A different kind of maths learning - Maths Olympiads

How many people think maths is fun?  My guess would be not many;  but I believe as with anything, it can be made fun. Maths is all about solving problems right from the basic up to the very complicated. If maths could seen more as doing puzzles and challenges, then perhaps it would have more appeal.



Puzzles and Challenges make Maths fun

I have already written about the Japanese KenKen puzzles which work on that theory that puzzles are fun, and help kids to develop their mathematical skills that way.

Maths can be made fun through games like Yahtzee, Monopoly and Top Trumps, use of numbers in cooking, and fun challenges. I was once looking after a friend's kids and had to take them grocery shopping with us. I set the kids a challenge to keep them occupied while I concentrated on my shopping list! In pairs they had to add up how much the shopping cost in total as we went around. Whichever team was closest to the correct answer at the end won.  They loved this challenge and when their mum came to collect them they told her how much fun they'd had food shopping! Who would have thought?


The key to getting kids to like maths, is the same as anything - make it fun, make it different, make it a challenge. Learning maths methodology then doing lots of example problems to practice and drill the method is one way to learn - and I do agree it has its place. Repetition is important in maths to gain skill and to be able to do things more easily, which will in itself make maths more enjoyable  (the easier something is, the more likely you are to enjoy it). But there has to be more to maths than endless repetitive sums!



What we are doing

I started out a few months ago, setting maths problems for our daughters, with a reward in a locked box that could only be opened by the combination number of the solution to the maths problem. 

You can read about that here.
The girls enjoyed this, so it grew into a maths advent calendar for Christmas, and now I've had to add an extra box so that they have one each and it's become part of their morning routine to solve a problem and unlock their boxes.

Many of the problems I use for these boxes are from the Maths Olympiad challenge that both girls have participated in at school.



Maths Olympiads

Both our daughters have participated in Maths Olympiads over the past few years at school. It's a 'competition' designed to teach major problem solving strategies and build mathematical intuition in  school kids.

The kids get practice at school in lunch times, and then over the year there are 5 Olympiad tests, each of which consists of 5 questions with around half an hour to solve them in.

The best part of this Maths Olympiads for me is the problem solving practice it gives the students. They learn to use trial and error, estimation and logic to find the answers. The questions are more than just maths problems, they are challenges and puzzles.

 Yes, they do use their mathematical skills to add, subtract, multiply, divide, and make various calculations; but they also learn some nifty mathematical 'tricks' and shortcuts.

For example..

To add consecutive numbers from 1 upwards, take the final number, multiply it by the next consecutive number and divide your answer by 2.

eg:  1+2+3+4+5=    (5 x 6) divided by 2 = 15

Or here's another one my younger daughter taught me:

How to know if any number is divisible by 3:

Add the individual digits and if their sum can be divided by 3, then the original number can be too.

eg  462   4 + 6 + 2 = 12 , which can be divided by 3, so 462 can be too!

There are other divisibility rules which can be found here.

By setting these problems each night I'm learning more myself and also enjoying the challenge of solving the puzzles!



A very tricky problem

When I found this 'viral maths problem' on the internet from last year's Singapore Maths Olympiad, I had to give it a try! It is aimed at Singaporean High School students, and is meant to be a difficult one.

Here is the problem:

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl marks 10 possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, or August 17.

Then Cheryl tells Albert the month of her birthday, but not the day. She tells Bernard the day of her birthday, but not the month. Then she asked if they can figure it out.

Albert: I don't know when Cheryl's birthday is, but I know Bernard doesn't know either.

Bernard: At first I didn't know when Cheryl's birthday is, but now I know.

Albert: If you know, then I know too!

When is Cheryl's birthday?

Tricky isn't it?

Well if you can't figure it out - here's a video to explain how you get the answer:

I had to listen to this and read other explanations a few times before I really understood how to work out the answer!



Make Maths Different and Fun!
Maths as we think of it traditionally - that is 'numbers' can be found in so many aspects of our daily life from shopping and cooking, to bills and banking.  But problem solving is so much more than a maths skill. It's a life skill that will prove a valuable asset to our kids if we get them to practice and enjoy puzzles and problem solving from a young age.

We will continue to look for and take advantage of opportunities to help our kids to develop these skills - whether that be Maths Olympiads or games and puzzles.

