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?









Try Something New week 6 - A Persuasive Writing Challenge



At the weekend, Euan decided to try a writing challenge with our girls - but not only for them, he did it with them too, which I think was part of the reason our girls enjoyed it so much! Our kids certainly enjoy when we play games and do things all together - even if it is writing!

He set a writing prompt, then he and the girls had 45 minutes each to write their own opinions and response to the prompt.  When they had finished, they read what they had all written together; then came my role.  Euan read out all 3 pieces ( so that I didn't know who had written each one as I would have recognised everyone's handwriting).  
 I had to listen, judge them and give feedback.

As it happened I guessed wrongly as to the two pieces written by our eldest daughter and Euan, which was the source of much amusement! But I was very impressed with all three answers and it provoked much discussion afterwards too, both about the topic itself and the different written responses to it.

This was a great way to get our girls practising their writing skills with no pressure of a 'test' or feeling like they were doing 'school work'.  They love challenges, particularly those where they can go up against Mum or Dad and we'll definitely be doing more of these!




So here was the chosen writing prompt for this challenge:

"Handwriting should no longer be taught in schools."


And here are the three responses
 (typed up by me, just as they were handwritten, no alterations have been made!).


1.
Handwriting is a vital part of human life. People use it for communication and for spreading ideas. It has been used for centuries and has still worked to people's satisfaction.

Handwriting helps people excel in reading and spell-checking. This can help students in exams and assignments. If students were not taught handwriting, when teachers went to check their students' work it would probably be messy and difficult to read.

Secondly, handwriting helps people develop uniqueness and creativeness. Handwriting does this because even though all students are taught to write the same way, their natural handwriting will show through. That is what makes everyone's handwriting different and special.

People may argue that technology is the 'new way of the future'. This is quite likely but that might still be another decade or two away, so for now there is no need to forget about handwriting. Also, there are still many people in the world that love the art of writing and, in some cases, despise the use of technology.

If people just stopped being taught handwriting the world would be a confusing place. Teachers might not agree with the fonts chosen by the students because they can't read it, this would bring the students grades down. If that student had been taught handwriting, they might have gotten better grades because they would have learned handwriting and practised it for a lot of their life.

When people hand-write, it shows their emotions. They might use quick , scribbly writing or careful, elegant writing. Technology is getting close and closer to taking over, but do we really want that? Handwriting is an essential part of life, which his why it should be taught in schools.

Students have the right to hand-write!




2.
Handwriting should no longer be taught in schools. I do not agree with that. Handwriting is a traditional method used for recording the past and communicating with others.

Firstly, handwriting should be taught in schools because if one day people don't have a computer to type but they do have paper and pen, they can still record stuff; whereas if they hadn't learnt handwriting they couldn't communicate or record stuff.

Secondly, it is vital that handwriting carries on being taught in schools because if it wasn't it would make it easy for students to cheat. They could just copy and paste from the internet into their writing. But with paper and pen, it is extremely hard to cheat.

Finally, handwriting must be taught is schools because if you get a virus on your device which you are writing with,  you might lose your work. But with pen and paper, it is very hard to lose your work.

In conclusion, handwriting should still be taught in schools because one day you might only have the devices used for handwriting with you, it makes it hard to cheat and it is unlikely that your work will get lost. And that's why handwriting needs to be taught in schools.



3.
In recent years, as computers have become more and more part of everyday life, many people think handwriting is becoming outdated and antiquated. The ability to write and compose your thoughts and arguments is as important as ever, however, the need to write is less important as computers take over from pencils and pens. Due to the rise of computers, handwriting should no longer be taught in schools.

As soon as you join junior school you are faced with computers. The sooner you can read the sooner you can make the most of computers. When you can understand letters and recognise them it is time to learn to type. Programmes such as Dance Mat Typing and Mavis Beacon provide great ways to have fun and learn the important skill of typing to allow writing to become easier and of higher quality through the use of software on a computer.

When you create a written document on a computer using a programme such as Microsoft Word, you can instantly edit it. the frustration of having to rub out mistakes and have a messy, smudged paper is no longer an issue. Using a clean, crisp screen is the new norm. tools such as spell check and grammar check which can be used to highlight and fix corrections , save time for both the writer and classroom teacher when editing and correcting written work. We cannot 'un-invent' the computer as a tool to help writing, we should embrace it and move forward with the times.

In contrast, people say learning with pen and paper helps develop a deep understanding of letters, spelling and even a love for language, but this is perhaps a dying idea, with phones, tables, i-pads and computers taking over every part of our free time, we should not waste our precious leisure time with old ideas that take away time from fun things like swimming and hockey.

