# Resources tagged with: Creating and manipulating expressions and formulae

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### There are 130 results

Broad Topics > Algebraic expressions, equations and formulae > Creating and manipulating expressions and formulae

### Hallway Borders

##### Age 11 to 14 Challenge Level:

What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?

### Top-heavy Pyramids

##### Age 11 to 14 Challenge Level:

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

### Number Pyramids

##### Age 11 to 14 Challenge Level:

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

### Magic W

##### Age 14 to 16 Challenge Level:

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

### Leonardo's Problem

##### Age 14 to 18 Challenge Level:

A, B & C own a half, a third and a sixth of a coin collection. Each grab some coins, return some, then share equally what they had put back, finishing with their own share. How rich are they?

### A Tilted Square

##### Age 14 to 16 Challenge Level:

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

### Christmas Chocolates

##### Age 11 to 14 Challenge Level:

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

### Unit Interval

##### Age 14 to 18 Challenge Level:

Take any two numbers between 0 and 1. Prove that the sum of the numbers is always less than one plus their product?

### The Simple Life

##### Age 11 to 14 Challenge Level:

The answer is $5x+8y$... What was the question?

### Plum Tree

##### Age 14 to 18 Challenge Level:

Label this plum tree graph to make it totally magic!

### Partitioning Revisited

##### Age 11 to 14 Challenge Level:

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

### Matchless

##### Age 14 to 16 Challenge Level:

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

### Painted Cube

##### Age 14 to 16 Challenge Level:

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?

### Interactive Number Patterns

##### Age 14 to 16 Challenge Level:

How good are you at finding the formula for a number pattern ?

### Chocolate Maths

##### Age 11 to 14 Challenge Level:

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

### Regular Hexagon Loops

##### Age 11 to 14 Challenge Level:

Make some loops out of regular hexagons. What rules can you discover?

### Multiply the Addition Square

##### Age 11 to 14 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?

### Crossed Ends

##### Age 11 to 14 Challenge Level:

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

### AMGM

##### Age 14 to 16 Challenge Level:

Can you use the diagram to prove the AM-GM inequality?

### Chocolate 2010

##### Age 14 to 16 Challenge Level:

First of all, pick the number of times a week that you would like to eat chocolate. Multiply this number by 2...

### More Number Pyramids

##### Age 11 to 14 Challenge Level:

When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

### Never Prime

##### Age 14 to 16 Challenge Level:

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

### Always Perfect

##### Age 14 to 16 Challenge Level:

Show that if you add 1 to the product of four consecutive numbers the answer is ALWAYS a perfect square.

### Your Number Was...

##### Age 11 to 14 Challenge Level:

Think of a number and follow my instructions. Tell me your answer, and I'll tell you what you started with! Can you explain how I know?

##### Age 11 to 14 Challenge Level:

Think of a number, add one, double it, take away 3, add the number you first thought of, add 7, divide by 3 and take away the number you first thought of. You should now be left with 2. How do I. . . .

### Summing Consecutive Numbers

##### Age 11 to 14 Challenge Level:

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

### Cubes Within Cubes Revisited

##### Age 11 to 14 Challenge Level:

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

### Think of Two Numbers

##### Age 11 to 14 Challenge Level:

Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?

### Magic Squares for Special Occasions

##### Age 11 to 16

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.

### Special Numbers

##### Age 11 to 14 Challenge Level:

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?

### Triangles Within Pentagons

##### Age 14 to 16 Challenge Level:

Show that all pentagonal numbers are one third of a triangular number.

### Triangles Within Squares

##### Age 14 to 16 Challenge Level:

Can you find a rule which relates triangular numbers to square numbers?

### Always the Same

##### Age 11 to 14 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?

### Triangles Within Triangles

##### Age 14 to 16 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

### ' Tis Whole

##### Age 14 to 18 Challenge Level:

Take a few whole numbers away from a triangle number. If you know the mean of the remaining numbers can you find the triangle number and which numbers were removed?

### Attractive Tablecloths

##### Age 14 to 16 Challenge Level:

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

### Hand Swap

##### Age 14 to 16 Challenge Level:

My train left London between 6 a.m. and 7 a.m. and arrived in Paris between 9 a.m. and 10 a.m. At the start and end of the journey the hands on my watch were in exactly the same positions but the. . . .

### Good Work If You Can Get It

##### Age 11 to 14 Challenge Level:

A job needs three men but in fact six people do it. When it is finished they are all paid the same. How much was paid in total, and much does each man get if the money is shared as Fred suggests?

### Is it Magic or Is it Maths?

##### Age 11 to 14 Challenge Level:

Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying. . . .

##### Age 11 to 14 Challenge Level:

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

### Special Sums and Products

##### Age 11 to 14 Challenge Level:

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.

### Diophantine N-tuples

##### Age 14 to 16 Challenge Level:

Can you explain why a sequence of operations always gives you perfect squares?

### Three Four Five

##### Age 14 to 16 Challenge Level:

Two semi-circles (each of radius 1/2) touch each other, and a semi-circle of radius 1 touches both of them. Find the radius of the circle which touches all three semi-circles.

### The Number Jumbler

##### Age 7 to 14 Challenge Level:

The Number Jumbler can always work out your chosen symbol. Can you work out how?

### Fibs

##### Age 11 to 14 Challenge Level:

The well known Fibonacci sequence is 1 ,1, 2, 3, 5, 8, 13, 21.... How many Fibonacci sequences can you find containing the number 196 as one of the terms?

### Marbles in a Box

##### Age 11 to 16 Challenge Level:

How many winning lines can you make in a three-dimensional version of noughts and crosses?

### Always a Multiple?

##### Age 11 to 14 Challenge Level:

Think of a two digit number, reverse the digits, and add the numbers together. Something special happens...

### Seven Squares

##### Age 11 to 14 Challenge Level:

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

### Janine's Conjecture

##### Age 14 to 16 Challenge Level:

Janine noticed, while studying some cube numbers, that if you take three consecutive whole numbers and multiply them together and then add the middle number of the three, you get the middle number. . . .

### Steel Cables

##### Age 14 to 16 Challenge Level:

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?