5 Ways to Build Number Sense in Your Classroom

For many of us, our kinders start the school year lacking number sense. It’s a challenge we face every year, and we feel like it’s going to take them forever to learn their numbers! These are some of the ways I have been successful in my classroom when it comes to teaching number sense. Even if you do not teach kindergarten, these teaching strategies can be used in all grade levels. You just have to change up the content and up the rigor.

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 1. Small Groups:

Just like in reading, I also pull a small math group daily. I try to make 4 small groups of 5-7 depending on my class size. Since our math center time is around 30 minutes, I cannot see every group daily, so I make sure to rotate them to every other day. In the beginning of the year, I have a huge gap of kids ranging from knowing numbers to 20 to only knowing the number 1. So, I make sure to group them by their skill level. I use a lot of manipulatives, white boards, and some math centers as well. For those struggling kiddos, I focus on numbers 0-5 for several weeks. Or if I need to dial it back further, I do 0-3. I make it fun by having them count cubes, writing the number on their white board, using number puzzles and putting the numbers in order. Basically, repetition over and over again until they have mastered 0-5. For those middle kids, I still focus on 0-5 but push them on numbers 6-10. We do the same kind of activities. Focusing on 1:1 counting, writing numbers and using some of the fun centers I have in my classroom. I really like to have the students use a center in my small group before I have them work on it independently, that way they can really be successful at it, and I know they are doing it correctly. For those higher kids, I still focus on numbers 0-10 but push them. Asking questions like what number comes before and after, what’s the missing number, using 10 frames, what’s one more or one less, and writing the numbers with nice and neat handwriting. Since we usually focus on numbers 0-10 in the first quarter, I don’t want to branch out into the teen numbers until we have a solid number sense of 0-10.


2. Mental Math: 

This is a great way to build number sense and it’s so quick and easy! In the beginning of the year, I usually have dot cards that replicate a dice. I flash them and they are to quickly tell me the number. I mix it up by asking girls, boys, hair color etc. This is also called subitizing. 

 
After they have a good grasp on the dice cards, I use more challenging cards where the dots are not in a specific pattern.
Also in the beginning of the year, I draw a 5-frame on my white board and have magnets that I interchange on the 5-frame squares. They are to close their eyes as I place them randomly on the 5-frame. I tell them to open their eyes and they are to shout out the number. I don’t always put them in order. I have boxes missing. In the middle of the year, I do the same thing, but with a 10-frame. If you want to add a written piece to it, you could always pass out white boards to the kids and have them quickly write the number down and then the teacher says: “3, 2, 1, show me your number!” Again, I make sure to mix up the magnets on my 10-frame so they are not always in sequential order.

Towards the end of the year, I start to use story problems. For example, I have 2 dogs and 3 cats, how many animals do I have all together? They are to think, and then write their answer on their white board. Then I say “3, 2, 1, show me your answer!”


3.  Math Review: 


This my number one way to increase number sense. I start math review pretty much the first week of school and do it EVERY day till the end of the year. It has a structure that is easy to follow once you get it down. I will break down the format so you can try this in your classroom. Math review should take between 15-20 minutes including passing out papers, pencils, etc.

A.     Math review has a 10-day cycle. Days 1-4 are teacher led and days 5-9 are student led. Day 10 is an assessment.
B.     It has 4 math problems with concept statements so they know what they are doing. This helps build that math vocabulary where they can explain it in their own words on the days that’s student led.
C.     Teacher led days (days 1-4): the teacher will read the concept statements and have the students chorally respond. The teacher will model how to solve the problem using metacognition. Then the teacher will give the student a few moments to fill in the answer on their paper. Then the teacher will read the closing statement for that problem and have the students chorally respond. This same process will be done for each number. I like to have the students self-correct their work, so after each problem I have them give themselves a dot under their answer if they got it correct.
D.    Student-led days (days 5-9): The teacher will still read the concept statements and closing statements as the students chorally respond, but when it comes down to solving the problem, the teacher will give the students a minute or so to complete the first problem. Then have the students talk with their partner how they solved the problem. You will need to model this many times before it’s done correctly. I give them a sentence starter like “I solved the problem by _______.” Then pick a student to come up and solve the problem. Make sure you pick someone who answered it correctly. They are to explain to the class what they did. You will probably need to walk them through this many times before that conversation comes easy to them. Then I tell the students, if you got that answer right, give yourself a dot, if you did not, circle it and write the correct answer. Continue this process for each problem.
E.     Assessment day (day 10): I spread the class around the room, and they have day 10 on their desks, floor, etc. They are to work quietly and do the problems on their own. I collect them and this is how I assess if they have mastered a concept or not. For those who haven’t, I go over it in a small group during our math block.
F.     Now you’re probably wondering what this all looks like, and the logistics of it. I print it out and make an individual packet for the student. They are labeled day 1-10 at the top. I keep a teacher copy and lay it under the document camera. Some years I have the class sit on the carpet, and some years I have them at their tables. It just depends on your class and how well they behave. So that part is up to you! Here is a sample from the first week of school:
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G.     Notice that each day has the same concepts, just different numbers. In the beginning of the year, I make everything teacher led. They are not ready for student-led yet! Usually after the first quarter, I start to have them try it out on their own. Here are a few samples from the last weeks of school:
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Al  All the skills covered in math review are all common core based standards that deal only with number sense, no shapes, measurement, etc.
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If you are interested in Math Review, I have it available to purchase in my store! I have bundled it for the ENTIRE year as well as sold individually for the beginning, middle and end of year. Click here to find Math Review in my store!


