Number operations and calculation methods

This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

problem

Favourite

Missing multipliers

Age

7 to 14

Challenge level

What is the smallest number of answers you need to reveal in order to work out the missing headers?

game

Favourite

The remainders game

Play this game and see if you can figure out the computer's chosen number.

game

Favourite

Countdown

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

problem

Favourite

Consecutive numbers

Age

7 to 14

Challenge level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

problem

Favourite

5 by 5 Mathdokus

Age

7 to 16

Challenge level

Can you use the clues to complete these 5 by 5 Mathematical Sudokus?

problem

Favourite

Remainders

Age

7 to 14

Challenge level

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

problem

Favourite

Method in multiplying madness?

Age

7 to 14

Challenge level

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

problem

Favourite

Two and two

Age

7 to 16

Challenge level

How many solutions can you find to this sum? Each of the different letters stands for a different number.

problem

Favourite

Largest product

Age

11 to 14

Challenge level

Which set of numbers that add to 100 have the largest product?

problem

Favourite

Cinema problem

Age

11 to 14

Challenge level

A cinema has 100 seats. How can ticket sales make £100 for these different combinations of ticket prices?

problem

Favourite

Consecutive seven

Age

11 to 14

Challenge level

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

problem

Favourite

Fractions jigsaw

Age

11 to 14

Challenge level

A jigsaw where pieces only go together if the fractions are equivalent.

problem

Favourite

Round and round and round

Age

11 to 14

Challenge level

Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

problem

Favourite

Keep it simple

Age

11 to 14

Challenge level

Can all unit fractions be written as the sum of two unit fractions?

$Countdown fractions$

problem

Favourite

Countdown fractions

Age

11 to 16

Challenge level

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

problem

Favourite

Going round in circles

Age

11 to 14

Challenge level

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

problem

Favourite

Magic letters

Age

11 to 14

Challenge level

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

problem

Favourite

Strange bank account

Age

11 to 14

Challenge level

Imagine a very strange bank account where you are only allowed to do two things...

problem

Favourite

Making a difference

Age

11 to 14

Challenge level

How many different differences can you make?

problem

Favourite

Cryptarithms

Age

11 to 14

Challenge level

Can you crack these cryptarithms?

game

Favourite

Up, down, flying around

Play this game to learn about adding and subtracting positive and negative numbers

problem

Favourite

Can you make 100?

Age

11 to 14

Challenge level

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

problem

Favourite

Almost one

Age

11 to 14

Challenge level

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

problem

Favourite

Have you got it?

Age

11 to 14

Challenge level

Can you explain the strategy for winning this game with any target?

problem

Favourite

Number daisy

Age

11 to 14

Challenge level

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

problem

Favourite

Egyptian fractions

Age

11 to 14

Challenge level

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

problem

Favourite

Twisting and turning

Age

11 to 14

Challenge level

Take a look at the video and try to find a sequence of moves that will untangle the ropes.

problem

Favourite

More twisting and turning

Age

11 to 16

Challenge level

It would be nice to have a strategy for disentangling any tangled ropes...

problem

Favourite

Connect three

Age

11 to 16

Challenge level

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

problem

Favourite

Weights

Age

11 to 14

Challenge level

Different combinations of the weights available allow you to make different totals. Which totals can you make?

problem

Favourite

Impossibilities

Age

11 to 14

Challenge level

Just because a problem is impossible doesn't mean it's difficult...

problem

Favourite

Overlaps

Age

11 to 14

Challenge level

Can you find ways to put numbers in the overlaps so the rings have equal totals?

problem

Favourite

Same answer

Age

11 to 14

Challenge level

Aisha's division and subtraction calculations both gave the same answer! Can you find some more examples?

problem

Favourite

Where can we visit?

Age

11 to 14

Challenge level

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

problem

Favourite

Consecutive negative numbers

Age

11 to 14

Challenge level

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

problem

Favourite

The greedy algorithm

Age

11 to 14

Challenge level

The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.

problem

Favourite

The root of the problem

Age

14 to 18

Challenge level

Find the sum of this series of surds.

You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.

Or search by topic

Number and algebra

Geometry and measure

Probability and statistics

Working mathematically

Advanced mathematics

For younger learners

Number operations and calculation methods