NARRATION:Back in the deepest, darkest depths of time, there lived a great mathemagician called Hypatia. Numbers fell under her spell one by one. With them, Hypatia could do anything. Now Hypatia is looking for people to share her powers with. She has forged a mathematical maze. Only true mathemagicians can solve the puzzles and find their way out. Join two young explorers, Oliviaand Hassan, to solve the puzzles, escape the maze and become the greatest mathemagicians of all time.
Multiplying using written methods.
OLIVIA AND HASSAN:Wahey! Wahoo!
ARCHIMEDES:Woo-aa-hhh.
HYPATIA:Shhh鈥 Welcome to the Galaxy Garden, where we shall all grow if you'll pardon鈥
ARCHIMEDES:The pun.
HYPATIA:What do you see amongst the stars? It shows the deepest desire of your heart.
HASSAN:A cat!
OLIVIA:Eating a cake!
HASSAN:On top of the Eiffel Tower?!
HYPATIA:I mean, I see a crab, but sure, why not? Whilst this is a lovely place, the Galaxy Garden can lull you to sleep. And if you don't solve my puzzle to open the portal, you too will become an eternal sleeping flower.
HASSAN:Doesn't sound too bad.
OLIVIA:Speak for yourself, Hassan.
HYPATIA:132 times 14, can you solve this multiplication?
OLIVIA:We're definitely going to try, aren't we Hassan? Huh?
ARCHIMEDES:To multiply two larger numbers together, we break it down into smaller, easier equations. Take 22 multiplied by 23 for example. First, we take our equation and put the numbers on top of each other. Larger number on top, smaller on the bottom. So 23 on top, 22 on the bottom. If we can't multiply by a big number like 22 in our heads, then we split the bottom number up into its ones, tens and hundreds, multiplying the top number by each column of the bottom numbers separately, starting with the ones.
OLIVIA:And then we take the number on the bottom right and multiply it by all the numbers on the top row one by one, working from right to left too?
ARCHIMEDES:Yes, well done Olivia. So first we times the three by two to give six, then we times the 20 by two to give 40. So that gives a total of 46. Then we move on to the number on the bottom in the tens column and do the same.
HYPATIA:But there's one big difference here. Can you think what that might be?
HASSAN:The bottom two is in the tens column, so we're actually multiplying by 20.
ARCHIMEDES:Exactly, so we write a zero in the ones column so that all the numbers we multiply after this are ten times bigger. Three times 20 equals 60, and 20 times 20 equals 400. So this is 460 altogether.
OLIVIA:If we've partitioned the second number into tens and ones and multiplied each part separately, we must need to add them back together?
ARCHIMEDES:Yeah, you're right. Note that when we add the 40 and the 60 together, we must regroup by taking this one hundred and adding it to our hundreds column to make our final answer, 506.
HYPATIA:But what about my puzzle?
OLIVIA:Hmph.
HASSAN:Hmm. I think we've got the answer!
OLIVIA:132 times 14 equals 660. Are we right, Hypatia?
HYPATIA:You're so close, but not quite. Think about how large each digit in the calculation is鈥
HASSAN:Oh that's silly, we forgot to add the extra space. We're multiplying 132 by ten, not one.
ARCHIMEDES:Oh, it's an easy mistake to make.
OLIVIA:So instead of 132, I need to put 1320.
HASSAN:Plus 528鈥
翱尝滨痴滨础:贰辩耻补濒蝉鈥
OLIVIA AND HASSAN:1848.
FLOWER:Ahh! Thank you.
OLIVIA:Yay!
HASSAN:Ha!
HYPATIA:But what about you young mathemagicians? What do you think of these equations? Can you spot the mistakes? 942 times 76 equals 69,582. 326 times 48 equals 3912.
Video summary
Finding themselves in space, Olivia and Hassan watch mathemagician Hypatia perform long multiplications in the sky by bending the stars.
After watching in awe, Archimedes comes to their aid and encourages them to bend the stars in the same way to perform a long multiplication written equation.
They find that placing the stars on top of each other, as with numbers, they can break down large multiplications and more easily find the answer.
This short animated film is from the 大象传媒 Teach series, Hypatia's Mathematical Maze.
Teacher Notes
Before watching the film:
Prior to this lesson you may wish to introduce students to other relevant topics, for example:
- Times tables up to 12x12
- Multiplying by 10 and 100
- Multiplying two digit numbers by partitioning
During watching the film:
Depending on the focus of your lesson you might wish to pause the film at certain points to check for understanding, asking questions such as:
- What does each digit in the number represent?
- Why does a zero appear in the second calculation? What鈥檚 different?
- What good mistake might people make when doing short and long multiplication?
- Can you answer Hypatia鈥檚 final question by working out the answers before finding her mistakes?
Final question:
Can you spot the mistakes?
- 942 times 76 equals 69,582
- 326 times 48 equals 3912
Answer to the final question:
- 942 x 76 = 69582 (two lots of regrouping not added). The answer is 71,592 / 326 x 48 = 3912
- (Second calculation not multiplied by 10). The answer is 15,648.
Following on from the film:
- Link to rounding to encourage pupils to check their answers by using estimation, e.g. check 207 x 29 by doing 200 x 30, so it will be roughly 6000.
- Add another skill by setting comparison questions, i.e. crayons can be bought individually for 29p or a pack of 6 costs 149p. Arvind buys 42 individual crayons and Bill buys eight packs of crayons. Who spends more money? Record your answer using < or >.
- Link to area by finding the area of rectangles with large measurements, e.g. a football field measuring 252 feet x 94 feet, or even the area of composite shapes with large measurements.
This short film is suitable for teaching maths at KS2 in England, Wales and Northern Ireland and 2nd Level in Scotland.
Adding and subtracting using mental methods. video
In a mythical temple full of obstacles, Olivia and Hassan learn simple mental maths and apply it to work out the passcode to open the door.
Adding and subtracting using written methods. video
Having been transported to a floating library, Olivia and Hassan's ability to solve large equations using written methods is tested.
How and why we round numbers. video
Olivia and Hassan are taught how to round to the nearest 1000, 10,000, and 100,000 when a disgruntled magic carpet demands money from them.
Using addition and subtraction in multi-step problems. video
Inside a giant computer created before the age of mathemagicians, Olivia and Hassan are faced with a multi-step problem to reach the labyrinth鈥檚 next stage.
Multiplying by 10, 100 and 1000. video
When Olivia and Hassan find themselves on the roof of an enormous skyscraper they learn how to multiply by 10, 100 and 1000 and work out the number of windows on the building.
Mental multiplication. video
While exploring a jungle, Olivia and Hassan learn the true nature of square numbers as being created when two of the same number are multiplied together.
Factors, multiples and primes. video
Trapped in a desert together with Archimedes, Olivia and Hassan learn what common factors, multiples, and prime numbers are.
Dividing using written methods. video
Olivia and Hassan learn how to perform long division in order to free gridlocked traffic on a bridge.
Recognising and comparing fractions. video
Olivia and Hassan are enjoying themselves in a world made out of pizza and learn how to work with numerators and denominators in fractions.
Adding and subtracting fractions. video
Amongst the ruins of an ancient city, Olivia and Hassan learn how to add and subtract fractions.
Multiplying and dividing fractions. video
In a mysterious crystal cave, Olivia and Hassan get to work dividing and multiplying fractions in order to find their way out.
