What is a good progression of Number Sense?
So number sense would start with concepts like recognizing numbers to 10, then 1-1 correspondence (counting), composing and decomposing numbers into parts and whole (number bonds, math triangles, etc.), basic addition & subtraction, estimation, missing addends and… the concept of place-value. This should be spiraled meaning that you go back and reteach it. Starting with smaller numbers for all of these concepts, then spiraling back for 2 digit numbers and teaching all of these concepts again, then the same for 3 digit numbers and so on.
- I created and found as many hands-on resources as possible.
- We played games and did activities
- We went over different skills at the beginning of class and during transitions
- We sang songs
- We always built on previous skills when we were learning new ones
- I differentiated my centers and math fact time.
1. Hands-On Learning
I created and found as many hands-on resources as possible. One of the resources I am most proud of are my Bead Sliders to 20! I made them for what I thought was a few students, but they ended up being one of our most used math tools for the entire class! They help kids compose and decompose numbers 1-20. We started out using them for our number bonds, then addition, missing addends & subtraction. So many other teachers and parents have loved them as well!
For counting, I of course used a lot of manipulatives. I also found that self-correcting puzzles and clip cards were amazing for the times that I couldn’t be there right in the moment as they were practicing. My city library has an amazing amount of educational games and puzzles that I can check out. I also love thrifting and have found lots of materials there! My favorite clip cards (for both math and literacy) come from Rachael @ Literacy with the Littles. You can find her on TPT, Instagram and her blog: https://literacywiththelittles.com/
Now, I have my own class set of base ten blocks that I use to teach how 10 ones make a ten stick (rod) and 10 ten sticks made a 100 square. I use 10 frames all. the. time. so I wanted a mat that had one. I couldn’t find one, so of course a I made it with printable base ten block manipulates.
1st use the mat and base ten block manipulatives to build numbers 0-10, then progressively teach double and triple digit numbers. I also use these to add and subtract, especially with regrouping. This math tool scaffold provides concrete understanding what regrouping is (in my childhood it was called borrowing) so that the child knows what the crossing out and making new numbers actually means.
2. Play
If you have read other blog posts of mine, then you probably know how much I love to play in the classroom! There are so many fun ways you can play with math, even during your instruction
COUNTING Ideas, Games & Activities
Counting: The possibilities for counting while playing are endless. Think of card games, dominoes, dice, board games, puzzles, clip cards, etc. I mostly used these items during centers and practice after workbook pages were complete.
While I was teaching, I loved using my “math monsters”. I put the math monsters (little monster cutouts that I laminated and glued on magnets) in a bag. The kids would take turns coming to grab a monster from the bag (I would pretend to eat their hand or give them a little spook for fun) and they would put the monster on the board. I usually had them place the monster in a ten-frame square. We would count and compare our monsters. Eventually they would also be used for basic addition and subtraction. If you haven’t signed up for my email list, you should do so now and get 8 FREE Math Games for K-3rd Grade
COMPOSING NUMBERS Ideas, Games & Activities
*Composing Numbers My kids were really struggling with composing numbers and knowing all of the combinations for any given number 0-10 (for example, 4=4+0, 1+3, 2+2). I had games to teach friends of 10, but not for the other numbers, so of course, I made them. We play with my Bead Sliders 1st (and some of my kids like to use the bead sliders to play the card games). This helps them add the 2 addends easily, but each card in the card games also have picture scaffolds to help students who need it. There are a variety of games to keep things fun, yet familiar games to make them easy to play like memory, go fish, & make a match.
MISSING ADDENDS Ideas, Games & Activities
*Missing Addends This concept can be sooo tricky for kids! The first thing I use are my Bead Sliders. We fill out the whole number in the number bond and then slide the beads to fill out the 1st part. Then we count the other beads to figure out the missing addend. Not sure what my bead sliders are? Scroll up and click on the image to see them in my TPT shop. When my students get pretty fluent with finding missing addends with the bead sliders we play a game as a class.
The game we play as a class is called “How many are hiding?”. 1st, tell them the whole big number of items (I use counting bears or counting cubes) and write it in the number bond. Then hide some under a cup or in an empty tissue box. The kids will count how many they can see, and write it in the number bond. Then they will use the “count on” strategy to figure out how many are hiding! They do a math talk to explain how they came up with their number either to a partner or the class. That kiddo then gets to check their answer by pulling out the hidden items and counting them with their peers! They love this! Eventually, this becomes a game they can play without me. I do a guided partner play with “friends of 10” to help them learn their Make a 10 facts. Do you need resources for making 10? I have some free materials in my store!
After we learn how to use number lines, I teach them how to find missing addends with that tool as well.
