If there’s one common thread that runs through every single thing we do in pre-k, it’s setting the foundation for all of our kiddos’ future learning! We set the foundation for their social/emotional learning, reading, writing, math… literally EVERYTHING! And it’s absolutely no different with the skill of decomposing numbers. Decomposing numbers is one of the most important math concepts for kiddos to grasp as they get older. And we can do a LOT to set the foundation for them in our pre-k classrooms! (If you’re wondering what decomposing numbers is and why it’s important, you can read about it HERE.)
What skills come before decomposing numbers?
There are several skills that should be firmly in place before you start introducing decomposing numbers to your kiddos. Here’s a quick look at what they are:
- Rote counting: Knowing the counting sequence in order.
- One-to-one correspondence: Counting objects by saying one number for each object counted.
- Cardinality: Knowing that the last number you say when counting a group of objects tells how many objects there are.
- Order irrelevance: Understanding that the order in which you count the objects in a group doesn’t change the number of objects in that group.
- Joining sets: Understanding that two groups of objects can be joined together to make a larger group.
- Separating sets: Understanding that one group of objects can be separated into smaller groups.
And once you’ve got all of those concepts in place, you’ll be ready to introduce decomposing at a very basic, conceptual level.
So now let’s take a look at each one of these concepts and what how you can teach them in your classroom!
To develop the skill of rote counting, kiddos needs lots and lots of opportunities to count! They need to learn that the words you say when you’re counting always stay the same and always go in the same order. This is definitely one area where the phrase “practice makes perfect” applies!
But… please note that rote counting does NOT require objects. You can always use objects for counting practice, but you can also teach the counting sequence without using a thing! The important thing with rote counting is simply being able to say the numbers in order!
Here are some ways you can incorporate rote counting into your classroom throughout your day:
- Counting songs: Singing songs that start at one and count up are a great way to teach the counting sequence! Songs like “One, Two, Buckle My Shoe” and “1, 2, 3, 4, 5, Once I Caught a Fish Alive” are great examples of songs that teach the counting sequence! You can download my free set of seven songs that teach counting by clicking HERE!
- Counting books: Books are a great way to teach the counting sequence! Plus, you get to sneak in some literacy too! Here are a few of my favorites!
Mouse Count by Ellen Stoll Walsh
Ten Black Dots by Donald Crews
How Do Dinosaurs Count to 10? by Jane Yolen and Mark Teague
Counting Crocodiles by Judy Sierra
Chicka Chicka 1, 2, 3 by Bill Martin Jr. and Michael Sampson
- Transition times: Moving from one activity to another can serve more than one purpose if you squeeze a little learning in! Count out loud during clean-up times, when lining up, during bathroom breaks, or when walking in line down the hall to keep your kiddos minds busy and engaged! Try counting at different volumes, in different voices, or with a puppet to keep it fresh and fun!
One-to-one correspondence is the ability to say one number for each object counted and to only count each object one time. When you are working with your kiddos on this concept, you’ll want them to master counting to 5 with one-to-one correspondence before you move on to 10, and 10 before you move on to 20. Keep in mind though… counting with one-to-one correspondence has nothing to do with matching quantities to written numerals! That’s another skill for another day! One-to-one correspondence is simply accurately counting objects.
Even though it seems like something very simple and natural to us, that’s not necessarily the case for our littles. It is VERY common in preschool and pre-k to have kiddos randomly moving their finger over a group of objects while saying the counting sequence. But the number they stop on is never the correct one! One-to-one correspondence does actually need to be taught and practiced when you have kiddos who come to you without a solid understanding of it.
So how do you do that in the classroom? You give your kiddos as many opportunities to count objects as you can!
- Manipulatives: The very best way to teach and practice one-to-one correspondence is using manipulatives! My absolute favorite for this is mini-erasers from Target! (I may have a slight obsession with these…) But, you can also use Unifix cubes, two-sided counters, linking chains, pattern blocks, transparent discs, craft sticks, dominoes, bear counters… Honestly, anything can become a math manipulative when you lay it on the table in front of one of your kiddos and ask her to count them!
- Classroom supplies: You already have crayons, markers, pencils, and glue sticks at your fingertips, so why not use them! Let your kiddos count the supplies each day to make sure everything is where it’s supposed to be! It helps you make sure your tables and centers are fully stocked AND gives your kiddos extra counting practice!
- Physical movements: Make a game out of counting by giving your kiddos a movement and a number. Have them do that movement that many times while they count. For example, you could ask them to take 5 steps, clap 7 times, or hop on one foot 9 times.
So, what if you have a kiddo who just isn’t grasping the concept of one-to-one correspondence? In that case, practicing in a whole-class or small-group setting may not be enough. You may need to do some individual teaching. You can teach them how to organize their counting by lining up the objects and moving each one as you count it. You may need to line up a set of objects for yourself and for your kiddo. Ask them to mirror what you are doing as you touch and count each object. You can also go a step further by holding their hand and physically moving it to touch each object as they count. This slows them down enough to help them only say one number per object.
