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Resources tagged with Visualising similar to Carroll Diagrams:

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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 > Visualising

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Domino Numbers

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

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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Neighbours

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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Alquerque II

Stage: 1 Challenge Level: Challenge Level:1

A variant on the game Alquerque

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Change Around

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

Move just three of the circles so that the triangle faces in the opposite direction.

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Dodecamagic

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

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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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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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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Painting Possibilities

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

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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Multiplication Series: Illustrating Number Properties with Arrays

Stage: 1 and 2

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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Red Even

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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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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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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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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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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Paper Patchwork 1

Stage: 1 Challenge Level: Challenge Level:1

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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Three Cubed

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

Can you make a 3x3 cube with these shapes made from small cubes?

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Overlaps

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

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

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Coded Hundred Square

Stage: 2 Challenge Level: Challenge Level:1

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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Rearrange the Square

Stage: 1 Challenge Level: Challenge Level:1

We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?

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Cubes Cut Into Four Pieces

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

Eight children each had a cube made from modelling clay. They cut them into four pieces which were all exactly the same shape and size. Whose pieces are the same? Can you decide who made each set?

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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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Posting Triangles

Stage: 1 Challenge Level: Challenge Level:1

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

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Tricky Triangles

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

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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Hundred Square

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

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?

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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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Shadow Play

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

Here are shadows of some 3D shapes. What shapes could have made them?

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Dragons and Swans

Stage: 1 Challenge Level: Challenge Level:1

A game for two players. You'll need some counters.

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Skeleton Shapes

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

How many balls of modelling clay and how many straws does it take to make these skeleton shapes?

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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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Nine-pin Triangles

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

How many different triangles can you make on a circular pegboard that has nine pegs?

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Start Cube Drilling

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

Imagine a 3 by 3 by 3 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will have holes drilled through them?

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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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Horizontal Vertical

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

Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?

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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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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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Paper Patchwork 2

Stage: 1 Challenge Level: Challenge Level:1

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

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Teddy Bear Line-up

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

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

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How Would We Count?

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

An activity centred around observations of dots and how we visualise number arrangement patterns.

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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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Circles, Circles

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

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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Move a Match

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

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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Triple Cubes

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

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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Cuboid-in-a-box

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

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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Square Corners

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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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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Four Triangles Puzzle

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

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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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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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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Tessellating Capitals

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

Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.

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Odd Squares

Stage: 2 Challenge Level: Challenge Level:1

Think of a number, square it and subtract your starting number. Is the number you’re left with odd or even? How do the images help to explain this?