A certain amount of memorization is required for youngsters to learn basic math facts. But it’s also important that children understand the rules, or properties, of addition and subtraction. This encourages them to think creatively about numbers and provides them with strategies that lead to increased facility when working math problems.

Teach the commutative property to your child. This property states that the order of the addends does not change the sum. Write two corollary addition problems, such as 2 + 8 and 8 + 2, on a piece of paper. Line up 10 small toys and have your child group them to represent the two problems. Point out that that the answer is the same no matter the order of the addends.

Teach the associative property, which states that changing the grouping of addends does not change the sum. For example, the problems 1 + 3 + 5, 3 + 1 + 5, and 5 + 3 + 1 all have the same answer. Place 10 pennies or other items on a table. Have your child practice placing the items in different groupings, then writing a math fact to demonstrate each grouping.

Explain the identity, or zero, property to your child. This property states that zero plus any other number is always equal to that number. For example, 2 + 0 = 2 and 0 + 9 = 9. Likewise, zero subtracted from any number is the original number, such as in the problem 10 - 0 = 10. Also, when any number is subtracted from itself, the answer is always zero, such as in the problem 8 - 8 = 0. Because the concept of zero can be difficult for a young child to grasp, you can help him understand by using real items such as raisins or apples to demonstrate. Show him that if he has five raisins and he gives them all to you, he'll have zero raisins left.

Explain to your child that subtraction is the opposite of addition. Have him group some small candy pieces to demonstrate an addition problem, such as 3 + 4 = 7. Then ask him to show you how the same items can be used to make the subtraction problems 7 - 3 = 4 and 7 - 4 = 3. Teach your child to always write a subtraction problem with the highest number on top.

Demonstrate to your child how he can use addition to check the answers to a subtraction problem. For example, if he worked the subtraction problem 10 - 3 = 7, show him that he can check his work by adding the answer, or sum, to the subtrahend -- in this case, 7 + 3. It’s a rule of addition that adding the sum to the subtrahend always equals the minuend.

#### Things You Will Need

- Small toys
- Pennies
- Raisins or other fruits
- Candy pieces

#### Tip

Discourage your child from counting on his fingers because that can inhibit math fact memorization and quick calculation. Instead, teach him to count forward when adding and count backward when subtracting.