# Multiplication and Division Fact Families

At the end of last term, the students in 4KM and 4KJ were learning about multiplication and practising their times tables.

We have started this term by exploring the relationship between multiplication and division. These are called inverse operations – that means they undo each other.

We have been making fact families with multiplication and division.

Click on the link below to watch this video to learn about fact families. Tip: right click and chose “open in new tab” so you can come back to the blog when you’ve finished watching.

Today all the students made a poster of a fact family to demonstrate their learning.

## 34 thoughts on “Multiplication and Division Fact Families”

1. Dear 4KM and 4KJ,

We think that the posters encourage numeracy skills and a very fun and organised way to show maths.
There’s an easy way to figure out what the answer is. e.g. The numbers are 8 and 6. The way that you can figure out the rest of the family is by simply multiplying both 8 and 6 together. 8 x 6 = 48. Then the answers would now be 8 6 48.
We’re going to make some fact families.
The numbers are 12 9 and 12 13.

From,
Some commenter’s,
Ethan & Brandon.

• Dear Brandon and Ethan,
Thank you commenting on the blog. I think that fact familys make things easier to work out divison. It is a good thing to learn. When I went to my cousins house last night she said that they said was called factors inseed of fact familys.

It was a lot of fun to make the posters yesterday.It is good have something new on our Numercy window. Fact familys do help you with your maths skills.I would love to learn more about fact familys.

That is a good way to learn fact familys as well. Here are some I made up
11,12,132
12,9,108.

Thank you for your reply. You can call fact families lots of different things like factors and I agree with you saying that making the families was very fun.
11 x 12 = 132
12 x 11 = 132
132 / 11 = 12
132 / 12 = 11

From Brandon.

• Dear Brandon,
Thank you for replying t my comment to you and Ethan. That is nice of you to put the answers to my sums.

2. Dear 4KM and 4KJ,

Hi guys,

I really like this post because I really like learning about fact families and this is my favourite maths subject even though I don’t know much about fact families.

from

shakira

• Dear Shakira,
Thank you for commenting on our class blog. The post is really well made and it must of taken a lot of time for Mrs Morris to edit it and put it on the blog

Fact Familys are fun to learn and it makes it easier for some people to learn their divison. It will take a while to learn fact familys. But so far were all doing pretty well.

3. Dear 4KM and 4KJ,

This looks like so much fun!
Really interesting topic.

Here is a Fact Family I thought of:
(because I like 6 times tables)
6 x 20 = 120
20 x 6 = 120
120 / 6 = 20
120 / 20 = 6

Have fun thinking of all the different Fact Families!

From Cassandra =) (Lilli’s Aunty)

• Dear Cassandra,
Thank you for commenting on the class blog. It has been so much fun.Doing the posters made it even better to learn. The posters was a fun activity.

They are really good fact familys that you have made are good fact familys I have made up last night.
11×12=132
12×11=132
132/12=11
132/11=12

12×9=108
9×12=108
108/12=9
108/9=12

Thank you for replying to my Aunty.

That is a great Fact Family you made up last night. 🙂
Here is one I thought of just then:
11 9 99
11 x 9 = 99
9 x 11=99
99 / 9 = 11
99 / 11 = 9
Now I’m going to make another one: =)
5 7 35
5 x 7= 35
7 x 5 = 35
35 / 7 = 5
35 / 5 = 7
And there you have it two “Fact Families.” 😆

From Lilli 🙂 : lol: =)

• Dear Lilli,
Thank you for replying to my commenting to your auntys comment. Those fact familys are great.

4. Dear 4KM and 4KJ,

Terrific post about fact families and inverse property! When I teach multiplication and division to my third graders, they are always relieved to learn that if you know your multiplication facts, then you automatically know your division facts. At first, they think it is another big set to learn and are thrilled when they understand the inverse. It is just like addition and subtraction are inverse!

My favorite fact families are the squares numbers because they are unusual.

Like 8. 8. 64

You only need to write two sentences:

8 x 8 = 64
64 ÷ 8 = 8

For anyone who is interested, I got the ÷ sign by pressing OPTION + backslash key.

Does anyone else like the square numbers?

Mrs. Y♥llis

• Dear Mrs. Yollis,

I like the idea of square numbers but we haven’t been taught them yet.
Thank you for supplying our blog with the division key.

See you soon. Hopefully…
Brandon.

5. Dear Mrs Yollis,
Thank you for commentinng on the class blog. It took Mrs Morris a long time to get this post onto the blog. Fact familys have helped a lot of people with their divison. And they will be an expert after a few days.Then they can tell their little brothers and sisters and they will be good at it as well.

