# 5 Days of Maths Playtime

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!

### 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?

Fabulous Fibonacci

# Let’s Play Math

Let’s Play Math by veteran homeschooler (and maths blogger) Denise Gaskins is the maths book I’ve been looking for ever since we began homeschooling.

Three things set it apart from any other maths book I’ve come across:

1.  It’s incredibly readable.  I found myself going to bed an hour early every night to enjoy it, and had read it cover-to-cover within a few days.

2.  It’s chock full of suggested resources. These alone are more than worth the cover price. The Kindle version allows you to click straight through to the linked websites – brilliant.

3.  It’s comprehensive. Combined with all the linked resources, this book is going to transform how I teach my kids maths. No more dabbling in “real maths” but then running back to the workbooks when anxiety strikes (me) – with this approach I can teach my kids to think like mathematicians without worrying about leaving gaps.

### Why Learn Maths?

Why do we teach our children maths? So they can become mathematically literate adults, able to calculate their taxes and mortgages? To pass exams which will allow them to get into college or the job market? Both good reasons.

The problem is, many of us are so anxious about failing to do these things that we deprive our children of perhaps the most important reason to learn maths of all: because maths is beautiful, and fun.

### The “Aha!” Factor

Humans are hard-wired to enjoy puzzles. When we learn something new, we receive a hit of the feel-good hormone dopamine. When the new information comes as a surprise, we get a double dopamine hit. That’s why “Aha!” moments, like when we get the answer to lateral thinking puzzles, feel so good.

Let’s Play Math is about cultivating the “Aha!” factor in our children.

### Living Maths  – Where to Start?

Anyone who surfs the educational ‘net knows that there are plenty of creative maths ideas out there. But this abundance of resources can be overwhelming. As Denise says, “It seems easier to shove a textbook across the table and say, ‘Work two pages'”, leaving someone else to make all the decisions.

Let’s Play Math cuts through the overwhelm.

Here are some of my favourite topics covered in the book:

#### Hands-On Maths

I use hands-on methods throughout our homeschool, but I’ve never felt very confident with maths manipulatives. (On the rare occasion I do manage to bring them in I get very excited and blog about it.)

Let’s Play Math has a section on buying manipulatives (ask questions like “is it strew-able?”, “is it worth the storage space?”) plus a section on homespun manipulatives, together with lots of ideas for using them.

#### Maths History

“I am sure that no subject loses more than mathematics by any attempt to dissociate it from its history”.

James Glaisher, quoted in Let’s Play Math

What is it about maths that has parents who use living books throughout our homeschools reaching for the textbooks?

History is full of men and women so fascinated by this subject that some of them overcame extremely oppressive circumstances to find a way to pursue their passions. When we share their stories we give our children a taste of the excitement of maths.

“What a shame it is that our children see only the dry remains of these people’s passion. Worksheet exercises are the bare, abstract skeletons of what once were living puzzles.”

Let’s Play Math suggests devoting one maths lesson a week to maths history, and offers plenty of ideas on how to choose good living maths books. There’s even a whole chapter entitled “4,000 Years of Stumpers” – puzzles that have challenged mathematicians throughout the ages.

#### Story Problems

Denise suggests that we might measure homeschool maths success by whether or not our children fear story problems, and the book is full of tips and resources for using story problems effectively. One of my favourite is to take turns, adults included – getting the chance to challenge Mum always goes down well in this house! Taking turns makes maths into a game.

#### Older Children

My two are only 8 and 9 at the moment but after reading the chapter on the “Transition to ‘Higher’ Math” I believe we can use this approach throughout all our homeschool years, including those when my children might be taking exams.

The book suggests different approaches for the teen years depending on whether a child has had a good taste of the “Aha!” factor during the elementary years.  Once a teen is ready for textbooks:

“Don’t be fooled by your own experience of dry or tedious math classes: textbook mathematics is still math the mathematician’s way, as mental play.  But it is no longer the play of a child dabbling in the shallows… No, this is the play of the athlete, who works hard at training and enjoys seeing his muscles grow firm, who can’t wait to test himself against a new and challenging opponent.”

### Let’s Play Math as a Supplement

I intend to use Let’s Play Math as our maths “spine” but, like Project-Based Homeschooling, I think you can do as much or as little of it as fits with your individual homeschool style.  Read the book, feel inspired, and do whichever activities sound like fun to you.

