Voiceover:
In a world without maths, a land where people forgot, who will save the day?
Baz:
Alright if I make some tea Dave?
Dave:
Sure thing Baz, help yourself.
Kitten:
Miaow
Baz:
Ooo hello
Kitten:
Miaowow
Baz:
And another.
Kitten:
Miaow
Baz:
Ooo cheeky, hehe.
Kitten:
Miaow!
Baz:
Ooooo!
Baz:
Dave, this is getting silly. You鈥檝e got to do something about all these kittens.
Kitten:
Miaow
Dave:
What kittens?
Kitten:
Miaow
Dave:
Yeah I know Baz, I started trying to sort them out. You, Charlie, Mrs Barker and Sally, all said you鈥檇 take some.So I got 4 boxes and wrote your names on them, but then I got stuck.I was trying to share them out equally, but I wasn鈥檛 sure how many to put in each box.
Baz:
Errr that鈥檚 a tough one.Don鈥檛 worry I know someone who can help. Scoop all them kittens up, I鈥檒l call鈥ivider Girl!
Kitten:
Miaow
Narrator:
Divider Girl can you help Dave and his brother Baz solve their problem?There are eight kittens that need to be shared equally between four people.Oh yeah, dividing time.
Eight divided by four.
Let鈥檚 start by sharing out the first four, that鈥檚 one kitten for each person and four kittens left to share. If everyone gets another kitten that makes two for each person with zero kittens left to share out.Eight divided by four equals two. Good work Divider Girl.
Baz:
Great, sorted, nice one.
Dave:
I鈥檒l call Sally.
Dave:
Alright Sally, how鈥檚 it going?
(offscreen) Sally:
Alright Dave.
Dave:
We鈥檝e just sorted out the kittens. There鈥檚 two for you, you can pick them up anytime.
(offscreen) Sally:
Kittens Dave?
Oh no, I thought you said mittens, cute, fluffy mittens. I can鈥檛 take any kittens, I鈥檓 allergic. Sorry.
Dave:
Oh, okay. No worries Sal.Now only three people want kittens.
Baz:
That鈥檚 okay Dave, we just need to share these two kittens equally between the other three boxes.
Kitten:
Miaow, miaow!
Dave:
Nice try Baz, but I don鈥檛 think that鈥檚 going to work.
Baz:
Hang on, Mrs Barker鈥檚 got all them dogs hasn鈥檛 she? I don鈥檛 think she鈥檚 going to be able to take kittens as well.
Dave:
Cats and dogs get on Baz.
Baz:
No they don鈥檛 Dave.
Dave:
Oh great, so we鈥檝e still got loads of kittens and now only two people want them. Let鈥檚 go back a step, pop those ones back.
Kitten:
Miaow
Dave:
Right then, we鈥檝e got one, two, three, four boxes with two kittens in each. How many have we got altogether?
Baz:
I don鈥檛 know Dave, I can鈥檛 count them, they keep moving around.
Dave:
Four lots of two that鈥檚 err, four times two that鈥檚 ummm, that鈥檚 errr鈥
Baz:
That鈥檚 multiplication Dave.
Dave:
You鈥檙e right Baz, that is multiplication. And I know just who we need for that.
Narrator:
Oh what鈥檚 this? I think Divider Girl鈥檚 got an idea. Ah yes, multiplication is the inverse of division.
Since we know eight divided by four equals two, we also know four times two equals eight.
Dave:
Of course, eight! That鈥檚 the number we started with, eight kittens.
Narrator:
Ooo she鈥檚 beaten Multiplication Boy to it, he鈥檚 not going to like that.
Baz:
Oh sorry Multiplication Boy, I think we鈥檝e sort of done it.
Dave:
Right then Divider girl, you鈥檙e up again.We鈥檝e got eight kittens but we want to share them equally between two people this time.
Narrator:
So you need to work out eight divided by two. Remember division is just鈥verything alright Multiplication Boy?
Yes, four times two equals eight, we鈥檝e done that bit already, keep up Multiplication Boy. Oh, you want to swap the four and the two over?
Well yes you can do that, Multiplication is commutativeso you can swap the numbers over, either side of the multiplication symbol and the answer is the same.So since we know four times two equals eight, we also know two times four equals eight.
Or in other words, we know four lots of two are eight, so we also know two lots of four are eight. Since division is the inverse of multiplication that means eight divided by two equals four.
He鈥檚 done it! Two people get four kittens each.Sorry Divider Girl he鈥檚 beaten you to it.
Dave:
Wow that鈥檚 impressive, Can you do that with division?
Narrator:
No division is not commutative.Eight divided by two equals four but two divided by eight does not equal four.Woo hoo hoo hoo, I love kittens! A woo hoo hoo ha, a woo hoo hoo, woohoohoohoo!
Video summary
Baz and Dave need to share out some kittens ready to go to their new homes!
At first it seems simple, eight kittens shared between four friends.
Things quickly get more complicated when they discover Sally is allergic to cats.
She can鈥檛 take any kittens, and Mrs Barker has all those dogs.
There are remainders involved, new calculations to solve and the inverse to be explored.
This sounds like a job for Divider Girl and Multiplication Boy!
The superheroes of A World Without Maths show Baz and Dave that they both have the skills to help solve this problem.
But who will be the first to get to the bottom of it? Will they manage to find new homes for all those cute fluffy kittens? And will Baz ever get that cup of tea he was after?
This clip is from the series A World Without Maths.
Teacher Notes
Key Stage 1:
You could present your class with the same problems as the story and give them toys and boxes or sorting hoops to act out the problem.
They might use an existing array to talk about how many dots are in each row, how many rows there are and how many dots there are in total.
They might write the related multiplication and division sentences for the array.
Pupils could use objects or drawings to create their own arrays to show the relationship between multiplication and division.
You could create number trios (placing three numbers on the corners of an equilateral triangle) to explore how these show related calculations in multiplication and division. For example, 4 and 7 at the bottom and 28 at the top show that 4 x 7 = 28, 7 x 4 = 28 and that 28 梅 4 = 7 and 28 梅 7 = 4.
Key Stage 2:
You could get your class to use drawings to create their own arrays to show the relationship between multiplication and division.
They could then write out all four calculations that the array shows.
Children might solve word problems that present multiplication or division problems. For example: Baz and Dave are going to share out all the cat food they have. They have 24 tins and each box can hold 4 tins. How many boxes will they need?
Or, Baz and Dave have some left over cat food to give away to the friends who are taking the kittens. They have 6 boxes. In each box are 4 tins. How many tins do they have in altogether?
This clip will be relevant for teaching Maths at KS1 and KS2 in England and Wales, and First and Second Level in Scotland.
How to use mental methods to multiply. video
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Multiples of two, five and ten. video
Multiplication Boy and Divider Girl keep their maths superpowers sharp with a competition to count in twos, fives and tens.
How to use arrays to multiply. video
Multiplication Boy helps Mr Sharma buy pencils for the school, using arrays to multiply.
What is multiplication? video
Multiplication Boy uses repeated addition to help Dave work out how many bricks he needs to build a new wall for Mrs Sharma.
Dividing using repeated subtraction. video
Divider Girl uses repeated subtraction to help Mrs Barker with a division problem involving some hungry pups.
How to use mental methods to divide. video
Divider Girl helps Charlie with a division problem, using her multiplication facts.
