Ready to make word problem struggles a thing of the past by implementing numberless word problems in first grade (or any grade for that matter)? Then you’re in the right place!
Stay with me.
Admit it. Most of us would rather do a week of recess duty than teach our first graders how to solve word problems. Time and time again we watch in horror as our students randomly add numbers in a word problem to get an “answer”. We feel hopeless, students feel hopeless, and we fight the urge to skip word problems altogether.
Am I right?
See if you can relate to this scenario:
We present our students with a word problem that is NOT a simple part-part-whole problem where the sum is the unknown. Why would we do this? Because, for most of us, our standards state that first graders must be able to solve all problem types for addition and subtraction with the unknown in all positions.
As we know, this is no easy task my friends.
The problem we present is this:
There are 6 students on the bus. More students get on the bus. Now there are 9 students on the bus. How many more students got on the bus?
We sit and wait – feeling like we’re underwater, holding our breath, waiting for just one student to truly process and comprehend what the problem is asking.
We squint our eyes and brace ourselves…hoping that we do not hear a very confident answer of 15!
But we do.
We almost always do.
The majority of our first graders have a tendency to randomly grab numbers in a word problem and add them together.
Because they are tiny humans who have not yet been taught how to process what is being asked in a word problem, as well as what important information is needed to solve the problem.
Numberless word problems!
Stay with me as I walk you through 5 simple steps to get you rocking and rolling with numberless word problems in your own classroom.
(Kudos to the brilliant Brian Bushart for coming up with this lifesaver of a strategy. This one strategy can completely transform our students’ abilities to solve word problems. It’s a game changer.)
But First…What Are Numberless Word Problems?
Numberless word problems are just that…word problems that are numberless. However, they do not remain numberless, they’re just initially presented that way.
By initially removing all numbers in a word problem, students are given the opportunity to process what is truly going on in the situation.
Let’s use the example shared above. The numberless version would look like this:
There are some students on the bus. More students get on the bus. Now there are lots of students on the bus.
Now imagine we just presented this scenario to our students.
As you can see, the numbers have been removed, as has the question. With the numbers and question removed, students are no longer rushing to add numbers together as quickly as bees swarming toward vanilla ice cream cones on a hot summer day.
What happens with their thought processes?
Suddenly, our students have to slow down and process what is truly happening in this situation.
They must visualize and think. Which is fantastic because, in real life, we are not handed tidy equations to solve. Real math involves thinking, processing, and problem solving.
So what does this look like from start to finish?
Here are the 5 easy steps for implementing numberless word problems in first grade – or any grade for that matter:
Step 1: PRESENT A NUMBERLESS WORD PROBLEM WITH NUMBERS AND QUESTION INITIALLY REMOVED
Select a word problem from your math curriculum or write one yourself. Remove the numbers and question, then read it to students.
Ask students what is happening in the story and have them look closely for any math they see.
Have them think, pair, share their ideas.
Here are some possible responses:
- There is a bus with kids on it.
- More kids are getting on the bus.
- There are more kids on the bus at the end of the story than the beginning.
- It’s a joining problem because more kids are getting on the bus.
(Note: It will take time and practice using the numberless word problem strategy before some of our students produce responses like these, but with a little patience, it will come.)
Step 2: BRAINSTORM WHAT THE QUESTION COULD BE, THEN REVEAL THE QUESTION
For this step we’re going to ask our students to think, pair, share what the question could be.
By encouraging our students to think about what “could be” asked, we’re encouraging them to identify and process important aspects of the problem.
The first time we ask our students to do this, we may be met with blank stares. Hold tight. Use wait time….like no tomorrow.
Your patience will pay off. This process gets much easier. As our students are exposed to more numberless problems, they become quite amazing “question detectives.”
You might hear responses such as these:
- How many students were on the bus at the end?
- It might be this. How many students were on the bus in the beginning?
- How many more students got on the bus?
After questions are brainstormed, reveal the actual question in the word problem and reread the problem to students.
Step 3: HAVE STUDENTS IDENTIFY WHAT INFORMATION IS NEEDED IN ORDER TO SOLVE THE PROBLEM, THEN REVEAL THE INFORMATION.
By this point, students know what the question is. Now ask them if they can solve the problem.
Of course they’ll say they can’t.
Here’s where we’ll ask them to think, pair, share what information they need in order to solve the problem.
Again….this part of the process will take great patience at the beginning of our journey into numberless word problems, but our patience will pay off ten-fold – guaranteed.
