Problem Solving: Part - Part - Whole Problem Group

Everyday, real-world math is problem solving.  That's why it is so important that our students understand the problem solving process.  I hope that you are enjoying this blog series and have gotten some helpful tips and ideas for teaching problem solving that you can use in your classroom.  Today we are moving to our next problem type, the Part-Part-Whole problem.  

Problem Solving in the Primary Grades

As teachers it is imperative that we give our students a solid foundation in problem solving.  This means moving beyond teaching key words and teaching our students how to think through what is happening in a problem in order to determine the appropriate math steps to take.  

If you missed the first few posts in this series, I highly recommend that you go back because there is so much great information to help you teach problem solving skills in your classroom.  If this is the first post you've seen, here's what you've missed:

1. The 11 Types of Addition and Subtraction Problems
2. The Joining Problems
3. The Separating Problems

What are Part-Part-Whole Problems?

Part-part-whole problems are those addition and subtraction problems where you have two parts that together make up a whole.  You might be wondering how this is different from the joining and separating problems...  Well, there's one important difference - CONTEXT!

In the joining and separating problems ,we focused on getting students to see the action that was happening.  One group joins another group to make a bigger group.  Or, some of a group leaves to make a smaller group. There is a start, a change, and an end.  There is action in these problem types, and we want our students to see that.

In the part-part-whole problem group, there is no action. The start and the end are the same because nothing is joining or leaving.  Instead, we focused on two different parts of a group that make up the whole.  

Here's an example:  

Look at this group of pumpkins.  The group is already formed.  No more pumpkins are being added and none will be taken away.  Instead of having one of those actions, we want to break down our information by the color of the pumpkins.   We have two orange pumpkins and one white pumpkin.  Now our focus will be on the total number of pumpkins.

You see, in the real world there aren't always actions happening.  Sometimes we just need to take inventory of what we have, and this often includes breaking down into "sub-groups" that we call parts.

While this example is really simple, a real world application could include much larger numbers or a group with more than 2 parts.

While the math concepts of addition and subtraction will remain the same, it is important that students see the different contexts in which the mathematical operations can be used.

Part-Part-Whole Problem Types

There are two types of problems that fall into this problem solving group.  The addition problems are where the whole is unknown and the subtraction problems are where one part is unknown.  Let's dig into each of these problem types and how you might teach them in your classroom.

1. Whole Unknown

When you have a problem where you know the two parts of a group but you don't know the total group, then you have a Whole Unknown problem type.  These problems are addition problems.  I actually like to teach these problems along with the Joining Problems since both use the the same addition concepts.  

Once students are comfortable with the joining process, they are ready to use addition to put two parts together without there being an actual joining action.  As you introduce these problems, make sure to have students visualize the problem.  It's important for them to see that addition is used in different situations.

Here's an example of how I might teach a Whole Unknown problem in my classroom:

2. Part Unknown

The second type of problem in this group is when one of the parts is the unknown.  These problems connect to your subtraction concepts and are great to teach along side the Separating problems.  Before introducing students to the fact that there are different types of problems, make sure that they are understanding the subtraction concepts first.  When we throw too many different things at them, we can cause confusion and frustration. So make sure to lay the groundwork first, then show them the different times that subtraction can be used.

When looking at part unknown problems you can find the missing part in both the first and second positions.  However, the math students will use will be the same. 

Here's an example of how I would teach this type of problem to my students and the strategies that I would use:

Helping Students Master Part-Part-Whole

Now that we have understanding of this problem type, it's important to provide students with the instruction and practice opportunities to help them reach mastery.  In my math classroom, 90% of my math instruction happens in the small group setting.  I love this because I can really tune into each student, their understanding and their needs.  

Start with Hands-On Learning

I always start instruction and practice with physical objects that the students can move.  For these problem types, using one manipulative that is available in two colors is perfect.  The goal is for the two groups to have something in common (the common group) but to also be separated in some way to make the different parts.  Another option is two different parts with a more common generality like two types of animals or two types of food.

Here's some hands-on manipulatives that are perfect for introducing part-part-whole problems:

• colored counting cubes
• buttons
• pom poms
• counting bears
• colored clothes pins 

These are all fairly easy to find and make for a great hands-on lesson.   As you introduce these, have students create the entire group first.  This is really important to help them differentiate these problems from a joining or separating problem.  If we have them add one color and then the next, they are likely to connect that to the joining action.  

A fun way to do this is to have some small paper or plastic cups with the manipulatives already inside.  Then have students dump them all on the table at one time to create the whole group.  Help students connect this as the whole.  Then have students separate the group into the two parts and help them connect this to the vocabulary term 'part'.  

Move into Paper Practice

Once students have an understanding of the concepts then they are ready to move into paper and pencil practice.  My favorite practice resource is Mega Math Practice because it is jam-packed with ready to use problems for each problem type.  I don't know about you, but sometimes I dream about word problems, but then when it's time to make one up while I'm teaching I draw a total blank!  That's why I love having these already made problems that are ready to go!  

When putting together Mega Math Practice, I also made sure to include a variety of different math strategies.  This way you can be confident knowing that your students are being exposed to numerous strategies and practice for each of them.  Students will work on drawing a picture, creating bar models, using ten frames and writing about the problem.  An easy way to create a well-rounded math program that will support students no matter their learning style.

Try Your Free Mega Math Practice for Part-Part-Whole Problems

I know how helpful these resources can be for teachers and students alike.  That's why I want you to try them out in your classroom for free.  These Free Part-Part-Whole resources will help your students practice these important problem solving skills.

You can also find the full Mega Math Practice in both printable and digital formats. You can find the Part-Part-Whole problem solving practice in my store at Teachers Pay Teachers.

And . . . if you are ready to fill your teacher toolbox with ready to use problems for all 11 types of problem solving problems, you can grab the Mega Math Practice Problem Solving Bundle and be ready for the entire year!

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