Estimating and approximating

problem
Equation attack

Age

16 to 18

Challenge level

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.
problem
Four go

Age

7 to 11

Challenge level

This challenge is a game for two players. Choose two of the numbers to multiply or divide, then mark your answer on the number line. Can you get four in a row?
problem
Building approximations for sin(x)

Age

16 to 18

Challenge level

Build up the concept of the Taylor series
problem
What do functions do for tiny x?

Age

16 to 18

Challenge level

Looking at small values of functions. Motivating the existence of the Maclaurin expansion.
problem
Little man

Age

5 to 7

Challenge level

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?
problem
Interstellar

Age

11 to 14

Challenge level

What number could replace * so that */5 is between 3 and 4?
problem
Shedding some light

Age

7 to 11

Challenge level

Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?
problem
Archimedes and numerical roots

Age

14 to 16

Challenge level

The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
problem
The magic number and the hepta-tree

Age

7 to 11

Challenge level

Find the exact difference between the largest ball and the smallest ball on the Hepta Tree and then use this to work out the MAGIC NUMBER!
problem
Back to school

Age

7 to 11

Challenge level

Mr. Sunshine tells the children they will have 2 hours of homework. After several calculations, Harry says he hasn't got time to do this homework. Can you see where his reasoning is wrong?