Do you know any other ways to make learning maths fun?

How to practice Japanese numbers in a fun way

Our girls learn Japanese at school. They started in prep (aged 4) and have had 2 lessons each week throughout junior school. 

Both girls enjoy learning a new language.

Our eldest moved up to high school this year and for the first half of the year she doesn't have any Japanese lessons - instead she is studying French. Although she enjoys the challenge of learning a third language, she doesn't want to forget the Japanese she has learnt so far.

In the recent school holidays we found some time to practice Japanese together. One game we played to do this was Bingo!

It was a nice simple game to play and a great way to practice both listening to and speaking the numbers in Japanese. 

We played mostly with 3 of us, sometimes 4, and all helped each other with the numbers.  It was definitely a great way to practice the numbers - it was more about playing a fun game than 'studying'.  Perhaps we might use it for French too in the future!

Have you ever played bingo in another language?

KenKen - fun puzzle arithmetic practice

Ken means Wisdom in Japanese, but the original name for this puzzle was, 

"The Kashikoku Naru Puzzle" 

which means 

"The It Makes you Smarter Puzzle"

(source) 

I first heard of these puzzles when my dad brought these KenKen books out from the UK for our girls. KenKen are a kind of sudoku type puzzle that works on arithmetic and logic. They were invented by a Japanese maths teacher as a way to train young brains in arithmetic in a fun puzzle type manner. In the foreword to each book, the creator, Tetsuya Miyamoto says,

 "It's important that the learning process is enjoyable. KenKen is ideal for making the learning process enjoyable and is perfect for all ages."

How to play

The logic part

Each puzzle has a grid, and like in sudoku and each square in the grid contains a number. If the grid has 3 squares across then those numbers will be 1,2 and 3. If it has 4 squares the numbers will be 1,2,3 and 4; and so on. No number can be repeated in any column or any row.  

Now for the arithmetic part

The small numbers found at the top left corner of a square is the answer to the particular maths function of the numbers in that block. The top of the puzzle will tell you if you are adding, subtracting, multiplying or dividing.

Here's an example of a small multiplication puzzle. In the top right of the page you see a 'x' sign telling you this is a multiplication puzzle.

If you look at the top left corner of each block - this tells you the answer of the numbers in that block multiplied together. So in the top left block there is a 2 which tells us the two numbers in that block must be 1 and 2,  the order of those numbers must then be determined.

If we look at the block on the left below, the number 3 tells us the two numbers in that block must be 1 and 3, so the number in the top left must then be 2, so that the left column has all three numbers present. In the centre of the square that block has a 2, so that one is simple - place a 2 in that box!

The puzzle is worked out using each block in turn.

Here's an example of another puzzle:

You can see at the top right of this page there is a '+'  and a"-" symbol, telling us it's an addition and subtraction puzzle. There are 5 squares across so each row and column must contain the numbers 1,2,3,4 and 5.

The top left block has 2 numbers that added together make 9. Of the numbers we can use, these must be 4 and 5.  Then again the order must be determined. 

Each block must be worked through to work out the numbers and positions,

Fun and educational

These puzzles really are fun to do. They help practice basic arithmetic skills, develop concentration, perseverance and logical thinking, and there are varying levels for all abilities.

You can find KenKen in newspapers, magazines, books and also online and in downloadable apps.

The official KenKen website has daily puzzles, customizable puzzles and free weekly printable email puzzles for teachers to use in classrooms.

Mr Miyamoto developed these puzzles based on his philosophy of 'Teaching without teaching".

Kids will far prefer doing puzzles and games to maths problems and worksheets - but if you find the right puzzles and games they teach the same things!

Have you or your kids ever tried KenKen?

I would definitely recommend giving them a try!

Scale drawings and new bedrooms

Our girls currently share a bedroom. They get on well together but they're getting older and beginning to want their own space. So at the end of this year, we're reorganising our house so they can have their own bedrooms. Needless to say the girls are very excited about this - especially the part where they get to choose the colour and decor for their rooms!

They're both saving up their money to be able to buy things for their new rooms. However, when we went out to the shops the other day, they were excited about buying things like storage ottomans, and comfy bean bag chairs - despite me trying to tell them that there wouldn't be enough space in their rooms.

