The math program we use, Singapore Math, teaches the concept of number BONDS from the very earliest books. This is similar, yet different in a subtle yet distinct way, from teaching number FAMILIES, as other math programs do.
A number bond is a mental picture of the relationship between a number and the parts that combine to make it. The concept of number bonds is very basic, an important foundation for understanding how numbers work. A whole thing is made up of parts. If you know the parts, you can put them together (add) to find the whole. If you know the whole and one of the parts, you take away the part you know (subtract) to find the other part.
Number bonds let children see the inverse relationship between addition and subtraction. Subtraction is not a totally different thing from addition; they are mirror images. To subtract means to figure out how much more you would have to add to get the whole thing. When we play Salute! in class, children are getting practice in seeing this relationship.
In my math group, we are continuing to work on number sense, place value, and quick ways to add and subtract. Quick ways to make 10 are extremely helpful to know automatically, and I soon found out that many of the children were adept at this. I figured it was time to challenge them with a higher level concept.
Recently, I passed out slips of paper with numbers written on them. Groups of children worked to see how quickly they could find pairs that added up to 100.
We talked about strategies - If you have a slip of paper with 47 on it, what ones place will you be looking for? If you find two number cards with a 3 in the ones place, would you choose 63 or 53. Why?
Here are some activities you can play at home to practice the concept of number bonds:
Throw two dice and tell how many more you would need to make 10.
(On the rare throws of 11 or 12, the answer is a negative number.)
Throw 3 dice and tell how many more it takes to make 20.
One player names any number 0-100, and the other tells how many more it takes to make 100.
You could also play the last game with math cards [take out the jokers and face cards, leaving just ace (1) through 9], turning up one for the tens place and one for the ones, to make a two digit number.
10′s Concentration — Turn all the math cards face down on the table. On her turn, each player turns up two cards. If they add up to 10, she gets to keep them and try again. If one of the cards is a 10, she gets to keep it and turn up another card. Whoever takes the most cards, wins.
These ideas were taken from Let's Play Math.