ask for the last number needed. Ask, “Can you solve the problem now? Will the answer be greater or less than the number revealed (e.g. 6 students)?”
It helps to reread the question and the story problem. If there is disagreement, allow a couple of students to share their reasoning. After a consensus is reached, reveal the last bit of information (numbers) they need and insert it right into the problem.
Again, be ready for some excited students bouncing up and down ready to share their answers!
Students solve the problem with a strategy of their choice.
Send students off to their desks to solve the problem in a way that makes sense to them. Having whiteboards and concrete objects available for them to use is very helpful. This freedom of choice allows them to work at their developmentally appropriate level.
After they solve the problem, have partners share their answers and how they got them. Then have them share aloud with the group. It’s pretty amazing to hear all the different strategies they use.
Okay, so how do you feel? Can you envision yourself using this strategy with your students? If you said yes, I so hope you take the plunge and give it a try.
You can easily write your own numberless word problems using story problems right out of your curriculum. However, if you’re looking to purchase a pre-made set, we have the following yearlong sets available.
- Numberless Word Problems – Addition & Subtraction within 20
- Numberless Word Problems – Addition & Subtraction within 100
- Numberless Word Problems – Multiplication/Division (1 digit by 1 digit)
If you are a first grade teacher looking for a quick way to get started, just click below to sign up for our email list and receive FREE Numberless Word Problem Samples and a Lesson Outline to give you a jump start.
Good luck giving numberless math word problems a try!
Becky at Primary Bliss Teaching