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?

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Quantum physics, GIMP and slime

C(10) learning to use GIMP

C(10) learning to use GIMP

I was going to write about our family’s approach to screen time last week. I must have been writing further outside my comfort zone than I realised, because I kept procrastinating and – well – here I am ten days later with a post about some other fun stuff we’ve been doing recently. Quantum physics, computer art and an old favourite, slime.

Slime

C(10) had a friend to sleep over on Thursday.  I find weekday playdates a great excuse to try fun projects we’ve been meaning to get around to. This week we made slime with borax, using Sci-Toys’ fun with boron recipe.  Everyone found it very cool to see their slime instantly coagulate when they added borax solution to their glue.

Polymers

Pretty slime. I love food colouring.

The older kids looked at the structure of the borax molecule and we talked about polymer cross-linking. Our slime didn’t turn out like the shop-bought kind. It wasn’t as stretchy and snapped more easily. We’ll have to experiment some more. :wink:

Do you know a good slime recipe? What makes for stretchier slime? I’m hoping one of these polymer recipes will work.

While making their slime, my kids reminisced about the many times they’ve mixed cornflour and water. C(10)’s friend had never made cornflour gak, so while I cleared away the borax mess, they made a bowlful each which they happily played with for ages.

Unschooling science - making slime

The best activities are always the messiest

Quantum physics

J(8) asked to learn about quantum physics this term, which led us to the Uncle Albert trilogy. In the first of these entertaining chapter books Uncle Albert and his niece Gedanken discover the theory of relativity. The second book is about black holes and the shape of the Uncle Albert and the Quantum QuestUniverse. And in the third book, Uncle Albert and the Quantum Quest, Gedanken finds herself in (Lewis Carroll’s) Wonderland, where she becomes small enough to examine close up the behaviour of electrons, photons and other tiny atomic components.

All three of us enjoyed the Uncle Albert books immensely. We now know a great deal more than we did about the science of the very big and the very small. We had fun testing our knowledge in the quizzes weaved into the end of each story.

On busy days when we have to leave the house at, say, 10AM, it’s easy to round everyone up for a few chapters of a good book (compared with, say, an open-ended maths session). Which makes for efficient use of time (and better maths later in the day, with a relaxed mum who isn’t watching the clock).  (How do people manage to get everyone out of the house for school by 8AM?)

What will we read next? It might be Albert Einstein and Relativity for Kids: His Life and Ideas with 21 Activities and Thought Experiments. Or perhaps The Mystery of the Periodic Table.

Learning to draw with GIMP

C(10) has spent many hours over the last few weeks creating art on the computer.  I don’t think I’ve ever seen my all-rounder daughter so passionate about one thing. She’s inspired by Canadian (homeschooled) artist Fin, whose FinsGraphics YouTube channel she’s been following for a long time.

Like Fin, C(10) likes to create Minecraft-style “blockhead” art. Fin uses Photoshop, but C(10) has found she can do most of what he does using the free GIMP software instead.

Watching C(10) learn how to use GIMP has been interesting. The complex interface frustrated her at first.  So I grabbed a computer and sat down alongside her, and we figured it out as we went along.

When C(10) saw me researching my queries I think she realised that (1) you need a bit more than intuition to use this kind of software, but (2) all the information you need is out there if you know how to look for it. Good learning.

Unschooling - computer art with GIMP

Blockhead art by C(10)

Unschooling - Computer art with GIMP

C(10)’s drawing of YouTuber Mumbo Jumbo

Here’s the picture I made on that first day we messed around together. I’m not at all artistic so I’m rather pleased with it as a first attempt, but you can see how unpolished it is compared with C(10)’s – that’s all the manual work-arounds I had to resort to because I don’t know my way around GIMP.

Unschooling - Learning computer art with GIMP

My GIMP picture (inspired by an avatar I found online but can’t find now, oops)

As well as leaving me behind on GIMP, C(10) has been using social media to share her creations with her global artist network in a way that has left me feeling rather technologically backward. Oh well, at least I know where to go for help.

March woods collage

We’ve  been enjoying the  recent spring weather too, playing outdoors with friends. (Although following our strange, wet winter it looks more like autumn, with all the leaves  still on the ground.)

