Boost Math Confidence with Number Sense Routines

Help More Homeschool Mamas Discover This!

Learn what number sense routines are, why they are essential, and how to implement them in your home and classroom! 

Number sense routines are one of the best ways to level up your child’s math abilities long-term! In this article, I’ll show you number sense routine examples that are fun and effective. Learn the importance of building number sense and understanding of mathematical relationships!

Number Sense 101

Number Sense is a broad term which refers to a child’s understanding of the relationship between numbers and math concepts, such as

• Counting
• Part-Part-Whole
• Proportional-Thinking
• And much more!

Number Sense Routines for Kindergarten, Preschool, and Struggling Students

Developing number sense in kindergarten is a good time to start but if your children show signs of being ready, you can also start teaching number recognition to preschoolers. 

Regardless of your child’s age, teaching number sense to struggling students or to students with poor number sense skills is always a good idea. Even if your child has strong number sense  skills, number sense activities should be a part of your child’s learning routine to keep progressing and their memory fresh.

What are Number Sense Routines?

Number sense routines are a series of daily activities and strategies designed to build a student’s understanding of numbers, operations and relationships between numbers. 

These routines help students develop their basic number sense and operations

skills, which are an essential prerequisite for all problem-solving and mathematical concepts. 

Benefits of Number Sense Routines

Learning The “Why” behind math

Teaching your kids number sense routines is so much more than just memorizing math facts! With number sense, your kids learn to not only “do” math, but to understand the “why” behind it. 

By visualizing numbers and their relationships before seeing them abstractly, students will use number sense to grasp the fundamental concepts behind what makes math processes and formulas work. With number sense, it’s not just memorizing the facts, it’s learning why the math problems work!

Prepare them for Other Math Concepts

Early number sense should be established before children move on to their main math curriculum or they will not be prepared to learn the material. 

By giving your students the time and space to practice foundational math skills like counting, comparing numbers, and recognizing patterns, they’ll be able to move on to higher-level concepts with ease. 

It may seem like a waste of time to slow down and go back to the basics when your plate is already so full but it is well worth your time.

Think of it as a race car driver slowing down around the corners to avoid spinning out then speeding up again for the straightaways. With number sense routines, you’ll be able to get your students to their math goals faster, and with more confidence!

Strategies for How To Teach Number Sense

Establish Routines

Number sense routines are meant to focus on learning the mathematical content, and minimize the distractions of explaining new games or processes. These routines are easy to keep fresh by adding variations to the numbers and ways to solve the math problems.

Choose activities that are easy for you to do regularly. It can be as easy as discussion, working with math manipulatives, or playing a quick game (activity ideas below!). It doesn’t matter the activity as long as you are working on the skills your child needs. 

Pair Visuals With Abstract Digits

Start developing number sense by giving your children the opportunity to visually explore numbers. Show them real objects to touch, move and compare so that they can start to make the connection between the physical number of objects and the abstract digit associated with that number. 

Below is the order of how your children should practice with numbers to establish real connections to the relationships behind numbers. 

Visually —> Visually + Abstract —> Abstract

When they start to make connections with the numbers visually, you’ll then add the abstract digits associated with those numbers to the visuals. 

Number Sense Examples

With practice associating the physical number with the digit, they’ll be able to understand the relationships between them. 

Use Math Number Sense Manipulatives

Manipulatives are one of the best ways to visually develop number sense! In reality, you can use just about anything as manipulatives from around your house or classroom.

We’ve started a list of the most popular manipulatives specifically for number sense routines.

Manipulatives

• Unifix Cubes
• Dice
• Double sided counters
• Number paths
• Counting bears
• Ten frames
• Rekenrek
• Math fingers

Ask Open-Ended Questions

Asking open-ended questions helps students find answers independently. This helps us, as teachers, to resist simply telling them the process or answer. You may be surprised with the processes they create and relationships they find!

Use Everyday Activities to Practice Math

Relating the day-to-day activities your children do to number sense is a great way to make learning natural and help them make real-world connections. 

For example, when you give your children a snack such as carrots, ask them questions like “How many carrots do you have?” then “If you ate one carrot, then how many will you have left?”. 

Help Your Kids See Number Relationships

Based on the book Teaching Student Centered Mathematics by John Van de Walle, making these four number relationships is essential to learning number sense. Here is an overview of this theory.

Spatial Relationships – Having a visual to go with a numeral and understand how they relate to each other.

Example: Using fingers to see that there are 2 fingers on one hand and 1 finger on the other and knowing it is 3 fingers without having to individually count all of the numbers.

One and two less and more – Instantly know the number that is one or two more and less when using visuals.

Example: Line items out and will kids understand how many are left. If you take away one or two and they have to go back and count them all they need more practice with this relationship.

