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# How to Teaching Composing and Decomposing Numbers

Updated: Oct 31, 2022

How do you explain decomposing numbers to kindergarten?

Cracking the Code to Teaching Decomposing Numbers

Decomposing Numbers Unit Plan

I think I've cracked the code. For the longest time, I did not understand how to teach decomposing numbers or what the purpose was, I wasn't sure why decomposing numbers was important in kindergarten. I remember teaching a game called Racing Bears, where the students had to roll a die and try to get their bear to land exactly on a specific spot and if they had numbers left over, they could split their bear with another one and make that bear finish off the number. Even typing that it doesn't make sense because I didn't understand what I was trying to show the kids or what skill they needed to know to play that game. It seemed like the kids who got it, got it, and the kids who didn't, didn't.

There has been a push in mathematics instruction to have your students be in a state of productive struggle. I personally think there is a time and a place for that, but because the idea of decomposing numbers is so abstract, I have found more success with more explicit instruction for this topic. In some cases, my students have just mastered the concepts of cardinality and one-to-one correspondence so asking them to then be flexible with numbers can be a challenge.

The Tools

I started to think about my students needing to be able to be flexible but also having concrete items to use to build their understanding of the flexibility of numbers, so now when I teach decomposing numbers, I use a variety of tools in similar ways to help their understanding.

Number Bond

The first tool I use is a number bond. A number bond is one big circle connected to two smaller circles the number you are working with is in the big circle and then its parts go into the small circles. I like to use double-sided counters for this so if I was doing the number 5 I might have 3 yellows in the small circle on the top and two reds in the small circle on the bottom.

Part-Part- Whole

The other tool I use is a part part whole mat. This is a rectangle cut in half longways and then cut it in half again on the bottom so there's a long half on top and two smaller parts on the bottom. Using the same number, I'd start with all five on top then move three yellows to the bottom part, and then two reads to the other part. (Side note I have used a tense frame also, but I haven't seen it be as impactful in this instance.)

The Lessons

Warm Up

For our warm-up I might play the game Bunny ears. In this game, the students need to show you three fingers and put them behind their heads like Bunny ears. Some students might use all three fingers on one hand, if so perhaps prompt them to use two hands and still make 3. I often get some students showing three on both hands which would equal 6 and then take the opportunity to have them count their fingers and make any corrections if need be. This serves to keep in mind the different ways we might make the number 3.

The Mini Lesson

For the mini-lesson I have all the students come to the circle and depending on your class give each student a number bond and three double-sided counters or have your students work in pairs so one set of manipulatives between two students. If possible, you can make a big number bond or show a number bond on the document camera so you can model what you're doing. I walk them through step by step putting all three counters in the big circle showing that three is the number we are starting with. I would then have them think back to our Bunny ears activity and think about the different ways we made the number 3. From there I would model for the students by putting some yellow and some red in the smaller circles and having students take turns making the combinations of three. As we find the combinations I'll record in a place where all students can see all the combinations we found in order so zero reds and three yellows, one red and two yellows, two reds and one yellow, three reds and zero yellows.

Then ask the students if they see any patterns or notice anything about those numbers. Some students might notice that they're opposites some might not, but as we go through each number, they'll start to see that this pattern repeats. That would be the end of my lesson and I would do it and activity like Shake and Spill, Drop the Cubes, or How Many More so they can start to really become familiar with combinations of three.

The Next Day

The next day I would repeat the same process but instead of doing 3 for our warmup with Bunny Ears, I would use the number 4. For the minilesson, instead of the number bond, I use the Part Part Whole mat and repeat the same process that we used for the number bond with the Part Part Whole Mat, modeling how to use it.

See if anybody could come up with those combinations of four but when I record them, making sure to record them in order so they could see the opposites that arise when you're decomposing numbers.

Continuing the Unit

Continuing the unit, continue with Bunny Ears and the number 5 and go back to the number bond and repeat the same process. Depending on how you run your math workshop, you can add a different decomposing number station.

The next day I would switch out Bunny ears for Quick Images as it serves a similar purpose but for Quick Images, I would use different arrangements of the same number, similar to Bunny Ears, so they start to see the combinations of numbers before we actually use our counting mats.

Final Thoughts

This was a bit of a longer post but I felt like it took me years to figure out how to teach this in a way that my students could understand how to work out decomposing numbers and understand the pattern that comes with decomposing numbers.

The real test for me was circling back to decomposing numbers and the students still remembered exactly how to do it and when we moved to story problems and addition and subtraction, they were able to recall those combinations and use their fingers and use the manipulatives very effectively to find out the answers that they needed. Being able to apply their knowledge to other situations was so rewarding to see and I was definitely doing my happy dance teacher cheer because I had cracked the code of teaching this concept.

Let me know if this works for you I have my full lessons available in my store as well as the stations that I used with my students so you can use exactly what I did. If you feel like you don't need that and you just want the number mats I also have them available for free! I hope you and your students have a great time with this unit and you feel your teacher joy just like I did!

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