I’ll keep at it with the screen time post. :wink:

***

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Hands-on Aztec History

Hands-on Aztec History - Lizard Daysign

The Aztecs dominated Central America from the 14th to 16th centuries. They founded the magnificent floating city of Tenochtitlan (modern Mexico City) and – more importantly – were among the first people to make chocolate.

We haven’t done much hands-on history lately, but discovering that the Aztecs used cacao beans as money captured our imaginations, and  soon we were off on a delightful rabbit trail.

Here are some of the activities we enjoyed during our hands-on Aztec history day.

Aztec numbers

The Aztecs used a base 20 number system. Numbers were represented with combinations of dots and symbols, grouped together in any order.

Hands-on Aztec History

Aztec numbers

I printed out copies of how the Aztecs recorded numbers. We practised with this Aztec maths activity sheet, and then had fun writing number puzzles for each other.

The Aztec calendar

The Aztec calendar consisted of three calendar wheels. The two wheels of the religious calendar interlocked in 260 different combinations, making up the 260 day sacred calendar.

The Aztecs also used a 365 day agricultural calendar. The two cycles together formed a 52 year “century”.

Hands-on Aztec History

Aztec calendar on amate by Pacofender

I’ve seen beautiful artwork based on the Aztec calendar and I was tempted to suggest that we have a go ourselves. But since we didn’t study how the calendar works in any detail, I didn’t want to dumb down a fascinating but complex subject with an over-simplified art project. We’ll enjoy exploring the maths of the Aztec calendar another time.

Instead, we used this Aztec daysign calculator to find out which (of 20) Aztec daysigns we were born under. We coloured our daysign pictures with watercolour crayons.

Hands-on Aztec history

J(8) colouring his alligator daysign

My kids love this sort of thing, and spent ages playing with the daysign calculator, working out the “daysign destinies” of everyone they know.

hands-on Aztec history

C was amused to discover that the body part associated with her daysign – the vulture – is her right ear.

Aztec chocolate

The Aztecs were among the first people to mix ground cacao seeds with seasonings to make a spicy, frothy drink they called chocolatl.  Cacao beans were such a luxury commodity that they were used as currency, so chocolatl was reserved for special occasions and important people.

Cacao or cocoa?

Have you ever wondered whether there’s a difference between cocoa and cacao? It seems that the word “cocoa” probably came about by mistake – a sort of linguistic typo that stuck. Today, we tend to refer to raw “cacao,” but processed “cocoa”.

From bean to bar

We watched this video about how cacao beans are harvested and processed. I like that it shows the cacao beans being pulled from the fruit.

The next video shows how cacao beans are processed and made into chocolate bars.

Tasting time

After watching all that chocolate being made, our mouths were watering.

Tesco sells chocolate made with beans from individual named countries. Each bar even comes with accompanying tasting notes.

Hands-on Aztec history

I couldn’t find any Mexican chocolate, but we did taste chocolate from Dominican Republic and Ecuador.

We used all our senses as we tasted, noticing how each type of chocolate looked, how it smelled, how it felt and sounded as it broke, and – of course – how it tasted.  As we tasted each bar, we looked up where its beans came from on our world map.

I recorded some of the children’s descriptions. J(8) described the chocolate from Côte d’Ivoire as “Nutty, creamy, and smooth”. C(10) thought it was “musty”!

Hands on Aztec history

Chocolate tasting notes

The children both liked the chocolate from Ecuador best.  My favourite was the Peruvian chocolate, which tasted like berries.

What about cocoa nibs?

Cocoa nibs are small pieces of cacao beans that have been roasted and removed from their husks. Cocoa nibs can be eaten raw (we weren’t impressed), or added to recipes as a healthy chocolate substitute.

C(10) decided to grind a spoonful of cocoa nibs into powder using a pestle and mortar. An hour later, she had new-found respect for the people who used to do this before modern machines were invented!

Hands-on Aztec history

C(10) grinding cocoa nibs

After all that grinding, C(10) decided to save the tasting for another day. :smile:

Aztec poetry tea

We drank Aztec-style hot chocolate for poetry tea. The recipe comes from the British Museum, but we were doubtful how closely this delicious beverage resembled the spicy drink consumed by rich Aztecs!

