Addition and       Subtraction Facts       to 20   Introducing the Concept   Developing the Concept

## Addition and Subtraction Facts to 20

The basic addition and subtraction facts are all the combinations of numbers (2 + 2, 6 + 9, 8 + 4, and so on) from 0 to 10 and the corresponding subtraction exercises (4 – 2, 15 – 6, 12 – 8, and so on). (See the fact chart at the end of this section.) To you, these are probably automatic. You don't need to think about them because you've memorized the answers. That immediate command is what you're striving to teach your students.

There are a variety of strategies that can be used to figure out or remember the basic facts.

Zero and Commutative Properties of Addition: The Property of Zero states that if zero is added to any number, the sum equals that number. The Commutative Property (Order Property) states that the order of addends does not change the sum: 3 + 4 = 7 and 4 + 3 = 7.

Subtracting With Zero: There are two rules for using zero in subtraction. Zero subtracted from any number is the original number. (This is the counterpart of the Zero Property of Addition.) Secondly, any number subtracted from itself equals zero.

Counting On and Counting Back: When adding 1, 2, or 3 to a number, for example, 9 + 1 or 7 + 2, you can add by counting on from the greater number. Similarly, for facts such as 6 – 1, you can subtract by counting back.

Doubles and Doubles Plus One: Doubles facts such as 4 + 4, 5 + 5, and 6 + 6 are easier to recall than other facts. Once children readily recall the sums for doubles facts, they can be used to help with facts that have an addend with one more. Since 8 + 8 = 16, the sum for 8 + 9 will be one more than 16, or 17. Children learn to apply their knowledge of doubles to subtraction. For example, children can use 9 + 9 = 18 to solve 18 – 9 = 9.

Add With Ten: The place-value system makes adding 10 to a one-digit number easy—just replace the zero in 10 with the digit being added. For example, 10 + 5 = 15. You can also add a number to 10 by counting on from 10 to find the sum.

Make a Ten to Add: When one addend is 7, 8, or 9, it might help children to break apart the other addend to make a ten, then add. For example, to add 8 and 5, first think how many more you need to add to 8 to make 10 (2). Then subtract 2 from the 5 (3). Add the 3 to the 10. (8 + 5 = 10 + 3, or 13.)

Use Addition to Subtract: A related addition fact can be used to help solve a subtraction fact. To solve 11 – 7, it can be helpful to think 7 +&nsbp;? = 11. Since 7 + 4 = 11, then 11 – 7 = 4.

Fact Families: A fact family is a group of related facts using the same numbers, such as 4 + 3 = 7, 3 + 4 = 7, 7 – 3 = 4, and 7 – 4 = 3. Fact families are a very powerful tool for mastering facts: Once you know one fact in a family, you can work out the other facts in the same family. Fact families are also useful for solving problems with missing addends, such as 4 + __ = 7. The fact table below shows the strategies that can be used with addition facts.