It is a fact!
When children understand essential patterns, they can progress to gain a deeper understanding of numbers. Teaching children facts and fact families can make mathematical calculations a lot easier to master.
When teaching, don’t teach just facts, teach them as families. For example,
1 x 7 = 7
10 x 7 = 70
100 x 7 = 700
When you teach 1 x7 = 7, then explain that since 10 is ten times larger than one, then the answer to 10 x 7, will be ten times larger. This is the same sort of explanation for 100 x 7. Using fact families helps pupils learn to work out what they don’t know by thinking about what they already know.
Another example is, if pupils know that 5 x 3 = 15, then they can work out that 6 x 3 = 18 (by adding another group of 3 to the previous answer) and 4 x 3 = 12 (by subtracting a group of 3 from the previous answer. Introduce this to the pupils and get them to investigate facts from a given family.
Using inverse is a powerful way to get children to reason about fact families. For example: what fact families can you derive from 7 x 4 = 28? If you know this, then you can do
28 ÷ 4 = 7
28 ÷ 7 = 4
When I have tried this in class, the children say things like, “oh you are just swapping the numbers around!” Then I extend their understanding by asking, “Why am I swapping the numbers around? Prove to me that the number sentence is right. Why is it right?”
Here are some other examples,
13 + 4 = 17
This means that
17 – 4 = 13
17 – 13 = 4
Once they have a hang of this, give children an investigative activity; write up the numbers 12, 7, 5. Ask the children to write up a fact family for these numbers.
Another favourite activity of mine is deriving fractions of numbers using fact families. For example,
4 x 6 = 24
5 x 6 = 30
So what is 5 ½ x 6?
This is where the issue of using the correct language comes in. Explain that, four *groups of six* is twenty-four and five *groups of six* is thirty, this means that *five and a half groups of six* is 33. This is because *half a group* of six is three. Add thirty to three to get thirty-three.
To use fact families properly, you have got to use the right language of maths, use the correct vocabulary and do not be afraid that the children may not be able to handle the correct terminology. If, it is within the programme of study for their year group, please use it. I will discuss mathematical vocabulary next. But before we do that, here are some questions for you. *Only use fact families to work these out.* No cheating!
1. How many sevens are in 35?
2. How many sevens are in 350?
3. If 4 x 7 = 28, what is 4 ½ x 7?
4. What families could you use to work out 128 x 7?