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Broad Topics > Information and Communications Technology > smartphone

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Consecutive Negative Numbers

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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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Consecutive Numbers

Stage: 2 and 3 Challenge Level: Challenge Level:1

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Weights

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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Make 37

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

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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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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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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Sweet Shop

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

Five children went into the sweet shop after school. There were choco bars, chews, mini eggs and lollypops, all costing under 50p. Suggest a way in which Nathan could spend all his money.

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Eight Hidden Squares

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

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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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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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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Children at Large

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

There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?

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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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Inscribed in a Circle

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

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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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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Who Is the Fairest of Them All?

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

Explore the effect of combining enlargements.

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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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Picturing Square Numbers

Stage: 3 Challenge Level: Challenge Level:1

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

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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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1 Step 2 Step

Stage: 3 Challenge Level: Challenge Level:1

Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?

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CD Heaven

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

All CD Heaven stores were given the same number of a popular CD to sell for £24. In their two week sale each store reduces the price of the CD by 25% ... How many CDs did the store sell at. . . .

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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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Route to Infinity

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

Can you describe this route to infinity? Where will the arrows take you next?

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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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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?

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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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An Unusual Shape

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

Can you maximise the area available to a grazing goat?

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Beelines

Stage: 4 Challenge Level: Challenge Level:1

Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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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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Fence It

Stage: 3 Challenge Level: Challenge Level:1

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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14 Divisors

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

What is the smallest number with exactly 14 divisors?

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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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Difference Sudoku

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

Use the differences to find the solution to this Sudoku.

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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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Keep it Simple

Stage: 3 Challenge Level: Challenge Level:1

Can all unit fractions be written as the sum of two unit fractions?

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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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Attractive Rotations

Stage: 3 Challenge Level: Challenge Level:1

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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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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Areas and Ratios

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

What is the area of the quadrilateral APOQ? Working on the building blocks will give you some insights that may help you to work it out.

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One and Three

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

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. . . .

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Matchless

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

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 ?

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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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What's it Worth?

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

There are lots of different methods to find out what the shapes are worth - how many can you find?

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Consecutive Seven

Stage: 3 Challenge Level: Challenge Level:1

Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

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Areas of Parallelograms

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

Can you find the area of a parallelogram defined by two vectors?

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Dating Made Easier

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

If a sum invested gains 10% each year how long before it has doubled its value?

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Tet-trouble

Stage: 4 Challenge Level: Challenge Level:1

Show that is it impossible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units...

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Sitting Pretty

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

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?

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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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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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