Here is a quick cake conundrum for you.
Two girls are decorating the christmas cake. It is a square fruit cake. They share the icing such that one girl ices the top and one face. The other girl ices the remaining three faces. What possible dimensions of the cake will make the icing areas equal?
It was the month before Christmas and all through the house not a creature was stirring – except for the senior elves who were on the brink of all out war. Father Christmas had picked up some leadership strategies on his travels and decided to send his management elves on a team building day … paintballing!
Don’t be fooled – this is no simple Christmas time-filler. This task requires problem solving strategies, two-way tables, averages, data analysis and logic. In fact, you might want to have a go yourself. There is a task sheet, support sheet and solution.
The Elf Challenge (pdf)
Enjoy the puzzled faces and watch the arguments when students try to justify their answers.
Hey … it’s that time of year again! Baubles and cheesy jumpers are creeping into the most mundane of places. How about a more mathematical festive season?
Image credit: http://technabob.com/blog/
Here is a round up of the Sandpit’s Christmas resources:
Twelve Days of ChrisMaths
Calling all creative thinkers!
What mathematical questions could you set from this picture?
Here are a few to start you off:
1. Sequences – do the increasing number of chocolates in each layer form a sequence (in 2D, in 3D)? If so, what is the general term? Is it geometric or arithmetic?
2. Series – if it is an arithmetic sequence, can you find the sum of a finite number of layers? Which layer would have the 1000th chocolate?
3. Geometry – what shape must the layers be in order to form this structure? Is there a pattern to the layers? Could you stack these in a different way to form an equally stable structure?
4. Money – if a standard box holds 12 chocolates, how many boxes would a 2D or 3D version of this require? What is the cost? What if they came in a larger box? Could you save money?
5. Health – how many calories are there in the tower? How far would you have to run to burn off the calories? How many ‘average’ meals is it equivalent to? How many fastfood burgers? How sick would you feel after all that chocolate?!
Instead of setting a question, why not ask your students or even your trainee teacher what questions they can come up with?
It’s amazing what maths you see when you go for a walk along a canal on a beautiful afternoon. After helping a canal boat through a lock, the following problem occurred to me: how many times must you turn the handle to raise the sluice gate?
Fact: The sluice is controlled by a series of cogs. The handle turns a ratcheted cog with eight teeth.
Fact: The handle turns a small cog with thirteen teeth.
Question: The next cog has ten teeth on a quarter of it’s circumference. How many is this in total?
Fact: This large cog is attached to a small cog with ten teeth, which lifts the vertical post.
Question: From the picture can you estimate how many teeth are on the vertical post?
Question: Given all this information how many turns does the handle need?
Extension: Look at this picture. What is the angle between the foot supports?
Don’t you just hate it when students forget basic key skills? Especially those at the higher end of Year 11 or studying A-Level, who should have a better core knowledge. What if there was a magic tool which began to address this issue?
Skills required
Equipment
You will not need:
Magic Tool
Activity
Quite simply draw the four diagrams below on the board and ask the following questions:
It takes moments to draw the questions on the board, but the discussion can take some time and addresses several basic skills. You can change the numbers to adjust the level of challenge.
Whether you are on half term holiday this week or next, I’m sure you’ll have time for this little number skills starter.
Image Credit: Jill Murphy, ‘The Worst Witch’ – a children’s classic, which I highly recommend.
Can you help Wanda, the Grand High Witch, to find the local reporter hiding at her Halloween Girls Night Out? Solve the number problems and unveil the imposter.
This starter or homework activity includes order of operations, factors, prime numbers, addition and multiplying (written method).
Happy Halloween!
(Updated: 1st Nov 2017)