What patterns do you see in them?
Suppose you have to share 9872 gold coins between 8 people.
You give the coins out in thousands until there are less than 8000 left.
Then you give out one hundred at a time until there are less than 800, then […]
He labelled each bag with the number of coins inside it.
He could then pay any sum of money from 1 coin to 15 coins using one or more of the bags without opening any of the bags.
Give a proof linked to this picture of the formula $a^2 – b^2 = (a + b)(a – b)$ .
2. What do you notice about the difference between squares of consecutive numbers?
Compare the differences between squares of numbers that differ by 1 […]
This picture shows how you can fit 2 identical copies of a triangle together to form a rectangle.
Can you use it to find the number of dots in the fifth triangle number without counting the dots?
Can you find any […]
Is there more than one?
It is quite easy to find a few solutions. The big challenge is to find all possible solutions.
Can you provide a convincing argument that you have found […]
Explore the pattern you get when you carry on these multiplications up to 37 × 54.
Click here for MAGIC OF 37 worksheet.
Click here for the Notes […]
How many lines are there in your diagrams? How many lines are there in the original diagram? Can you find a way of working out […]
You might like to start by investigating the patterns you get when you shade multiples of a number on a grid. Download here
For the prime sieve investigation use a 100 square grid (download here):
Circle the number 2. Put a line through every multiple of 2 up to 100.
Can you find the chosen number from this square using the clues below?
1. The number is odd.
2. It is a multiple of three.
3. It is smaller than 7 x 4.
4. It has an even tens digit.
5. It is the greater of the two possibilities.
Suppose a newly-born pair of rabbits, one male, one female, are put in a field. Rabbits are able to mate at the age of […]