Number Bonds/ Fact Families/ Complements of Numbers and Guided Math

Posted on August 30, 2010. Filed under: Graphic Organizers, Guided math, Math Centers | Tags: , , , , , , , , |

Number bonds, fact families and complements of numbers basically are names for the same concept. They describe the relationship between pairs that make up a number. So for instance, 1+4, 2+3, 0+5 are all number bonds of five. For children to develop automaticity with number facts they need to learn their number bonds up to 18. They should learn these first through 5, then through 10, then through 18  cut and paste this url to arrive at this page…

The key component to this is to build understanding at the three levels: concrete, pictorial and abstract. Too often math textbooks jump right to the abstract level, asking students to make connections that they don’t really understand. I have written a post on fact families and ten frames but I would like to discuss this idea further here (be sure to see those posts for further discussion).

Concrete: It is important to start with concrete materials.

1. Use a 5 frame and two sided markers. So students can see the relationships of building numbers that build five. They toss the markers and see the different ways to make five.

 2.  Use snap cubes.  For example, I would use 2 green snap cubes and 3 blue ones.  I would then lead the students through activities where they explore the relationships.

3. Explore other numbers up to ten.

4. Use a 10 frame and two sided markers.

5. This is an excellent site that shows how to build through the 3 levels:


Pictorial- The children follow the steps above but then color in their answers on the templates.

At the pictorial level have them make cards that illustrate the bonds:


Some printouts that are colorful and engaging.

Abstract – At this level, add the number sentences. You can also add the fact family triangle. Superfun Power Point Game:

Interactive Powerpoints:  (All these power points you have to cut and paste the url to see…they can all be found on this website


These you can link to instantly: (great visuals some at pictorial and some at abstract level)

Practice sheets: Great Booklet to Make:

(Again you have to cut and paste these urls into the browser to arrive at exact page)

Great Links  cut and paste (most of the links above come from this site –there are tons more here…I just organized them and highlighted the ones I like)

Other Links

Also in this blog search:

ten frames, ten frame, fact families

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3 Responses to “Number Bonds/ Fact Families/ Complements of Numbers and Guided Math”

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Greetings –
The most common concern from Grade 1-5 is the lack of automaticity of math facts. I can’t imagine a teacher not wanting to engage students in an otherwise boring task with these activities and the rationale you provided is clear and easy to explain to teachers. One of the 2nd grade teachers labored over fact families last year and really didn’t achieve the learning outcome she expected. I know these suggestions will be well-received. I really don’t use the term number bonds, but I will now. Thanks

Hi Lisa,
Here in the U.S. we don’t use the term so much but in other countries, i.e. Britain, they do. I think you bring up an important issue about automaticity. I am going to write a post about the difference between automaticity and fluency. We have to work on both.

[…] *Be sure to see the other post about Number Bonds! […]

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