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.
How and why we round numbers.
HYPATIA:Ha ha ha!
OLIVIA:Wait up! Hypatia!
HASSAN:Where did she go?
OLIVIA:Where's the portal to get out of here?
HASSAN:Let's solve this puzzle. Maybe that will reveal the exit.
OLIVIA:Hmm, rounding.
HASSAN:What's rounding? Is it this?
CARPET:Oh no! You are joking me. My favourite vase, who would do such a thing? You!
HASSAN:Us?
CARPET:You owe me a vase.
OLIVIA:We don't have any money.
CARPET:Wow. Clumsy and unprepared.
HASSAN:I don't even know how to do rounding.
ARCHIMEDES:Hey cranky carpet, it's okay.
OLIVIA AND HASSAN:Archimedes!
ARCHIMEDES:I got this. How much?
CARPET:Well, it's 10 pounds for the vase…
ARCHIMEDES:Oh, I think I have some 10 pound notes, so that's ideal.
CARPET:Emotional distress, 50 pounds.
OLIVIA:Come on!
CARPET:Being rude, 30 pounds. Plus interest, plus tax, plus a tip, that's 126 pounds.
OLIVIA AND HASSAN:What?!
CARPET:I'm sorry, but at the end of the day that is business.
ARCHIMEDES:Okay, here's…130 pounds.
CARPET:Thank you for shopping at Cranky Carpet's Vase Megastore. And here's your change.
HASSAN:Sorry Archimedes, I didn't mean to knock the vase over.
ARCHIMEDES:That's okay, I'm glad I could help.
OLIVIA:How come you gave so much?
ARCHIMEDES:Well I only have 10 pound notes, so I round up, going to the nearest 10 from 126, which is 130 pounds.
OLIVIA:How do you mean?
ARCHIMEDES:Well, let's take a look.
If we want to round to the nearest 10, we first visualise our number, 126. The two nearest 10s it sits between are 120 and 130, which 10 is it nearer to?
OLIVIA:Uhh… 130?
ARCHIMEDES:Exactly. Such mathematical wizardry!
From 120 to 126, there's a difference of six. From 126 to 130, there's only a difference of four. If our number ends in five or more, we round up to the next 10 above. But if it ends in one, two, three or four, we round down to the nearest 10 below. We can apply rounding to any size of number, not just for rounding to the nearest 10. So for example, 1256 would be closer to 1000 on the line if we were rounding to the nearest thousand. And 72,351 will be rounded to 100,000. If we rounded to nearest 100,000, as it is on this half of the line. If we put 1256 on this line and rounded it to the nearest 100,000, the answer would actually be zero as it is so small on this line.
OLIVIA:So, you used rounding to work out how much money to give?
HYPATIA:Exactly! Rounding also allows you to make data easier to understand.
ARCHIMEDES:Oh. Like I've spent about six hours in the market buying about 20 cookies and I'm wanting zero judgement.
HASSAN:So for Hypatia's question… Argh! It's so difficult with so many numbers.
HYPATIA:Be careful to pay attention to the correct column.
HASSAN:So to round to the thousands we go along to the fourth number along because 1000 has four numbers too.
OLIVIA:So we can ignore the first two numbers?
HASSAN:And then we see which thousand 688 is nearer to - 5000 or 6000. 5688 is closer to 6000 than 5000, so the answer is 6000. Is that right?
OLIVIA:Oh wait, we have to add back in the first two digits.
HASSAN:Ahh, so the answer is 346,000. How about the others?
OLIVIA:If we round the nearest 10,000, it's 350,000, as 45,688 is closer to 50,000, and to the nearest 100,000, it's 300,000.
HASSAN:Because 345,688 is closer to 300,000.
HYPATIA:Congratulations, that's correct!
OLIVIA:Alright!
HASSAN:Nice!
CARPET:And 20 pounds for your mystical door magic.
HYPATIA:Now that we have explored rounding, I have a question for my young mathemagicians. Fill in the gap so each number rounds to 120,000 when rounded to the nearest 10,000.
Video summary
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.
Our great mathemagician Hypatia adds further rounding problems for the duo to complete before they can continue through the mathemagical maze, challenging them to round to the nearest 1,000, 10,000, and 100,000.
The episode ends with a final rounding question for pupils to answer in the classroom.
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 wish to introduce students to other relevant topics, for example:
- Place value appropriate to the year group
- Estimation of placing numbers along a number line
- Finding multiples of 10, 100 and 1000 above and below a number
During the film:
Depending on your lesson’s focus, you may wish to pause the video at certain points to check for understanding, asking questions such as:
- Do you understand what is meant by the nearest 10 / 100 / 1000?
- Do you know which digits round up, and which round down?
- Why does rounding make things easier to understand?
- Can you tackle Hypatia’s final question?
Final question:Fill in the gap so each number rounds to 120,000 when rounded to the nearest 10,000:11?,6231?1,92812?,054
Answer to the final question:Gap 1: 5,6,7,8 or 9Gap 2: 2Gap 3: 0,1,2,3 or 4
Following on from the film:
- Practise procedural variation by giving pupils numbers with the same digit ending to round and asking them what they notice, e.g. 27, 427, 727, 1827 rounded to the nearest 10.
- Round the same number to the nearest 10, 100 and 1000 to show what changes in the method when the digit we are rounding to changes.
- Give digit cards and set a problem in the inverse, e.g. I make a number using the cards 2, 8, 8, 2. It rounds to 8200 to the nearest 100. What number did I make?
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.
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.
