Delight your friends with this cunning trick! Can you explain how it works?

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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?

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

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?

There are nasty versions of this dice game but we'll start with the nice ones...

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

This article suggests some ways of making sense of calculations involving positive and negative numbers.

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

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

This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.

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

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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?

Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

If you have only four weights, where could you place them in order to balance this equaliser?

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

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

Use your logical reasoning to work out how many cows and how many sheep there are in each field.

This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

Got It game for an adult and child. How can you play so that you know you will always win?

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.

Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number. Cross out the numbers on the same row and column. Repeat this process. Add up you four numbers. Why do they always add up to 34?

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

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

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

An environment which simulates working with Cuisenaire rods.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?