So, when we got home, we got out the tape measure and some squared paper and made scale drawings of their new bedrooms and the furniture they're going to put in them so they have more of an idea of the space they have.

They'd never made a scale drawing before, so it was a good maths exercise for them too.  The squared paper we had was the perfect size to scale our drawings down to a tenth of the original size of the rooms and furniture.  With all our measurements in metres and centimetres, dividing everything by 10 was nice and easy.

We had fun measuring all the various items of furniture. They learnt that they only had to measure the length and width as height wasn't important for a 2 dimensional drawing!

They are now having fun 'moving the furniture' around in their rooms and deciding who will get which bookcase, and desks etc.   Since we still have a couple of months to go before everything happens, I'm sure there will be lots of different plans get made for their rooms before then.

Now all they have to do is decide on colours!

Do your kids have their own bedrooms? Did you let them choose their own colour and style?

Mastermind - a game of logic

Have you ever played this game?

Mastermind is a two person code-breaking game that was invented in the 1970s as a board game.  

The code-maker chooses a combination of 4 coloured pegs, and the code-breaker tries to guess this combination.  For each guess, white and red pegs are used to signify if the colours guessed are correct or not and in the right place or not. 

White means the right colour but the wrong position, 

Red means the right colour in the right position.

This game is similar to a much older paper and pencil game called 'Bulls and Cows". This time the code-maker writes down 4 single digit numbers and the code-breaker tries to guess this. Instead of coloured pegs, the words bulls and cows are used to tell the code-breaker which numbers are correct and in the right or wrong place. 

We used to have this board game when I was a child, and I remember enjoying playing it often with my brother or parents.    When I found the game in a charity shop here - I bought it and our girls now love playing it too!

I'd never heard of the paper and pencil version of this game - but love the idea that we can play this when we're out and about - perhaps waiting for something - with nothing more than paper and pencil which I always have with me !

You can of course play this game online.  I have the game as an app on my phone, and my girls have played it on there too. This of course is a way you can play it on your own - against the computer, if you don't have a friend with you!

This is a great game for developing and practicing logic and reasoning skills. Super simple and lots of fun!

What simple games do you and your kids like to play?

Minecraft - providing geometry practice for Naplan?

Last week our daughters asked to download the game Minecraft onto their tablets to play.

It's an interesting game where you get to use your imagination to build whatever you want mostly using cubes.

There doesn't seem to be a particular goal to reach to end the game - a bit of survival, some adventure and lots and lots of creativity.

One thing that did strike me when I was looking at this game - was the fact that you build things using cubes - and get to see those buildings in 3D.  This reminded me of some of the numeracy questions on Naplan tests for both Grade 3 and Grade 5:

\

Playing Minecraft and building 3D shapes using cubes will give kids at least an awareness of these structures and because in the game, then can walk around them and see them from different sides - this should help them with the above type of question as it will give them an experience of their own to relat the question to.

My girls will be pleased to know that they are practising for their Naplan tests whilst playing this new game!!

Do you or your kids play Minecraft?

Number sequencing - Naplan numeracy practice

Looking for number sequences is something that kids practise through junior school years.  It helps develop their logic thinking skills and in recognising patterns. It's also great practice for their mental arithmetic - adding, subtracting and multiplying.

 They may start out with very simple patterns like this:

2, 4, 6, 8, 10.........

Here the rule is to 'add 2'

And then move on to patterns that involve subtraction, multiplication or combinations of calculations.

Questions involving number sequences can be found on both Grade 3 and Grade 5 Naplan numeracy tests:

Here's an example from a Grade 3 paper:

46, 40, 34, ?

What is the next number in counting pattern?

Is it 26, 28, 30 or 38?

And here's one from a Grade 5 paper:

What is the next number in this pattern?

810, 910, ?

There are some great online games for kids to practice number sequencing.

This Caterpillar ordering and sequencing game is great for kids to build up their skills from simply putting the number in order numerically up to simple sequences in multiples.

(source:  www.topmarks.co.uk)

For a more advanced game - more suited to those Grade 5 kids - there is a great game to crack codes by finding the number sequence rule. You have to find the correct numbers or rule for the sequence to collect bio rods - and get them before the Wardroid attacks you!   

