Differentiation in Math

Number Bonds: How to Teach Number Sense the Right Way

Image of a task card, number bonds worksheet and manipulatives to show concrete, representational and abstract demonstration of number sense.

“Number bonds?!  I don’t get it.  I mean, I have seen them before, but is it necessary to teach them to the kids?”

This was my thinking about number bonds as I stepped into the world of teaching primary math.  I am no math whiz, but math was not a challenge for me. Well, not until algebra, but …. you know.

When I was a student manipulatives in math were not a thing. Very few people thought that there was more to teaching math than rote memorization and number sentences.  

Even now when I explain to people that the numbers are just an abstract representation of concrete items, their eyes just kind of glaze over in confusion.  

“Say, what?”

Now more than ever I believe our students need to be grounded in a concrete understanding of what a written number represents.  And number bonds are an essential part of the.

Even this morning my husband asked me what he should use as his “hook” for teaching financial literacy to high school students.  

My immediate response was that he needed to make sure that they realized that money  was not as simple as tapping a plastic card on a machine.  

What is the concrete connection between credit cards and money?

I am such a primary teacher.  🥴

Image of a large potted fern with a puff at the bottom and text overlay that reads, "Number bonds: how to teach number sense the right way."
Number bonds are a wonderful strategy that support mathematical. Find games and activities using number bonds in my store.

Number bonds definition

A number bond is the bond between two numbers and the sum of the two numbers. They are useful in many more ways than I considered as a primary teacher.

As I dug deeper, I began to grasp an understanding of when we teach our students the true number bonds meaning we have provided a tool that is useful for all of the students in the class. 

I learned  that they can be used to:

  • Explore higher level operations
  • Problem solve and use critical thinking
  • Understand geometric shapes and fractions
  • Break down larger numbers into component parts to add or subtract

All of these relationships are part-part-whole relationships.  And number bonds are all about the connections between the parts and the whole.

Teaching number bonds does not start with teaching the 3 circles we see on number bonds worksheets and number bonds pictures.  and how they are connected. 

However, those number bonds images  are a very powerful visual tool to demonstrate the relationship between the parts and the whole.

But only once we are ready for them.

image of an icon for a resource for teaching make ten with a number bond worksheet included inside. the caption reads, " Number Bonds Knowing where to begin. it may not be where you think.
Prior to learning about number bonds students need a solid grounding in counting and adding numbers first. Find games and activities using number bonds in my store.

A number bonds example

When we teach our students all the ways to make 5, (or 10, or 1,996, or any number for that matter), we are teaching them how those two numbers partner together to make a bigger number.  

We need to teach them that the number bonds part part whole relationship is what makes math work.

Number besties … that is what number bonds are. 🙂

Imagine you are at the orchard (I live close to one so indulge me) buying caramel apples, and you need 5 altogether.  You have 4 in your cart.  There is only one “bestie” for you to get to that magical number 5.  

Amazingly 😉, those are not the only besties for 5!  These numbers are besties too:

  • 2 + 3
  • 0 + 5 

Of course, as students start to understand number bonds they will add a couple more to the list:

  • 3 + 2 
  • 5 + 0
  • 1 + 4

And they aren’t wrong, but that is a different math lesson. 

How important are number bonds in math?

Number bonds in math lay the groundwork for understanding more advanced mathematical concepts.

Learning that there are specific numbers that work together to form another whole number is an essential building block for math.

And I do mean essential.

I know a beautiful little girl.  She is quite clever.  She can skip count to 100, and she is even beginning to multiply without really understanding that she is doing it. 

However, she does not truly, deeply understand that there are ten ones in that ten rod.  It’s true.  I gave her a little informal assessment.

Now, when she reads a word problem she may be able to do the word problem because 

she has been taught how to decipher one in class.

But will she know what to do when she is standing in front of caramel apples at the orchard?

She is clever, so for this little girl the lights will go on, and she will figure number bonds in math out on her own.

But this is not the case for all of our students.  We need to teach them all about number bonds in math and help them to make the connection.

Number bonds: how to teach them

Before starting with written number bonds, your students need to be comfortable with basic counting and addition.

I am certain you have resources for teaching math, but, again, it is best to make sure everyone understands each other.

Using counting collections for basic counting.

A beloved activity in my class for counting was “counting collections”.

