Thursday, September 28, 2017

Mastering Multi-Step Word Problems

How many of you cringe at the thought of teaching your students multi-step word problems?  (RAISES HAND!)  I get it. I know.  It's tough.  It is overwhelming, and it's not necessarily something that just "clicks" for kids.  They need practice, they need time to think through problems, and they need to start really thinking like mathematicians in order to become proficient at more difficult problems.  Luckily, over the years, I've come up with a few different ideas and activities for helping students master multi-step word problems!  There are TONS of freebies in this post.  Enjoy!

I always begin problem solving (not just multi-step) by teaching my students CUBES.  This has been around for years, in many different variations.  An oldie but a goodie, if you will!

I REALLY, REALLY emphasize the "E" because this is where kids get stuck.  I created the three "What" questions that they need to be able to answer before they can move on and solve the problem.  Before they try to solve the problems, they need to ask themselves:

• What label will my answer have? (This helps them narrow down exactly what they are doing with the problem, and maybe, just maybe, it helps them remember to include a label!)
• What information do I HAVE to answer the question?
• What information do I NEED to answer the question?
I have found that kids are almost always able to figure out the answers to these questions when they are required to stop and think about it, and this step ALWAYS helps to set them up for problem solving success!

I also teach my students to use a pretty specific format for showing their work and solving word problems.  I have been using some variation of this for years, and it has evolved the more and more I have used it.

The sample problem I used in this anchor chart is a SINGLE-STEP problem, and I would highly encourage you to teach this format using a single-step format, then move on later to using it for multi-step (hang tight! I will address using this format with multi-step problems soon!).

Now, do I recommend you use this format for every single word problem students use? Absolutely not.  However, we do at least one or two a week this way simply because of the "answer" section and how important it is for students to be able to explain their math process.

Students always have to begin their written answers with "To solve this problem, I..." and they always have to end it with "Therefore, I know..."  Students are always very tempted to say, "To solve this problem I added 1,098 and 530.  Therefore, I know the answer is 1,628 calories."  Is this right? Sure! But is it the best answer and explanation they could have given? Nope.

I always encourage my students to be VERY specific about what the numbers are that they are addressing when they write out their answer.  This helps them really evaluate their thinking and see if it made sense.  There is a big difference between telling me which numbers you added and what those numbers represent.  This also encourages students to restate the question in their answer and make sure they have actually answered the question that is being asked.

**THIS IS ALWAYS A CHALLENGE!** It takes my students several examples to catch on to explaining their answers in this way, but it is so, so worth it once they truly understand.  Here is another student sample:

Now, before I have them use this model for multi-step problems, there are a few activities we do to prepare for that challenge and to get them comfortable with multi-step problems.

First, I have them do a little sequencing sort.  I give them a completed multi-step problem with all of the steps out of order.  The steps are written in the same format as described above, with very specific instructions walking the reader through how they solved the problem.  The students put the directions back in order and make sure it all makes sense.  They aren't actually having to do any math here, so it frees them up to simply think about the process. (These sorts are free! See link at the end of my blog post.)

Once I feel like students understand the basics of solving multi-step problems, we move on to some scaffolded practice using these handy little foldables that I created! (I have created ten pages of varying levels, and they are FREE for you to use with your students!  Click the link at the end of the post to access the freebies.)

Each page is split in half.  Students fold the paper in half, cut across the dotted lines on the right side, and fold the right flaps under.  They always start with the left side, where they read the problem, following the CUBE steps (with a special place for the Examine step, because I think it is SO important), and then they open the flaps to reveal step-by-step how to solve the problem.  The flaps give the student hints about what step they need to complete and sometimes how to do it.  It serves as a scaffolded guide for solving these tricky word problems.

The purpose of the flaps is to guide students through the steps, but to also give them time to think about what the next steps are and then see if they are correct.

Now, the only tricky part about this is that students might solve problems differently (and possibly in a different order) and get the same answer and THAT IS OKAY.  These are meant to be used as an introduction to multi-step problem solving only!  There are so many ways you can let your students use them.

Once we have done several of these together, I let them start working on their own with task cards and our four square format I mentioned above.  I have them glue task cards in their notebooks and work through each problem.  Once they have done a few like this, I let them move on to working on them without the four square format.

Some students even like to create their own foldables (like those that I showed above) with the task cards!

When kids are ready, we then move on to multi-part problems.  Kids LOVE these, and they seem to really thrive on the challenge of not only having a multi-step problem, but also a multi-PART problem.

...and when your students are really ready for an even bigger challenge, it's time to present to them... Math Detectives!  This is a new spin on Error Analysis that requires students to really analyze solutions and see which solutions and problem solving steps are the most reasonable.  Each card has a task on it (usually multi-step) and there are two different explanations for a solution.  The students have to figure out which explanation is correct and then solve the problem.  This is such a fun activity for my students!  They love being detectives.

Well, there you have it!  All of my ideas and resources for teaching students to love solving multi-step word problems!  It doesn't have to be (too) scary.

If you'd like to download the THIRTY pages worth of freebies featured above, please click the image below.  This freebie includes the two tasks mentioned above as well as anchor chart templates and printable posters.

ENJOY, and please share your multi-step word problem tips in the comments!