## An Introduction

Have you heard of a number bond? My first exposure to it was through the Singapore Math curriculum. I used this curriculum in a US school, however, as the name implies, it was developed from the curriculum used by the country who scores high in math. When I became more familiar with the common core math standards, I began to see the correlation between Singapore math and these new standards.

## A Number Bond

Whether or not you have heard the term, the concept of a number bond should be very familiar to you. I like the illustration of the banana above. You can still see the whole banana, but you can also see parts. A number bond is also made of parts and a whole. A basic number bond consists of three connected circles.

In the above example, the top circles are the “parts.” The bottom circle is the “whole.” A number bond could also be turned upside down or on it’s side. No matter the direction, the two parts will always join with the whole. Any numbers can be used in these circles, as long as the whole equals the total of the two parts combined. Here is an example:

You can see that together, 5 and 3 make 8. The two parts equal the total. This could easily be written as 5 + 3 = 8. You might be asking yourself, why do we need to use such an abstract picture to show an addition problem? Here is the beauty of a number bond. It makes addition and subtraction interconnected, as you already know they are, however to a young student, they can see the connection right from the start. From this one picture they can also determine that 3 + 5 = 8, 8 – 3 = 5 and 8 – 5 = 3. To make it even easier for a younger student, you can use objects. Place 5 blocks and 3 blocks into the parts. Have them move those parts to the total to see that it makes 8. Reversely, start with 8 blocks and have them see what happens when you take some of them away (to put in a part). This is a very simple example. Let’s take a look at a little more complex number bond.

Now you can see that we have some larger numbers in our number bond. For older students, they may be able to quickly solve the 5 and 3 number bond, but this one might take some additional work. If the whole was missing, they might need to write out an addition problem to find the total. Even better, try covering one of the parts and see how they can solve through subtraction.

## Number Bonds and Place Value

I love to use number bonds when talking about place value. It is a great way to show tens and ones (or even hundreds and thousands) in a new way.

You might think that a child has a good grasp on place value when they are using a traditional place value chart and base 10 blocks. By mixing it up with a number bond, you can see who really understands the concept. Here is a way to separate 57 into tens and ones. It also helps to integrate addition into the conversation on place value. Want to stretch your child even further? Try this out. Separate the tens even further. Here is another way to show 57:

Now we have taken our tens of 50 and broken into 30 and 20. We combined our 30 with the ones of 7 to make 37, then left 20 in the second part. See how many ways your student can make a number by splitting apart the tens.

## Place Value in the Hundreds or Thousands

The great thing about number bonds is that they can change and morph into whatever you need. If you are working on larger numbers, try a number bond with more than two parts. A number bond can have as many parts as you need, as long as they still add up to the whole.

In this case we have taken a three digit number and created a part for each place value. Imagine how you could use this with even larger numbers, or to challenge a child who understands traditional place value.

## Different Forms of Number Bonds

Be on the lookout for this concept of number bonds as you are working with your child. You may have already worked with the number bond concept without even realizing it. They do not have to look like the three circle examples you have seen above. Number bonds can be in the form of circles, squares, dominoes, fingers, pictures, or anything else that might have parts and a whole.

These are all ways to show the number bond of 4 and 6 make 10. Look familiar?

### Common Core Math Standards

Kindergarten: CCSS.MATH.CONTENT.K.OA.A.2

Solve addition and subtraction word problems, and add and subtract within 10, e.g., by using objects or drawings to represent the problem.

1st Grade: CCSS.MATH.CONTENT.1.OA.D.8

Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. *For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = _ – 3, 6 + 6 = _*.