There is also another number sequencing game on this same website with slightly less fancy graphics - but still good fun - cracking codes to open the safe door!

These games are from BBC's KS2 Bitesize website which has lots of brilliant educational games for English, Maths and Science.

These are great short games you can encourage your kids to play when they go on the computer.  When I find these fun games I often email the links to our girls. They get the excitement of getting a new email - and a new game to play!

Have fun with number sequencing!!

Lemon Cookies - and more Naplan practice!

Recipes 

Our youngest daughter is a budding cook and loves making cookies and cakes.  She has a page-a-day calendar with recipes for cookies on. Here's one batch she made last week:

Ingredients:

For the Cookies:

1 cup butter

1/2 cup sugar

1/2 tsp vanilla extract

grated zest of 3 lemons

1 1/2 cups plain flour

3tbsp cornflour

For the Filling:

4 tbsp butter

1 cup sugar

grated zest of 2 lemons

juice of 1/2 lemon

Preheat oven to 350F (175C). Beat the butter, sugar, vanilla extract and lemon zest together until light and fluffy. Sift the flour and cornflour together and stir into the creamed mixture. Roll into balls and press flat on a baking sheet. Bake for 12 minutes. Allow to cool.

To make the filling, beat the butter and sugar together with the lemon zest and juice until light and fluffy. Spread the filling onto the flat side of one cookie, then put another cookie on top and sandwich together.

Baking as a way to practice numeracy skills

Baking is a great way for kids to practice a number of skills - not just the skill of baking!

Measurements are well practised as ingredients are weighed etc. Depending on the unit of measurement, sometimes fractions are sometimes practiced - as they are here, when things are measured in cups, and half cups etc.  This is something that can come up on the Naplan test in Grade 3 too. For example - here is a question I found on one of the past papers:

Thomas needs 3 cups of flour to make a cake.

He only measures 1/2 cup at a time.

How many 1/2 cups of flour will he need?

1   2   3   or 6 ?

When a student is faced with a question like this, of course they are being tested on their knowledge of basic fractions, but if they have had the real life experience of measuring flour using half cups for a recipe, then the question becomes so much more familiar and so, easier.

We have a large and varied selection of recipes that the girls can bake from - with measurements in cups, grams and ounces, depending on where the recipes come from !  It is great for the kids to be exposed to all these different measurements and to also be able to understand how they relate to each other. Many recipes have 2 different measurements shown, so the kids get used to seeing for example 100g (4 oz), and so gradually learn to convert between different units of measurement.

Estimation

The more kids bake and weigh ingredients, the better they become at estimating weights. It is not only important that kids can read and use units of measurements, but also that they have a rough idea of what, for example 1 kg might feel like.

Another way of practising this is by helping at the shops when buying say - a bag of sugar, and feel the weight of it when they put it in the basket. Or perhaps they know their own weight and so then have a reference point to compare other things to.

Estimating real weights and lengths etc is something else that may appear on the Naplan test, where the students may have to choose the most sensible or likely option from the answers as to what something might weigh or measure.

Here is another example of a question from a past paper:

Which of these is the closest to the length of a real shoe?

5cm

25cm

75cm

100cm

To answer this question, students need to understand what 1cm is actually like and be able to relate this to real life objects. I remember always using my 'big' 30cm ruler at school to compare things to when estimating lengths. It's helpful for kids to have a point of reference like this to refer to - something that they can think, "Is this object longer or shorter than my 30cm ruler?"; thus making it easier to estimate the length of something they don't know.

Real life is often the best practice

I hope these examples show that written tests not only test the student's knowledge of facts - but can be a measure of their understanding of some basic things they encounter in real life.

Sometimes the best practice for basic numeracy and literacy skills for young kids is doing something 'real' - like baking!

So - take a look in your recipe books, and see what tasty delights your kids could bake with you, for some 'homework'  today!

Digital vs Analogue watches for kids

Should you get your kids an analogue or a digital watch?

When we got our girls their first watches, we chose to get analogue ones (shown here in the picture).  We wanted them to learn to tell the time this way first - not just simply read the numbers on a digital watch.

We also have analogue clocks around our house - so the girls did learn this way initially.

