In maths lessons in Year 3-6, there is so much to learn, practise and master that it can sometimes be a bit tricky to get the time needed to develop many of the problem-solving skills further; however, post Satsy McSatsface is a perfect time to take on this challenge in fun and engaging ways - the way maths is meant to be enjoyed! In this section of my super-duper whizzy website, I will be sharing with you some great ideas that are perfect for taking these skills further.
What to be ready for Year 7? Of course you do!
Have lots of knowledge? Of course you have!
Possess a range of problem-solving skills? Without a doubt - YES!
Ready to use them in extended task? Of course you are!
Brie-Anna de Mouse, Star of Maths with a Mouse (and nemesis of TdM - my older brother)
Finding all possibilities: One of the challenges that mathematicians often face is trying to find all the possibilities. The difficulty arises when an organised system is not used. The following tasks are designed to help develop approaches to mastering this skill. They can be attempted using actual concrete materials - such as pupils, socks and sweets; online using pictures and games; completed on paper using organsised lists and working systematically. For initial ideas of how to practise this skills, click on the bright yellow button below and you will find some great ideas to help you develop this useful skill. There's ice-cream there too!
Once you are an expert (or at least on the way to that status), it is time to use those skills to save the planet...or at least to solve some maths problems! Below are a few of my favourite challenges (mostly from NRich and Transum - legends!) AND even further below you will find some Classic puzzles to do before you leave Year 6!
Before trying those, I have a great suggestion for you: visit Alice in Fractaland from Mathigon.
Alice in Fractaland is such a fascinating presentation and many of the special number sequences within it are really important in mathematical puzzles and investigations too!
Warning: It becomes more and more confusing as you wander deeper into Fractaland.
Recognising special sequences such as the Fibonacci sequence or triangular numbers becomes easier with practice so the button below is here just for that reason!
Extended problem solving tasks
Classics puzzles to do before you leave Year 6!
Whether you use actual pieces or this great online version from Transum, the classic puzzle The Towers of Hanoi is a wonderful challenge for all mathematicians.
The level of challenge can increase also by:
increasing the number of pieces
using the fewest possible moves
recording your method clearly - great mathematicians can develop effective ways of sharing their thinking
predicting how many moves it will take based on patterns. This might even lead to generalising patterns/nth term
What a great puzzle!
Guess what? Transum have a great version of Jugs with lots of different levels to challenge you! The best thing about this version is that no water is wasted - it seems that Transum is environmentally conscious as well!
With each challenge, you need to create a certain amount of liquid - the only problem is, you can't measure it as the jugs you have are not the correct size and have no scale! How inconsiderate of the jugs! Time to start filling and pouring and emptying. Once you get the hang of what needs to be done, the next challenge is communicating what you have done and even recording your methods, Hope you remember what you did!
Once again, Transum has a wonderful online version relating to the classic puzzle River Crossing Challenge. Lots of other versions exist and can be completed physically or using objects on a smaller scale. Either way, there are many maths skills that can be used. Have a go!
Can you find solutions? Can you communicate your method? Can you explain your process to other mathematicians?
I love watching little frogs leaping - it looks like so much fun! This classic puzzles, Leapfrog, which is available as an online activity from Transum, is not as easy as it first appears but this is a task any mathematician can attempt.
Ideas:
Too tricky? Make it easier by having fewer frogs
Too easy? More leaping frogs please.
Don't want to use an online version? Use counters, plastic frogs, pictures, you and some friends pretending to be different colours of frogs!
Want to be an even better mathematician? Communicate your methods with another mathematician. You can even look for patterns and try to make predictions. The guide from Nrich below has some great suggestions of how to tackle and extend this puzzle.
More great ideas coming soon...