# Decomposing Numbers Into Three Parts

I’ve been working with my Firsties on composing and decomposing numbers, and we are currently working on combinations for eight. I decided to take it in a different direction this week and work on decomposing into three parts, so I made a part/whole mat with three parts. You can download a free mat at the end of this post.

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The lesson started as I handed out the materials. I handed out the part/whole mats, and I gave the first student a handful of teddy bear counters, which turned out to be 5. How many bears do you have?ย Five.ย How many should I give you if you need 8?ย Three. This was a great formative assessment. I gave each student a different number of bears, and most counted on to determine how many to make 8. One student was clearly stumped. I had given him 3 bears, and he guessed several different numbers. I suggested that since we needed to make 8, he might try counting on from 3 to 8. He was able to do that with prompting. Next time, I would probably give him a number closer to 8.

I asked the students what was different about this part/whole mat, and they all quickly answered that it had three parts. I always like to insert questions that allow students to make and communicate observations. We started will all of our bears in the Whole section. I directed the students to move 3 bears to the first part and 2 bears to the second part. I then asked how many bears would be in the third part. Some students seemed confused by this, while others immediately realized it would be 3. This was a great opportunity to allow the students who understood to share their thinking: I knew it was three, because there were three bears left in the Whole section. Next, I modeled writing an equation to match our model. Again, some students were confused that we could have two plus signs. They wanted to put an equal sign after 3 + 2. By the way, they love writing with markers on the tabletop. So much better than a piece of paper!

After we practiced several like this, I told them excitedly that we were going to try something different. I gave them only the first part, and let them choose how many bears to put in the other two parts. I reminded them that they might have a different combination than their neighbor, and that was okay. I gave them 1 for the first part to allow them maximum flexibility in their other parts. After they completed their equations, I had them read them and I wrote the equations on my easel. I pointed out that within 1 + 4 + 3, I saw 1 + 7. I also asked them to describe how their equations were alike and different. ย For example, SJ and Malik both used 4 and 3, but they “flip flopped” them.

To end the lesson I told them I had a WILD idea! I was not going to give them any of the parts–they could totally make up their own. You would have thought it was Christmas.

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1. Becky Maxwell says:

I noticed that your part/part/whole chart had the whole on the top. Is there a reason it’s on the top instead of being underneath the parts?

1. Donna Boucher says:

No, Becky, I think that’s just the way I’ve usually seen and done it. I think it could be either. What do you think?

1. Kristina Sanchez says:

Becky and Donna, I think its a good idea for kids to be exposed to the chart both ways. Typically we add two numbers together and then find the sum. But like Donna said many show the whole on top to show how many there are all together, but it would be an awesome lesson to show it both ways. After all don’t we need to teach kids there is more than one way to do many problems.
In fact in our math lessons, and as part of Common Core standards kids need to know that 4+3=7 and 7=4+3. So why not do whole, part, part and/or part, part, whole (or in this case whole, part, part, part and or part, part, part, whole).

1. Rae says:

2. Rae says:

Could this work on higher year levels with larger numbers?

1. Donna Boucher says:

It’s not usually used with larger numbers, because you wouldn’t want students counting larger amounts of counters one-by-one.

2. Catherine Howard says:

i teach 2nd grade and as part of our moring routine the children decompose the number of the day. They can use up to four addends. We start on day 2 so it’s just 1+1 & 2+0 . It’s always a big revelation when they realize how many ways there are to make even a 1 digit number. It’s nice because as they grow stronger mathematically, the numbers grow with them. We also talk about strategies they use ( counting on, doubles, doubles + 1, make a ten, compensation, etc). All the students participate using whiteboards but the student of the day gets to choose 4 equations to explain to the class. They also know at least one must be expanded form.

1. Vicki Zweibohmer says:

Catherine, Does your morning work only include the Number of the Day work? Or does it include more? I also teach second grade and I am looking for a daily morning work for math that does not include paper consumption. Thanks!

3. Margaret Benedetto says:

I have been doing a lot of number bond work with 3 addends with first graders in my enrichment group. I use different part-part-part-whole templates too. We have used number bonds with circles with the whole on the top, then on the bottom vertically, then we try circle number bonds horizontally.We use number bonds as shown in your blog post which is a great introduction to bar modeling. I vary the missing parts. Today I had students choose one number as the whole (sum) and show me four different p-p-p-w combinations for that number. There has been great enthusiasm and engagement throughout these explorations.

4. Tracey says:

Hi Donna, I love the three-part mat. Did you free-draw them or is there a template you could share (or link to one where one could be made?)?

Thank you – I love this idea for reinforcing our mental addition strategies. ๐

1. Donna Boucher says:

Actually, Tracey, I did just free-draw it! Very unusual for me, but I kind of thought of it spur of the moment.