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Resources tagged with Visualising similar to Extending Great Squares:

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Intersecting Circles

Stage: 3 Challenge Level:

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

Like a Circle in a Spiral

Stage: 2, 3 and 4 Challenge Level:

A cheap and simple toy with lots of mathematics. Can you interpret the images that are produced? Can you predict the pattern that will be produced using different wheels?

Framed

Stage: 3 Challenge Level:

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

Fence It

Stage: 3 Challenge Level:

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

Tetra Square

Stage: 3 Challenge Level:

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.

Pyramid Numbers

Stage: 2 Challenge Level:

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

Dissect

Stage: 3 Challenge Level:

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

Tied Up

Stage: 3 Challenge Level:

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

Trice

Stage: 3 Challenge Level:

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

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?

An Unusual Shape

Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

More Pebbles

Stage: 2 and 3 Challenge Level:

Have a go at this 3D extension to the Pebbles problem.

Two Squared

Stage: 2 Challenge Level:

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

Stage: 3 Challenge Level:

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?

Isosceles Triangles

Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Redblue

Stage: 2 Challenge Level:

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

All in the Mind

Stage: 3 Challenge Level:

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. . . .

Muggles Magic

Stage: 3 Challenge Level:

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

Dodecamagic

Stage: 2 Challenge Level:

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?

Nine-pin Triangles

Stage: 2 Challenge Level:

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

Map Folding

Stage: 2 Challenge Level:

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?

Jomista Mat

Stage: 2 Challenge Level:

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

Folding Flowers 2

Stage: 2 Challenge Level:

Make a flower design using the same shape made out of different sizes of paper.

Regular Rings 1

Stage: 2 Challenge Level:

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

World of Tan 1 - Granma T

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Granma T?

Folding Flowers 1

Stage: 2 Challenge Level:

Can you visualise what shape this piece of paper will make when it is folded?

Weighty Problem

Stage: 3 Challenge Level:

The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .

Midpoint Triangle

Stage: 2 Challenge Level:

Can you cut up a square in the way shown and make the pieces into a triangle?

Regular Rings 2

Stage: 2 Challenge Level:

What shape is made when you fold using this crease pattern? Can you make a ring design?

Coordinate Patterns

Stage: 3 Challenge Level:

Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?

Putting Two and Two Together

Stage: 2 Challenge Level:

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?

Take Ten

Stage: 3 Challenge Level:

Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3. . . .

Triangular Faces

Stage: 2 Challenge Level:

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

Concrete Wheel

Stage: 3 Challenge Level:

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

The Old Goats

Stage: 3 Challenge Level:

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .

World of Tan 11 - the Past, Present and Future

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of the telescope and microscope?

World of Tan 19 - Working Men

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

Stage: 3 Challenge Level:

How many different symmetrical shapes can you make by shading triangles or squares?

World of Tan 6 - Junk

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this junk?

World of Tan 20 - Fractions

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the chairs?

World of Tan 21 - Almost There Now

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

World of Tan 5 - Rocket

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of the rocket?

World of Tan 13 - A Storm in a Tea Cup

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of these convex shapes?

Cutting a Cube

Stage: 3 Challenge Level:

A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?

World of Tan 9 - Animals

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this goat and giraffe?

Counting Cards

Stage: 2 Challenge Level:

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?

World of Tan 8 - Sports Car

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this sports car?

Making Tangrams

Stage: 2 Challenge Level:

Here's a simple way to make a Tangram without any measuring or ruling lines.

Playground Snapshot

Stage: 2 and 3 Challenge Level:

The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?

World of Tan 22 - an Appealing Stroll

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of the child walking home from school?