I read Aztec poems as we enjoyed our hot chocolate, while J(8) entertained us with an old favourite, Michael Rosen’s Chocolate Cake.

Hands-on Aztec history

Aztec hot chocolate

Websites

Aztecs at Mexicolore

Learning-Connections – Aztecs Primary Project Pages

Aztec chocolate

Videos

BBC Education (KS2) – The Aztec Empire - Good quality clips covering a variety of topics, including where the Aztecs came from and why they made human sacrifices (J(8)’s favourite).

Horrible Histories Aztecs videos

Books

The Story of the World Volume 2: The Middle Ages

The Usborne Encyclopedia of World History

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How to make a Multiplication Tower

Multiplication tower

Do you have projects pinned that you’ve been meaning to do for years? Multiplication towers was one of mine. When I first saw them on The Map is Not the Territory I knew we’d all learn something from playing with this 3D multiplication model.

The catalyst for getting around to it was a Christmas gift. My lovely parents-in-law sent us some fine meat which arrived from Scotland packaged in polystyrene and dry ice. The steaks were delicious – but you know you’re a homeschooler (or a toddler) when you get even more excited about the packaging than the gift itself. Yes, that giant slab of polystyrene was the perfect base for our multiplication tower.

What you need

Here’s where my learning curve began. (Skip this bit if you are an instructions-reader, you won’t get it.) You know how you sometimes start gathering materials for a project without consciously thinking it through?

So I had my polystyrene base, a pack of beads, and now I needed some skewers. How many? I thought of the multiplication grids we’ve been working on recently. Should our multiplication tower go up to 10 x 10, or all the way to 12 x 12? “Oh, why not go for it?” I thought, throwing caution to the wind and putting two 100 packs of bamboo skewers in my basket.

Back home, I used a sharpie to mark out a grid of 144 dots on the polystyrene. It wasn’t until I began inserting the skewers that I saw the flaw in my plan, and realised that (a) no skewer would be tall enough to hold 144 beads, (b) the 12 times table alone would use up almost all our 1000 beads and (c) as enthusiastic as my kids are about hands-on maths, I may not be able to persuade them to spend a week threading beads.

At this point it occurred to me to refer back to the project, where I discovered that Malke made a 5×5 multiplication tower, requiring 225 beads. Good idea.

Bead multiplication tower

Bead multiplication tower

I thought about making the model myself first, to make sure I understood how it worked. But after a few beads I remembered that sometimes a student learns more if the teacher doesn’t know all the answers.

So I called C(10) and we figured it out as we went along. (See the labelled photo of our Lego multiplication tower below if you’re not sure of the reasoning behind the colour-coding.)

Multiplication tower

Of course this isn’t difficult maths – many people make multiplication towers with slightly younger kids as an introduction to the concept – but it does get you thinking logically about number patterns and the commutative property.

Multiplication tower

Different views. Front left: 1 one, 1 two, 1 three, 1 four and 1 five. Front right: 4 ones, 3 ones, 2 ones (1 is offscreen)

Lego multiplication tower

I showed J(8) the Lego multiplication tower Frugal Fun for Boys made.  He enthusiastically set about gathering 2×2 Lego bricks to make his own. He only had enough bricks to make up to 4×4, but it was enough to get the idea.

Lego multiplication tower

J(8) making his Lego multiplication tower

When we compared C(10)’s bead tower with J(8)’s Lego one, we noticed they were different.  In our bead tower we had used the same colour beads for the “ones” on both the x and y axes, as they did at The Map is not the Territory. In the Lego tower, we had used different colours for each “one” on the y axis (as Frugal Fun for Boys did).

Labelled lego multiplication tower

So in the photo above, on the x axis we have a blue Lego for “1 one”, two blues for “1 two”, three blues for “1 three” and four blues for “1 four”.

Meanwhile, on the y axis, we have one blue and one white Lego representing “2 ones”, a blue, a white and a red for “3 ones” and a blue, a white, a red and an orange for “4 ones”.

The children and I discussed the two models, and decided the Lego model made more sense to us. C(10) changed her bead tower.  More great learning.

Minecraft multiplication tower

Next, C(10) decided to make a multiplication tower on Minecraft. You can’t write numbers on Minecraft so she decided to use colours to represent the numbers (the small dark blue blocks along the axes in the picture below).

