What are number bonds? Number bonds are just another way to visualize addition facts and are a huge component of Singapore math. What is Singapore math? It is a collection of computation strategies that arose out of Singapore, where students are supposedly ranked among the best in the world in math achievement. So are number bonds all they are cracked up to be? I think they might be! But I’ll let you decide. First, here is a video of Rory discovering number bonds for the first time so you’ll know what I’m talking about.

#### THE GOOD…

“Emphasizing number relationships is key to helping children fully develop number sense.” Van de Walle

And the most important relationship to develop? Part-part-whole. Number bonds are a great visual to see the part-part-whole relationship.  Focusing on a quantity in terms of its parts is a major milestone for young children and number bonds can help them get there. Just make sure you keep the big idea in mind by consistently using the “part-part-whole” terminology.

The building block of number sense is to think of numbers flexibly. Number bonds help develop number sense by showing different ways to decompose and recompose numbers. By showing different number bonds for one whole number, children see multiple ways of making (or unmaking!) a number. 5 can be made from 2 and 3, or by 4 and 1. Number bonds show this connection well.

However, what is my favourite attribute of number bonds? Number bonds are a great way to teach addition and subtraction at the same time. Rory and I continued our lesson with questions such as: “With 5 whole cars, if you had 4, how many did Philian get?” (one). Number bonds allow children to link the inverse operations easily so that they develop the two skills together. This creates fluency in both operations at the same time, and not a weakness in subtraction, which we often see when the two operations are taught separately.

“Primary teachers have the tendency to rely too heavily on textbooks, workbooks and photocopied support materials.” Charlesworth

Number bonds lend too easily to this. It is too easy to photocopy a bunch of circles and have the students fill it in with little attention to problem solving. As a result, students are not given the chance to discover the meaning of the relationships on their own. Instead, why not have the students choose their number and discover the number bonds that connect it? Or why not use number bonds as a method to record their work for a problem, but not as the problem itself?

Number bonds shouldn’t be presented independently; use manipulatives to make it real. Adding is putting together groups of objects to find out how many, and students need practice actually doing this with concrete objects. Notice with Rory, I don’t start with the number bond visual – I start with the concrete manipulative to mimic a real life situation. I use that to build the number bond and whenever Rory got stuck, where did he go? He referred back to his concrete manipulatives: the cars. Number bonds help you to see the two parts, but manipulatives make the two parts real.

“Research has demonstrated that when kindergarten and first-grade children are regularly asked to solve word problems, not only do they develop a collection of number relationships, but they also learn addition and subtraction facts based on these relationships.” Van de Walle

Number bonds should not be presented first and then problem-solving second. Instead, allow students to discover the facts for themselves and then use number bonds to make sense of their work. Rory was able to solve the problem for himself and will have a deeper understanding of ways to make 5. Using real problems makes the learning more engaging for the child, especially if the problem involves them. And as the research shows, it also helps them achieve mastery as well!

#### THE UGLY…

You might be tempted to use number bonds as flashcards for a drill or a timed test or prolonged practice. Number bonds used as drill creates anxiety and stress and doesn’t encourage an understanding of the part-part-whole relationship. Children should learn facts through discovering patterns and relationships. By focusing on families of facts and their relationships, in a problem-solving environment, you are encouraging mastery of facts through exposure. Rory quickly noticed the patterns that make 5 – as one part gets smaller, the other gets bigger. He giggled when he saw that 3+2 is the same as 2+3, but he was discovering these relationships under the guise of a real problem. There was no anxiety or pressure for him to memorize number bonds.

Some kids aren’t going to be ready for number bonds because they are too abstract. To aid with this, start with 5 or 10 frames and concrete manipulatives to help them see the facts more easily. Keep the manipulatives going and don’t switch to the abstract (pencil and paper) until much later. Allow the child to determine the pace of the learning….as long as you are providing opportunities for them to engage in problems that reinforce the facts, you’re good!, You will know mastery is achieved when they don’t have to count how many are in each group, they just know and this typically doesn’t happen until 3rd grade!

#### THE BOTTOM LINE…

So are number bonds good, bad or ugly? Well, you always need to keep in mind your big idea…you are trying to build number fluency which involves efficiency, accuracy and flexibility. Number bonds are another tool in your toolkit to help students visualize part-part-whole relationships. As long as you remember to focus on those relationships and surround the students learning in problem-solving and not drill, then number bonds are a great resource. Just beware of what could make them bad or ugly as well.

What does Rory think? He loved creating them so much, he carried on and made his own number bonds independently afterwards…some more abstract than others!

Have you had any experience with number bonds: good, bad or ugly?! I’d love to hear about it! Tell me in the comments section below!