# The Property of Zero for Addition (for every number a, a + 0 = a and 0 + a = a) This property can be used to easily find the answer to any fact with a 0. These facts are shown in the 0 row and 0 column of the addition table.

Counting on by 1, 2, or 3 Children use this strategy, and the Commutative Property (for all numbers a and b, a + b = b + a) to find the answer to any fact with a 1, 2, or 3 by counting on by 1, 2, or 3. These facts are shown in the 1, 2, and 3 rows and 1, 2, and 3 columns of the addition table.

 + 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 4 5 6 7 8 9 10 11 3 3 4 5 6 7 8 9 10 11 12 4 4 5 6 7 8 9 10 11 12 13 5 5 6 7 8 9 10 11 12 13 14 6 6 7 8 9 10 11 12 13 14 15 7 7 8 9 10 11 12 13 14 15 16 8 8 9 10 11 12 13 14 15 16 17 9 9 10 11 12 13 14 15 16 17 18

Doubles The doubles are 1 + 1, 2+ 2, 3 + 3, 4 + 4, 5 + 5, 6 + 6, 7 + 7, 8 + 8, and 9 + 9. These are easily learned by counting 2s: 2, 4, 6, 8, 10, 12, 14, 16, 18. These facts are on the left to right downward diagonal in the chart.

Doubles plus one An example of a doubles-plus-one fact is 8 + 9. The sum for this can be easily found by thinking of the fact as a double plus one: 8 + 8 + 1 = 17.

Combinations to 10 Recognize numbers with sums of 10: 6 + 4, 4 + 6, 5 + 5, 3 + 7, 7 + 3, 8 + 2, 2 + 8, 9 + 1, and 1 + 9.

Adding with 9 Thinking of 9 + 8 as 9 + 1 + 7 = 10 + 7 can make finding the answer to any fact with 9 easy. In general, 9 + a, where 0 ≤ a ≤ 9, 9 + a = 10 + (a − 1).

Using these strategies leaves the following facts to be learned by drawing pictures, using a number line, or using counters: 4 + 7, 7 + 4, 4 + 8, 8 + 4, 5 + 7, 7 + 5, 5 + 8, 8 + 5, 8 + 6 and 6 + 8.

Teaching Model 19.3: Make a Ten to Add