Minecraft multiplication tower

Minecraft multiplication tower

She spent some time viewing the tower from different angles in a way that made me slightly dizzy. At one point she exclaimed, “Hey, look at this pattern here, on the diagonal – 1, 4, 16, 25!” She’d discovered the squares.

C(10)’s Minecraft tower reminded me to show her the computer-generated multiplication towers at Moebius Noodles. Click over to see quite how high 12×12 multiplication towers get.

C(10) decided to save her Minecraft multiplication tower in a new “Maths World” and went on to demonstrate some maths puzzles she could play with there. {I see more fun ahead.}

If you didn’t get polystyrene for Christmas

If you don’t have a polystyrene or foam block, you could perhaps use sand to support the skewers, or follow the example of Highhill Homeschool and use cotton. Or make a Lego tower.

Have you ever made a multiplication tower? Did you learn anything surprising?

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Maths – Why Faster Isn’t Smarter

Maths - Why Faster Isn't Smarter

Although both my kids are good at maths, neither of them do well under time pressure. I can relate – they get their relatively slow processing speeds from me. We enjoy mulling over puzzles, not quick-fire quizzes.

So I was immediately drawn to  Faster Isn’t Smarter: Messages about Math, Teaching and Learning in the 21st Century,  a collection of essays about teaching maths, when I saw it recommended by one of my favourite maths authors.

Faster Isn’t Smarter is set out as 41 independent messages that can be read in any order.  I personally read the whole book from start to finish on a Turkish beach (back in October, not last week – shame). I came home inspired and enthusiastic to continue our living maths adventures.

Here are a few of the many ideas I took from the book:

Faster isn’t smarter

The book’s eponymous essay, Faster Isn’t Smarter: The Trap of Timed Tests, talks about how some of the world’s greatest thinkers, scientists and mathematicians weren’t fast at arithmetic, but went on to be very successful at higher-level maths.

Maths - Why Faster Isn't Smarter

This message paves the way for a discussion about what skills are important for mathematical thinking.

Depth over breadth

In Seven Steps Toward Being a Better Math Teacher, the author suggests that most maths curricula try to cover too many topics in one year, leading to superficial coverage and little depth.  To counteract this, she advises maths teachers to identify priority topics for each grade level.

As homeschoolers we’re free to choose what our children learn, when, and how. Faster Isn’t Smarter‘s “depth over breadth” discussion has encouraged me to do what feels right for our family, despite the extensive list of topics presented in schools each year.

This doesn’t mean we have to stay on one topic for months. It just means we don’t have to rush from one topic to the next in order to get through vast amounts of material at a pace dictated by someone who doesn’t know how the individuals in our family learn best.

For example, C(10) and I spent several months exploring fractions. During our journey we played with multiples and factors, prime numbers, multiplication table tricks and probability – all led by C(10)’s interest.

She’s now using Math Mammoth worksheets to consolidate her knowledge of multiplication facts and division procedures. Most curricula would do this the other way around, teaching the facts before their fancier applications. But because we are not trying to check off a long list of other topics this year, we were able to work in the way that best suited C(10).

Knowledge is not the same as creativity

The chapter Creativity: An overlooked element in school mathematics observes that it’s not enough to teach mathematical facts and processes. Children need something more to equip them with the creativity and innovation skills they will need in the 21st century workplace.

Knowledge must blend with:

(1) “How the person approaches problems (critical thinking or problem-solving skills)”

and

(2) “The person’s motivation to be creative (especially intrinsic interest and passion)”

before we have a student who knows how to think creatively.

As homeschoolers we have the luxury of being able to spend at least as much time developing our children’s problem-solving strategies and stimulating their interest in maths as we do providing access to knowledge.

When we’re not trying to get through a hefty curriculum or long list of topics each year, we have time to play with the kind of mathematically relevant puzzles and games used by the best maths teachers throughout history.

These are exactly the kind of activities that, in our family, were too often pushed aside as “extras” back in the days when we used a maths curriculum.

