A Question of International Law - Puzzle

If an aeroplane crashes right on the border of the United States and Canada, in which country would you bury the survivors?

From: "What is The Name of This Book?" by Raymond Smullyan.

The Racetrack - Puzzle

A certain snail takes an hour and a half to crawl clockwise around a certain racetrack, yet when he crawls counter-clockwise around the same racetrack it takes him only ninety minutes. Why this discrepancy?

From: "What is The Name of This Book?" by Raymond Smullyan.

A Question of Slope - Puzzle

On a certain house, the two halves of the roof are unequally pitched; one half slopes downward at an angle of 60 degrees and the other half at an angle of 70 degrees. Suppose a rooster lays an egg right on the peak. On which side of the roof would the egg fall?

From: "What is The Name of This Book?" by Raymond Smullyan.

A Rate-Time Problem - Puzzle

A train leaves from Boston to New York, An hour later, a train leaves from New York to Boston. The two trains are going at exactly the same speed. Which train will be nearer to Boston when they meet?

From: "What is The Name of This Book?" by Raymond Smullyan.

Two Indians - Puzzle

Two American Indians were sitting on a log - a big Indian and a little Indian. The little Indian was the son of the big Indian, but the big Indian was not the father of the little Indian.
How do you explain that?

From: "What is The Name of This Book?" by Raymond Smullyan.

Maths and Music

Below, I would like to share some of our favourites maths songs -we are playing these during our daily school rides.

Circle and Square: A simple shapes song by Readeez

Source:
https://youtu.be/tjgoAMbPFOM?list=RDtjgoAMbPFOM

Number Songs by StoryBots

Source:

https://youtu.be/Huggdy7ohb4?list=PLPphPHIzdSQOpn7CNolFiqCAB4EQnbUtr

Let's Go to School: Count with Me Song from Learning DVD | LeapFrog

Source:

https://youtu.be/jIZGxk4UWUs

'Penny You're The One' Penny Counting Song (Money Math) by Readeez

Source:

https://youtu.be/0h946YYlH1M

'Odd and Even' by Readeez

Source:

https://youtu.be/aW-0M8uWrjM

'Special Name for Twelve' by Readeez

Source:

https://youtu.be/8VUMDu6bdZ4

1,2,3 or first, second, third..

As we are mathematician, we like to keep the mathematical concepts consistent through out the educational upbringing of our kids. I will explain this using the following example.

It is natural that we are introducing young kids to the word of letters and numbers. With letters, people tend to use letter naming root (using the letter's names) or phonics root (using the sounds that the letter make). With numbers, well, we all tend to start with one, two, three.. of course.

However, have you ever thought about what you want your kid to have in mind when you say eg. five?

I believe that you would like them to be able to associate with the word FIVE a group of five objects. This is because it is what 5 stands for - a group of five objects.
However, to keep this concept consistent in our kid's heads, we should be using the word five ONLY when they are indeed looking at 5 objects at a time.
So, in similar way, we should be saying 'one', when they can see a single object; saying 'two', when they are looking at two objects; saying 'three', when they are looking at three objects.. etc.

Seams logical, doesn't it?

Unfortunately, there is one crime on the mathematical development of our kids that we adults make all the time. This is that when we are counting and pointing to single objects, we call out cardinal numbers (which represent quantity) instead of ordinal numbers (which represent position or rank in a sequential order).

What is the difference?

Each of the ordinal number describes a single object, ei.:

• 'first', means an object which starts the line;
• 'second', describes a single object which is second in line;
• third, describes a single object which is third in line, etc. 

Whereas each of the cardinal numbers represents different quantity of objects.

We've tried to keep these differences in mind, when our toddlers were starting on their mathematical journeys. Will you?

Pocket Money

Parents might have different views on whether or not to give pocket money to their young kids. The reasons behind our decision to go for it were:

• we knew our four year old son will use the collected money well (our son loves LEGO, and the only thing he asks for are new LEGO sets)
• he has already started to understand the concept that when you have money you can exchange it for various things (he understood money has special value)
• we wanted our son to practise counting in a real situation (in order to know how much he can spend he first needs to know how much he has saved)
• we didn't want to offer him money in exchange for his work (eg. completing chores) but decided to explain to him the concept that money can be earned, too, in case he asks for an increase in pocket money in the future.
• the amount being given was chosen by us so that getting to his saving aim did not seam to be an endless journey
• we decided to give the pocket money daily, so that we could provide frequent opportunity for counting.

Our son has quickly realised that he needed a way of keeping track on which days he has already received his pocket money. He decided to use his wall calendar for that. By marking the days he has helped us to make the track on the giving pocket money process.
Additional benefit: familiarisation with the calendar year structure.

Counting money for 4 years old seemed difficult at first. But we advised him that he could get some help from a calculator. Working with a calculator is still his favourite way of doing the sums.
Additional benefit: familiarisation with counting devices.

Our son has developed preference of not having too much separate notes or coins in his savings (so that the process of counting the entire savings is quicker). He often asks us to exchange his lower denominations for higher denomination notes.
Additional benefit: developing a sense for exchange of units.

As our son has dealt with money almost daily, he was able to learn very quickly the "money time tables", eg. five 20Kc go into one 100Kc note, ten 100Kc notes go into one 1,000Kc note, etc.. (we are lining in Prague, in Czech Republic,and we use Czech crowns here).
Additional benefit: learning in natural way the time tables (or at least its parts).

As counting the money itself has stopped to be difficult for our son, we decided to upgrade the process. We decided to give out different amounts of daily pocket money, the amount depending on the total amount of the money saved by our son. The more he has in his bank, the higher his daily amount of pocket money is. Our son worked with us to develop a table with different thresholds of the money in his bank, and corresponding daily money amounts.
Additional benefits: familiarisation with a saving account principle. The more money you have saved in the bank, the higher the interest payments you receive.

The natural step now for the pocket money process will be an upgrade to a percentage interest rate structure. However, in order to do that we must make sure that our son:
- is familiar with percentages principle
- is able to use his calculator to work out the percentage of a given sum
- get familiar with rounding up the numbers

Once we introduce the improved structure, I will update our pocket money story for you.