Fractions come early in the new Primary Maths Curriculum

This week sees the start of a new primary maths curriculum in England – here’s my previous article summarising the changes.

One change is that fractions are to be introduced earlier – in year 2. This makes sense since children have a pretty intuitive understanding of fractions by age 6. 

As our “Introduction to Fractions” video suggests, children become aware of fractions at the dinner table - so don’t miss this opportunity to discuss them. Of course if there are always four of you sharing the pizza it can get a bit predictable – so mix it up and ask some “what if” questions such as “what fraction would you get if there were five of us?”

Welcome back Roman Numerals

Another quirky addition to the curriculum is Roman Numerals up to “XII” in year 3 and “M” in year 6.  The rationale is to help preparation for algebra because we have letters representing numbers – however Roman numerals have a pretty unique pattern. Let’s see if you can remember or guess some of these:

IV

VII

IX

XI

MCXII

 

Answers at the bottom of the page.

Fluency and Number Sense

The new curriculum has a welcome emphasis on fluency and frequent practice in maths. This is something we also see as essential for success in maths.

Here’s what the new curriculum says:

“AIM:

become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately”

It’s worth remembering that the changes to the curriculum aren’t everything. More significant is their teacher, the school and last but by no means least, home and family support for learning. Meanwhile here at Komodo we’re incorporating the relevant changes to the curriculum to ensure we continue to complement classroom maths.

And the Roman Numeral answers are:

  • IV (4)
  • VII ( 7)
  • IX   ( 9)
  • XI  (11)
  • MCXII   ( 1112 )  the primary curriculum goes up to 1000  ( M) but most Y6 pupils will be able to work this out.

 

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Parent’s Tips for Summer Holiday Learning

tramore

Having returned from a great weeks holiday in Donegal on the North West tip of Ireland I’d like to share a few thoughts and – hopefully useful –  tips on learning in the summer holidays.

Our annual holiday to Donegal is always tinged with trepidation because the weather, even in July, can be appalling. This year, thanks to a last minute shift in the jet stream, we lucked out on blue skies and freak temperatures in the low twenties. Add this to the usual beautiful clean empty beaches and who could ask for more! This year James and Kate’s holiday highlight was a trip to Tory Island. Not so much for the island itself, but for being tossed around and drenched by the swell on the tiny ferry boat that took us there and back. It was refreshing that the boat’s Captain had an old fashioned attitude to health and safety – or the fun would have been missed.

The Summer Slide

“The summer slide” is the term given to children’s educational gains evaporating during the summer holidays. Some writers have described this in a pretty alarmist way. In his book Outliers Malcolm Gladwell makes much of the “agricultural school calendar” being responsible for the US and European education systems falling behind Asia. His solution – have a two week break instead.

It’s no doubt true that 6 weeks – or 8 weeks in Northern Ireland & Scotland -  of summer holidays without stimulating our children’s brains is not going to do them any favours when they return to school. That said, having say 2 weeks of complete down-time while away from home is invaluable for de-stressing our kids and ourselves. Like all things parenting it comes to common sense and moderation. Here are a few tips & ideas for learning activities that will keep little minds active during the summer holidays - apologies in advance for stating the obvious:

2014-07-24 09.49.54

Reading Hour

Reading is one of the best habits we can pass to our kids and its educational value is immense. Of course these days kids will default to grabbing the ipad or watching TV – so I think it’s important to switch all screens off for a while each day. Here are some some reading suggestions from James – suitable for ages 9,10,11:

  • The “Percy Jackson” Books by Rick Riordan – no cover photo because he’s passed them all on
  • The “Alex Rider” books by Anthony Horowitz
  • Everything by Michael Morpurgo

Kate’s favourites include:

  • The “Pippi Long Stocking” Books by Astrid Lindgren
  • The Borrowers books by Mary Norton
  • everything by Michael Morpurgo too
  • Matilda – Roald Dahl

What about the 5,6,7  year old reading list?

I’m a big fan of clearing out the cupboards so we’ve passed most of our early reader books on to younger cousins. I would certainly recommend everything Roald Dahl, especially The Twits, Matilda and Charlie and the Chocolate Factory, but beyond that I’m hoping you guys might help by posting some suggested reading on our Facebook page or using the comments below - please add the age too!

All Things Crafty

Kids love a craft project but it can be difficult for parents to organise. The good news is it gets easier as kids get older. Here are a few great craft products that require little parental organising.

