Solving Word Problems: A Boot Camp!

Solving word problems is an essential part of elementary math, but so often we fail to give students the tools needed to be successful. One strategy to help is to do a word problem “boot camp” to get them off on the right foot!

Solving Word Problems "Boot Camp"

Here’s what I mean.

We know students have been solving problems since kindergarten (we hope!), but often in the primary grades, we don’t showcase different strategies and help students learn to recognize different word problem types and the strategies that can be useful in tackling them.  Here’s where a boot camp can come in handy!

Most students have been exposed to strategies for solving word problems such as “draw a picture” or “make a table”.  (Sidenote:  Not ALL students have, so do some digging to see what background YOUR students really have!)

Unfortunately, these lessons may have been sprinkled in here and there over the years and rarely revisited.  What can solidify these strategies in students’ minds is to really study them, first one strategy at a time and then later in a more “mixed” setting.  When students do an in-depth study of the different problem types, practice the strategy, and then later have to apply those strategies on their own, we have a perfect example of how a gradual release model can make a huge impact.

Getting Started With Problem Solving Strategies

So here’s what I do!  First, decide which strategies are important for you to explore.  Here’s a list to get you started!

  • Make a list
  • Guess and check
  • Use objects to model
  • Make a table
  • Find a pattern
  • Work backward
  • Draw a picture

Now, these strategies are all useful in different types of problems, so we need students to understand how and when they are effective.  We also want students to recognize that there is no “right” strategy.  If students have a full “toolbox” of strategies to try, they have a much better chance of selecting a good starting point for their problem.

Some of these strategies are more sophisticated than others as well.  Let’s look at two: “Use objects to model” and “Draw a picture”.

Helping Push Students to Think Deeply

One of the most useful strategies we can teach is to “use objects to model”.  We begin this when children are very young. When we use real objects (ex. crackers) to model a problem such as, “Benny has 3 crackers.  His teacher gave him 2 more. How many does he have now?”, students can “see” the problem.  They can see the “joining” action.  We gradually move student to realize that objects such as unifix cubes can represent objects like crackers.  This is still modeling and is a very tangible, concrete way for students to solve problems.

Unfortunately, we often move past this modeling as students get older and the numbers get larger.  Students in upper elementary see using objects as “babyish” instead of a useful tool that can help them get unstuck! Having manipulatives handy and modeling their use can be exceptionally beneficial.

Now, do we want students having to pull out a bag of plastic cubes forever?  Absolutely not.  One strategy to start to move them past the concrete objects is the “Draw a picture” strategy which is one level more abstract.  Instead of having crackers or cubes to represent the problem, students can learn to make tallies or other marks to represent the problem.  This becomes exceptionally useful as the problems get more advanced.  Check out this problem geared for third and fourth graders.

Use objects problem solving strategy

Think about how using objects (scraps of paper, plastic cubes, etc) could help a student model exactly what the problem is asking.  Now check out this one!

Draw a picture problem solving strategy

Do you see how a drawing would be an excellent way for students to “show” the action of the word problem.  This is certainly not a problem that can be done effectively in one’s mind, and the numbers in the problem are only a part of the story.  Using problems like these to show students the strategies helps students understand the value of adding them to their own problem solving toolbox to access for ANY type of problem they encounter through the years.

Modeling Our Thinking

So let’s chat about modeling.  So often we skip this step entirely or don’t dedicate enough time to it. Whether you are working with your entire class or small groups, modeling different problem solving strategies and tools (like manipulatives) is key.  In a boot camp like this, you will want to make sure to take your students through each and every strategy you want to teach and go through the gradual release.  Model your thinking, have them work together, and then try it on their own.  This may take several days–especially if the strategy is new.

If you are working with a large group, consider projecting problems onto your Smartboard or device and walk through the steps you use to make sense of the problem and dig in.  Use a document camera and show the same thing.  No technology?  Print a copy of the problem out nice and big and bring the students close to watch you think, talk, and solve.  The key here is to let them in on the secrets!

  • Let the students know what you notice when you read the problem.
  • Show them confusing parts.
  • Wonder aloud about what strategies might be useful.
  • Ask them for their input.
  • Showcase how you keep track of your work and organize it.
  • Reflect on your answer and whether or not it seems reasonable.

All of these stages are intuitive to us as adults–but certainly are NOT to most elementary students.  The more they see it, the better chance they have of applying it to their own work.  This leads me to…

Students Solving Word Problems Together

The “we do together” step is such a powerful intermediary step.  After seeing a teacher model a strategy, letting partners or trios try it together gives the perfect blend of “I’ll try now!” and the support of peers.

Of course, it is essential to help students learn how to work together. (I talk about this a little more in THIS POST if you want some details.) Once you have established expectations, it’s great to take problems similar to what you have just modeled–whether working on drawing pictures or making tables or guessing and checking–and then have students work together to try some.

One tip I love to give is simple but SO powerful.  Before you let the partners work together, give them a few minutes of alone “think time”. This can help students who tend to be more reserved collect their thoughts and wrap their heads around the problem.  Without this wait time, some students tend to take over a partnership.  You know you’ve seen it!  This gives everyone a little chance to get their background–and gives you a few minutes to walk around, coach, get students started, or even “prime the pump” with students who you know are slow to get going or who may need a hint to get started.qx

Students Solving Word Problems Alone

Once students have had some practice with a specific strategy, feel free to send them off to try on their own.  If needed, bring a small group together for additional coaching and modeling.  Ideally, we want to get to a place where students can apply what they have learned in their “boot camp” to any problem they encounter.

I also think it’s important to find ways to work problem solving into every single math class.  Consider…

  • A problem every day as a warm up
  • Math centers with differentiated problems set up
  • Partner problems
  • Small group interventions or challenges for students needing differentiation
  • Problems on a variety of topics and skills–not just what you are working on at the time.  This forces students to use those tools you taught them!

Need Some Help?

I know this can seem like a lot, so over the years I have worked to create a collection of problems that are perfect for this “Solving Word Problems Boot Camp”!  If you are interested in having problems that are geared toward each strategy listed above with enough problems to model, have partners work, and have some for independent work, check it out.  It even includes a collection of problems at the end where no strategy is identified so students need to reach into the toolbox and choose on their own!  The cards can be printed as task cards (color or black and white), projected, or even used digitally through Google Classroom.  CLICK HERE or the image below to check it out.

Teaching Problem Solving Task Cards

Want to read another post about teaching problem-solving?  This is a great one–and there’s even a freebie waiting for you!