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

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

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

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.

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.

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

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

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

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

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?

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?

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

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?

In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.

Three dice are placed in a row. Find a way to turn each one so that the three numbers on top of the dice total the same as the three numbers on the front of the dice. Can you find all the ways to. . . .

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.

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

Choose any three by three square of dates on a calendar page. Circle any number on the top row, put a line through the other numbers that are in the same row and column as your circled number. Repeat. . . .

Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

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.

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?

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

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

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

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

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

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

This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.

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

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?

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?

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

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

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

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

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.

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

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

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

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

If you wrote all the possible four digit numbers made by using each of the digits 2, 4, 5, 7 once, what would they add up to?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.