Search by Topic

Resources tagged with Visualising similar to Differences:

Filter by: Content type:
Stage:
Challenge level:

Picturing Square Numbers

Stage: 3 Challenge Level:

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Painted Cube

Stage: 3 Challenge Level:

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?

Route to Infinity

Stage: 3 Challenge Level:

Can you describe this route to infinity? Where will the arrows take you next?

Christmas Chocolates

Stage: 3 Challenge Level:

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

Marbles in a Box

Stage: 3 Challenge Level:

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

On the Edge

Stage: 3 Challenge Level:

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

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?

Cuboids

Stage: 3 Challenge Level:

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Tourism

Stage: 3 Challenge Level:

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.

Convex Polygons

Stage: 3 Challenge Level:

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

Picturing Triangle Numbers

Stage: 3 Challenge Level:

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

Hidden Rectangles

Stage: 3 Challenge Level:

Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?

Threesomes

Stage: 3 Challenge Level:

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?

An Unusual Shape

Stage: 3 Challenge Level:

Can you maximise the area available to a grazing goat?

AMGM

Stage: 4 Challenge Level:

Can you use the diagram to prove the AM-GM inequality?

Konigsberg Plus

Stage: 3 Challenge Level:

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.

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?

Cubes Within Cubes Revisited

Stage: 3 Challenge Level:

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?

Concrete Wheel

Stage: 3 Challenge Level:

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

Partly Painted Cube

Stage: 4 Challenge Level:

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?

Eight Hidden Squares

Stage: 2 and 3 Challenge Level:

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?

Squares in Rectangles

Stage: 3 Challenge Level:

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?

Is There a Theorem?

Stage: 3 Challenge Level:

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?

Seven Squares

Stage: 3 Challenge Level:

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

Cuboid Challenge

Stage: 3 Challenge Level:

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

Chess

Stage: 3 Challenge Level:

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?

Clocked

Stage: 3 Challenge Level:

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?

Tessellating Hexagons

Stage: 3 Challenge Level:

Which hexagons tessellate?

Stage: 3 Challenge Level:

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

Squares, Squares and More Squares

Stage: 3 Challenge Level:

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

Yih or Luk Tsut K'i or Three Men's Morris

Stage: 3, 4 and 5 Challenge Level:

Some puzzles requiring no knowledge of knot theory, just a careful inspection of the patterns. A glimpse of the classification of knots and a little about prime knots, crossing numbers and. . . .

A Tilted Square

Stage: 4 Challenge Level:

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

How Many Dice?

Stage: 3 Challenge Level:

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. . . .

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.

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. . . .

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. . . .

Frogs

Stage: 3 Challenge Level:

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

Triangles Within Pentagons

Stage: 4 Challenge Level:

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

Triangles Within Triangles

Stage: 4 Challenge Level:

Can you find a rule which connects consecutive triangular numbers?

Square Coordinates

Stage: 3 Challenge Level:

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?

Stage: 3 Challenge Level:

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

Steel Cables

Stage: 4 Challenge Level:

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Troublesome Dice

Stage: 3 Challenge Level:

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

Bands and Bridges: Bringing Topology Back

Stage: 2 and 3

Lyndon Baker describes how the Mobius strip and Euler's law can introduce pupils to the idea of topology.

Khun Phaen Escapes to Freedom

Stage: 3 Challenge Level:

Slide the pieces to move Khun Phaen past all the guards into the position on the right from which he can escape to freedom.

Stage: 3 Challenge Level:

Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?

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?

One and Three

Stage: 4 Challenge Level:

Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .

Three Frogs

Stage: 4 Challenge Level:

Three frogs hopped onto the table. A red frog on the left a green in the middle and a blue frog on the right. Then frogs started jumping randomly over any adjacent frog. Is it possible for them to. . . .

Natural Sum

Stage: 4 Challenge Level:

The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .