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

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

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

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

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

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In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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.

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?"

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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

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

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

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. . . .

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

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?

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?

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

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?

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?

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

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

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

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.

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

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?

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

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

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?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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

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

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

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

Use the differences to find the solution to this Sudoku.

An activity making various patterns with 2 x 1 rectangular tiles.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

This challenge extends the Plants investigation so now four or more children are involved.

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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.

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?