Overall, it is clear that writing is as important as ever but how we do it is changing. We do not need to waste time in school focussing on old ideas such as handwriting when computers can be our paper and 'Word' our assistant. Let's take the technological plunge, get rid of time wasting activities such as handwriting and use computer typing programmes and editing software to write as we move into the 21st century.



Can you guess which was written by a 10 year old, a 12 year old and an adult?






Try Something New Week 5 - Cheesecake and Gift Boxes


This year (2016) as a family we're aiming to try something new each week.  So far this is what we've done:

Week 3: Made marshmallows

From now on I'll be posting on the blog each week about the new things we're trying.

So this week, what did we do?

Our eldest daughter tried out a new cardboard gift box net. We printed the free PDF from this site.
The first time she tried pasting it onto some card from an old chip box, with some pretty paper on the other side.
This didn't work so well as the card was too thick and didn't fold too well.
So she tried again, this time just printing the template direct onto some thin cardboard. This worked much better!
 These little gift boxes are so easy to make and look so pretty, I think we'll be exploring and making more of them!

Our youngest daughter tried baking something new this week - a cheesecake!  I picked up this recipe book years ago from a charity shop.

She decided to make the basic uncooked cheesecake first, and did a great job, especially with separating the eggs!

The cheesecake tasted delicious, and I'm sure she'll be making more from this recipe book.

Did you try anything new this week?

We'd love to hear about your new experiences - do leave us a comment here - or alternatively tell us about it on our 









A stronger wooden rubber band car

After making several different 'cars' a couple of weeks ago, our daughter had one final try at making a stronger faster rubber band car before she goes back to school next week.

She decided to stay with the simple design she'd used before 
(you can see her previous creations and how well they worked here).



New Materials

This time she used a thin piece of plywood for the base instead of cardboard. The reason she did this was because she wanted to add more rubber band 'engines' to her car after a discussion and suggestion from Granddad! She had tried adding more rubber bands to her previous cardboard car, but the card just bent with the force of the wound up rubber bands!

So - wooden it was - and we found some wooden dowel rods to make the axles stronger too. We used cut up sections from an old board marker pen casing to slot the dowel rods through so they would run smoothly.


Here is her completed final rubber band, wood and CD car. If you can see on the back axle there are three small screws to attach the rubber bands to and notches on the front of the car to loop the other ends around. So this is her '3 cylinder' car! More engines, more power!



Test run

Here is how far it managed to travel, carrying a tuna can, up a slope we had built from cardboard.

Although the car didn't make it quite to the top of the slope as we'd hoped, we'd spent enough time on the cars and so decided to stop there and take stock of what we've learned.  Maybe we'll revisit making cars after a few weeks break!


What we learned

So what did we learn (and I say we because I've never made cars before and learned just as much as our daughter did!)?

  • We learned how to make a rubber band car and how it works with potential and then kinetic energy. 

  • We learned how different sized wheels affect the movement of the car.

  • We learned about friction - adding sections cut from rubber gloves to the CD wheels to allow them to grip the tiles.

  • We saw the difference when putting the car on different surfaces, and with different weights on the car. 

  • We also learned about the strength needed in the construction materials and tested various different types. 

  • We had to use lots of creativity to make these cars - choosing materials and learning how best to cut, shape and attach them together.

  • We made lots of mistakes and persisted with trial and error, making the successes and achievements so much more exciting and satisfying!


Give it a go yourself!

I would highly recommend spending time with your kids learning how to make something like a rubber band car.  I watched several you tube videos myself first to get the basic idea of what to do, so that I could help as best I could.  We also did things in small stages so that neither of us got too fed up or frustrated. 
Building up the project over 3 weeks was also definitely a good thing to do, as it gave us time to process each step and everything we had learned before trying to apply and build upon that when we tried again.  
We used materials we found in the house so it didn't cost us anything other than a little time, but it was time well spent, learning and experiencing something new with my daughter - and not only that, it was great fun!


Inspired by

This project was inspired, partly by a balloon car kit our daughter got for Christmas, and partly by the Opti-minds challenge our daughter took part in last year. She and her friends did the Language Literature Challenge last year but are considering doing the Science Engineering Challenge this year and so I thought it would be fun to have a go at last year's Science Engineering Challenge together in these summer holidays to give her an idea of what to expect. They had to move a tuna can at least 1.5 metres in distance and upwards at least 0.5 metres.  Although we didn't quite manage this, I think our daughter learned enough in terms of science principles and also the need for persistence and trial and error, so that if her team chooses the Science and Engineering challenge this year, they will have at least some ideas on where to start!

Have your kids ever done a challenge like this before?
I think Opti-minds, or other challenges like this are a great thing for kids to do to learn all kinds of skills. I will be interested to see which challenge our daughter's team chooses this year.




 

Origami and following instructions - Transforming Ninja Star


In this week's newsletter, I included a link to these instructions for making origami transforming ninja stars. My girls, who I gear the newsletter for, asked me to include things to make, and I thought these looked pretty cool!

