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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Given the products of adjacent cells, can you complete this Sudoku?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Use the differences to find the solution to this Sudoku.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Can you replace the letters with numbers? Is there only one solution in each case?

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

What happens when you round these three-digit numbers to the nearest 100?

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

Have a go at balancing this equation. Can you find different ways of doing it?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

Number problems at primary level that require careful consideration.

Can you work out some different ways to balance this equation?

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

The clues for this Sudoku are the product of the numbers in adjacent squares.

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

An investigation that gives you the opportunity to make and justify predictions.

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Find out about Magic Squares in this article written for students. Why are they magic?!

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

This Sudoku, based on differences. Using the one clue number can you find the solution?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .