Creating and manipulating expressions and formulae

problem

Sum Equals Product

Age

11 to 14

Challenge level

2 out of 3

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 × 1 [1/3]. What other numbers have the sum equal to the product and can this be so for any whole numbers?
problem

Even So

Age

11 to 14

Challenge level

2 out of 3

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
problem

Good Work if You Can Get It

Age

11 to 14

Challenge level

2 out of 3

A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?
problem

Is It Magic or Is It Maths?

Age

11 to 14

Challenge level

2 out of 3

Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying them. Can you explain how they work?
problem

Multiple Magic

Age

11 to 14

Challenge level

2 out of 3

Think of any whole number. Each time you perform a sequence of operations on it, what do you notice about the divisors of your answer?
problem

Christmas Chocolates

Age

11 to 14

Challenge level

2 out of 3

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?
problem

Symbol

Age

11 to 14

Challenge level

2 out of 3

Using the new operator $\oplus$, can you solve this equation?
problem

Regular Hexagon Loops

Age

11 to 14

Challenge level

2 out of 3

Make some loops out of regular hexagons. What rules can you discover?
problem

Always the Same

Age

11 to 14

Challenge level

3 out of 3

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?
problem

Fibs

Age

11 to 14

Challenge level

3 out of 3

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?