Benchmarks of 5 and 10 – Knowing how a number relates to numbers 5 and 10. This is knowing the relationships of how numbers relate to a benchmark number. 

Example: Take a set of numbers and put it into a 10 frame, and see if they can see the relationship to ten. (9 is only one away from 10).

TIP: Start by solidifying relationships to the 5 benchmark before moving onto 10. If they are struggling to tell you the relationships between 10, they need more practice with 5. 

Part to part whole – Understanding how and where a whole can be broken into parts and the relationships of one number.

Example: 7 can be represented as 4 and 3 or 5 and a 2. Help your kids see that the parts can change but the amount stays the same. 

Assess Understanding and Address Learning Gaps

It’s a good idea to keep tabs on how your children are grasping number sense. One way to see how your child is understanding number sense is to give them simple number sense tests. 

Try this assessment by The Recovering Traditionalist to see what areas they need math interventions for number sense.

Once you know where your students are, you can then plan activities around improving number sense for the math concepts your child needs. 

Celebrate Math Achievements

Pay attention to the positives and successes of your children. Help them see their progress and puff up their math confidence by focusing on what they are doing right. Use this time to listen and guide your students rather than teach. You can always make improvements and build from there. 

Number Sense Routine Examples

Below are just a few examples of number sense in mathematics that you can incorporate into your routine. If you want more number sense and counting activity ideas, I’ve written a separate blog post with a ton of fun number sense games and activities inside! 

I Spy

How to Play:

One player picks an item then says “I spy with my little eye___”  then adds a clue such as  “3 things”.

Player two tries to guess the right group of items. 

This helps students practice grouping objects and finding numbers around them. 

Here is a video of how to play this game!

I wish I had

How to Play:

Player one says “I have ___ # of objects (candies, blocks, etc.), I wish I had __# of objects”. 

Player two then solves the problem by figuring out how many more or less objects they need to make the total. 

Ex: Player 1 – “I have 3 blocks, I wish I had 5 blocks. What do I need to do to have 5?”

Player 2 – “You need two more blocks to have 5 blocks!”

Show and Hide

Materials: Number cards, cup, small objects, die

How to Play:

Player one draws a card and puts that number of objects underneath a cup. Player one briefly shows the objects to player two then covers the objects with the cup and places the card next to the cup. 

Player two then tries to remember the number of objects under the cup. 

Variation to learn addition: Play the same as explained above, except after the cup is placed over the objects, have player two roll a die. Place that number of objects next to the cup.

Players work together to figure out how many objects are in total. (Some kids may have to lift the cup and count the object individually.  

Count and Clap

Materials: Action die and regular die

How to Play:

Prep the action die by writing actions that your child can do. We have a free printable action die here! Or you can use a white erase die.

Players roll both dice and follow the instructions. If the dice lands on “jump” and the number 4, the players will jump 4 times. Repeat as many times as you want. 

Use math story problems & Stories

Practicing math skills using word problems and situations using stories help make connections and inspire discussion. Number sense is about finding relationships and word problems/situations guide students to them.

The Bet Lines strategy is especially useful for helping students build numerical sense. For this strategy, you simply read the story problem like you would a story and ask follow up questions and make predictions after each line. Asking follow up questions line by line helps children focus on the meaning behind the story problem, not just “getting the answer”. 

3 PRO TIPs

TIP 1: Every child should be practicing number sense every day.

It doesn’t matter the age of your child, EVERY child should be practicing number sense daily. The only difference is the difficulty of the numbers you use. Teaching number sense to older students is still very important.

For developing early number concepts and number sense, start with numbers 1-5 or 1-10. Older children who have a solid understanding of the smaller numbers can practice with larger numbers. 

TIP 2: Consistent Routines

Your number sense routines should be consistent so children can focus on the math concepts. 

TIP 3: Vary How You Present the Material

Vary how you present the problems to your children. Vary the language you use for your questions, switch up the layouts or grouping of visual numbers, and present them with different types of visual representations of a number or problem.

For more great ideas on establishing and understanding number sense routines, check out the book Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3.

Final Thoughts

I hope you have found this blog post helpful in understanding the importance of number sense routines and incorporating them in your child’s learning. Number sense routines are an invaluable tool for helping children understand the world of mathematics, and with a bit of practice, you will be well on your way to developing number concepts confidently.

What’s Next?

Get your number sense routines going and grab your free Printable Number Sense Games!

These easy, 5-minute games are perfect for kindergarten math centers for number sense practice or simply to make a part of any child’s regular learning routine to help build number sense concepts and operations. They include number sense cards, matching games, Bingo, building number sense activities, number sense counting games, and more hands-on number sense activities!

Learn what number sense routines are, why they are essential, and how to implement them in your home and classroom! 

Help More Homeschool Mamas Discover This!