I am in love with number bonds. Last year when I piloted the Singapore Math in Focus curriculum, I was mildly irritated with number bonds. They seemed to be just another version of the fact family.
Last week I was lucky enough to attend the SDE Singapore Math Conference in Las Vegas last week. And now the scales have fallen from my eyes! I know the power of number bonds!
Yes, number bonds are similar to fact families, but they’re a model that sets students up for understanding fact families, addition, subtraction, combinations of a whole, expanded notation, place value and so much more!
If you’re unfamiliar with what a number bond is (like I was a year ago) check this out:
A number bond includes a whole and two or more parts. This is why I confused it with a fact family at first. At the most basic level the main circle holds the sum of the parts and the two smaller circles hold two parts that combine to make the whole.
When we introduce number bonds to little guys in Kindergarten or first grade we start with using objects like popsicle sticks, beans, or some other counter. Each student is given a number bond with “5” written in the larger circle that shows the “whole” and five beans. We count the beans together – yep, there are five! Then we show them how putting the beans in two groups doesn’t change that there are still five beans. Now they get to show a way to make two groups with their beans. We count them up and sure enough they still equal five.
Next they take their two parts and put them inside the two small circles in the number bond. Now we count them again and point out to the five (in the “whole” circle) to show that the sum of their two groups is five. At this point they want to change their groups and see what other ways they can make five. This is where I record each of their discoveries on the board using vocabulary like: and, plus, together, make, equal, and are the same as.
In the first and second grade they write numbers inside the circles to show the parts and whole. A great use of the number bond is to show combinations to make ten. Understanding how to make ten is foundational for understanding place value and developing mental math strategies.
In my morning Calendar routine I have the students write the number of the day in standard form and expanded notation. The number bond lends itself beautifully to breaking a number up into tens and ones to write expanded notation. Just turn it on its side like this. Between the parts write a plus sign.
In the second and third grade the number bond will travel with the students into problem solving and measurement. Number bonds can be used to add measurements of length, weight, and time.
In the video below I show a basic measurement addition problem: 6 inches + 8 inches. It’s not complicated, but converting the answer from inches into a mix of feet and inches can be. But watch what happens when we use the number bond model to help us solve.
Now many people naturally think this way even without having been taught how to use number bonds, but there are many students and adults who don’t. I did pretty well in Math as a student, but I’ve always struggled with mental math and quick problem solving. That’s why I’m in LOVE with the number bond model!
How about you? Did you learn to use the number bond model? Can you think of other uses for number bonds?