Kate, and lately James, are fixed on creating multi-coloured bracelets with her rubber bands and loom. The patterns are quite intricate and need a bit of mathematical thinking – and there are hours of dedicated weaving ahead!

loom

 

As you may already know we’re big fans of the Paper Toy Monsters book. This was a life-saver a few years ago when we weren’t so lucky with the Donegal weather. Suitable for age 5 to 9, all you need is glue and scissors and away you go.  Here’s a nice French site with some great free paper-toys to get you started:

Papertoy-Monsters

There are endless crafty possibilities – here’s a site with hundreds of craft projects split into age ranges. If you have any crafty tips please post them on our facebook page or in the comments below.

 

chess

Chess

Chess is a great way to develop mathematical thinking because it’s all about patterns and strategies. If your kids are new to chess it’s useful to start by using an app which shows you all the possible moves when you select a piece - this is a great way to learn the rules & moves while playing. Here’s a great free chess app for android and here’s one that looks good for ipad / iphone.

Komodo

Komodo is a great way to avoid sliding back in maths during the summer holiday. There’s no need to double the effort just because there’s no school. I’d recommend - after two weeks of complete downtime - continue using it as normal for twenty minutes, five times per week. Komodo is designed to be effective in a short time – minimising the time kids spend at the screen – so once they’ve used it your kids can get outside to burn off some energy.

Happy Holidays!

Jane,

Co-founder of Komodomath.com & mother of James & Kate

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The Mathematical Brain – How Children Learn to Count

Learning to Count

 

Counting is easily taken for granted but there’s a lot of fascinating research into how we learn to count – and there’s more to it than you may think.

The Mathematical Brain

It’s first worth considering where our capacity to do mathematics comes from. Neuropsychologist Brian Butterworth in his book “The Mathematical Brain” suggests we’re born with an innate sense of number hard wired into our brain and he attributes this to a small region of the brain behind the left ear he calls “the number module”. He compares this idea to colour – in the same way we perceive the “greenness” of a leaf we can also perceive the “twoness” or “threeness” of a group of objects. Take counting. Like times tables and algebra, we tend to think it’s something kids have to be taught. Wrong, says Butterworth – it’s an instinct. Sure, we have to learn the names and symbols of numbers to develop that instinct, but, because the number module is hard wired into the brain, basic counting comes naturally. Remote tribes can count even when they have no words for numbers. In maths as in language he believes, “kids start off with little starter kits” And their maths starter kit is the number module. There are other theories too – such as maths being an extension of our spatial awareness – but there’s something nice in the idea of a “little maths starter kit”.  A Word of warning - All this doesn’t mean a child is predestined to be either good at maths or not. Far from it, we’re all born ready to learn maths – and it’s what happens in the first 10 years or so that sets us up.

Counting With Toddlers

Research suggest that toddlers – even as young as 12 months – have a sense of how many there are in a set – up to around three objects. This comes from their innate sense of number. Counting is learned when the toddler starts making the connection between this innate sense of “how many there are” and the language we use to count “one, two, buckle my shoe”. This is the first stage in learning maths and it’s the building block for many early concepts. Should parents count with their toddlers? Absolutely, using a variety of real objects. And since counting and language are interlinked reading to your toddlers is equally if not more important.

Counting – early learning milestones

Here are some stages of learning to count that you may notice your child going through at ages 3 to 5:

  • Recognising how many objects are in a small set without counting. So if you show your child four apples they won’t have to count them to tell you there’s four.
  • Knowing the “number words” from one to ten and their order.
  • Know the sequence regardless of which number they start on. So if you say “start counting at four” they will count “four, five . .” as opposed to always counting from one.
  • Conservation of quantity – This is where children realise that the number of objects in a set stays the same unless any are added or removed. So if they count six cans of beans in a straight line, then you rearrange the beans ( in front of their eyes ) into say two stacks of three – they will realise there’s still six without recounting.
  • Counting non-visible objects – your child will realise they can count things they can’t touch or even see – such as sounds, members of someone else’s family, or even ideas.
  • Cardinality, not to be confused with carnality - This is knowing that the last number counted is equal to the quantity of the set. If your child counts six oranges 1,2,3,4,5,6 and then you ask “how many oranges are there”? and they count them again then they haven’t grasped “cardinality”.

Counting on – as a step towards adding

Learning to add comes as an extension of counting. Here are some stages a child goes through to make this connection:

  • Counting all – For 3 + 5, children will count “one, two, three” and then “one, two, three, four, five”  to establish the quantity of the sets to be added – for example, three fingers on one hand and five fingers on the other. The child will then count all the objects “one, two, three, four, five, six, seven, eight”
  • Counting on from the first number – Some children come to realise that it is not necessary to count the first number to add. They can start with three, and then count on another five to get the solution. Using finger counting, the child will no longer count out the first set, but start with the word ‘Three’, and then use a hand to count on the second addend: ‘Four, five, six, seven, eight’.
  • Counting on from the larger number –  It’s more efficient when the smaller of the two numbers is counted. The child now selects the biggest number to start with which is “five”, and then counts on “six, seven, eight”.
  • The final stage isn’t really counting – it’s where learners know their number facts and skip the time consuming counting altogether.

