I wrote last week about how the excellent book Let’s Play Math inspired me to establish a living maths routine in our homeschool.

So – here’s what our first week of maths playtime looked like.

### Day 1 – Discovering the Fibonacci Sequence

We read Blockhead: The Life of Fibonacci, a gorgeous picture book about the twelfth century mathematician Leonardo Fibonacci.

We learned how Fibonacci brought Hindu-Arabic numerals to Europe, which had until then been using Roman numerals. Here we paused to talk about place value and how much harder it must have been for kids to do written arithmetic without a zero!

Next we puzzled over Fibonacci’s famous rabbit problem. (In short, if a pair of rabbits has two babies every month, how many rabbits do you have at the end of the year?)

J(8) got overwhelmed and ran off to the trampoline at this point. But I was delighted that C(9) – who also has “if I can’t do it perfectly straight away, I’m outta here” tendencies – stayed with the puzzle long enough to spot the pattern which gives us the Fibonacci Series. (J(8) will be ready for this level of engagement and reasoning in his own time!)

### Day 2 – Fibonacci Numbers in Nature

We’d read in Blockhead how the Fibonacci Series is found throughout nature, so on our walks for the rest of the week we looked for examples.

Most daisies, for example, have thirty-four petals (a Fibonacci number).

(Top tip: don’t split the petals, thinking they’re two. The first time I counted fifty-nine. Next daisy, I carefully kept each petal intact and I got thirty-four exactly.)

Daisies have 13 (easier to count) sepals (another Fibonacci number).

Fibonacci numbers are found in so many places besides plants – they crop up everywhere, from fine art, to galaxies, to pineapples. What a lot we still have to explore!

### Day 3 – KenKen Puzzles: Arithmetic and Logic Practice

KenKen – Japanese for “cleverness” – is an arithmetic logic puzzle invented by a Japanese maths teacher. It’s a similar to Sudoku but the digits in each mini-grid combine together to make a given number, using prescribed operation signs. Hard to explain but once you’ve done one or two you get it!

We downloaded the free KenKen iPad/iPhone app, which allows you to start with very easy puzzles using just addition and the numbers 1-3. I can see this providing hours of maths fact practice!

### Day 4 – Pattern Blocks: Exploring Symmetry and Tessellations

Let’s Play Math suggests investing in manipulatives that are, among other things, strew-able. Pattern blocks have definitely passed that test this week.

Pattern blocks give kids the chance to explore pattern building, geometric shapes, tessellation, symmetry and all that other mathematical stuff in an open-ended way. I’m looking forward to looking at these concepts in greater depth over the course of our maths playtimes.

### Day 5 – Story Problems

This was the simplest day in terms of set-up, and perhaps the most fun, which came as a welcome surprise to me. All we needed was a portable whiteboard and our imaginations (and a bit of patience waiting for J(8) to finish each of his long complicated stories!).

We took turns, and I think the children learned at least as much from setting me problems (and watching me work through them out loud and on the whiteboard) as they did solving them.

Here are some of the problems we came up with:

#### Story problem I started with

“If our puppy Harvey can skateboard at 5 metres per second, and the playground of our home ed centre is 20 metres long, how long would it take Harvey to skate from one end to the other?”

#### Story Problem by C(9)

(Who has recently been caring for her first flowering pot plant.) “If you water a plant every day, it grows one new flower every three hours. But you only water it every other day, so it grows half the number of flowers. How many flowers does it grow in a fortnight?”

#### Story Problem by J(8)

[Brace yourself.] “A man digs a hole 5 metres deep in 24 hours. If he sleeps 12 hours a night and has two 11 minute tea-breaks a day, how deep is the hole after 10 years?”

[I gave you the condensed version. The digging man (an escaping convict?!) ended up doing so many other things, we lost track. Once we’d negotiated relevant facts, I gamely worked out how far into the Earth’s core the man had burrowed.]

**Verdict on Week One**

We enjoyed each of our maths playtime sessions SO MUCH.

