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Resources tagged with Visualising similar to Dicing with Numbers:

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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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Painted Cube

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

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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Christmas Chocolates

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

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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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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Marbles in a Box

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

How many winning lines can you make in a three-dimensional version of noughts and crosses?

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Route to Infinity

Stage: 3 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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Concrete Wheel

Stage: 3 Challenge Level: Challenge Level:1

A huge wheel is rolling past your window. What do you see?

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On the Edge

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

If you move the tiles around, can you make squares with different coloured edges?

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Triangle Inequality

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

ABC is an equilateral triangle and P is a point in the interior of the triangle. We know that AP = 3cm and BP = 4cm. Prove that CP must be less than 10 cm.

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Seven Squares - Group-worthy Task

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

Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?

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Tourism

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

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

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Drilling Many Cubes

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

A useful visualising exercise which offers opportunities for discussion and generalising, and which could be used for thinking about the formulae needed for generating the results on a spreadsheet.

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Clocked

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

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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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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Picturing Triangular Numbers

Stage: 3 Challenge Level: Challenge Level:1

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

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Intersecting Circles

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

Three circles have a maximum of six intersections with each other. What is the maximum number of intersections that a hundred circles could have?

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Threesomes

Stage: 3 Challenge Level: Challenge Level:1

Imagine an infinitely large sheet of square dotty paper on which you can draw triangles of any size you wish (providing each vertex is on a dot). What areas is it/is it not possible to draw?

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Konigsberg Plus

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

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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Convex Polygons

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

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

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Keep Your Distance

Stage: 3 Challenge Level: Challenge Level:1

Can you mark 4 points on a flat surface so that there are only two different distances between them?

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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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Chess

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

What would be the smallest number of moves needed to move a Knight from a chess set from one corner to the opposite corner of a 99 by 99 square board?

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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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Cuboid Challenge

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

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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Seven Squares

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

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?

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How Many Dice?

Stage: 3 Challenge Level: Challenge Level:1

A standard die has the numbers 1, 2 and 3 are opposite 6, 5 and 4 respectively so that opposite faces add to 7? If you make standard dice by writing 1, 2, 3, 4, 5, 6 on blank cubes you will find. . . .

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Cubes Within Cubes Revisited

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

Imagine starting with one yellow cube and covering it all over with a single layer of red cubes, and then covering that cube with a layer of blue cubes. How many red and blue cubes would you need?

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Is There a Theorem?

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

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

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Tic Tac Toe

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

In the game of Noughts and Crosses there are 8 distinct winning lines. How many distinct winning lines are there in a game played on a 3 by 3 by 3 board, with 27 cells?

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All in the Mind

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

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

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A Tilted Square

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

The opposite vertices of a square have coordinates (a,b) and (c,d). What are the coordinates of the other vertices?

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Painting Cubes

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

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

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Sea Defences

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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Tetra Square

Stage: 3 Challenge Level: Challenge Level:1

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

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Königsberg

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

Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?

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Coloured Edges

Stage: 3 Challenge Level: Challenge Level:1

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

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Flight of the Flibbins

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

Blue Flibbins are so jealous of their red partners that they will not leave them on their own with any other bue Flibbin. What is the quickest way of getting the five pairs of Flibbins safely to. . . .

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Squares, Squares and More Squares

Stage: 3 Challenge Level: Challenge Level:1

Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

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Zooming in on the Squares

Stage: 2 and 3

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

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Pattern Power

Stage: 1, 2 and 3

Mathematics is the study of patterns. Studying pattern is an opportunity to observe, hypothesise, experiment, discover and create.

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Dice, Routes and Pathways

Stage: 1, 2 and 3

This article for teachers discusses examples of problems in which there is no obvious method but in which children can be encouraged to think deeply about the context and extend their ability to. . . .

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Square Coordinates

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

A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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Triangles Within Pentagons

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

Show that all pentagonal numbers are one third of a triangular number.

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Partly Painted Cube

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

Jo made a cube from some smaller cubes, painted some of the faces of the large cube, and then took it apart again. 45 small cubes had no paint on them at all. How many small cubes did Jo use?

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Troublesome Dice

Stage: 3 Challenge Level: Challenge Level:1

When dice land edge-up, we usually roll again. But what if we didn't...?

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3D Stacks

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

Can you find a way of representing these arrangements of balls?

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Auditorium Steps

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

What is the shape of wrapping paper that you would need to completely wrap this model?

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Triangles Within Triangles

Stage: 4 Challenge Level: Challenge Level:1

Can you find a rule which connects consecutive triangular numbers?

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Conway's Chequerboard Army

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

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

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Travelling Salesman

Stage: 3 Challenge Level: Challenge Level:1

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

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Frogs

Stage: 3 Challenge Level: Challenge Level:1

How many moves does it take to swap over some red and blue frogs? Do you have a method?