Number lines are great visual tools for making this connection between “counting on” and addition or subtraction – we use them in Komodo a lot. Here’s an earlier blog article all about number lines.

The number line

Beyond basic counting

Counting is the first mathematical pattern learners encounter. From here they soon begin to count backwards which is a step towards subtraction and they’ll also count in twos, fives and tens which is a foundation for multiplication. The next big step is the idea of place value and counting to base 10. Learners often make this leap simply because it’s an obvious and efficient way to count large numbers. In Komodo we use practice examples like this to help learners make the connection to counting in tens and ones.

counting in tens

 

It’s easy to forget that counting is a key concept in maths with many stages before it’s mastered. There’s certainly a lot more to it than one, two, three!

I’m Ged McBreen, Co-Founder of Komodo and a qualified Maths teacher. If you found this article interesting sign up to our email list.

 

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Introducing the Komodo Bronze, Silver and Gold Medals

Komodo-Bronze-Silver-and-Gold-Medals

 

Some parents have asked what comes after the Black Belt and suggested a few great ideas. We didn’t want to downgrade the super-coolness of the Komodo black belt so we’ve gone for a way learners can keep on wearing it. After the black belt learners go onto Bronze, Silver and Gold Medals that pin onto their black belt. Here’s a little technical note – if you’re using an ipad or android tablet you’ll have to upgrade to the latest version 1.9 of the app to claim your medals.

Congratulations to our latest Black Belt Learners

Well done to our latest Komodo Black belt learners – all seventeen of you deserve a big cheer!

17-Komodo-Black-Belt-Certificates

 

 

 

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What’s Changing in the Primary Maths Curriculum in 2014?


DOE

 

There’s a recurring debate about the best way to teach maths in schools. It involves teachers, politicians and the media – who of course love to whip up the intensity. The usual trigger for the annual frenzy is publishing the PISA international test tableswhich this year saw the UK a fair bit behind Shanghai, Singapore and Hong Kong. The debate also focuses on the merits of various teaching approaches. Should maths teaching be more traditional? Should the emphasis be more hands on group activity ?  More arithmetic? More creative problem solving?  In the midst of this debate the Government is soon changing the primary maths curriculum in England. All this may be disconcerting for parents, like us, who have children in the primary school system – so here is some useful information that sheds light on the maths curriculum changes coming in September 2014:

What’s Changing?

The government has published a new primary maths curriculum for Key Stages 1 and 2 which is to start in September 2014. The full document is here but here’s the gist:

  • It affects Key Stages 1 & 2 ( that’s all the primary maths curriculum) If you’re in Scotland, Ireland or elsewhere in the world these changes aren’t relevant – They’re just for England.
  • There’s more to learn – quite a few topics that used to be in secondary maths have been moved forward – such as long division and a more complex understanding of fractions
  • Fractions are introduced earlier, multiplication tables up to 12x are expected by age 9
  • There is an increased emphasis on practice. “So pupils develop the ability to recall and apply knowledge rapidly and accurately”
  • Calculators are out!  - to be replaced by “mental fluency and the use of efficient written methods in the four mathematical operations”
  • The National Curriculum Levels are out! -  Schools will be free to decide how to report to parents on children’s progress. They will also be expected to report to parents on their children’s SATs results using 10 ability bands worked out on a national level. More here

What’s does this mean?

It’s always difficult to predict how changes will affect learners in schools. At first glance there appear to be many sensible changes however the real test is in how schools implement the new curriculum – and we won’t know this for a year or two. It’s worth remembering that curriculum is not everything – the biggest influence on your child’s learning will still be their teacher, the support they get at home and the school experience in general.

Where Next?

If you have a spare 30 minutes – yes I know how unlikely this is – you may find this BBC Radio 4 iPlayer programme interesting. It’s an overview on maths teaching today and it touches on some of the same issues in more detail.

howtoteachMaths

 

 

 

 

 

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A Parent’s Guide to Visual Learning in Maths

visual models in maths

Half plus half equals one!

When we learn maths we develop understanding through visual models – these are “mental pictures” that explain a particular idea or concept. A “visual model” can be as simple as a using the slices of a cake to represent fractions, but they can explain some pretty complex ideas in advanced maths too. In this article I’m going to explore a few of the visual models we use in primary maths.

