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### 3388

##### Stage: 3 Challenge Level:

Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

### Countdown

##### Stage: 2 and 3 Challenge Level:

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

### Have You Got It?

##### Stage: 3 Challenge Level:

Can you explain the strategy for winning this game with any target?

##### Stage: 3 Challenge Level:

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?

### Digit Sum

##### Stage: 3 Challenge Level:

What is the sum of all the digits in all the integers from one to one million?

### Got it Article

##### Stage: 2 and 3

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

### Hot Pursuit

##### Stage: 3 Challenge Level:

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

### Largest Number

##### Stage: 3 Challenge Level:

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

### Pair Sums

##### Stage: 3 Challenge Level:

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

### Got It

##### Stage: 2 and 3 Challenge Level:

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.

### Consecutive Negative Numbers

##### Stage: 3 Challenge Level:

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

### More Plant Spaces

##### Stage: 2 and 3 Challenge Level:

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.

### Constellation Sudoku

##### Stage: 4 and 5 Challenge Level:

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

### Two and Two

##### Stage: 3 Challenge Level:

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

### Making Sense of Positives and Negatives

##### Stage: 3

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

### Kids

##### Stage: 3 Challenge Level:

Find the numbers in this sum

### First Connect Three for Two

##### Stage: 2 and 3 Challenge Level:

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.

### Arrange the Digits

##### Stage: 3 Challenge Level:

Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

### Reach 100

##### Stage: 2 and 3 Challenge Level:

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.

### Cayley

##### Stage: 3 Challenge Level:

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

### Making Maths: Double-sided Magic Square

##### Stage: 2 and 3 Challenge Level:

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

### Countdown Fractions

##### Stage: 3 and 4 Challenge Level:

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

### Weights

##### Stage: 3 Challenge Level:

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

### Number Pyramids

##### Stage: 3 Challenge Level:

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

### More Children and Plants

##### Stage: 2 and 3 Challenge Level:

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

### Pole Star Sudoku 2

##### Stage: 3 and 4 Challenge Level:

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

### Number Daisy

##### Stage: 3 Challenge Level:

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?

### First Connect Three

##### Stage: 2 and 3 Challenge Level:

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?

### Football Sum

##### Stage: 3 Challenge Level:

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

### Adding and Subtracting Positive and Negative Numbers

##### Stage: 3

How can we help students make sense of addition and subtraction of negative numbers?

### Consecutive Numbers

##### Stage: 2 and 3 Challenge Level:

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

### Chameleons

##### Stage: 3 Challenge Level:

Whenever two chameleons of different colours meet they change colour to the third colour. Describe the shortest sequence of meetings in which all the chameleons change to green if you start with 12. . . .

### The Patent Solution

##### Stage: 3 Challenge Level:

A combination mechanism for a safe comprises thirty-two tumblers numbered from one to thirty-two in such a way that the numbers in each wheel total 132... Could you open the safe?

### Alphabet Soup

##### Stage: 3 Challenge Level:

This challenge is to make up YOUR OWN alphanumeric. Each letter represents a digit and where the same letter appears more than once it must represent the same digit each time.

### As Easy as 1,2,3

##### Stage: 3 Challenge Level:

When I type a sequence of letters my calculator gives the product of all the numbers in the corresponding memories. What numbers should I store so that when I type 'ONE' it returns 1, and when I type. . . .

### Like Powers

##### Stage: 3 Challenge Level:

Investigate $1^n + 19^n + 20^n + 51^n + 57^n + 80^n + 82^n$ and $2^n + 12^n + 31^n + 40^n + 69^n + 71^n + 85^n$ for different values of n.

### 2010: A Year of Investigations

##### Stage: 1, 2 and 3

This article for teachers suggests ideas for activities built around 10 and 2010.

### And So on and So On

##### Stage: 3 Challenge Level:

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?

### Connect Three

##### Stage: 3 and 4 Challenge Level:

Can you be the first to complete a row of three?

### Always the Same

##### Stage: 3 Challenge Level:

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?

### Cunning Card Trick

##### Stage: 3 Challenge Level:

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

### 4 Dom

##### Stage: 1, 2, 3 and 4 Challenge Level:

Use these four dominoes to make a square that has the same number of dots on each side.

### Domino Square

##### Stage: 2, 3 and 4 Challenge Level:

Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

### Make 37

##### Stage: 2 and 3 Challenge Level:

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.

### Crossed Ends

##### Stage: 3 Challenge Level:

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

### Playing Connect Three

##### Stage: 3 Challenge Level:

In this game the winner is the first to complete a row of three. Are some squares easier to land on than others?

### Card Trick 2

##### Stage: 3 Challenge Level:

Can you explain how this card trick works?

### Top-heavy Pyramids

##### Stage: 3 Challenge Level:

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

### Eleven

##### Stage: 3 Challenge Level:

Replace each letter with a digit to make this addition correct.

### Cubes Within Cubes

##### Stage: 2 and 3 Challenge Level:

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?