One of the great joys about homeschooling is the ability to pull in different resources and the freedom to explore all the different rabbit holes of knowledge. For us, maths is not limited to what is prescribed in text-books, but is a fundamental way of seeing the world around us (hello two maths majors in the family - my kids don't stand a chance).
Here are some of our favourite maths resources - that both teach and inspire kids to learn and understand maths.
For Younger Kids
The Number Devil: A Mathematical Adventure, by Hans Magnus Enzenburger
This is a fantastic chapter book about a boy who doesn't like maths until a little number devil takes him on a tour of numbers. It is an amazing introduction to some of the great ideas in mathematics with cute drawings along the way and puzzles to keep you thinking. Think Klein bottles and Fibonacci.
The Boy who Loved Maths: The Improbable Life of Paul Erdos, by Deborah Helligman
This is an adorable little book about Paul Erdos, one of the great mathematicians of the 20th Century. He was also a homeschooling 2e kid, so great for showing that being unconventional doesn't need to stop you following your dream. Also, each page has a different maths idea embedded in each page (with a handy key at the back to help you understand what is going on). It is beautifully illustrated as well. A real treat.
Dragon Box Elements
This is a great way to introduce geometry proofs to even the youngest child. Really! It works - my 5 year old adores creating little triangle warriors to 'fight' the evil tentacle monster. It's intuitive and your little ones don't need to know how to read to play - it's all done visually.
These are so old-fashioned, but I adore them. Yes, I am the kind of homeschool mum who buys Cuisenaire Blocks for Christmas presents! Let your kids explore with them and they will find new ways of using them and learning number sense along the way. My two spontaneously decided to sort them into small groups after a mini-lesson on division, and then they had so much fun discovering how many different coloured blocks they could match together. They've also loved building houses and pools out of them as well.
Kahn Academy can be hard to use for little ones who are not yet reading, but they have recently expanded so there are more options for younger children. You may have to sit and supervise / read the questions for your pre-readers. My son loves reading questions out for my daughter, which is adorable.
If you really must do work-sheet type maths, Singapore Maths is pretty decent. It has lovely illustrations and breaks down the maths into digestible bite-sized portions. It also uses a mastery-based approach, rather than a spiral, so it teaches maths in a different order from typical school books. There are also editions for American and International maths - very useful for the currency sections (Singapore currency is very similar to Australia in denomination so it works well.) Be warned though- they are very expensive! And if you have a voracious maths kid they may power through them a little fast. My son did 5 years worth of their books in 3 months. That's when I called it quits on buying books by grade level!
For Older Kids
Kahn Academy is really quite excellent for older kids. They have also added in mastery challenges, which means kids can pre-test on different areas. This is great for kids and particularly for parents who may not know exactly where their child is mathematically, and saves on endless repetition. Kahn Academy also has some great back-end resources for parents and tutors so you can craft the direction you want your kids to work towards.
Dragon Box Algebra
This is a great resource introduced to us by our wonderful maths tutor (see below) that turns algebra into a visual learning experience. The goal is to solve mini-problems by feeding your dragon. It's a drag and drop game that slowly builds up algebraic knowledge step by step, and only towards the end does it introduce standard notation. Once you have finished the whole game, there is also the option to redo the whole thing using standard algebraic notation. This is a really excellent resource and helped by son get over his road-block on algebra by turning it into something he could visualise. It's also a lot of fun.
This is our go-to resource for cool new videos on maths ideas. It's a YouTube channel run by Brady Haran from Nottingham University, where mathematicians in Britain get to talk about wonderful puzzles and conundrums in mathematics - all in easily accessible form and designed for lay audiences. You won't find a better introduction to the world of maths possibilities than here.
. . . Except for maybe Vi-Hart. Vi-Hart's clever videos on visual maths are something we come back to again and again. From fractals to Fibonacci through to hexaflexagons, there is going to be something here that will both entertain and enlighten. Also, we were swamped with hexaflexagons for weeks once we watched her video as the kids loved making their own over and over again.
Mr Gelston's One Room Schoolhouse
Mr Gelston is my son's maths tutor - yes, with two mathematicians in the house we also use a maths tutor! Sometimes, it's just as important to get different perspectives on maths as it is to read different types of literature. The wider the exposure, the more nuance that your kids can understand about the wonders of mathematics. This is something that Mr Gelston does masterfully. He is also a whizz at understanding how to teach 2e kids who may jump from detailed explanations of the infinite prime number conjecture, or algebra from first principles to answering only in beeps.
Adam Spencer's Number Books
Adam Spencer is a mathematician in Australia who is both knowledgeable and funny. His books are fun and pitched to a lay audience, but they don't skimp on maths detail. They are a visual feast and his books have been my son's go-to bed time reading for many many months now.
His books include: Adam Spencer's Big Book of Numbers, Adam Spencer's World of Numbers, Adam Spencer's Enormous Book of Numbers, and Adam Spencer's Time Machine. Yes, they are different books.
We have used other resources over the years, and one that is still a favourite is Cool Maths Games. This is actually more logic puzzles than strictly obviously maths learning, but it is a great supplementary resource for learning about numbers.
Minecraft is also been a boon for introducing Boolean Algebra in a more game-friendly form as well as helping my daughter understand multiples of two!
I hope some of these resources are useful for your homeschool - and help to give a glimpse at the vast possibilities that are available for homeschooling mathematics. Happy Mathing!