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Resources tagged with Working systematically similar to Holes:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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

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Brush Loads

Stage: 2 Challenge Level: Challenge Level:1

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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Map Folding

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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Single Track

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

What is the best way to shunt these carriages so that each train can continue its journey?

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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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Shunting Puzzle

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

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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Tangram Tangle

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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Three Sets of Cubes, Two Surfaces

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

How many models can you find which obey these rules?

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Display Boards

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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Waiting for Blast Off

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

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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Open Boxes

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

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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Knight's Swap

Stage: 2 Challenge Level: Challenge Level:1

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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Tessellate the Triominoes

Stage: 1 Challenge Level: Challenge Level:1

What happens when you try and fit the triomino pieces into these two grids?

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Celtic Knot

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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Cover the Camel

Stage: 1 Challenge Level: Challenge Level:1

Can you cover the camel with these pieces?

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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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Cuisenaire Counting

Stage: 1 Challenge Level: Challenge Level:1

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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Two by One

Stage: 2 Challenge Level: Challenge Level:1

An activity making various patterns with 2 x 1 rectangular tiles.

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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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Putting Two and Two Together

Stage: 2 Challenge Level: Challenge Level:1

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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Growing Garlic

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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3 Blocks Towers

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

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

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Coloured Squares

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

Use the clues to colour each square.

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Cubes Here and There

Stage: 2 Challenge Level: Challenge Level:1

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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Routes 1 and 5

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

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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Snakes

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

Explore the different snakes that can be made using 5 cubes.

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We'll Bang the Drum

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many different rhythms can you make by putting two drums on the wheel?

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Dienes' Logiblocs

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

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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Cover the Tray

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

These practical challenges are all about making a 'tray' and covering it with paper.

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Creating Cubes

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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Homes

Stage: 1 Challenge Level: Challenge Level:1

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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Quadrilaterals

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

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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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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Teddy Town

Stage: 1, 2 and 3 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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Briefcase Lock

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

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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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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Counting Cards

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

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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Here to There 1 2 3

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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Zargon Glasses

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

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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Paw Prints

Stage: 2 Challenge Level: Challenge Level:1

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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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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Whose Sandwich?

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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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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Adding Plus

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

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

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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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Calcunos

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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A City of Towers

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

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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Mrs Beeswax

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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Jumping Cricket

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

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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Rabbits in the Pen

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

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

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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?