A balanced mathematics program

Another essay I found especially useful was A 21st-Century View of a Balanced Mathematics Program, which describes how we can help children develop the skills to:

  • make sense of maths (understand concepts and ideas)
  • do maths (know facts and how to perform skills) and
  • use maths (solve a wide range of problems and apply the maths they’ve learned).
Faster Isn't Smarter
The author concludes by encouraging readers to combine the ideas from Faster Isn’t Smarter with other ideas in our communities. She calls for visionary, ambitious thinking and positive, connected actions to take on some of the greatest challenges in mathematics and in education in general.As homeschoolers we’re not weighed down by the bureaucracy that hinders schoolteachers from responding effectively to these challenges.  I’d recommend this very readable book to any parent in search of some fresh maths inspiration - whether you are homeschooling or supporting your child outside school.

***

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A Day in the Life of our Homeschool – With an 8 year old and a 10 year old

dayinthelife22

Each day of the week is very different for us. Some days we’re with friends all day, or we might spend a whole day immersed in a hands-on science project.

But the day I’m sharing here – Thursday – follows a similar pattern each week. Because we’re out over lunch, there’s no time for big projects. Instead, we fit in lots of shorter activities and reading aloud. It might be my favourite day of the week!

7 – 8 AM

I wake up and meditate, then come downstairs to let the dogs out.

After I’ve unloaded my part of the dishwasher, I savour the day’s first cup of tea and a bowl of porridge in my study.

P1270007  Version 2

Greeting the day. Blue(ish) sky!

8 – 9 AM

I do my daily German Duolingo lesson.

Usually I catch up on emails and blogs at this time, but today C(10) gets upset while practising her guitar and needs a pep talk. She’s having difficulty adjusting to her new teacher, and is being a bit tough on herself. I give her a cuddle and remind her that she can’t solve anything when she’s feeling down. She agrees we’ll talk about it again later when she’s feeling better.

9 – 10 AM

J(8) asked to learn about quantum physics this term. The Uncle Albert books are a wonderful introduction to the subject. Last week we heard about special relativity in The Time and Space of Uncle Albert.

Today I read aloud from Black Holes and Uncle Albert, a story about “the exploding universe …  black holes that swallow up everything, speeded-up time, light that is yellow but also red and blue … and how it is that you are made of stardust.”

Lots of big ideas to talk about as we read!

Day in the Life of a Homeschool  Read Aloud time

J(8) asks to try tea, so I make him a cup of lemon and ginger with a dash of agave. He’s not impressed!

10 – 11 AM

C(10) and I do Latin and then maths together. Right now we’re working through Math Mammoth’s Division 2. Although we don’t follow a curriculum, individual books from the Math Mammoth Blue Series are great value when a child needs extra practice on a particular topic.

C(10) fills in the answers on her iPad using Notability  ”This is fun and kind of relaxing,” she casually comments as she works. {I mentally punch the air.}

A Day in the Life of a Homeschool  Latin  Maths

J(8) plays with Lego in his room. He tells me about the RPG game he’s invented with them.

P1270041  Version 2

11 AM – 12 PM

We leave for French class at 11:40 and we’re not back until 1:40, so we eat pancakes before we leave. I read aloud from Puddles in the Lane, a lovely story about a family of children evacuated from the London Blitz during World War II.

P1270046  Version 3

Pancakes and reading aloud

12 – 2 PM

C(10) has 15 minutes one-to-one with the French teacher before J(8) join them for an hour. I walk the dogs in beautiful nearby woods. The children emerge from their class with Valentines “coeur” cookies.

Day in the life of our homeschool  French  woods

French Valentine cookies and dog walking

2 -3 PM

After lunch (soup and sandwiches), I practise guitar while the children play Minecraft together.  J(8) is paying her Minecraft gold to build houses for him in a world he’s created.

P1270058  Version 2

Playing Minecraft together

3 – 4 PM

I do maths with J(8).  I suggest that he tries the division pages C(10) enjoyed earlier.  As soon as I read out the first question, J(8) starts to roll around the floor on a space hopper.

I have an epiphany. It occurs to me that J(8) has as much difficulty concentrating on maths while he’s sitting still, as I do when he’s leaping around the room. (Sometimes I need to be reminded of something a thousand or so times before the penny finally drops.) I decide that as the grown-up, I need to to overcome my difficulty focusing, and find a way to accommodate J(8)’s wiggles.

It works! We actually manage to maintain enough momentum for him to learn some new maths.

