Arithmetic Of The Infinite

Infinite numbers are weird. They gnash their teeth against our intuition. They don’t behave how, deep down, we think numbers ought to behave.

That should not be surprising, since our intuition was formed around tiny little numbers like 3.1, 4000 or seven billion and two.

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Movie Ticket Puzzle Solution

[This is a back-issue of one of this site’s newsletters]

It’s Monday Morning Math Time!

If you’re hungry, have a look at this yummy breakfast math video. You’ll see there’s more than one way to cut a bagel, and maybe learn a bit of topology too.

I promised to give you a solution to the movie ticket problem.
If you missed it, have a read here and see if you can solve it before you read on here!

Continue reading Movie Ticket Puzzle Solution

Two, One, Zero, Blast Off! (or, How To Teach Subtraction)

Last week, I got to help my son learn subtraction with borrowing. He’s already learned how to subtract two-digit numbers when borrowing is not needed, as you can see from the picture below.

Continue reading Two, One, Zero, Blast Off! (or, How To Teach Subtraction)

Another Way To Teach Fraction Division

The classic way to teach fraction division is like this. To work out, say,

we ‘turn the second fraction upside-down’, to get

and then the division question becomes a multiplication question.

Continue reading Another Way To Teach Fraction Division

Coconuts and Diamonds

One of my favourite puzzles of all times is a bit tough for a typical lower-school kid. It goes like this :

Five men and a monkey are stranded on a desert island. They spend the day searching for food, and by evening, they have collected a big pile of coconuts. Too tired to do anything but sleep, they agree to share the coconuts out in the morning.

However, one of the men wakes up just before midnight. He doesn’t trust his companions, so he goes to the pile of coconuts to take his share. he divides the coconuts into five equal piles, with one left over. He takes his share and hides it, gives the spare coconut to the monkey, collects the rest back into a pile, and goes back to sleep. Continue reading Coconuts and Diamonds

Pumpkin Puzzle

A Young Pumpkin Plant
A Young Pumpkin Plant

We have some pumpkin plants growing in our yard. I counted them at one point, and there were 24 plants. This inspired a little puzzle –

If I have 24 pumpkin plants, and half of them grow a pumpkin, and half of those that grow a pumpkin grow another, and half of those that grow another grow yet another still – then how many pumpkins do I get in the end? Continue reading Pumpkin Puzzle