Resources tagged with: Creating and manipulating expressions and formulae

Filter by: Content type:
Age range:
Challenge level:

There are 131 results

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

Screen Shot

Age 14 to 16
Challenge Level

A moveable screen slides along a mirrored corridor towards a centrally placed light source. A ray of light from that source is directed towards a wall of the corridor, which it strikes at 45 degrees. . . .

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. . . .

' 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?

Simplifying Doughnut

Age 14 to 18
Challenge Level

An algebra task which depends on members of the group noticing the needs of others and responding.

Consecutive Squares

Age 14 to 16
Challenge Level

The squares of any 8 consecutive numbers can be arranged into two sets of four numbers with the same sum. True of false?

Snookered

Age 14 to 18
Challenge Level

In a snooker game the brown ball was on the lip of the pocket but it could not be hit directly as the black ball was in the way. How could it be potted by playing the white ball off a cushion?

Algebra Match

Age 11 to 16
Challenge Level

A task which depends on members of the group noticing the needs of others and responding.

Always Two

Age 14 to 18
Challenge Level

Find all the triples of numbers a, b, c such that each one of them plus the product of the other two is always 2.

Triangles Within Triangles

Age 14 to 16
Challenge Level

Can you find a rule which connects consecutive triangular numbers?

Salinon

Age 14 to 16
Challenge Level

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

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?

Your Number Is...

Age 7 to 14
Challenge Level

Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?

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?

Perfectly Square

Age 14 to 16
Challenge Level

The sums of the squares of three related numbers is also a perfect square - can you explain why?

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?

Pair Products

Age 14 to 16
Challenge Level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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?

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.

Sitting Pretty

Age 14 to 16
Challenge Level

A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?

Triangles Within Squares

Age 14 to 16
Challenge Level

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

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?

Lower Bound

Age 14 to 16
Challenge Level

What would you get if you continued this sequence of fraction sums? 1/2 + 2/1 = 2/3 + 3/2 = 3/4 + 4/3 =

How Big?

Age 11 to 14
Challenge Level

If the sides of the triangle in the diagram are 3, 4 and 5, what is the area of the shaded square?

The Pillar of Chios

Age 14 to 16
Challenge Level

Semicircles are drawn on the sides of a rectangle. Prove that the sum of the areas of the four crescents is equal to the area of the rectangle.

One and Three

Age 14 to 16
Challenge Level

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

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.

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. . . .

AMGM

Age 14 to 16
Challenge Level

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

How Many Miles to Go?

Age 11 to 14
Challenge Level

How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

Pick's Theorem

Age 14 to 16
Challenge Level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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.

Gutter

Age 14 to 16
Challenge Level

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

Triangles Within Pentagons

Age 14 to 16
Challenge Level

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

Square Number Surprises

Age 14 to 16
Challenge Level

There are unexpected discoveries to be made about square numbers...

Algebra from Geometry

Age 11 to 16
Challenge Level

Account of an investigation which starts from the area of an annulus and leads to the formula for the difference of two squares.

Puzzling Place Value

Age 14 to 16
Challenge Level

Can you explain what is going on in these puzzling number tricks?

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?

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?

Generating Triples

Age 14 to 16
Challenge Level

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Training Schedule

Age 14 to 16
Challenge Level

The heptathlon is an athletics competition consisting of 7 events. Can you make sense of the scoring system in order to advise a heptathlete on the best way to reach her target?

Difference of Two Squares

Age 14 to 16
Challenge Level

What is special about the difference between squares of numbers adjacent to multiples of three?

Robert's Spreadsheet

Age 14 to 16
Challenge Level

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

How Do You React?

Age 14 to 16
Challenge Level

To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...

Reversals

Age 11 to 14
Challenge Level

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