ESTIMATION Ideas, Games & Activities
*Estimation we play a couple of games throughout the year, the numbers just get bigger. I start with numbers within ten. I put some items in a clear jar and sing a song “estimate, estimate, I take my best guess and I estimate”. The kids show me on their fingers about how many they think. We then check by counting together. We play this same game, but I put the items on a paper under my doc cam, then quickly cover them up so the kids can’t count before they make their estimation. After they show me their guess, we count together.
COMPARING NUMBERS Ideas, Games & Activities
*Greater Than / Less Than By far, our favorite game to play is with my puppets! I have an alligator and shark puppet that I take turns playing with. Again, we start with small numbers, then eventually I use the puppets as I teach place-value and the actual greater than & less than signs. Of course, the alligator and shark want to eat the greatest number. The kids love holding the number cards and having a turn with the puppet! I make sure that we all say sentences like “4 is less than 9 and 9 is greater than 4” to make sure they are using the vocabulary words.
As a whole class, my kids build either towers or trains with unifix cubes. We line them up to compare numbers as partners and as small group tables. Again, we make sure to use our vocabulary words. I will have kids stand up at their table if they built the greatest or least number.
When my kids are practicing in centers, they love playing war. I have uno cards that I use (I make the special cards different numbers with a marker). I also bought some place value war cards on TPT forever ago when we start learning about place value.
PLACE-VALUE Ideas, Games & Activities
* Place-Value like I just mentioned, we have some place value war cards that we play with, but that is for centers. When I teach and play, I have kids take turns giving us a number within a range like 0-50 and we all build the number using our place value mats pictured above. If someone chooses my special number that I write down on a note ahead of time, then they get to hang out with a beanie baby for the rest of class!
We also love playing mystery numbers using the 120 chart. I cover up several numbers with the small sticky notes and students have to say what they think the number is and explain their thinking using the numbers on the sides, above & below the mystery number. One of their favorite centers is from Bite-Size Teaching. It is this game, but with a desert theme and they love it! I also let them play with blank 120 charts and mini erasers. They play in partners. 1 partner covers a few numbers for the other child and then they switch.
3. Transitions
This is both a classroom management hack and not wasting any time to practice previously taught skills and concepts! I actually do this throughout the whole day, but in math I make it math focuses. Our math starts right after recess. Of course it takes a few minutes (if I’m lucky) to have everyone in class. When my kids come in from recess, they immediately get to their math fact practice. I created an addition fact fluency program called Balloon Math because I was tired of just drill and kill. To read how I ran my Balloon Math Fact Fluency Program, click here!
As we transitioned to whole group learning I had a variety of things I did including self made subitizing cards (with colored dot stickers from the dollar store), ten frame cards that I bought from lakeshore, songs from my math songs cd, read aloud books about the concept for the day and number of the day! We only did number of the day during our place-value units that spiraled. I printed a set of blank posters and wrote each child’s name on one to make sure everyone would eventually have a turn. We found the number on our 120 chart, counted to it using whatever action or voice the special helper wanted, found 1 more/ 1 less, 10 more/ 10 less, wrote it in words, and expanded form. We hung the poster up for the day and the student got to take it home at the end of class. If we found the number of the day in our centers or workbook we happily shared the news with our friends!
4. Songs & Chants
My kids learn so much from songs and chants because they just stick! Some of the songs we made together like our song “friends of 10” that goes over each combination for 10 or chants for our count bys. Other songs we listen to from an old CD I have and Youtube.
I especially love the songs and videos by Jack Hartman kids music channel & Harry Kindergarten Music. There are sooo many good ones! My favorite of Jack’s is numbers to 100 with movement & my favorite of Harry’s is numbers in the teens have a group of ten.
5. Activate Schema
I always, always build on concepts that we have already learned whether it is building number sense or another academic area. It all starts with me going over our learning target (learning objective) and unpacking it. For example, if we were learning about making friends of 10, then I would have a target like: I can make all the friends of 10. Then I would ask, what do we know about 10? Maybe some kids would show their fingers or bring up a 10 frame that we have used. Whatever it is, we activate schema because we know that when people make connections with what they have already learned, they can use those same pathways to store new information in the brain. Later, at the end of the lesson or class, the students rate themselves on their own understanding of the learning target.
6. Differentiate
Let’s face it, some kids will pick up on number sense pretty quickly. Others might really struggle and need repeated teachings & practices to understand. In my class this looked like differentiating during our math centers and the beginning of class. Like I mentioned above, most of my kids were doing BALLOON MATH to practice their addition fact fluency, but a few of my kids did not. They came to work with me for those 10 minutes on number sense concepts that they were struggling with. We always had our BEAD SLIDERS to help if they needed them. When we differentiate, we are trying our best to give every student what they need to be successful!
I hope you got some ideas & resources to help you teach Number Sense. I'd love to hear from you!
Did you find anything particularly helpful?
Do you have some of your own ideas to share with other educators?
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