Day in the Life  J doing maths

This much movement in 30 seconds of maths!

Meanwhile, C(10) mixes up a batch of chocolate chip cookie dough. We bake six cookies and freeze the rest.

P1270069  Version 2

C(10) making cookies

4 – 5 PM

We enjoy C(10)’s cookies at Poetry Tea. She reads an extract from The Pied Piper, from our new poetry book, A Child’s Introduction to Poetry (thanks, Lisa), and “Double, double, toil and trouble” from Macbeth.

J(8) chooses poems from A Children’s Treasury of Milligan, which he received for Christmas. J(8)’s comic narration and Spike Milligan’s poetry are a match made in heaven; C(10) and I are very grateful to Santa!

Day on the Life of our Homeschool  Poetry Tea

Poetry teatime

After poetry tea, C(10) asks me to join her while she practises guitar. She plays beautifully, this morning’s upset long forgotten.

Thank you, Hwee, for the inspiration to join Simple Homeschool’s Day in the Life series!

***

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Love in 18 Languages (+ printable)

Love valentines project

When I came across the book Creative Lettering  at Mothers Daughters Sisters, I knew C(10) and I would enjoy doodling with the fun fonts it contains.

I also love foreign languages, and dabble with them at every opportunity. So I was most over-excited when I had the idea for this Valentines-inspired art project: writing “love” in 18 different languages.

Love Valentines Project

I put together the “love” translations in this document {free printable PDF} and made us each a copy. The languages include German, Italian, Spanish, Portuguese, Swedish, French, Japanese, Chinese, Russian, Arabic and Greek, plus seven more.

Love Valentines Project

Then we sat doodling together for a happy hour or so. We used Creative Lettering for font inspiration but if you don’t have the book you can find plenty of instant, free inspiration with a google image search for fun fonts.

As we wrote the different words, we commented on the similarities and differences between the different languages. We contrasted the word for “love” in the Romance languages (amor, amore, amour) with the Germanic words (Liebe, Liefde). We noticed how similar the Russian and Croatian words are.  And how alike the Mandarin Chinese and Japanese characters are.

Love Valentines Project

Once we had checked off all the languages, we doodled in the blank spaces.

Love Valentines Art Project

Then, after C(10) had wandered off to compose a song, I carried on tinkering with our creations. I photocopied them onto pastel coloured paper and put eight together to make a poster which is now adorning one of our homeschool supply cupboards!

Love Valentines Art Project

We had so much fun with this project. We might repeat it another time with other words – perhaps, “happy”, “spring”, or “joy”.

Do let me know if you try it!

Love Valentines Art project

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The Science of Flying

 

science of flying

“What makes aeroplanes fly?” asked C(10) a few weeks ago. We’ve had fun finding out.

An aircraft flying in steady forward motion is subject to four forces:  thrust, drag, lift and weight.  Aviation for Kids: A Mini Course For Students in Grades 2-5 (free online) contains dozens of ideas for experimenting with these forces.

Thrust

Thrust is the force that moves a plane forward through the air. To investigate thrust, we made three different “aircraft”, each powered by a different thrust mechanism.

1. Elastic band thrust

First, we made elastic band-powered planes. We experimented with thrust by observing the distance our planes flew when we changed how far we pulled our elastic bands before we released them. {Instructions are on p3 of Aviation for Kids.}

science of flying

science of flying

Rubber-band powered planes

In real aircraft, of course, thrust is created by a jet engine or propeller.

2. Air pressure thrust (blowing through a straw)

science of flying

Air pressure-powered planes

Our second aircraft was powered by blowing through straws, one inside the other.  {For instructions see p7 of Aviation for Kids.}

We experimented with placing the wings at different points along the straw and observing the effect on our aeroplanes’ flight.

C(10) suggested a competition to knock down unifix cubes with the planes.  It was more difficult than she’d expected!

science of flying

3. High air pressure thrust (balloon power)

We made a balloon-powered rocket when we learned about space travel last year. The kids were delighted to recreate it as part of our investigation into thrust and drag. {See p 10 of Aviation for Kids for instructions.}

science of flying

Balloon-powered plane

Newton’s third law states that for every action, there is an equal and opposite reaction – as the balloon deflates, it whizzes along the wire. It’s very cool!

