Resources tagged with: Ratio and proportion

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Broad Topics > Fractions, Decimals, Percentages, Ratio and Proportion > Ratio and proportion

Bus Stop

Age 14 to 16 Challenge Level:

Two buses leave at the same time from two towns Shipton and Veston on the same long road, travelling towards each other. At each mile along the road are milestones. The buses' speeds are constant. . . .

Rule of Three

Age 11 to 14 Challenge Level:

If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall?

Triathlon and Fitness

Age 11 to 14 Challenge Level:

The triathlon is a physically gruelling challenge. Can you work out which athlete burnt the most calories?

Circuit Training

Age 14 to 16 Challenge Level:

Mike and Monisha meet at the race track, which is 400m round. Just to make a point, Mike runs anticlockwise whilst Monisha runs clockwise. Where will they meet on their way around and will they ever. . . .

Washing Elephants

Age 11 to 14 Short Challenge Level:

How long will it take Mary and Nigel to wash an elephant if they work together?

Ratio or Proportion?

Age 7 to 14

An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.

Straw Scaffold

Age 11 to 14 Challenge Level:

Build a scaffold out of drinking-straws to support a cup of water

Hello Again

Age 11 to 14 Challenge Level:

Anne completes a circuit around a circular track in 40 seconds. Brenda runs in the opposite direction and meets Anne every 15 seconds. How long does it take Brenda to run around the track?

Speeding Boats

Age 14 to 16 Challenge Level:

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

Cereal Mix

Age 11 to 14 Challenge Level:

A farmer is supplying a mix of seeds, nuts and dried apricots to a manufacturer of crunchy cereal bars. What combination of ingredients costing £5 per kg could he supply?

Roasting Old Chestnuts 3

Age 11 to 16

Mainly for teachers. More mathematics of yesteryear.

A Scale for the Solar System

Age 14 to 16 Challenge Level:

The Earth is further from the Sun than Venus, but how much further? Twice as far? Ten times?

Slippage

Age 14 to 16 Challenge Level:

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance. . . .

Tray Bake

Age 11 to 14 Challenge Level:

My recipe is for 12 cakes - how do I change it if I want to make a different number of cakes?

Around and Back

Age 14 to 16 Challenge Level:

A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .

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. . . .

Burning Down

Age 14 to 16 Challenge Level:

One night two candles were lit. Can you work out how long each candle was originally?

Ratios and Dilutions

Age 14 to 16 Challenge Level:

Scientists often require solutions which are diluted to a particular concentration. In this problem, you can explore the mathematics of simple dilutions

Triangle in a Triangle

Age 14 to 16 Challenge Level:

Can you work out the fraction of the original triangle that is covered by the inner triangle?

Square Pegs

Age 11 to 14 Challenge Level:

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

Pythagoras’ Comma

Age 14 to 16 Challenge Level:

Using an understanding that 1:2 and 2:3 were good ratios, start with a length and keep reducing it to 2/3 of itself. Each time that took the length under 1/2 they doubled it to get back within range.

Make Your Own Solar System

Age 7 to 16 Challenge Level:

Making a scale model of the solar system

Rati-o

Age 11 to 14 Challenge Level:

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

Fractions Rectangle

Age 11 to 14 Challenge Level:

The large rectangle is divided into a series of smaller quadrilaterals and triangles. Can you untangle what fractional part is represented by each of the ten numbered shapes?

Ratio Sudoku 2

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

Ratio Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

Dilution Series Calculator

Age 14 to 16 Challenge Level:

Which dilutions can you make using 10ml pipettes and 100ml measuring cylinders?

Exact Dilutions

Age 14 to 16 Challenge Level:

Which exact dilution ratios can you make using only 2 dilutions?

Mixed up Mixture

Age 14 to 16 Challenge Level:

Can you fill in the mixed up numbers in this dilution calculation?

Nutrition and Cycling

Age 14 to 16 Challenge Level:

Andy wants to cycle from Land's End to John o'Groats. Will he be able to eat enough to keep him going?

Tin Tight

Age 14 to 16 Challenge Level:

What's the most efficient proportion for a 1 litre tin of paint?

Six Notes All Nice Ratios

Age 14 to 16 Challenge Level:

The Pythagoreans noticed that nice simple ratios of string length made nice sounds together.

Temperature

Age 11 to 14 Challenge Level:

Is there a temperature at which Celsius and Fahrenheit readings are the same?

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?

Arrh!

Age 14 to 16 Challenge Level:

Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. . . .

Do Unto Caesar

Age 11 to 14 Challenge Level:

At the beginning of the night three poker players; Alan, Bernie and Craig had money in the ratios 7 : 6 : 5. At the end of the night the ratio was 6 : 5 : 4. One of them won $1 200. What were the. . . .

Contact

Age 14 to 16 Challenge Level:

A circular plate rolls in contact with the sides of a rectangular tray. How much of its circumference comes into contact with the sides of the tray when it rolls around one circuit?

Rhombus in Rectangle

Age 14 to 16 Challenge Level:

Take any rectangle ABCD such that AB > BC. The point P is on AB and Q is on CD. Show that there is exactly one position of P and Q such that APCQ is a rhombus.

Oh for the Mathematics of Yesteryear

Age 11 to 14 Challenge Level:

A garrison of 600 men has just enough bread ... but, with the news that the enemy was planning an attack... How many ounces of bread a day must each man in the garrison be allowed, to hold out 45. . . .

Gift of Gems

Age 14 to 16 Challenge Level:

Four jewellers share their stock. Can you work out the relative values of their gems?

The Fastest Cyclist

Age 14 to 16 Challenge Level:

Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

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?

Semi-square

Age 14 to 16 Challenge Level:

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?

Wedge on Wedge

Age 14 to 16 Challenge Level:

Two right-angled triangles are connected together as part of a structure. An object is dropped from the top of the green triangle where does it pass the base of the blue triangle?

Zin Obelisk

Age 11 to 14 Challenge Level:

In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.

Conical Bottle

Age 14 to 16 Challenge Level:

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

A Shade Crossed

Age 14 to 16 Challenge Level:

Find the area of the shaded region created by the two overlapping triangles in terms of a and b?

A Chance to Win?

Age 11 to 14 Challenge Level:

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

Star Gazing

Age 14 to 16 Challenge Level:

Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star.

Golden Thoughts

Age 14 to 16 Challenge Level:

Rectangle PQRS has X and Y on the edges. Triangles PQY, YRX and XSP have equal areas. Prove X and Y divide the sides of PQRS in the golden ratio.