### Putting it into Practice

My favourite section of the book is “One Week of Real Mathematics”, which contains examples of what one week’s worth of math playtime might look like. I love having this starting point to show me what a balanced “maths diet” might look like.

My kids have a low tolerance for boredom and are very outspoken when something isn’t working for them, one consequence of which is that we threw out maths curriculum some time ago.  Since then we’ve read maths biographies, played with platonic solids, and enjoyed solving story problems – with the odd workbook thrown in here and there when I get the “Argh! I’m leaving gaps!” anxiety.

I feel like I’ve been ambling in the woods – enjoying the journey but a bit anxious about where we’re going to end up and whether we’re going to reach our “destination” “on time” (whatever that means!).

I knew the well-travelled road (maths curricula) wasn’t for us, but I lacked confidence in my ability to guide my children through uncharted territory. Let’s Play Math is the map and the guidebook I’ve been looking for. With it in my hand I can’t wait to take my children by the hand and head off to explore the wonderful world of maths.

* I was not paid for this review.  I bought my own copy of the book and I’m writing to share this great resource with other parents.

# Logic Game – Mastermind

Our favourite resource this week was a charity shop find – the game Mastermind.

Mastermind is a logic game in which one player (the codemaker) places four differently coloured pegs (out of a possible eight colours) in a row, and the other person has up to twelve chances to crack the code.

The codemaker gives feedback by scoring each guess according to how many pegs of the correct colour it contains, and how many of those are also in the correct position.

I was amazed at how educational this game is – something I hadn’t noticed at all when I played it as a child.  Playing recently my brain has at times felt quite scrambled figuring out the logic of my next guess!

One of the reasons Mastermind works so well in our house is because it’s not directly competitive. The codebreaker’s goal is to crack the code in as few guesses as possible and although theoretically the codemaker’s goal is for the code not to be guessed at all, in practice we were all rooting for the codebreaker!

If you don’t have the game, you can play Mastermind with pen and paper. There’s also an online version and a free iPhone app. A great way to develop logic skills and have fun together at the same time.

# Popsicle Stick Fractions

We got out the popsicle sticks this week to help C(9) understand the meaning of fractions like 5/8 of 24.

### Memorising Algorithms v. Understanding

C had no trouble calculating one eighth of twenty-four. There’s an easy-to-understand algorithm:

1/8  of  24  =  24  ÷ 8  =  3

But algorithms don’t facilitate real understanding.

This became apparent when we changed the numerator of the fraction. C is a bright girl and it wouldn’t have taken her long to memorise the extra step in the algorithm:

3/8  of  24  =  (24  ÷ 8)  x  3  =  9

But I wanted her to understand what was actually happening here.

Bring on the popsicle sticks!

The equation C was working on at this point was 3/10 of 70 (because of the numbers involved, the answer “30” kept jumping in to her head). This was going to take a lot of popsicle sticks!

### A Maths Story

We gathered 70 plain popsicle sticks.  These, we decided, were 70 new children starting out in kindergarten. (Don’t ask me how this metaphor got into our homeschooling house.)

Then we found 10 coloured popsicle sticks. These were helpful grade 5 children who were looking after the kindergarteners for the day.

One by one, we distributed the seventy plain sticks equally between the ten coloured sticks, until each “older child” had seven “kindergarteners” to look after:

1/10  of  70  =  7

This step, naturally, involved many imaginary conversations between the children, some of whom were rather wilful!

Next step – different numbers of groups of “children” were taken “to see different parts of the school”. Of course it was important to count the number of children at each point, to make sure we didn’t lose any!

So:

• Two of the groups went to see the science room. “Now then, how many children do we have here? Are you all going to fit in the science room? Let’s count. One, two, three … fourteen. Yes, you should be all right. Off you go.”

2/10  of  70  =  14

• Seven of the groups went to see the gym. “How many children is that? Goodness – forty-nine!”
7/10  of  70  =  49
• Three of the groups visited the art studio. “How many paintbrushes do we need for you all? One, two, three … twenty-one.”
3/10  of  70  =  21

And so on. So much fun!

### From Concrete to Abstract

C went on to complete a page of abstract problems with no trouble. As she practised, she came to recognise the algorithm as a convenient shortcut.