It is a bit tricky to undersand sometimes. And then they will get used to it and they will do very well.And if you give them a sum and they will say it straight away.

That is what Mrs Morris and Miss Lordan told us that addion and take aways are inverse and multiplication and divison are inverse as well.

Mrs Morris and Miss Jordan said that you carn’t turn around (as an example) 9,9 and they are very interesting fact families. I like square number they are very interesting.

Thanks for commenting back to me!

It was worth the hard work that Mrs. Morris put into this post because it is terrific!

Yes, I know what you mean about some families, there are only two sentences. Like with the products of 1, 4, 9, 16, 25, 36, 49, 64, 81, 100… There would only be two sentences. For example, with 9 you’d have 3×3=9 and when you reverse the two factors it looks the same, 3×3=9. The same is true with the division. 9÷3=3 looks the same as 9÷3=3.

We call them square numbers because if you make an array of “square numbers” with tiles, they make the shape of a square instead of a rectangle. I guess you could also call them square products.

One thing I love about square numbers/products is that they can be found along the diagonal of a multiplication chart. 🙂

Mrs. Y□llis

• Dear Mrs Yollis,
Thank you for replying to me. It did take a lot of time for Mrs Morris to finish this post. When we started free time Mrs Morris was already on it.

The whole class learnt something new even the teachers because of when you said that two numbers the same and then the answers which is called square numbers.

If there’s one thing I know about Mrs. Morris, it’s that she gets busy on tasks right. That is a character trait that I admire in her, among many other wonderful traits! 🙂

I’m glad everyone is learning. I learn from all of you too!

Mrs. Y♥llis

• Dear Mrs Yollis,
Thank you again for replying to me.

Mrs Morris is always busy excxpeserly today because she has the parent teacher interveiw. We had to mix things up.

6. Dear 4KM and 4KJ,

I love the post! I think all the posters are great!
My poster isn’t there because I didn’t get it finished in time. Anyways, I don’t care. I think fact families are a great way to learn division.

I could never get division right in grade 2 and 3.
I like division so much now I might do a sum right now.
8,9 and 72.
8×9=72
9×8=72
72÷8=9
72÷9=8

I must go now!

Iesha 😀 😳

• @ Iesha,
I agree what a great post, I also agree about the posters!
I doesn’t matter abotu not getting you poster done in time, as long as you tried you’re hardest.

Yes, the “Fact Family” idea, is a creative and fun way to learn you’re multiplication and division facts.

Happy Blogging.
Libst☀r

• Dear Iesha,
Wow what a great post,
I liked it how you put a fact family up so we could see it.

I bet your poster was still very good. Even know it did not get up on the blog.

I love division as well. When I heard about fact familys I thought it was going to be fun.

I used to think division was hard but now it seems easy.

I think division is fun.

What is your favourite tipe of maths?

Happy blogging,
Hannah

• Dear Iesha,
Thank you for commenting on the class blog. Mrs Morris has put a lot of effort into this post. Everyone did a great job on their posters and everyone that looks on the blog will think wow what a great job those students in 4KM and 4KJ.

That means you are a good person because you don’t care that your poster is not on the blog not like everyone else.

I could never get division right in grade 2 and 3.
I like division so much now I might do a sum right now.

7. Dear 4km and 4kj,

I like how you have made a post about fact familys because it can help people under stand the fact familys that video realy helps people learn easy I was surprisde that my dad, nan and my sister did’nt know about fact familys so I had to tell them but now my dad can under stand them my sister and my nan still dont realy under stand it is prety easy to under stand just like this,

3,6,18
3×6=18
6×3=18

18÷6=3
18÷3=6

there done its easy

bye for now
from Heath

• Dear Heath,
Thank you for commenting on the blog. There is a lot of ways to show little kids what fact familys are and mean. This is a good post to help people that are not very good at divison.

They didn’t know what it meant because lots of schools back then didn’t call them fact familys. Like when I went to my grandma’s house my cousin was there and I told her about fact familys and she said when she was at school they called it factors.

It is really easy to undersand when you have been tought a lot but like your sister and your dad don’t undersand because they haven’t been tough as much as you have. That’s why we have great teachers because undersand every thing they teach us

They are very good exemples that you have done. 😳

8. Dear 4KM and 4KJ,

I love then new post about the Fact Families. And the posters that everyone did, they look amazing. I know most of my fact families now, it is a great way to learn division.

I didn’t even know what division was in grade 2! I enjoy learning about Fact Families in 4KM and 4KJ all the time. I hope everyone enjoys it too.
What is your favourite sum using fact families ❓

Thats all for now.

