I've written before about why I believe number bonds are a far superior way to teach basic math facts, and I still stand by that claim. All my children have learned their math facts this way (through the Singapore math curriculum), and they still think of math operations in terms of number bonds, even in algebra.
What are Number Bonds?
Number bonds offer a concrete visual representation of the relationship between addition & subtraction or multiplication & division. Instead of thinking of each fact family as a list of four equations containing 12 numbers like this:
…the child pictures each fact family simply as a number bond of the three numbers like this:
No longer are there four different operations of addition, subtraction, multiplication, and division. With number bonds, the child sees that addition & subtraction or multiplication & division are simply two sides of the same coin.
I've created a teaching chart that helps explain the number bond concept, as well as a blank number bond worksheet that you can use with your child.
Download the number bond chart and worksheet here.
How to Use the Blank Number Bonds Worksheet
Here are a few suggestions for using the blank number bonds worksheet. Of course you're not limited to using just these suggestions.
What's Missing? Circle either addition/subtraction or multiplication/division at the top, and then fill in two circles in each number bond like in the example below. Your child will then need to fill in the missing circles.
The Same "Whole." Circle either addition/subtraction or multiplication/division at the top. Then fill in the top circle and one of the other circles in each bond, making sure the "whole" — the top circle — is the same each time.
Addends & Factors. Have your child fill in all the possible addends or factors (the "parts" for addition and multiplication) for a particular number. For example, you give the child the number 63 for multiplication, and he has to fill in all the possible factors — the "parts" — for 63. See the example below.
More Practice with Basic Math Facts
Once your child is comfortable with thinking of addition & subtraction or multiplication & division in terms of number bonds, you may want to move on to the more traditional missing number worksheets (such as 3 + ___ = 8 or ___ X 12 = 84). You can generate free missing number worksheets here.
When completing these missing number worksheets, encourage your child to continue to think of the problem in terms of the number bonds (specifically whole vs. parts) by looking at each problem and identifying which number is the "whole."
Number Bond Flashcards
We got rid of regular flashcards a long time ago. We now own only two sets of triangle (or three-corner) flashcards: one for addition/subtraction and one for multiplication/division. I just cover up one of the corners of the card, and my child has to figure out the answer by performing the correct operation. Triangle flashcards really help reinforce the number bond concept.
Do you use the number bond concept when teaching basic math facts? Or is this a totally new concept to you?
Thank You!
Ooh – genius! What a simple way to teach the facts. Thank you as always!
You never cease to surprise me! This is wonderful and just what we needed. Thank you so much for taking the time to not only come up with great lessons but to share them as well.
THANK YOU for this!
It was hard to find extra practice pages for this concept when we worked on it earlier this year. Thank you for making one!!
Number bonds are something I hadn't heard of prior to seeing them on your blog. But I believe this will help my visual learner A LOT! 🙂 Thanks so much for sharing these great printables…can't wait to use them!
Many blessings!
Thanks for this worksheet. We call them "Fact Families" at our house b/c these numbers stick together no matter what, just like families do. This worksheet will fit great with our math curriculum. Thanks so much!
My daughter was in public school for the past 3 semesters, and they made and used their own triangle flash cards in 3rd grade. Glad to find this number bond printable page. I will be drilling my now 4th grader on her multiplication/division facts regularly!
Just what I was looking for…simple, but cute. Thanks!
I couldn't understand the bonds @ first thanx a million u are a life savior.
Thank you for posting this!! My little artist may have better luck remembering this way.
This is my first exposure to these, and I'm thinking they might be good for my great-grandsons. But I'm curious to know why the bottom two circles are not joined? Is there some principle involved there?
@Lane Lester, The principle is that the bottom two are the parts that make the whole at the top. I suppose it would still be okay to join the bottom two, but I want to make it obvious WHICH is the whole and which are the parts.
Thank you for this! We use MEP math and I've been trying to teach my DD "Number Bonds" but I've not found the best way to explain them–until now! Thank you!
Thank you so very much!!!! <3
This is a nice a idea. I believe it is the easiest and fun way to teach part and whole relationship of numbers. It is also great to teach kids with basic maths principles.
I Have a question. Does the higher number always go on the top of the triangle, regardless of whether it is addition or subtraction?
I'm so sorry for taking so long to reply! The top number is the 'whole' number (the sum or the product). You would use the same triangle arrangment for 3 + 6 = 9 as you would for 9 – 3 = 6. 9 would be on the top and 3 and 6 would be on the bottom. It's the part + part + whole that the triangle structure demonstrates. Hope that makes sense!