# Abacus or Number Bonds?

Quite a few parents have come to me with the question of whether they should send their children for abacus classes.  From my discussion with them, I gathered that on one hand, many are impressed with the apparent effect abacus classes have on the speed of doing mental sum; on the other hand, they have also heard stories of how children get confused as abacus method is vastly different from number bonds, which seems to be the method of choice being taught at primary level.

I thought I would take the opportunity to clarify on this and hopefully to reach out to as many parents as possible with regards to this confusion.

What is Number Bond?

Firstly, number bond is an extremely important foundational mathematical concept.  Number bond is about number composition.  It explains how numbers work and the relationships between numbers.  It provides a mental picture to help children understand that every number can be broken into smaller parts, and when these parts are combined, they make the whole (a bigger number).  So number bonds let children touch the abstract, inverse relationship between addition and subtraction.

Consider the following four-fact family :

4+2=6

2+4=6

6-2=4

6-4=2

The idea of a four-fact family is to help students understand that once they know one of the facts in the family, they know all of them.  However, many students never see the connection and tend to think of these equations as separate bits of abstract information, all of which have to be memorized.  This can overload their minds and many along the way, lose interest in maths as a result.

Number bonds help students to make that connection and facilitate their understanding as it shows students a single mental picture that depicts all four of the fact family relationships.

Therefore, for those parents who are thinking of sending their children for abacus classes, by all means, do so.  However, it is important that your child already has a strong grasp of the foundational concept of number bond before they start abacus class.  There should not be any confusion if the child understands the concept behind number bond.  There will only be confusion if number bond is taught mechanically as a method of doing arithmetic.

For parents who want to know how they can teach the concept of number bonds to their children, I strongly suggest that you start with physical items that could physically be put together and taken apart.  For example, there is a lovely story about the number of bananas a monkey likes to have.  I would place 7 bananas in front of a toy monkey and said that I suggested to the monkey that he should have 3 bananas in the morning and 4 bananas in the evening.  As I tell the story, I would separate the bananas into two piles, one of 3 bananas and another of 4 bananas.  But monkey did not agree and wanted 5 bananas in the morning.  I then pulled apart the two piles and made a new pile of 7 bananas.  I then ask the child to tell me how many bananas monkey could have in the evening?  As the negotiation between the story teller and the monkey goes on, the child gets practice in terms of pulling a number apart (separating the 7 bananas into 2 piles) and how different combination of smaller numbers give 7.

After one to two physical demonstrations, children should be ready to move to number bond pictures and games.  I have written about number bond games using fingers in a previous article, but there are many ways in which one could invent number bond games.  For parents, my advice is that instead of drilling your child with number bond worksheets, it is much better to play games with your child as they will enjoy it more as they gain confidence in manipulating number bonds.

Here are some examples of games I play with my daughter and my students :

Dicey Game

Put a card with a number between 6 and 10 between your child and you.  Let your child roll the dice.  When it stops, the child must say the number which when combined with the number on the dice will make the number on the card.  For example, if the number on the card is 8 and your child rolled the number 5 on the dice, then your child should say 3.  The trick is to get your child to answer as quickly as s/he can so sometimes, it is helpful if this is made into a little competition.

Card Game

Retain only the number cards from a pack of cards and remove the rest.  Deal 2 cards to each player (you and your child).  Then in the middle, start flipping over cards, one at a time.  The minute someone sees a card s/he can use to combine with the two cards in his/her hand to make a number bond, s/he shouts “snap”. If s/he says the correct number bond, s/he wins the entire pile of cards.  For example, if your child holds 9 and 3, then, s/he should be looking out for 6.  But if your child holds 4 and 2, s/he could be looking out for 6 or 2.  6 as 4 and 2 makes 6; 2 as 2 and 2 make 4.