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.
Using addition and subtraction in multi-step problems.
OLIVIA AND HASSAN:Ahh! Woohoo!
HASSAN:Olivia, I think we're inside a computer.
HYPATIA:How did you get here? This is the computer that runs my mathematical maze. Oh! There must be a bug. We have been experiencing technical difficulties all day. Hmm鈥 Now that you're here, perhaps you can help solve this puzzle to fix the computer.
A super computer has 350 cables. A robot connects 120 more, but 375 cables frazzle. How many cables are left?
HASSAN:But what abou- How did she do that?
OLIVIA:Archimedes, what happened to you?
ARCHIMEDES:What? Oh no, it's happened again. Oh, this looks like a fun one.
OLIVIA:I think I've got the answer.
HASSAN:Here we go鈥
OLIVIA:Ah, I was so sure.
ARCHIMEDES:No worries, noone gets to be a great mathemagician without making mistakes. What?
HASSAN:Okay, let's take another look. The supercomputer has 350 cables. Then the robot attaches more, so we have to add first. 350 plus 120.
OLIVIA:470.
HASSAN:Right. And then 375 cables frazzle, so we'll need to minus those. The computer has 470 cables in total. Then we minus 375.
OLIVIA:470 minus 375. We can't minus five from zero, so we'll borrow one from the next column. 10 minus five is five. We can't do six minus seven, so we'll regroup from the next column again. 16 minus seven is nine and the next column cancels itself out. So that gives us 95.
OLIVIA AND HASSAN:Three, two, one鈥
OLIVIA:Oh no!
HYPATIA:More bugs. Solve the puzzles so you can escape.
HASSAN:It's on my screen!
OLIVIA:It's here too!
HASSAN:Any ideas?
OLIVIA:The sum of two numbers is 2309. The difference between these numbers is 129. What are the numbers? Hmm鈥
ARCHIMEDES:Try drawing it out.
OLIVIA:So, altogether it's 2309. We have two mystery numbers, mystery number one and mystery number two, which is the mystery number one plus 129. So if we take 129 away from 2309.
HASSAN:We know the total of two lots of mystery number one.
OLIVIA:Exactly, so 2309 minus 129, nine minus nine is zero. We'll have to borrow a 10 from the hundreds for the next row. So, 10 minus two is eight, two minus one is one and the 2000 stays the same. So, 2180 is the total of two lots of mystery number one.
HASSAN:Now what?
OLIVIA:Hmm鈥 Mystery number one is half of 2180, two divided by two is one. You can't divide one by two, so we take that hundred across to make 18 tens. 18 divided by two is nine and the zero doesn't change.
HASSAN:1090. So mystery number two is 1090 plus 129, it's 1219. Three, two, one, go!
OLIVIA:It's working! We're going through to the next staaa -
HYPATIA:They're getting better and better all the time.
ARCHIMEDES:Do you think they might make it to the centre of the mathematical maze?
HYPATIA:We'll see. One day they might be as mathemagical as you or even me.
And what about you? Can you answer this question? My maze originally had 342 sections. Olivia and Hassan have solved 123 of these. If I create an extra 21 sections, how many rooms do Olivia and Hassan have left to go before they reach the heart of my labyrinth?
Video summary
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.
Having answered correctly by using 鈥榖ar modelling鈥, Hassan is transported to another level, where he must work with Olivia through holograms to answer further multi-step problems.
After the pair have worked through a series of mistakes and questions to find the correct solution, mathemagician Hypatia asks pupils to answer a final multi-step question in the classroom.
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 maybe wish to introduce students to other relevant topics, for example:
- Mental and written addition and subtraction.
- Representing problems using bar modelling.
During watching the film:
Depending on your lesson鈥檚 focus, you may wish to pause the video at certain points to check for understanding, asking questions such as:
- Are your answers the same as those in the film?
- When would you use regrouping, and why?
- How many stages would you break this problem into?
- What are the different mathematical processes this question is asking you to perform?
- How can you answer Hypatia鈥檚 final question?
Final question:My maze originally had 342 sections. Olivia and Hassan have solved 123 of these. If I create an extra 21 sections, how many rooms do Olivia and Hassan have left to go before they reach the heart of my labyrinth?
Answer to the final question:342 - 123 = 219, then 219 + 21 = 240
Following on from the film:
- Give the pupils some two-step calculations and ask them to write the problems to accompany them.
- To support, have pre-drawn bar models for pupils to fill in with the correct numbers.
- To challenge, give questions in the inverse, e.g. Two numbers have a difference of 600 and a total of 4,284. What are the two numbers?
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.
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.