3/8  of  24  =  (24  ÷ 8)  x  3  =  9

But thanks to ten minutes of popsicle stick fun, she now understood what the numbers represented.

Do you use stories in your maths lessons?

For more maths ideas, visit the Math Monday Blog Hop at love2learn2day, and the Math Teachers at Play monthly carnival at Learners in Bloom.

# What we’re Doing for Grade 2 and 3 Maths

I last wrote about how we found our perfect math curriculum back in March, so I thought it might be time for an update…

### Jasper (7, Yr3/Gr2)

#### Life of Fred

Maths is still Jasper’s favourite subject, thanks to Life of Fred.  This term we finished Life of Fred (Edgewood) and began Life of Fred (Farming).  I love the way the Fred series mixes up basic fundamentals (such as subtraction with borrowing) with more sophisticated concepts (like union of sets, median averages and simple algebraic equations) in a way that introduces young children to advanced mathematical vocabulary in a very natural way. And, of course, we all love “Fred’s” delightfully quirky story and offbeat humour.

#### Games

Because we’re not doing a traditional curriculum, I make sure Jasper gets plenty of extra opportunities to learn his maths facts. Luckily he loves games, which are a great way of getting the job done.  Recently we’ve played Yahtzee  and War . (My favourite maths website, Let’s Play Math has lots of ideas for maths games. I’ve just noticed Contig, which looks great – we’ll be playing Contig Jr next week!)  We also play games like Tug Team Addition  at Math Playground, and Jasper practises multiplication using Arithmemouse and Timez Attack.

One benefit of working with a child one-to-one is that you get instant feedback on how easy or challenging he finds each concept.  So in Life of Fred (Edgewood) I noticed Jasper was a bit confused about the differences between rhombuses, trapeziums and parallelograms, so I set him some exercises on Study Ladder.  He loves working online, especially on specific exercises (rather than working his way through an online curriculum in a linear way – for example, Maths Whizz didn’t work so well for us for any length of time) so this is win/win.

### Cordie (8, Yr4/Gr3)

Cordie recently decided to take a break from Life of Fred (she was on “Farming”) to explore some other resources.  She did a few exercises from a Schofield & Sims KS2 workbook we had on the shelves and asked me to set her some “surprise” Study Ladder exercises.  One day she asked me to make her a page of clocks so she could brush up on telling the time, and another day she wanted a page of multi-digit subtraction sums.  She played around on Khan Academy for a while, watching videos on decimal place values and then setting herself some problems to solve. And she dipped into Math Mammoth’s Division 1 (filling in the answers on the iPad using the Notability app).

Following her explorations, Cordie says she’s ready to go back to more of a maths routine with Life of Fred.  Before that, though, we’re doing some times tables practice using Maria Miller’s structured drill system from Math Mammoth Multiplication 1.

I’ve looked ahead at all the Life of Fred elementary level books (up to “Jellybeans”) and they seem to cover everything on the English KS2 curriculum. As with Jasper, if Cordie needs or wants extra practice on a particular topic as we go along, there are plenty of other resources we can dip into.

Writing this post has also reminded me how much we all like Primary Grade Challenge Math which teaches mathematical thinking and problem-solving in a fun way.  We haven’t used Challenge Math in a while but I’d like to get back to using it regularly, perhaps once a week.

Isn’t it great how many fabulous homeschool maths resources are out there? There really is something to suit everyone, at every age and in every mood!

# Marshmallow Geometry Fun

Cocktail sticks and a pack of stale mini marshmallows are perfect supplies for some 3D marshmallow geometry.
We started out with simple shapes.

I wanted to make a fractal tetrahedron like these, but it turned out  trickier than  anticipated, especially without the instructions to hand.

My creation wasn’t very geometric! I’ve since read that the trick is to start with a flat base instead of a single tetrahedron.

Kinaesthetic learners will love this hands-on activity.  You end up with lightweight, tactile shapes that, thanks to the squidgy marshmallows, are strong enough to play around with until you’re satisfied with your shape.

J made me think of those creativity tests as he reeled off things his simple models could be (radiator, ladder, goalpost…).

As we played J asked if  we could have “Poetry Breakfast”.

It occurred to me how different my children’s first hearing of “Macavity The Mystery Cat” was to my own, in a classroom!