AIMSSEC Puzzles for learners age 8 to 12

A hundred square has been printed on both sides of a piece of paper.

One square is directly behind the other.

What is on the back of 100? 58? 23? 19?

Can you see a pattern?

How many squares can you make by joining four points on this grid?

What can you say about the areas of the squares?

Look for squares of different sizes and also tilted squares

What do the digits in the number fifteen add up to?

How many other numbers have digits with the same total if we only include numbers without zeros?

Click on Advent Calendar to go to the NRICH website to find 24 Making Maths activities. These are equally good for all the year round. On the NRICH site this month the Advent Calendar has links to one Making Maths activity a day from the beginning of December until Christmas. You will find instructions for making all sorts of mathematical models and learning aids from very cheap materials that will help you to learn, understand and enjoy mathematics more than ever.

Try a few of these:
Do human beings live for as long as a million hours?
If you have been alive for a million seconds, how many birthdays have you had?
What year was it one billion minutes ago?
How long would it take to count to a million ?
Could you run one thousand metres in one minute?
Could you eat exactly one tonne of food in a year without getting either very thin or very fat?
Could you walk as much as one hundred thousand kilometres during your lifetime?
Could one thousand drink cans fit into one cubic metre?

The questions are taken from Tony Gardiner's Maths Challenge, Book 1, Oxford University Press 2000.

Little Man is much smaller than you and me. Here is a picture of him standing next to an ordinary mug.

Can you estimate how tall he is? How tall do you think Little Man's mug might be?

Can you estimate how many "Little Man mugs" of tea might fill one of our mugs?

This month we have a link to an Advent Calendar on the NRICH website which gives you a mathematical game when you click on any day in December up to Christmas Eve. Some of the games you can play on the computer but for many of them do not need a computer. Enjoy!

For example with rods of lengths 3, 4, and 9 the measurements are:
4-3; 9-4-3; 3; 4; 9-4; 9-3, 3+4; 9+3-4; 9 and 9+4-3 (as illustrated).

A school photographer is taking a photograph of the two basketball teams.
She has to arrange ten people, all of different heights, in two rows of five, one behind the other.
Each person at the back must be taller than the person directly in front of them.
Along the rows the heights must increase from left to right.
In how many ways can the people be arranged like this for the photo to be taken?

What if there are four people to be arranged in this way, or six, or eight,
or twelve, or any specified even number?