## Addition Facts Through 20

**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