When I first heard the term “counting collections” I was intrigued.  

Once again this was something that I had not experienced in my education, but I was certain that this very respected math professor knew what she was talking about.

I have shared about my journey with counting collections on an earlier blog post . And I have also elaborated upon how to get them started in a subsequent blog.  

Counting collections are quite wondrous actually. 😍 They are literally what the name indicates.  

Simply put, they are little collections of things, quite literally anything.  Pencils, chopsticks, hot wheels, math counters all work.  

You provide a structure and expectation, and they count.  As they count you visit the students and notice their strategies for arriving at various numbers.  

The larger the collection the more elaborate the strategies. Speaking to that, counting collections are not just for primary. They are good right through upper elementary, and further if you want to go there.

Image of a counting collection with the caption that reads, "Counting collections are uite wondrous. They are little collections of things; quite literally anything."
Counting collections do not have to be expensive or elaborate. Use paper from recycling for mats, and have students count the crayons in the class. Find games and activities using number bonds in my store.

Prioritizing basic addition first

Maybe you are, and maybe you are not aware, but basic addition does not mean number sentences.

As I have mentioned, I did not start from a place of knowing these things, and so I want to make sure everyone understands before going forward.

Basic addition means using small collections, and having students learn how to combine two parts of that collection to make one larger collection.

This may sound like counting collections again, and it certainly can be. 

However, depending upon the student you may be starting with collections as small as 5, or even 2.  

Although I have never worked with a student who needed to start at 2 except in a Special Education pull out situation.

For example have your students find all the different ways they can reach 5 with multicoloured  plastic teddy bears.  

Then they find out how many red teddy bears they need if they already  have 2 yellow teddy bears. 

Etc.

And you continue working with collections of 5 until they understand, before moving on to collections of 7 or even ten.

This is basic addition.

Counting and addition are the sidekicks that show our students who the number besties are that make the number bonds. 

This is kind of like having all of the ingredients (the parts) before making a recipe (the whole).  

You can’t have one without the other. 🎶

Teaching number bonds addition and subtraction

Of course, counting collections are not the only way to teach number bonds in math. There are oh, so many ways to provide number bonds practice.

Use ten frames for number bond practice. If you use two different colours (as in the example with teddy bears above) you have a very effective tool for reaching your visual, tactile, and possibly auditory students.

For ten frames you can use the more expensive kind from the store, or just cut off two of the cups on an egg carton. Just be careful to wash, or somehow disinfect,  the carton to avoid making the children sick.

Cuisennaire rods provide a different angle on number bonds, and the colours and differing sizes can be powerful for both visual and kinesthetic learners.

My students had their own little rekenrek on a painting stick. There were two pipe cleaners attached to the paint stick, and each pipe cleaner had 10 beads, 5 red and 5 white on each pipe cleaner. 

An abacus works well too!  But I think you get the idea.  Anything hands on is effective. 

And, of course, once the students finish adding the pieces they are counting together, then it is very easy to show them how to subtract.

Touching on subtraction with number bonds is so important.  Many students get confused when subtracting larger numbers.

Giving them a rock solid grasp of how number bonds in math work together is powerful.

image of a blank number bond worksheet that reads, "Number bonds: so much more than worksheets."
In and of themselves, worksheets are not enough to differentiate. However, some types of worksheets can be a part of a well differentiated math station. Find games and activities using number bonds in my store.

Number bonds activities for the win!

Imagine having a versatile worksheet for learning number bonds that cater to every learning style.

Except it does not work.  At least not at the beginning. 

The number bonds activities and number bonds centers I have discussed in this post are better than those number bonds sheets for establishing your students’ basic understanding of numbers bonds.

However, there comes a time when students need to transfer this understanding onto paper, so that they can communicate their knowledge of numbers with the world.

If you are looking for more information on the impact of teaching number bonds using worksheets, then read my next post. 

I will be doing a short series on number bonds, because there is more to share. 

There is a reason I include a number bonds worksheet in almost all of my Write the Room activities in my TPT store. 😊

Share a question you have about number bonds, or an activity that you find successful.  We are better together!

Related blog posts:

What is classroom management? Why is it Important? Exploring why differentiation is a key to classroom management.

Tales of : Why is Differentiation in the Classroom Important?

How to Unlock the Mystery of Differentiation in Math

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