The Number Line

The number line

Most young learners are introduced to the number line at age 5 or 6. It’s a valuable visual model for progressing learners from counting one by one with their fingers towards memory recall of their number facts. Number lines really come into their own when learners see how they can split a calculation into two stages - making it easier to do:

numberline2

I’ve written a previous blog article on number lines which goes into more detail. You can check it out here.

Arrays

When learners first encounter multiplication they are usually introduced to Arrays.  An “Array” is  just 2D stack of counters as you can see:

Multiplication with arrays

Arrays are great because they also explain why it doesn’t matter which way round the numbers go in multiplication. In the case above you can see that four rows of six is the same as six rows of four – which explains why 4 x 6 is the same as 6 x 4  - otherwise known as the commutative law.

The Hundred Square

9-times-tables hundred square

The hundred square allows learners to create patterns out of ideas in maths. Take for example the nine times tables in the image above – the pattern shows us an easy method for learning the 9 times tables – you could get to 4 x 9 = 36  in two steps by thinking  4 x 10 = 40  and then 40 – 4 = 36.

In Komodo we use a variety of visual models for learning concepts in maths. This helps develop understanding and it also teaches children to think visually about maths – so when they’re faced with a tricky maths problem they’re equipped with a range of visual tools to apply. Using visual models also helps learners develop an intuitive feel for numbers – a “number sense”  that will stay with them for life.

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Design a Guy Competition

guys-together

 

The Komodo guys are a weird bunch. They’re all shapes and sizes, half animal, half vegetable, super-heroes and monsters. No one really knows where they came from – some say they have special powers, others say they’re just plain crazy.

The Design a Guy Competition

All Komodo learners are invited to design and name their very own Komodo guy. Here are a few early entries to get your child’s imagination flowing:

 

palmGuy

Palm Guy by James

 

Clumsy the Clown

Clumsy the Clown by Kate

Flat Fish Guy

Flat Fish by Kate

 

The Prizes

  • The Winner will have their guy recreated by our illustrator and included in Komodo
  • The top 3 entries will get a copy of the super-cool “Papertoy Monsters” book
  • Parents of the Winner will receive a £20 Amazon gift code to help with last minute Christmas prezzies
  • There’ll be lots of certificates too

Papertoy-Monsters

How to Enter

If you’re on Facebook:

  1. Take a photo of the picture
  2. Go to our Facebook Page https://www.facebook.com/komodo
  3. “Like the Komodo Page”  - so you’re allowed write / add photos
  4. On the main page add each picture and write the name of the guy and the child’s first name
  5. Click on this thumbnail for a guide:

how-to

 

 Not on Facebook:

  1. Take a photo of the picture
  2. Attach and email it to hi@komodomath.com along with the Guy’s name and the child’s first name
  3. We’ll then add the picture to the Facebook page https://www.facebook.com/komodo

The Rules

  1. The competition is open to Komodo subscribers only
  2. Clare, our illustrator chooses the Winners
  3. Entries must be made before Wednesday 18th December
  4. Winners will be announced on Friday 20th December
  5. Maximum 3 entries per child
  6. By submitting an entry you agree to us publishing the image on our Facebook page or blog
  7. We’ll refer to children by first name only

[Update]  And the Winner is Zogger by Zahra

zogger_zahra

zogger

 

Look out for Zogger inside Komodo!

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Exam Time

exam_girl

All of our children will have to sit exams at some stage in their school career, for some of you it starts with SATs, here in Northern Ireland it’s the 11+  and our son James sits the second of his three papers tomorrow morning. It’s been a fairly tense time in our house, hence the pause in blogging recently, apologies.

But what is the best way to prepare your child for an exam when they are still only primary school age?

I’m guessing that our experience getting James ready for the 11+ isn’t that different to any other parents with children sitting exams, you want them to do well but you don’t want to pressure them too much, you want to help them but you don’t really know what the best way to do that is. I should say that doing the 11+ is in no way compulsory, though it is very common here and in our area of Belfast there are twice as many grammar schools as comprehensives. Perhaps that makes the whole thing harder for parents, the knowledge that we don’t have to put ourselves and James through this awful exam, but he wants to go to a particular grammar school and we want him to have that choice.

Our first dilemma was to tutor or not to tutor?

Well, with our backgrounds in Maths and English we decided we really ought to be able to give James any extra help he needed, and the primary school he is at do their own preparation in class.
So far so good.