Cardinality is the understanding that the last number counted tells how many objects are in the set. For example, if you have four cubes and you count them, 1 – 2 – 3 – 4, the last number you say when you’re counting is 4. So, you know there are four cubes in the set. This is another concept that seems like second nature to us, but that’s not the case for our preschool kiddos. You can tell if they’ve got a firm grasp on cardinality by simply asking them to count a set of objects then asking, “So how many are there?” You’ll know right away if they understand this concept by their answer. If they are able to consistently tell you how many objects are in the set, they’ve got it! If they answer with a random number or give no answer at all, you’ll need to spend a little extra time working with them on this one.
The best way to teach cardinality is to practice, practice, practice! The first few times you work on it, do a whole LOT of modeling. I like to do this with a variety of manipulatives to keep it fresh. Mini erasers are my favorite! Put out several objects, line them up, touch them while you count, and make sure that EVERY time you count you say, “1 – 2 – 3, so I have three cubes.” That last part is the critical part for this concept! After you’ve counted and told how many, ask your kiddo to do it with you. You still point and you still count, but she does it with you. When you say how many there are, ask her to repeat what you’ve said. Gradually work towards your kiddos being able to do it without your example first as you see that they are ready for more independence.
Order irrelevance is the understanding that I can count a set of objects in any order and the amount doesn’t change. I can move them around. I can start on the left. I can start on the top. But no matter how I count them, there will still be the same number of objects.
To see if your kiddos have an understanding of order irrelevance, show them a set of five objects. Count them together starting on the left. Ask how many there are. Then say, “What if I start here and count?” as you point to the right side of the group. If they can tell you there will still be five, they understand that the order in which you count the objects is irrelevant. If they tell you the amount will change or if they aren’t sure, this concept is still developing and they need some more opportunities to practice it.
The best way to help your kiddos develop this concept is to spend time counting the same group of objects in different orders. You can do this with groups of students during circle time, with wooden blocks during centers, or with manipulatives during small group time. Honestly, you can do this anytime you are counting a set. Just make sure that after you’ve counted the set in a different order you point out to your kiddos the fact that the number of objects stayed the same!
Joining and Separating Sets
Joining and sets is the precursor to addition, and separating sets is the precursor to subtraction. They are both very important when we’re laying the foundation for decomposing numbers. Here are some basic understandings that we want our preschool and pre-k kiddos to have:
- If I join to sets together, the new set will be larger.
- If I separate a set, the new sets will be smaller.
- I can make a set larger by adding objects to it.
- I can make a set smaller by taking objects away from it.
Again, this comes with TONS of experiences with joining and separating. Giving your kiddos opportunities to count two sets, push them together, and count them again will develop the concept of joining sets. Giving them one larger set, asking them to take some away, and counting each new set will develop the concept of separating sets.
Now… listen to what I am NOT saying that this concept is! This is NOT written addition and subtraction facts! This is NOT memorization! This is NOT a concept you can effectively develop with worksheets! That will all come later as they get older, but for now they need to join & count and separate & count REAL OBJECTS over and over and over again to build a conceptual understanding of joining and separating! Trust me, their first grade teachers will thank you for this!
So… What Comes Next?
Once your kiddos are rocking these early math concepts and you think they’re ready for the next step, you’ll want to introduce the game, “How Many Hiding?” This is always a favorite with my pre-k kiddos! It’s fun to use as a large-group game during circle time, and it’s also fantastic to use with your small groups! Once they they learn how to play, you can add it to your math center and they can play independently! Here’s how it works! I’m using my Fall How Many Hiding game as an example.
- First, lay the fall background on the table.
- Choose a kiddo to be the squirrel, and give him the squirrel cut out.
- Start with three acorns. Lay them on the table and count them together with your kiddos. Ask how many there are and make sure they know you’ve got three acorns.
- Ask all the kiddos except the squirrel to hide their eyes.
- Ask the squirrel to hide part or all of the acorns under the fall background.
- Ask the other kiddos to open their eyes.
- Say the chant together. (This is definitely optional, but my kiddos always love it!) Ask them to count how many acorns they can still see.
- Help them figure out how many are hiding. For example, if they can still see one acorn, that means the squirrel hid two.
Once your kiddos have mastered this game using three acorns, you can start with four and then five and so on. Once they’ve gotten a pretty good hold on the concept of decomposing numbers at this conceptual level, they are ready to start using Number Pockets! But… please keep in mind that this probably will NOT happen in preschool or pre-k. Number Pockets are designed for late kinder and first grade, so do not feel like you need to push your pre-k kiddos into that level of skill! If you’ve worked on all the concepts in this post to set the foundation, your kiddos will be set in kinder and first grade!
If you teach older kiddos, or you have a rare pre-k kiddos who is ready for Number Pockets, you are ready to check out my next post!
Number Pockets: Getting Started