Creating and manipulating expressions and formulae

problem
Sums of pairs

Age

11 to 16

Challenge level

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”
problem
Alternating sum

Age

14 to 16

Challenge level

Given that the number 2008 is the correct answer to a sum, can you find n?
problem
Algebraic average

Age

14 to 16

Challenge level

The mean of three numbers x, y and z is x. What is the mean of y and z?
problem
Interactive number patterns

Age

14 to 16

Challenge level

How good are you at finding the formula for a number pattern ?
problem
'Tis whole

Age

14 to 18

Challenge level

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?
problem
Three fruits

Age

14 to 16

Challenge level

Quince, quonce and quance are three types of fruit. Can you work out the order of heaviness of the fruits?
problem
Average surroundings

Age

14 to 16

Challenge level

Can you work out Ali's age based on the diagram?
problem
Multiple magic

Age

11 to 14

Challenge level

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
Divisible expression

Age

14 to 16

Challenge level

Can you show this algebraic expression is divisible by 4?
problem
Symbol

Age

11 to 14

Challenge level

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