We all sat down together to try making them a couple of days ago.

The instructions were very clear and easy to follow for making the 8 basic parallelograms that the stars are made from.

Then when it came to putting them together, we were fine up until the last two pieces - where it took us a while and some trial and error before we finally got it right!

I then made one more using squares cut from some of our junk mail.

 This worked pretty well, but the thinner paper didn't slide and pull apart and together quite as easily as the sturdier origami paper.
Still, they were neat to make and play with, transforming them from stars....

........



...to rings


Both of which we found flew pretty well across the room when we threw them like Frisbees!


Making these origami stars, has me want to find more cool origami projects to try with my girls.  
Having to read the instructions carefully, look at the diagrams and orient your paper in the correct way can provide quite a challenge. 
This has to be helping them improve their spatial awareness, logical thinking, basic geometry and who knows what other skills.

So watch out for more origami in the coming weeks!




Making more cars - propeller and rubber bands

After our younger daughter's success last week making her own Balloon Car Racer, we decided to try making some more different cars powered by other means.

The first we tried was a plastic bottle propeller car, made following this video. Our daughter made it herself, figuring out the best way to punch holes and cut the various materials.


Here it is all finished - looking good!

Unfortunately when we wound up the propeller, the car didn't race forward as we'd hoped!


We asked for help on Facebook, and were given plenty of suggestions like adding weight, cutting more holes and rubber bands on the wheels.  We tried a lot of the suggestions and persisted for a long time until the rubber bands snapped and we put it aside for the day, frustrated!

A couple of days later, we decided to try again with another rubber band powered car. 
We found a great YouTube channel called 'GrandadIsAnOldMan' and watched several of his videos for inspiration and ideas.

First - and now I'm going to stop writing 'we' as our daughter well and truly made these ones by herself!
She made a cereal box car with rubber bands that wound around the back axle to power it. The wheels were milk bottle tops and the axles were kebab sticks.  This car worked but only ran slowly and couldn't carry any weight inside it.





Next she tried with larger mayonnaise jar lids for wheels - and rubber bands around them to gain traction on the tiled floor. This worked much better! The car was faster, but unfortunately still couldn't carry any weight!




Finally, she tried a flat bed car just made with cardboard, drinking straws to push the kebab stick axles through and CDs for wheels.  This worked REALLY well and was strong enough to carry a small tuna can!  Success!!





The cars our daughter made over the past week have provided lots of fun, entertainment and learning experiences.  Seeing and sharing the joy of success when she has made something that works as expected is amazing. 
She has learned some physics principles, for example kinetic and stored energy, friction and traction. 
She's learned persistence and perseverance to not give in when things didn't work - instead to look at why they aren't working and how can she improve it.
She has also learnt to make things for herself from materials we had on hand in the house - enjoying this and gaining far more satisfaction than from the initial plastic car kit she started with a week ago.


But the challenge isn't complete. There is a motive for making this car and transporting a tuna can. The next step being to make it go up a slope! For that we'll be revisiting the propeller car to see if we can add more force to power the car.

I will post on the progress of this project again in a few days!

Have you ever made a small DIY car like any of these?





Balloon Car Racer - a kit and a DIY!


A few days ago, our elder daughter made a solar helicopter from a kit she received for Christmas. Yesterday was our younger daughter's turn to try her Christmas kit - a Balloon Car Racer.


It was fairly simple to construct using the instruction booklet - just a few plastic pieces to fit together, and the balloon on top.
Pump up the balloon with the pump provided and let it go!

It worked really well, as you can see on this short video clip.



Since this car was such a simple concept, my daughter decided to see if she could make one herself.

She used the box that the kit came in for the body of the car. For the axles and wheels she tried wooden kebab sticks and buttons first of all.

The car did move, but as the holes in the buttons aren't in the centre of each button, the car kind of bounced up and down and the force of the air from the balloon wasn't strong enough to move the car in this bouncing motion.

The balloon was attached to the end of an old ballpoint pen casing, taped to the box with duct tape.

Cardboard circle wheels were tried next, but worked no better - then we thought of plastic lids.  They were easy to punch holes in the centre to push the kebab sticks through and were much sturdier than the previous 'wheels'.
Finally, the new DIY balloon racer worked!




The excitement we both felt when the car actually moved after blowing up the balloon was brilliant! Such a sense of satisfaction having constructed the car from scratch - and far better than simply constructing a pre-prepared kit!

My daughter then tried putting things in the box car to see what it could hold, but it's not strong enough to move when carrying anything of noticeable weight.

This has piqued an interest in my daughter though - and next we're going to try a different way to propel her newly built car and how to make it stronger.

Have you ever made your own model car? 
Do you have any tips or suggestions for us?






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