There are 53 NRICH Mathematical resources connected to Estimating and approximating, you may find related items under Calculations and numerical methods.
Broad Topics > Calculations and numerical methods > Estimating and approximating
Which two items of fruit could Kate and Sam choose? Can you order the prices from lowest to highest?
Choose some fractions and add them together. Can you get close to 1?
How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?
How could you estimate the number of pencils/pens in these pictures?
These Olympic quantities have been jumbled up! Can you put them back together again?
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.
Have you ever wondered what it would be like to race against Usain Bolt?
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
There are nasty versions of this dice game but we'll start with the nice ones...
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Here is a chance to play a version of the classic Countdown Game.
In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
See how the motion of the simple pendulum is not-so-simple after all.
My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.
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.
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?
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?
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.
Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?
Get some practice using big and small numbers in chemistry.
Analyse these beautiful biological images and attempt to rank them in size order.
Examine these estimates. Do they sound about right?
How might you use mathematics to improve your chances of guessing the number of sweets in a jar?
How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?
An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.
Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Work out the numerical values for these physical quantities.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
From the information you are asked to work out where the picture was taken. Is there too much information? How accurate can your answer be?
How many generations would link an evolutionist to a very distant ancestor?
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Work in groups to try to create the best approximations to these physical quantities.
Build up the concept of the Taylor series
Looking at small values of functions. Motivating the existence of the Taylor expansion.
Can you deduce the pattern that has been used to lay out these bottle tops?
Make an estimate of how many light fittings you can see. Was your estimate a good one? How can you decide?
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!
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?
Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make an estimate.
Can you work out how many of each kind of pencil this student bought?
Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?