## What is number bond?

## What is number bond?

Most textbooks define number bonds as the different pairs of numbers which make up the same number. For instance, the number bonds for 10 are 1+9, 2+8, 3+7, 4+6 and 5+5. Number bond is typically represented using a picture consisting of 3 circles connected by 2 lines. An example is given below and the picture is to be read as "7 and 3 make 10":

Number bond uses a part-whole-part concept to present the relation between the 3 numbers. In the above example, 10 is the "whole" and both 7 and 3 are the "parts".

## Is number bond important?

Here are the usefulness of number bonds:

### (1) Number bonds aim to ease your child's learning of more advanced addition.

For instance, to compute 8+7, the method is to add by forming a ten first. This requires your child to know "What plus 8 make 10?". After he derives 2 as the answer, he will need to breakdown 7 into 2 parts and this requires your child to know "What plus 2 makes 7?". The representation in number bond as shown below presents the idea clearer to a young child than you were to present it in the form of an equation: 8+7 = (8+2)+(7-2) = 10+5=15.

When he moves on to more advanced addition like 36+7, number bond still comes in handy in forming tens for the addition. For instance, your child will ask himself "What plus 6 makes 10?" and then "What plus 4 makes 7?" to do the addition.

If your child knows number bonds well, he can easily breakdown a number into the correct set of 2 parts for forming a ten.

### (2) Number bond makes it easy for your child to see the link between addition and subtraction.

For instance, the following number bond shows 3 equations 7+3=10, 10-7=3, 10-3=7. So, in effect, there is no need for your child to memorize any subtraction fact because he can always get the answer from the addition sentence. For instance, when your child needs to do 10-7, he no longer needs to do subtraction because he can use his knowledge of 3+7=10 to get the answer 3 for 10-7.

### (3) Number bond presents an elegant way to solve some complex problems.

For instance, solving a set of 2 equations like x+y=12 and x-y=4 as given in some Primary 1 Math test paper can be presented in a clear manner using number bonds that your child can understand. In the past, we are taught to eliminate one variable by adding up the 2 equations to solve for the value of x first and then substituting the value of x into one of the equations to get the value of y (known as Gaussian Elimination Method). Using number bonds, it is easy to illustrate to your child how to solve the equations using the following steps:

Step 1: Represent the equations x+y=12 and x-y=4 using number bonds.

Step 2: Substitute x in the first number bond with the two parts for x in the second number bond.

Step 3: Write down the number bond for 12, with 4 as one of the 2 parts.

Step 4: Compare the 2 number bonds in steps 2 and 3 and write down y+y=8.

Step 5: Derive that y=4 from y+y=8.

Step 6: Put the value of y back into the 1st number bond and derive x=8 using the number bond.

Date created: 8 May 2010