One array can tell four stories. You have seen turn-around facts and division as a missing factor. Put them together and three numbers give you four facts.
Why it works
The array has 21 dots, 3 rows and 7 columns. Read it as rows or as columns and you get the two multiplications. Ask "21 in 3 rows: how many in each?" and "21 in rows of 7: how many rows?" and you get the two divisions. All four describe the same dots.
Key idea
A fact family is the four facts made from one array: for 3, 7 and 21 they are $3 \times 7 = 21$, $7 \times 3 = 21$, $21 \div 3 = 7$ and $21 \div 7 = 3$.
Worked example: Write the family
Write the fact family for 6, 7 and 42.
- Multiplications: $6 \times 7 = 42$ and $7 \times 6 = 42$.
- Divisions start with the biggest number: $42 \div 6 = 7$ and $42 \div 7 = 6$.
Answer: four facts
Worked example: Find the missing number
A fact family uses 8, $\square$ and 72.
- 72 is the product of the other two: $8 \times \square = 72$.
- $8 \times 9 = 72$.
Answer: $9$
Common mistake
Dividing the small number by the big one. $7 \div 42 = 6$ is not in the family. In every division of the family, the biggest number (the product) is the one being divided.