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Resources tagged with Working systematically similar to Winning the Lottery:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

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Winning the Lottery

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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Arrangements

Stage: 2 Challenge Level: Challenge Level:1

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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Junior Frogs

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

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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Colour in the Square

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

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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Twinkle Twinkle

Stage: 2 Challenge Level: Challenge Level:1

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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Teddy Town

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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Combining Cuisenaire

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

Can you find all the different ways of lining up these Cuisenaire rods?

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A Bit of a Dicey Problem

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

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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Difference

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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Roll These Dice

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

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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Multiples Grid

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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A Square of Numbers

Stage: 2 Challenge Level: Challenge Level:1

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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More Transformations on a Pegboard

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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One to Fifteen

Stage: 2 Challenge Level: Challenge Level:1

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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Code Breaker

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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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Factor Lines

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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Counters

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

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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How Long Does it Take?

Stage: 2 Challenge Level: Challenge Level:1

In this matching game, you have to decide how long different events take.

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Dicey Perimeter, Dicey Area

Stage: 2 Challenge Level: Challenge Level:1

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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Calendar Cubes

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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Tri.'s

Stage: 2 Challenge Level: Challenge Level:1

How many triangles can you make on the 3 by 3 pegboard?

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Sticks and Triangles

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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Symmetry Challenge

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

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

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Is a Square a Rectangle?

Stage: 2 Challenge Level: Challenge Level:1

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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Seven Flipped

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Snails' Trails

Stage: 2 Challenge Level: Challenge Level:1

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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Palindromic Date

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

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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Buying a Balloon

Stage: 2 Challenge Level: Challenge Level:1

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

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Seven Pots of Plants

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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Egyptian Rope

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

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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All the Digits

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

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

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The Pet Graph

Stage: 2 Challenge Level: Challenge Level:1

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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Ancient Runes

Stage: 2 Challenge Level: Challenge Level:1

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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Six Is the Sum

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

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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Making Cuboids

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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Eight Queens

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

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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5 on the Clock

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

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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1 to 8

Stage: 2 Challenge Level: Challenge Level:1

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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Two on Five

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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Room Doubling

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

Investigate the different ways you could split up these rooms so that you have double the number.

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Pouring the Punch Drink

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

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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Octa Space

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

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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Sealed Solution

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

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Stairs

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

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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The Pied Piper of Hamelin

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

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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Consecutive Numbers

Stage: 2 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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It Figures

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

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Ice Cream

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

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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Making Boxes

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

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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Numerically Equal

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

Can you draw a square in which the perimeter is numerically equal to the area?