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

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

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

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...

What happens when you round these numbers to the nearest whole number?

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?

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

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

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?

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

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

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

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.

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

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?

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

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?"

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

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

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

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?

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

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. . . .

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.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.