   SEARCH HOME Math Central Quandaries & Queries  Question from Camasha, a parent: I am trying to help my daughter with fact families. I understand the premise from your previous explanation on the site . Generally when applying addition and subtraction their are two add and two subtraction utilizing all three numbers. However what do you do when you have a series like like 9, 9, 18 Hi Camasha,

The first fact family your daughter saw was probably made up of something like 2, 3 and 5, that is two positive numbers and their sum. There are then four members in the family.

1. The sum of the two smaller numbers to give the larger number
2 + 3 = 5.

2. The sum of the two smaller numbers in the reverse order give the larger number
3 + 2 = 5.

3. The largest number minus one of the smaller numbers
5 - 2 = 3.

4. The largest number minus the second smaller number

5 - 3 = 2.

If you apply the same rules to 9, 9 and 18 you get

1. The sum of the two smaller numbers to give the larger number
9 + 9 = 18.

2. The sum of the two smaller numbers in the reverse order
9 + 9 = 18.

3. The largest number minus one of the smaller numbers.
18 - 9 = 9.

4. The largest number minus the second smaller number.

18 - 9 = 9.

Facts 2 and 4 are redundant so the fact family only has two members

1. 9 + 9 = 18

2. 18 - 9 = 9

This shouldn't be surprising. There are many kinds of families, average families (a man a woman and two and a half children), extended families, single parent families, blended families, ...

Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.