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There are **53** NRICH Mathematical resources connected to **Estimating and approximating**, you may find related items under Calculations and numerical methods.

Problem
Primary curriculum
Secondary curriculum
### Fruity Pairs

Which two items of fruit could Kate and Sam choose? Can you order the prices from lowest to highest?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Almost One

Choose some fractions and add them together. Can you get close to 1?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Can You Make 100?

How many ways can you find to put in operation signs (+, −, ×, ÷) to make 100?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Count the Crayons

How could you estimate the number of pencils/pens in these pictures?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Olympic Measures

These Olympic quantities have been jumbled up! Can you put them back together again?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Place Your Orders

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Discuss and Choose

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.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speed-time Problems at the Olympics

Have you ever wondered what it would be like to race against Usain Bolt?

Age 14 to 16

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Dicey Operations

Who said that adding, subtracting, multiplying and dividing couldn't be fun?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Nice or Nasty

There are nasty versions of this dice game but we'll start with the nice ones...

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Back Fitter

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?

Age 14 to 18

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Countdown

Here is a chance to play a version of the classic Countdown Game.

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Power Countdown

In this twist on the well-known Countdown numbers game, use your knowledge of Powers and Roots to make a target.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### A Question of Scale

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?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Not-so-simple Pendulum 1

See how the motion of the simple pendulum is not-so-simple after all.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### All in a Jumble

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Root Hunter

In this short problem, try to find the location of the roots of some unusual functions by finding where they change sign.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Equation Attack

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.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Four Go

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Little Man

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?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Ladder and Cube

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?

Age 14 to 16

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Dicey Operations in Line for Two

Dicey Operations for an adult and child. Can you get close to 1000 than your partner?

Age 7 to 11

Challenge Level

Game
Primary curriculum
Secondary curriculum
### Nice or Nasty for Two

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your opponent.

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Fastest Cyclist

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Big and Small Numbers in Chemistry

Get some practice using big and small numbers in chemistry.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Biology Measurement Challenge

Analyse these beautiful biological images and attempt to rank them in size order.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Does This Sound about Right?

Examine these estimates. Do they sound about right?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Counting Sweets

How might you use mathematics to improve your chances of guessing the number of sweets in a jar?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Archimedes Numerical Roots

How did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Branching Processes and Extinction

An advanced mathematical exploration supporting our series of articles on population dynamics for advanced students.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cobalt Decay

Investigate the effects of the half-lifes of the isotopes of cobalt on the mass of a mystery lump of the element.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Approximately Certain

Estimate these curious quantities sufficiently accurately that you can rank them in order of size

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Big and Small Numbers in Physics

Work out the numerical values for these physical quantities.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Today's Date - 01/06/2009

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Where Am I?

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?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Time to Evolve

How many generations would link an evolutionist to a very distant ancestor?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Big and Small Numbers in Biology

Work with numbers big and small to estimate and calulate various quantities in biological contexts.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Big and Small Numbers in Physics - Group Task

Work in groups to try to create the best approximations to these physical quantities.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Building Approximations for Sin(x)

Build up the concept of the Taylor series

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What Do Functions Do for Tiny X?

Looking at small values of functions. Motivating the existence of the Taylor expansion.

Age 16 to 18

Challenge Level

General
Primary curriculum
Secondary curriculum
### Building Patterns

Can you deduce the pattern that has been used to lay out these bottle tops?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Shedding Some Light

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Magic Number and the Hepta-tree

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!

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Back to School

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Squaring the Circle

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Whole Numbers Only

Can you work out how many of each kind of pencil this student bought?

Age 11 to 14

ShortChallenge Level

Problem
Primary curriculum
Secondary curriculum
### Growing

Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### What's My Weight?

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?

Age 7 to 11

ShortChallenge Level