Resources tagged with: Creating and manipulating expressions and formulae

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

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?

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 ?

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!

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?

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?

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?

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?

Triangles Within Pentagons

Age 14 to 16
Challenge Level

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

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?

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?

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?

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...

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?

Regular Hexagon Loops

Age 11 to 14
Challenge Level

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

Interactive Number Patterns

Age 14 to 16
Challenge Level

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

More Mathematical Mysteries

Age 11 to 14
Challenge Level

Write down a three-digit number Change the order of the digits to get a different number Find the difference between the two three digit numbers Follow the rest of the instructions then try. . . .

Can They Be Equal?

Age 11 to 14
Challenge Level

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Triangles Within Triangles

Age 14 to 16
Challenge Level

Can you find a rule which connects consecutive triangular numbers?

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.

Triangles Within Squares

Age 14 to 16
Challenge Level

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

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. . . .

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?

DOTS Division

Age 14 to 16
Challenge Level

Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.

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?

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.

Multiplication Square

Age 14 to 16
Challenge Level

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Harmonic Triangle

Age 14 to 16
Challenge Level

Can you see how to build a harmonic triangle? Can you work out the next two rows?

AMGM

Age 14 to 16
Challenge Level

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

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. . . .

More Number Pyramids

Age 11 to 14
Challenge Level

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

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?

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.

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?

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

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?

Hot Pursuit

Age 11 to 14
Challenge Level

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

The Number Jumbler

Age 7 to 14
Challenge Level

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

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?

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?

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?

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?

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. . . .

Pareq Calc

Age 14 to 16
Challenge Level

Triangle ABC is an equilateral triangle with three parallel lines going through the vertices. Calculate the length of the sides of the triangle if the perpendicular distances between the parallel. . . .

Sum Equals Product

Age 11 to 14
Challenge Level

The sum of the numbers 4 and 1 [1/3] is the same as the product of 4 and 1 [1/3]; that is to say 4 + 1 [1/3] = 4 � 1 [1/3]. What other numbers have the sum equal to the product and can this be. . . .

Reversals

Age 11 to 14
Challenge Level

Where should you start, if you want to finish back where you started?

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?

Adding in Rows

Age 11 to 14
Challenge Level

List any 3 numbers. It is always possible to find a subset of adjacent numbers that add up to a multiple of 3. Can you explain why and prove it?