Parents whose kids had already been through the exam told me how stressful it was, how difficult, and I thought, no, not in our house, it can’t be that hard, and I certainly won’t allow it to become a stressful experience for James. How naive I was. It was all going so well until the new school term in September. James’ test paper results weren’t very good and he seemed to be having a real crisis of confidence. I began to panic. What were we doing wrong? Should we have got a tutor? Virtually all of his friends are being tutored, were we missing out? It’s probably the first time I considered that James might not get where he wants to go and we’ve got to be ready for that too.

So what did we do?

I talked to other mums – over many cups of coffee and breathless conversations it seems we were all going through the same thing – which is kind of reassuring. Then we went to see his teacher. He was fantastic – he didn’t say everything was going to be fine but he did give us some pointers for things we could work on with James reminded us that encouragement is crucial, something we had lost sight of a bit and told us that we had to let James take ownership of this exam, he was the one sitting it, not us.

Now that we are in the midst of the exams a calm has descended on our house – James has done his very best, we have done ours and what will be will be. We aren’t through yet but if I were to share some tips on what has worked for us, in keeping us all sane it’s these:  Encourage, encourage, encourage. Even when they’ve misread half  the questions for the tenth time and you feel like screaming at them, find the positives, praise them for what they got right. I think sometimes with James I focused too much on what he was getting wrong and it demoralised him.

Give them ownership of their work.

To get James back on track in the month before the exam I sat down with him and between us we came up with a weekly work plan, we decided  how many hours a week we thought was fair, how we would split it up, half an hour there on maths, 20 mins English another day. We drew up a chart so we could tick off the work as he did it.

The Carrot

condor-black-new

This really helped with getting the work plan going. We decided to reward James not for success in passing the 11+ but for the effort he puts in preparing for it. If he worked really hard we’d buy him the bike he wanted.  Wow – that one worked! Once there was something tangible for him to work towards it really focused his mind.

Keep things in perspective and keep your routine and theirs.

James has kept up all the sport and music he does after school and we’ve made sure that he has plenty of play time. This is an important exam but the world won’t end if he doesn’t get it and we can’t put life on hold for it – we have a happy, healthy son who will do fine whatever the outcome. Don’t  ‘Go Compare’

It’s hard not to be drawn into what other parents are saying about how their children are doing, and the kids themselves compare their marks to their friends’,  but ultimately nobody else matters – and as I’ve found out, you can’t always believe that they tell you anyway!

A last word

Exams at 7 or 11 are hard, something like the 11+ requires a degree of mental toughness that comes with maturity and I believe that at this stage some kids have it and some don’t, yet, but that doesn’t mean that you can’t help them do achieve their very best. If you’re going through an exam like us right now then I wish you and your child the very very best of luck – we will get through it!

Jane, Co-Founder of Komodo.

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Multiplication – The Half and Double Method

A tool kit for maths

Learning maths at primary school age is a little bit like collecting tools for a tool kit. Each maths skill has to be practised and perfected before it becomes part of the kit.

It all sounds very arduous but it’s really worth it – because once mastered, you’ll have these maths skills at your disposal for the rest of your life.

Here’s a super-useful tool for multiplying:

Multiplying using the Half and Double Method

When you’re faced with a multiplication like:

4 x 16 =

You have a number of methods to use:

  1. Short Multiplication  - the written method we all learned at school – here’s a video to remind you
  2. The Grid Method as discussed in this article
  3. The Distributive Law – which sounds scary but basically means “Splitting” it into two easy multiplications – so 4 x 16 becomes (4 x 10 ) + (4 x 6 )
  4. Or Sometimes, such as in this example, it’s just perfect for the Half and Double Method

 Using the Half and Double Method we can halve one side of the multiplication as long as we double the other – and the answer remains the same.

4 x 16

becomes

8 x 8 = 64

Here’s another example that looks a bit tricky at first:

34 x 5 = 

But after using the half and double method it becomes:

17 x 10 = 170

The method also works very well with some fractions like this:

3½  x 12 = 

Doubling removes the fraction:

3½  x 12 =  7 x 6 = 42

Likewise with decimals

4.5  x 8   =  9 x 4  = 36

 

The key to using the half and double strategy is choosing when it makes the problem easier.

Here are a few guides:

  • Is one of the sides 5 – if so doubling will give 10 which is easy ?
  • Is the side I need to halve even ?
  • Does one side include a half or 0.5 – if so doubling will remove it?

 

 

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Komodo – Award Winning Maths

Komodo Wins the at the DANI Awards

Left to Right: Barry Adams (Award Sponsor) Jane & Ged Co-Founders of Komodo

We’re proud to say that Komodo won the E-learning Award at last week’s DANI Awards – a UK City of Culture Event.

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