After students have brainstormed and shared what information is needed in order to find a solution to the problem, begin to reveal numbers one at a time, and discuss.
An example conversation might look like this:
“Okay my little mathematicians. You are right! We need to know how many students were on the bus at the beginning of the story. And I’ll tell you.
Six students were on the bus at the beginning of the story. I’m going to cross off the word “some” and write a 6.
Let’s read the story problem now.
‘There are 6 students on the bus. More students get on the bus. Now there are lots of students on the bus. How many more students get on the bus?’
Can you solve the problem now? Why not?”
This is where you’ll have students think, pair, share what additional information they need in order to solve the problem. Then continue your conversation with them.
It might look something like this:
“Yes! You’re right. We also need to know how many students were on the bus at the end of our story.
I’m going to tell you that information.
There were 9 students on the bus at the end of our story. (We’ll want to write the number 9 in the proper place.)
Okay boys and girls, do you need any more information in order to solve this problem?” (Have students think, pair, share.)
Step 4: GIVE STUDENTS TIME TO SOLVE THE WORD PROBLEM USING THE STRATEGY OF THEIR CHOICE
By now our students have taken the time to truly comprehend the word problem, they’ve identified what information they need in order to solve the problem, and they’re ready to go.
This is where we step back and give our students time to engage in some productive struggle as they work through the problem using whatever strategies make sense to them. Some will want to draw pictures. Some will want to use manipulatives. And some will want to write and solve equations.
This freedom of choice allows our students to work at their developmentally appropriate level and engage in some solid problem solving.
As our students are busily solving the problem, we want to wander around the room and do our thing. For students who are “stuck”, we will want to gently budge them using strategic questioning. For example:
- What is happening in the story?
- Is it a joining or separating problem?
- What do you know and what are you trying to figure out?
- What strategy could you use to solve the problem?
For students who have quickly solved the problem, we’ll want to see if they can solve it using a different strategy.
Step 5: HAVE STUDENTS SHARE THEIR ANSWERS AND STRATEGIES FOR SOLVING THE WORD PROBLEM
Once students have solved the problem, we’ll want them to share their answers as well as how they solved the problem. First, let’s have them share with a partner, then we’ll want to strategically choose a few students to share with the whole group.
We’ll want to choose a few students who have used different strategies to solve the problem.
For one, it honors all students’ mathematical thinking. We never want students to feel embarrassed about using manipulatives or drawing pictures. And we don’t want to force students who are in the representational stage to feel they have to use manipulatives or draw pictures. So we’ll choose students to share who solved the problem using different strategies – manipulatives, pictures, and equations.
It’s also a way to model a variety of strategies in a nonthreatening way. When we model a strategy, students tend to think that’s the right way to solve a problem. When students see a variety of strategies shared by their peers, they begin to internalize the fact that there are many effective strategies for solving math problems and this may encourage students to spread their wings and try them.
Finally, when students share their mathematical reasoning, whether it be with a partner or to the whole class, it deepens their own mathematical understanding.
NUMBERLESS WORD PROBLEMS IN FIRST GRADE – THE BOTTOM LINE
If you have students randomly adding numbers in word problems to “produce” answers, the BEST WAY to cure that disease is to use numberless word problems.
When the numbers and questions are initially removed from a word problem, students are forced to stop, think, and truly process what exactly is going on in the situation.
Which is what we want.
If we’re baking a cake and the recipe calls for a cup of flour, but we only have a one-fourth measuring cup, we’ve got to figure out how to solve our problem. We’re not handed an equation to solve. Real life just doesn’t work that way.
Real life math is all about solving real life problems in ways that make sense to us. So our job is to nurture mathematical thinkers. And the numberless word problem strategy is the way to do that.
Good news…you don’t need anything fancy in order to implement this strategy. You can just use word problems you have, remove the numbers, and don’t reveal the question right way.
However, if you’re looking for a thorough DONE-FOR-YOU resource that will save you time and is guaranteed to keep your students highly-engaged, we have the following yearlong sets available. These sets include numberless word problems to process through in a whole group or small group setting using your interactive whiteboard, as well as printable independent practice word problems. All problem types are represented with the unknown in all positions – which really gets students thinking. Click on the links to learn more.
- First Grade Numberless Word Problems – Addition & Subtraction within 20
- Numberless Word Problems – Addition & Subtraction within 100
- Numberless Word Problems – Multiplication/Division (1 digit by 1 digit)
Until next time,
Lets’ stay positive and enrich the minds and hearts of those around us.
First grade teachers, ready to give numberless word problems a try today? We have a FREEBIE just for you!