4. Problem Solving: 


This a really fun way to build number sense, and the kids love it too! I don’t usually start this until the 3
rd quarter, but it can definitely be done sooner if you choose to do so. I do this every Friday morning, and it follows a structure that is the same each week. Problem-solving days include solving a story problem with either addition or subtraction. I type out a problem with room for student work, a place to record their answer, and how they solved the problem. Slide19
The first time we do problem-solving, I create an anchor chart with the class. We choose different strategies to solve a math problem. Then they can refer back to this when working independently.

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This is the format I follow when doing problem solving:

A. Read Together: Have the students sit on the carpet, and read the problem several times. I point out the numbers and circle them. I don’t want to give away what method to do or if the question is asking for addition or subtraction. So I keep it pretty basic when I introduce the problem.
B. Student Work: 
Students work independently for about 3-5 minutes at their tables. At the tables, I provide buckets full of manipulatives. Inside are Unifix cubes, 10-frames, number bonds, and their pencils and crayons. Students are able to choose whatever method works for them.
C. Solve With Partner:This part is tricky, but since we have been doing math review for 2 quarters, it’s not that difficult for them to discuss with their partner how they solved the problem. I had to model it a few times pretending like I was a student. Basically, they are to show their partner how they solved it, and I give them the sentence starter, “I solved the problem by _____.” This should be roughly 1-2 minutes.
D. Class discussion: I have the students bring their paper and pencil and I usually pick one manipulative to bring to the carpet. Usually, I say bring 10 cubes. Then I call on about 6 students to give me their answer. That’s it. No explanation yet. I write down correct answers and incorrect answers. Then I go back and call on the students so they can tell the class how they solved the problem. I usually illustrate or model what they are saying on my white board or doc camera. For example: If the student says, “I drew a picture of 5 balloons.” I ask them, “why did you draw 5?” They can explain that it says 5 in the sentence. So then I go ahead and draw 5 balloons on the board. Then the student continues to explain, “then I crossed out 2 balloons.” I again ask why. I proceed to cross out 2 balloons. Then I ask what did you do after that? They say, “I got 3 balloons.” I ask the class if that makes sense. I love it when they go further and write it into a number sentence. 5-2=3. Then I move on to the next kid. I make sure to pick kids who solved the problem differently this way the class can see multiple ways to solve a problem. I make sure that the students who provided the incorrect answer explain their way. Then we realize that their way didn’t make sense and I cross out their answer.
E. Class Solution: We pick one way to solve it and have everyone try it together with their own manipulatives, paper, and pencil. Most of the time, I just pick it. I have everyone count out 5 cubes and then take 2 away. We then all write the number sentence on our paper.
F. Class Write Up: This is teacher led and can be done on your white board or on chart paper. I pretty much sequence our steps in order using First, Next, Last. For example: “First, we counted out 5 cubes because Jack had 5 balloons. Then, we took 2 away because have gave them to his friend. Last, we counted how many cubes we had left.” We know that Jack has 3 balloons left so we wrote the number sentence 5-2=3. Then after we come up those steps, we all read it together, and that’s problem-solving! This process should take about 30-40 minutes, but don’t be surprised if it takes you up to 45 minutes to even an hour the first few times!

I was actually filmed teaching these problem-solving steps as a model for the district! Kindergarten problem solving takes a lot of practice, but once you and your class get the steps down, it’s like clockwork, and it’s really beneficial!



5. Assess and reassess:

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Last but not least, I make sure I am on top of my students and what they know or do not know. This way I can move them around in their math groups if needed. As we know, some start slow, but really pick up the pace once they are in school and fully submerged in our classroom content. I usually assess them every 2 weeks. Assessing also helps me direct instruction on what I need to teach. If 90% of the class has mastered a skill, then I feel it’s ok to move on, and I will attend to that 10% who still do not have it. I love to use my common core math assessments as well. They are not just geared towards number sense, they assess every common core standard in a very organized manner. If you are interested in my assessments, they are available for purchase here in my store!

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Comments

  1. Brooke Stuart says

    Hi Sarah! I’m a kindergarten teacher from Kentucky. My students are really struggling this year with number sense. I came across your blog and love the ten minute math review. The math program my district uses has a daily review but it focuses on the lesson and I would really like to just do a quick number sense review at the start of each math lesson! I was wondering if you had it available to purchase? Thanks!

    • sarahcasady says

      Hi Brooke! I am so glad you came across this post! I currently do not have the math review for sale, however, I am thinking this may be my next project! The examples I have posted are samples from a math review that we created with our kindergarten team. I appreciate the feedback, and the minute I create a math review for purchase, I will let you know 🙂

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