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

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?

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?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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.

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Can you substitute numbers for the letters in these sums?

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

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

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

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

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?"

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

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.

Number problems at primary level that require careful consideration.

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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?

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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?

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.