However - we equally found that once they had grasped analogue time - they had to learn to equate that to digital time.  It was all very well to be able to read the numbers on a digital watch and say, "It's 3.45"  but how do you say the same time in 'analogue'.

Which ever way a child learns first - they do have to learn both ways and be able to switch between them both.

Being able to switch between analogue and digital time is also something that comes up in questions on the grade 3 Naplan tests.

Learning analogue times also helps kids become aware of other basic maths concepts like fractions and even pie charts!. An analogue clock gives them a familiar point of reference to start from when learning further maths concepts at school.

Last year we explored when kids begin to understand time and found some activities to play with our girls using stopwatches - and some fun websites for them to play on to practise as well. I found another simple game here for some quick practice of converting between analogue and digital times.

I'm definitely glad we chose to start the girls off with analogue watches and clocks. We do live in a digital age with digital clocks on everything from phones, to microwaves and computers, but there are also still plenty of analogue clocks and watches to be found!

What kind of watch do you and your kids have?

Naplan numeracy practice Grade 3 - Geometry

Geometry is a branch of mathematics concerned with questions of

 shape, size, relative position of figures, and the properties of space

(source - Wikipedia)

Geometry is one of the areas covered by the Grade 3 Naplan test.

   One type of question I've noticed a few times is identifying a 

specific person in a 'photo' . For example the question may ask 

what number jumper the person in the back row, second from the

 right is wearing.  This is basic geometry - in terms of identifying 

relative position of figures.

To practice this basic skill, we got out some of the girls school class

 photos from the last few years. We then practised by asking them

 who was sitting or standing, for example - third from the left in the

 front row. We also reversed this by asking them to describe to us

 where a particular friend was in the photo. The girls enjoyed

 looking back over the years to see how they and their friends have

 grown and changed - this provided a good distraction from the

 'maths' aspect of this activity!

Another great and fun way to practice some basic geometry is to

 play Battleships.   There are also often questions which ask the 

kids to identify locations and items on a grid - using battleship

 ideas to plot co-ordinates.

A couple of years ago I made our girls their own Battleships folders

which are a great thing to have with us with ready printed sheets

 and a pencil each to play any time, anywhere! You can print your

 own Battleships grids here! Or just draw your own on scrap paper.

 This is another great, easy activity that needs very little 

preparation.

Naplan year 3 and 5 Numeracy - Fun Money practice

Both Year 3 and Year 5 Naplan numeracy tests may contain questions related to money and working out costs and change.  To practice these skills in a fun way I got out some cash and the junk mail from the letterbox!

First of all for our Year 3 daughter, I would grab a handful of random coins, pass them to her and she would add up the total value of the coins.

This is one type of question that we have found on several year 3 Naplan tests.

The next step was to grab a catalogue for one shop from the junk mail pile. We started out with supermarkets.  I told both girls they had $10 each to spend. They had to choose what they would buy from the catalogue, work out how much they choices cost and how much change they would then have from their original $10. This is to practice working out total costs and change which can come up in questions in both year 3 and 5 Naplan tests.

It was interesting to see the different ways both girls did this task. Our youngest chose her items and one by one subtracted their cost from her $10 so she saw exactly how much money she had left after each choice.  This meant she got lots of practice at subtraction!

Our elder daughter wrote down each item and it's cost on a separate piece of paper, then added up the total which she then subtracted from the original $10. So she only had to do one addition and one subtraction calculation - but it also meant she had to be able to estimate how much she was spending as she was choosing!

Both girls really enjoyed this task - they went through most of the junk mail catalogues - shopping for all sorts of things - sports gear, toiletries and lots of chocolate! They bought things for themselves and gifts for others too!  For the supermarkets I allowed them $10 each, but for bigger shops I allowed $100 each!   You could also use $1000 or larger values for furniture shops for example.

This gives them practice with money, addition, subtraction, decimal points and estimation.  Both grade 3 and 5 need these skills - grade 5 kids just need to be able to do all of this with larger numbers than grade 3 kids. From information I found on a Naplan website - for year 3 kids need to be able to perform money calculations up to $10, and year 5 kids up to $1000.

This is a great activity that you can do with your kids any time with no preparation other than having some junk mail in the house!  Our kids really enjoyed it and kept on shopping after I'd left them to it by themselves!