 

Drag

Next, we investigated drag – the air resistance that slows an aircraft as it moves forward. If drag is greater than thrust, the aircraft cannot move forward.

To see the effects of drag, we attached a foam plate to the front of our balloon aircraft.

science of flying

Investigating the force of drag

When it was subject to the increased drag of the plate, the balloon only managed to travel halfway across the room before it ran out of air.

Apparently it was hilarious to lie underneath the wire as the balloon zoomed to a halt.

science of flying

“It’s coming at us!!”

 

Lift

The other pair of forces that operate on an aircraft are lift and weight. Lift is provided by the airfoil shape of an aircraft’s wings.

If you look up how planes fly, you find many references to Bernoulli’s principle. But some scientists think that lift can be explained perfectly well by Newton’s laws – that aircraft are forced up by the vast amount of air that the wings throw down.

Bernoulli’s principle

Whatever role it plays in helping planes fly, Bernoulli’s principle is fun to demonstrate, partly because it’s counter-intuitive.  We demonstrated Bernoulli’s principle in two ways.

First we placed a sheet of paper between two books. We blew through the gap.

science of flying

Investigating Bernoulli’s principle

The children had predicted that the paper would lift up as they blew underneath it. Instead, the paper sagged down. Bernoulli’s principle says that within a stream of fluid (such as air), pressure goes down as speed of flow goes up.  So when we blew, the air pressure under the paper decreased and atmospheric pressure from above pushed the paper down.

We also demonstrated with ping pong balls and a hairdryer. J(8) especially liked this one as he got to use a gadget.

science of flying

Demonstrating Bernoulli’s principle with a hairdryer and ping pong balls

When the hairdryer blows fast-moving air between the ping pong balls, air pressure between the balls decreases. Atmospheric pressure outside the balls pushes them together. (This doesn’t happen when you aim directly at the ping pong balls, but J(8) had fun doing it anyway.)

How do wings produce lift?

Lift is created by the curved shape of an aeroplane’s wing. This “airfoil” shape causes air to move faster over the top of the wing than the bottom. When lift is greater than the weight of the plane, the plane will move upwards.

We made paper airfoils and attached them to thread (see p25 of Aviation for Kids).

science of flying

Airfoil shape

When we ran with our airfoils, they moved up the thread.

 

The airfoil also lifts when you spin around very quickly. This one was repeated many times!

 

(Aviation for Kids also suggests pointing a hairdryer at the airfoil. We did this but found it difficult not to blow the paper wing directly up or down.)

Weight

To experiment with weight, we made the world’s best paper aeroplane. This plane has great lift!

science of flying

“The world’s best paper aeroplane”

Then we increased the plane’s weight by attaching paperclips. It was easy to see that the extra weight reduced the plane’s lift. One paperclip actually had a stabilising effect, making the plane easier to direct. Two or three clips seriously impacted our planes’ ability to stay in the air.

science of flying

Investigating the force of weight

What next?

C(10) has been making notebook pages about the science of flying. She’s come up with lots more questions as she’s been writing!

Science of flying

C(10)’s notebook pages

Our science this month is going to focus around the exciting engineering box we’ve just received on loan from the James Dyson Foundation, but we’ll definitely be continuing with the science of flying after that.

Further resources on the science of flying

Up, Up and Away: The Science of Flight (favourite)

Flight aerodynamics video  Explains how the four forces of flight operate (turn up the volume to compensate for the narrator’s monotone)

Bernoulli’s paper airplane experiment

Airfoil lifting force misconception

BBC Bang Goes the Theory Bernoulli’s principle and wings

Science kids – Flight lesson plans

A physical description of flight; revisited Technical article on how aeroplanes actually generate lift, and the Newton v. Bernoulli debate

***

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Chinese Year of the Horse Art Project

chinese year of the horse art project We celebrated Chinese New Year by doing a really simple, fun art project. First we reminded ourselves what we learned last year about how Chinese (lunar) New Year is calculated.

What Determines the Date of Chinese New Year?

Chinese New Year always falls between January 21 and February 21. Within this range, there are two rules of thumb used to calculate the exact new year date.

The first rule of thumb is that the new year falls on the new moon closest to the beginning of spring (in the northern hemisphere). But if the beginning of spring falls halfway between two new moons (as in 1985 and 2015), the second rule of thumb is used.