See you soon.

Indi♥

• Dear Indiana,
Thank you for commenting on the blog. Everyone loves the new post about fact familys. The posters are wonderful everyone did a great job.

9. Dear 4KM and 4KJ,

All of the posters are very colourful, everyone did a good job!

here is a fact family that I know,
11 12 132
11 x 12 = 132
12 x 11 = 132
132 / 11 = 12
132 / 12 = 11

happy blogging
L♥ren 😀

10. Dear Mrs.yolls I love Olympics! I watched them in 2008 it was cool I ratted it 9/10 by for now from Ethan

11. @ Loren,
Thanks for commenting on our blog. What an awesome comment.
Yes, the posters are very colourful and also a great job done.

Wow, great Fact Family. I know heaps, but I’ll just choose one:
2, 5, & 10
2×5=10
5×2=10
10/5=2
10/2=5

Happy Blogging.
Libst☀r

12. Dear 4KM and 4KJ,

What a wonderful post! I love Maths.

I like the maths topic division! If you know what multiplication is you know what division is.

Here is fact family:

7×6=42
6×7=42
42/7=6
42/6=7

From,
Skye

13. Dear 4KM and 4KJ,
I really like your class’s posters. My class (4PR) is learning division as well, I enjoy it. I think “Fact Families” are a great way to learn division, with the multiplication and division together.
Here are some fact families that I know:
♥ 11 times tables
♥ 9 times tables
♥ 5 times tables
♥ 10 times tables

Bye for now,
Laura

14. Dear 4KM and 4KJ,

I think all of your Fact Family posters are very interesting. Maths is an interest of mine although I only studied one year of it at university when studying for my science degree. I do have many interests. 🙂

It seems maths looks at ways of doing then undoing things. As you know, addition and subtraction can undo each other.

5 + 8 = 13
13 – 8 = 5

Multiplication and division can act the same way…

5 x 6 = 30
30 ÷ 6 = 5

You will find as you learn more, maths will show you a number of ways to do and undo.

When looking at multiplication, I loved to find patterns in answers. I found the more I practised, the faster I became at calculating multiplication facts. Because I knew my multiplication facts, I could use them to work out division facts. As your charts show, they work together.

When I was in Year 4, we had to learn by heart up to the x12 tables. This was because we used pounds, shillings and pence as money. It took 12 pennies to make one shilling so we had to be able to quickly work out x12.

0 x 12 = 0
1 x 12 = 12
2 x 12 = 24
3 x 12 = 36
4 x 12 = 48
5 x 12 = 60
6 x 12 = 72
7 x 12 = 84
8 x 12 = 96
9 x 12 = 108
10 x 12 = 120

Did you notice the units (or ones) column counts by 2s?
0, 2, 4, 6, 8, 0, 2, 4, 6, 8, 0
Now look at the other digits to the left of the units (for 0 x 12 you have 0) …
0, 1, 2, 3, 4, 6, 7, 8, 9, 10, 12
Notice they jump a number every fifth one
0, 1, 2, 3, 4, (5), 6, 7, 8, 9, 10, (11),12

x12 might be a little harder than multiplying by up to 10.

Can you see any patterns in the answers when multiplying by up to 10?

@RossMannell
Teacher, NSW, Australia

• Dear Ross Mannell,

Thank you for leaving a fantatic comment on our blog! Maths is also an interest of mine! Was it fun studying it in university?

I was very suprised when I heard multiplication and division fact families can undo each other. But I didn’t know if addition and subtraction could!

I also like looking at multiplication like it was patterns. Learning by charts help a lot and learning tricks about how to do times tables make it easy.

Using pence, pounds and shillings is a good way of doing it because, as you wrote,12 shillings equal 1 pound.

I actually do notice the ones column conting by 2s!

Wow! What a good way of learning your 12s!

I can see the pattern when multiplying by ten!

Maha

• Dear Maha,

I think I was in Year 5 when we started to calculate money in dollars and cents. Decimal currency took over on February 14, 1966.

Look at these…

\$ 5.36 +
\$ 7.85
——-
\$13.21

Now here is the same amount in pounds, shillings and pence…

£ 2 / 13 / 7 +
£ 3 / 18 / 6
—————
£ 6 / 12 / 1

12 pence (12d) = 1 shilling (1s)
20 shillings = £1

I was glad when we changed over to decimal currency. It’s much easier to calculate. 🙂

@RossMannell

15. Your fact family posters were very nice. We live in the United States and found your website when searching for examples of great fact family problems.
We truly enjoyed viewing all of your hard work!! Great job!!

Elizabeth
Georgia
United States of America