How we do maths without a curriculum

how we do maths without a curriculum

Back in January I shared our maths plans for this term. Our plans are always flexible. One of the joys of not following a curriculum is that if something isn’t working we can switch topic or try a different approach.

Maths with one of my children has far exceeded my hopes and expectations this term. C(10) has matured in so many ways over the last six months, and being her maths mentor has become a real delight. She’s developed genuine enthusiasm to engage with mathematical ideas and persist with challenging problems. And she’s always willing to listen to my suggestions for improving her working methods.

We started in January reading Awesome Arithmetricks, whiteboards to hand. This worked well as a recap of addition and subtraction (with some fun interludes like this simplifying equations puzzle). Awesome Arithmetricks also explained long multiplication in a way that made sense to C(10).

The long division question

Then we came to long division.  Before she started using the standard algorithm, C(10) wanted to know how it worked. Great question, but not one which is explained in Awesome Arithmetricks. {Tangent: according to one of my favourite books about teaching maths, The Elephant in the Classroom, one of the main reasons girls do less well than boys in maths at school is because girls so often want to know “Why?”, a question there is rarely enough classroom time or teacher skill to address.}

You don’t have to be a maths genius to teach your kids maths without a curriculum

So what did I do? I did what I always do when one of my kids asks a tricky question – I turned to google. “How does the long division algorithm work?” I found plenty of helpful websites, but – to be completely honest – I didn’t follow many any of the explanations!

I didn’t panic. You really don’t need to be a maths genius to teach your child maths without a curriculum. I’m certainly not! If I’d devoted a bit of time to understanding how the long division algorithm works I’m sure I would have got there. But I decided it would be more fun to figure it out alongside my daughter.

{Edit: The Cookie Factory Guide to Long Division at Let’s Play Math is a brilliant explanation of how long division works. I now understand it, yay!}

C(10) knows my attitude to learning maths. She knows that I got top maths grades up to “A” level but that I mostly learned by unquestioning memorisation, rather than fully grasping the mathematical concepts. She trusts me, not to know all the answers, but to help her discover them for herself, in a way she deeply understands.

At this stage of her maths education it would be easy for me to swot up in advance and pretend I know it all. Instead, though, I’m aiming for a long-term approach which will create a foundation of trust. A foundation which will, I hope, continue through our homeschooling days, as C(10) becomes more independent but continues to trust me as her learning mentor.

How we approached long division

So what did we do about long division? I downloaded Math Mammoth’s Division 2 which teaches long division in several small steps, over many lessons. C(10) completes the exercises on her iPad using Notability. A side benefit is that she’s been getting lots of multiplication fact practice.

{A tangent about learning multiplication facts: C(10) prefers to figure out each multiplication fact when she needs it rather than rote-learn the times tables up front.  I fully support this way of working because I can see how it develops her number sense. And I’m delighted that she can now instantly recall many facts thanks to having calculated them so many times. That’s seems a sensible order for learning multiplication facts.}

Fun maths to break up the worksheets

Division 2 is great value at $5.10 for 70 pages of well-structured teaching and practice. I’m sure by the time we’ve completed it we’ll both know everything there is to know about the hows and whys of long division. But there was no way C(10) was going to work through 70 consecutive pages of division and emerge with her love of maths intact. So, we’re taking our time.

Each day I ask what she’d like to do for maths. Usually a few times a week she chooses to work on Division 2. Other times we do something different. We have plenty of resources – many of them free –  to choose from.  Here are some we’ve enjoyed this term.

An unexpected treasure trove – SATs papers

This SATs-papers website contains all the past test papers sat by English schoolchildren. I usually take one look at SATs papers (especially science and English ones) and run a mile, thanking our lucky stars that we home-educate and my kids don’t have to waste their time on this kind of stuff.

But we love the KS2 Level 6 Maths problems.  These questions are deceptively short but they all require thinking, and that’s why C(10) loves them.  You can download as many SATs papers as you want, you just have to register (free).

Becoming a problem solving genius

How we do maths without a curriculum

Like Primary Grade Challenge Math, Becoming a Problem Solving Genius is made up of short chapters, each of which introduces a topic in a fun way and is followed by four sets of problems which range in difficulty from “easy” to “super-Einstein”.

While we love the problems in this book, we find some of the strategies a bit formulaic.  C(10) likes to have a go at the problems and then refer back to the notes when she needs a pointer. As with our multiplication facts approach, this seems to me to be the most sensible order of doing things. Instead of being told how to do something and then being tested on it, don’t we learn better once we’ve experienced a need for a piece of information or technique?

Measuring Up: Prototypes for Mathematics Assessment

Measuring Up (free download) is another source of interesting games and problems on subjects ranging from probability to geometry.

According to its publishers, the book “features 13 classroom exercises for fourth grade students that demonstrate the dramatic meaning of inquiry, performance, communication and problem-solving as standards for mathematics education.”

Each of the 13 exercises is followed by an explanation of what it has been designed to achieve.  Examples of high, medium and low level responses are also given. We just enjoy the puzzles!

The Man Who Counted

how we do maths without a curriculum

When The Man Who Counted popped through my letterbox I briefly wondered if Amazon had sent it by mistake, or perhaps as a bonus for my generous contribution for their bottom line. When my brain finally clicked into gear I remembered coming across it on Math Mama Writes‘ list of a dozen delectable math books.

C(10) and I have only read a few chapters so far, but already we’ve found some delightful problems. (Really! The kind you have so much fun with you want to share them with friends and family.)

Maths art

Highhill Homeschool has been sharing a wonderful series of posts based on the geometry of circles. Their most recent activity was based on Islamic Art and Geometric Design from the Metropolitan Museum of Art (yet another free download). This ties in perfectly with our forthcoming trip to Spain, where we’ll be visiting the Moorish palace, the Alhambra.

alhambra art

Photo: The way of beauty (click image for more)

We’ve enjoyed looking at photos of the exquisite geometric designs at the Alhambra. And C(10) has found a reason to learn how to draw circles with a compass. We’re looking forward to moving onto  finding geometric shapes within our circles.

how we do maths  without a curriculum

Circle art

Do you have any fun maths resources to share?


I’m appreciatively linking up here:

After School Link Up at Planet Smarty

The Hip Homeschool Hop

Wonderful Wednesdays at Solagratia Mom

Collage Friday at Homegrown Learners

Weekly Wrap Up at Weird Unsocialized Homeschoolers

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