In addition to our living maths, J(8) also asked me to read Life of Fred: Goldfish to him every day. We worked buddy style through the questions at the end of each chapter.

There was also a lot of spontaneous maths play – and not just by the children!

So where are we going with this?

My goals for this term are for C(9) and J(8) to play with maths concepts, have fun with numbers and discover a bit of maths history.

My role will be to strew interesting materials, make suggestions, read aloud and – most importantly – observe. I love quietly playing detective, noticing what each child is drawn to, what comes naturally, and what might benefit from more ~~practice~~ playtime.

By the end of term in July I’ll have a lot more information about how the maths playtime approach is going. Then we’ll talk over our experiences and take it from there.

I’ll post more about our maths playtimes soon.

### Want to find out more?

My Let’s Play Math Pinterest Board

How exciting, I love how you’ve embraced this with so many different aspects of maths but also in a cross-curricular manner. Fascinating for me as a teacher!

Thank you! Yes I think maths in our house is going to look fairly scatter-gun this term – we’re going to cover a lot and then over time dig deeper. I want my kids to have a glimpse at what maths is really about – I’m looking forward to it!

I love the whole week, but I particularly like how you explored the Fibonacci sequence. So, so good. I’m stealing that for a bit of living maths in our school! Our guys would love it!!

Ooh fab – do share when you do it! I love the connection between maths and nature!

I love this! My kids’ math curriculums include lots of manipulatives & a few games, but we haven’t really looked into “living math.”

Thanks, Nichole. I love your Pinterest boards!

I love this, especially the digging man story!

What are the triangles in the first picture, and the other polygons again later? Are those a purchased manipulative, or bendy straws stuck into each other? (We had a lot of fun making similar shapes with bendy straws in our co-op group awhile back. And Maria Droujkova’s group made stars, too.)

Thank you Denise – I’m glad we’re on the right track. 🙂

Yes the triangles and polygons are bendy straws (great idea from your book!). We had started to play with them but then the postman delivered the pattern blocks and the kids couldn’t wait to get stuck into those.

I love that photo of everyone with their bendy straw polygons!

I absolutely love this post! Fibonacci sequence is such an interesting topic, and I really enjoy seeing the different ways you’ve appraoched the topic each day. I get so many good ideas here. 🙂

Thank you for your enthusiasm, it really makes a contribution over here! 🙂

When you play with Fibonacci again, Wild Fibonacci : nature’s secret code revealed, by Joy Hulme and Carol Schwartz, is a really great book (for kids) too.

I’d been wondering how to segue into golden spirals and that book looks perfect – thank you!

Thanks for all of the great math ideas. I have a math obsessed child, so I’m pinning your post and we are going to explore some of these ideas soon!

So glad you link with Collage Friday 🙂

Thanks, Mary! And thanks for hosting the wonderful link up 🙂

This is a great math post. Thanks for putting the pin button at the bottom. I pinned it and requested the Fibonacci book from the library.

We do lots of hands-on math, but follow a curriculum with the older kids. I know the hands-on approach is more fun and just as effective, but I’m interested to know how difficult it is for you to put together. I imagine it to be time consuming?!?

Thanks, Julie. It’s actually been surprisingly easy to put together so far, mainly because we already have so many resources that have been rather neglected back when I was more concerned about curriculum.

I expect someone more organised than me could spend hours planning activities in a more logical way, but if I let that stop me I just wouldn’t get around to it. So my philosophy at the moment is just to dive in and let the children explore in a fairly open ended way.

I’m better at routines than plans. My routine for this term is to play games once a week for maths fact practice (I plan to download Speed on our iPad!). Another day we’ll make up story problems. Another we’ll read a living book (see eg today’s Pythagoras post – I did make sure I had rope and lego bricks handy for that). Another day we’ll play with manipulatives (I have lots of ideas here). The final day is our crazy Tuesday so actually not much formal maths then, though they do cooking at the home ed centre so some measuring, I guess!

Stopping by from Collage Friday- great post!! I love all your math fun.

Thank you so much Laurie!