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.
Adding and subtracting using mental methods.
OLIVIA:What are we dealing with Hassan?
HASSAN:Eight trip wires, three spike traps, five swinging blades, six crocodiles, four lurking crocodiles and one custard pie.
OLIVIA:Hmm, okay.
HASSANThat's… Hmm… 27 traps, so we need to be super care - ful.
OLIVIA:Come on then.
HASSAN:Hmm, lemon.
OLIVIA:Hmm! Some kind of code?
HYPATIA:In order to solve my puzzle and find the combination, you'll need to do a bit of calculation. Get it right and your journey continues. Get it wrong, and you're trapped forever.
HASSAN:That's way too big a number.
OLIVIA:Wait, we can do this I'm sure. Hey, Archimedes.
ARCHIMEDES:It's just like when you counted the traps, the number might be bigger but you've definitely got the basics.
HASSAN:Oh yeah.
HYPATIA:Break it down into smaller equations. Split the large number into its parts. That is indeed the best way to start.
ARCHIMEDES:You've got this. Let's split out our first number, 15,712.
HYPATIA:Two ones, One ten, seven hundreds, five thousands and one tens of thousands.
ARCHIMEDES:Then we split 2200. It doesn't have any ones or tens, just two zeros, so we just had two hundreds to the seven already there. That's 900 and 2000 to the 15 already there. That's 17 thousands.
HYPATIA:Then, we add everything back together. So the answer is 17,912.
For subtraction and taking away, it's the same but the amount decreases. So if we want to minus 2300 from 12,462, we take away three from the hundreds and two from the thousands.That leaves 10,162.
HASSAN:So we just work through the numbers column by column, doing a bunch of mini additions to create one big addition?
ARCHIMEDES:Yeah.
HASSAN:We can do it all in our heads?
ARCHIMEDES:Yeah.
OLIVIA:You can press the button now, Hassan.
HASSAN:Let's do it together.
HYPATIA:Not so fast. Let's see how you do without Archimedes.
ARCHIMEDES:Mmm, lemon.
HYPATIA:And now a little question for my young mathemagicians… I am thinking of a number, I subtract 1400. I get an answer of 4567. What was my number?
OLIVIA:Hmm, let me think. Hang on, you've not said the question right, you've given us the answer.
HASSAN:That's the point, we've got the answer, but not one of the original numbers. Let's see.
Something minus 1400 is 4567. Well, 567 plus 400 is 967, and 4000 plus 1000 is 5000. So, I've got it!
OLIVIA:Are you sure? If we get this wrong, we won't be able to go to the next section.
HASSAN:I think so. Hypatia, the number you were thinking of is 5967.
HYPATIA:I see you've learned a lot today. You are correct. Nice one!
OLIVIA AND HASSAN:Woohoo!
ARCHIMEDES:Ah! Ay! Oof!
Video summary
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.
Hypatia, our great mathemagician, sets a question which they must work out correctly to open the door: 15,712 + 2200.
With the help of mathematical companion Archimedes, the pupils learn simple mental maths and apply it to work out the answer.
Once they have left the temple, Hypatia and Archimedes leave pupils with a further mental subtraction question.
This short animated film is from the BBC Teach series, Hypatia's Mathematical Maze.
Teacher Notes
Before watching the film:
Prior to this lesson you may want to introduce students to other relevant topics, for example:
- Place value including naming columns and recognising the value of individual digits, up to the 100,000s
- Partitioning numbers using standard and non-standard partitioning
- Counting in steps of powers of 10 from any number
During watching the film:
Depending on your lesson’s focus, you may want to pause the video at certain points to check for understanding, asking questions such as:
- Which digits change and which don't? Why?
- Which column are you tackling first? Why? Does it matter?
- How can we solve Hypatia's question at the end?
Following on from the film:
You could practise conceptual variation and represent problems using a variety of concrete materials, e.g. dienes blocks and place value counters.
You could practise procedural variation and give a sequence of questions and ask the pupils when the method or thinking changes, e.g.
- 17,245 + 1500
- 17,245 + 1600
- 17,245 + 1700
- 17,245 + 1800
- 17,245 + 1900
When does the pattern change? Do we need a different method?
You could present some problems with some 'good mistakes' made, and ask the pupils to spot and correct them, e.g. 43,372 + 2400 = 45,870
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 written methods. video
Having been transported to a floating library, Olivia and Hassan's ability to solve large equations using written methods is tested.
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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’s 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.
Multiplying using written methods. video
Finding themselves in space, Olivia and Hassan watch mathemagician Hypatia perform long multiplications in the sky by bending the stars.
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.
