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Rabbit Run

Age 7 to 11 Challenge Level:

Ahmed has some wooden planks to use for three sides of a rabbit run against the shed. What quadrilaterals would he be able to make with the planks of different lengths?

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Rabbits in the Pen

Age 7 to 11 Challenge Level:

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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Race Time

Age 11 to 14 Short Challenge Level:

Frank and Gabriel competed in a 200m race. Interpret the different units used for their times to work out who won.

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Rachel's Problem

Age 14 to 16 Challenge Level:

Is it true that $99^n$ has 2n digits and $999^n$ has 3n digits? Investigate!

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Racing Odds

Age 11 to 14 Challenge Level:

In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair?

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Radioactive Triangle

Age 11 to 14 Short Challenge Level:

Weekly Problem 41 - 2014
Three straight lines divide an equilateral triangle into seven regions. What is the side length of the original triangle?

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Raffles and Strings

Age 16 to 18

How much are you likely to win from a raffle? How many loops will you make with some strings? Here, two guided examples can be found for you to work through.

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Rail Network

Age 7 to 11 Challenge Level:

This drawing shows the train track joining the Train Yard to all the stations labelled from A to S. Find a way for a train to call at all the stations and return to the Train Yard.

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Rain

Age 11 to 14 Short Challenge Level:

How many dry days did Aisha have on her holiday?

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Rain or Shine

Age 16 to 18 Challenge Level:

Predict future weather using the probability that tomorrow is wet given today is wet and the probability that tomorrow is wet given that today is dry.

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Rainstorm Sudoku

Age 14 to 16 Challenge Level:

Use the clues about the shaded areas to help solve this sudoku

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Raising the Roof

Age 14 to 16 Challenge Level:

How far should the roof overhang to shade windows from the mid-day sun?

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Ramping it Up

Age 16 to 18 Challenge Level:

Look at the calculus behind the simple act of a car going over a step.

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Random Inequalities

Age 16 to 18 Challenge Level:

Can you build a distribution with the maximum theoretical spread?

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Random Pattern

Age 14 to 18 Challenge Level:

Make your own random patterns

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Random Squares

Age 16 to 18 Challenge Level:

What is a random pattern?

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Random Variables - Continuous

Age 16 to 18

Resources to support an advanced course of statistics

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Random Variables - Discrete

Age 16 to 18

Resources to support an advanced course of statistics

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Randomness and Brownian Motion

Age 16 to 18

In Classical times the Pythagorean philosophers believed that all things were made up from a specific number of tiny indivisible particles called ‘monads’. Each object contained. . . .

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Rangan's Theory of Cycles

Age 14 to 18

In this beautifully written-up investigation Abhay describes his discovery of a 'theory of cycles'.

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Range of Averages

Age 11 to 14 Short Challenge Level:

Find these 4 numbers, given their mode, median and range.

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Rarity

Age 16 to 18 Challenge Level:

Show that it is rare for a ratio of ratios to be rational.

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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?

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Ratio and Proportion

The Ratio and Proportion collection of STEM resources

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Ratio and Proportion KS2

Age 7 to 11

This collection of activities for KS2 children focuses on ratio and proportion.

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Ratio Cut

Age 14 to 16 Short Challenge Level:

Cutting a rectangle from a corner to a point on the opposite side splits its area in the ratio 1:2. What is the ratio of a:b?

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Ratio of Areas

Age 14 to 16 Short Challenge Level:

What is the ratio of the area of the hexagon to the area of the triangle?

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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.

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Ratio Pairs 2

Age 7 to 11 Challenge Level:

A card pairing game involving knowledge of simple ratio.

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Ratio Pairs 3

Age 11 to 16 Challenge Level:

Match pairs of cards so that they have equivalent ratios.

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Ratio Riddle

Age 14 to 16 Short Challenge Level:

Can you work out the ratio b:c given the ratios a:b and a:c?

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Ratio Sudoku 1

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

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Ratio Sudoku 2

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios.

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Ratio Sudoku 3

Age 11 to 16 Challenge Level:

A Sudoku with clues as ratios or fractions.

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Ratio Swap

Age 11 to 14 Short Challenge Level:

How many adults would need to join this group of people to reverse this ratio?

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Ratio, Proportion & Rates of Change

Working on these problems will help your students develop a better understanding of ratio, proportion and rates of change.

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Ratio, Proportion & Rates of Change

Working on these problems will help you develop a better understanding of ratio, proportion and rates of change.

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Ratio, Proportion and Rates of Change - Short Problems

Age 11 to 16

A collection of short problems on ratio, proportion and rates of change.

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Rational Integer

Age 14 to 16 Short Challenge Level:

Weekly Problem 39 - 2012
For how many values of $n$ are both $n$ and $\frac{n+3}{n−1}$ integers?

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Rational Request

Age 16 to 18 Challenge Level:

Can you make a curve to match my friend's requirements?

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Rational Roots

Age 16 to 18 Challenge Level:

Given that a, b and c are natural numbers show that if sqrt a+sqrt b is rational then it is a natural number. Extend this to 3 variables.

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Rational Round

Age 16 to 18 Challenge Level:

Show that there are infinitely many rational points on the unit circle and no rational points on the circle x^2+y^2=3.

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Rationals Between...

Age 14 to 16 Challenge Level:

What fractions can you find between the square roots of 65 and 67?

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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

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Ratty

Age 11 to 14 Challenge Level:

If you know the sizes of the angles marked with coloured dots in this diagram which angles can you find by calculation?

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Reach 100

Age 7 to 14 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.

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Reach for Polydron

Age 16 to 18 Challenge Level:

A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.

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Reach for the Stars

Age 16 to 18 Challenge Level:

Some graphs grow so quickly you can reach dizzy heights...

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Reaction Rates

Age 16 to 18 Challenge Level:

Explore the possibilities for reaction rates versus concentrations with this non-linear differential equation

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Reaction Rates!

Age 16 to 18

Fancy learning a bit more about rates of reaction, but don't know where to look? Come inside and find out more...