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Broad Topics > Information and Communications Technology > smartphone

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Hexy-metry

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?

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Where to Land

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Chris is enjoying a swim but needs to get back for lunch. If she can swim at 3 m/s and run at 7m/sec, how far along the bank should she land in order to get back as quickly as possible?

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Think of Two Numbers

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Funny Factorisation

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Some 4 digit numbers can be written as the product of a 3 digit number and a 2 digit number using the digits 1 to 9 each once and only once. The number 4396 can be written as just such a product. Can. . . .

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Circles in Quadrilaterals

Stage: 4 Challenge Level: Challenge Level:1

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

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Dozens

Stage: 3 Challenge Level: Challenge Level:1

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?

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Shady Symmetry

Stage: 3 Challenge Level: Challenge Level:1

How many different symmetrical shapes can you make by shading triangles or squares?

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Two and Two

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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On the Edge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here are four tiles. They can be arranged in a 2 by 2 square so that this large square has a green edge. If the tiles are moved around, we can make a 2 by 2 square with a blue edge... Now try to. . . .

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Can They Be Equal?

Stage: 3 Challenge Level: Challenge Level:1

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

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Summing Consecutive Numbers

Stage: 3 Challenge Level: Challenge Level:1

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

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Legs Eleven

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Take any four digit number. Move the first digit to the 'back of the queue' and move the rest along. Now add your two numbers. What properties do your answers always have?

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How Old Am I?

Stage: 4 Challenge Level: Challenge Level:1

In 15 years' time my age will be the square of my age 15 years ago. Can you work out my age, and when I had other special birthdays?

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Going Round in Circles

Stage: 3 Challenge Level: Challenge Level:1

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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The Spider and the Fly

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?

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Inscribed in a Circle

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

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Semi-detached

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

A square of area 40 square cms is inscribed in a semicircle. Find the area of the square that could be inscribed in a circle of the same radius.

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Special Numbers

Stage: 3 Challenge Level: Challenge Level:1

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?

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Marbles in a Box

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

In a three-dimensional version of noughts and crosses, how many winning lines can you make?

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Number Daisy

Stage: 3 Challenge Level: Challenge Level:1

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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Napkin

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A napkin is folded so that a corner coincides with the midpoint of an opposite edge . Investigate the three triangles formed .

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Largest Product

Stage: 3 and 4 Challenge Level: Challenge Level:1

Which set of numbers that add to 10 have the largest product?

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Curvy Areas

Stage: 4 Challenge Level: Challenge Level:1

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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Product Sudoku

Stage: 3, 4 and 5 Challenge Level: Challenge Level:1

The clues for this Sudoku are the product of the numbers in adjacent squares.

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Elevenses

Stage: 3 Challenge Level: Challenge Level:1

How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

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American Billions

Stage: 3 Challenge Level: Challenge Level:1

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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Repetitiously

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The number 2.525252525252.... can be written as a fraction. What is the sum of the denominator and numerator?

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Sending a Parcel

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

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Differences

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

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How Much Can We Spend?

Stage: 3 Challenge Level: Challenge Level:1

A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

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Counting Factors

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Is there an efficient way to work out how many factors a large number has?

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Take Three from Five

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?

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Litov's Mean Value Theorem

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...

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Cuboids

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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M, M and M

Stage: 3 Challenge Level: Challenge Level:1

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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Quadrilaterals Game

Stage: 3 Challenge Level: Challenge Level:1

A game for 2 or more people, based on the traditional card game Rummy. Players aim to make two `tricks', where each trick has to consist of a picture of a shape, a name that describes that shape, and. . . .

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Searching for Mean(ing)

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?

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Ben's Game

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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Partly Circles

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the same and what is different about these circle questions? What connections can you make?

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Squares in Rectangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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Handshakes

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

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Nicely Similar

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

If the hypotenuse (base) length is 100cm and if an extra line splits the base into 36cm and 64cm parts, what were the side lengths for the original right-angled triangle?

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Days and Dates

Stage: 4 Challenge Level: Challenge Level:1

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

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Trapezium Four

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

The diagonals of a trapezium divide it into four parts. Can you create a trapezium where three of those parts are equal in area?

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Two Ladders

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Two ladders are propped up against facing walls. The end of the first ladder is 10 metres above the foot of the first wall. The end of the second ladder is 5 metres above the foot of the second. . . .

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Compare Areas

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Which has the greatest area, a circle or a square inscribed in an isosceles, right angle triangle?

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Mirror, Mirror...

Stage: 3 Challenge Level: Challenge Level:1

Explore the effect of reflecting in two parallel mirror lines.

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Arclets

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

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Salinon

Stage: 4 Challenge Level: Challenge Level:1

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?

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Painted Cube

Stage: 3 Challenge Level: Challenge Level:1

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?