The second rule of thumb is that most of the time Chinese New Year will fall eleven (or sometimes ten or twelve) days earlier than the previous year, but if that means that the event would be outside of the possible range (January 21 to February 21), a leap month is added, so Chinese New Year jumps nineteen (or sometimes eighteen) days later.

Story: The Great Race

We read The Great Race: The Story Of The Chinese Zodiac, a beautifully illustrated picture book which tells the story of how Emperor Jade, the King of Heaven, holds a race to decide the order in which to name the twelve years of the Chinese calendar. The Great Race

Art

2014 is the Year of the Horse. We watched Artchoo’s tutorial on how to draw the Chinese character for “horse”, and did the simple watercolour painting project there.

year of the horse art

C(10) used a paintbrush dipped in ink to write “Happy New Year”

J Chinese New year

J(8) has broken his writing wrist, so he stuck to cutting and pasting most of his Chinese characters!

chinese year of the horse collage

Chinese New Year Homeschool Project

Making Year of the Snake art last year

Goodbye, Year of the Snake – hello Year of the Horse!

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Awesome Arithmetricks – Simplifying Equations

awesome arithmetricks - simplifying equations

My children (8 and 10) don’t spend as much time doing sums as other children. Whereas most elementary maths curricula focus on arithmetic, we work on a balance mathematical skills, including critical-thinking and problem-solving. One of my main aims is to stimulate my kids’ interest in and passion for maths.

A place for arithmetic algorithms

But I do want my kids to be number-confident – they need to be able to use arithmetical algorithms. I have two priorities here. I want them to be proficient at using algorithms (to accurately follow step-by-step procedures). I also want them to know how the algorithms work (why they are using them).

Murderous Maths: Awesome Arithmetrics

Murderous Maths: Awesome Arithmetricks is the perfect way to review arithmetic skills and develop number sense.  C(10) and I are reading the book at the moment. We enjoy the jokes and the story, and stop to practise procedures whenever we need to.

(We got our copy of the book as part of the Murderous Maths boxset.)

How we use Awesome Arithmetricks

We do maths side-by-side on the sofa, mini-whiteboards and hot cups of tea to hand (we’re English, after all). We keep manipulatives and iPads within easy reach, and grab them to work through concrete examples, play a game or do a few drills. (C(10) used this free subtraction app yesterday, for example. Maths apps don’t get much more basic but it provided the instant, no-frills practice she wanted.)

Awesome Arithmetricks is divided into four sections –  addition, subtraction, multiplication and division. But it contains a lot more than the basics. Examples are given within entertaining stories, and questions are posed as puzzles.

Simplifying equations

This week we worked through the section on simplifying equations. We learned four tricks to making an equation prettier:

  • Always treat both sides the same
  • An operator sign must stay with the number that comes after it
  • You can swap both sides over completely if you want
  • If you move a number to the other side, you must change its sign. (I drew a diagram of balance scales and we went through the in-between steps that make this so.)

Puzzle – Spot the lethal equation

Students then test their understanding by tackling this puzzle (taken from Awesome Arithmetricks):
“You have just been bitten by a fearsome two-headed Arctic ice snake. Already your blood is starting to freeze solid, but in front of you is a cabinet of mathematically prepared antidotes which were made up from the equation:

awesome arithmetricks - simplifying equations

Three of these bottles have correct equations on them, but the fourth could be LETHAL! You haven’t time to work all the sums out, but by altering the original formula using the tricks, can you see which three equations are correct?”

awesome arithmetricks - simplifying equations

C(10) enjoyed this puzzle so much she worked through it several times over the course of a week.

Dragon Box Algebra – An algebra game

Dragon Box Algebra 5+ is a fun puzzle game that teaches kids the principles of algebra. It perfectly complements a study of simplifying equations. (The game is available for most computers and mobile devices.)

C(10) worked through all the levels of the app a few months ago (for fun). So, after we’d read about simplifying equations in Awesome Arithmetricks, we played with a few algebraic equations.  C(10) enjoyed solving them using what she’d learned playing Dragon Box Algebra and reading Awesome Arithmetricks.

Awesome Arithmetricks - simplifying equations

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