Resources tagged with: Visualising

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Broad Topics > Thinking Mathematically > Visualising

Reflecting Squarely

Age 11 to 14 Challenge Level:

In how many ways can you fit all three pieces together to make shapes with line symmetry?

Fred the Class Robot

Age 7 to 11 Challenge Level:

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

Coloured Edges

Age 11 to 14 Challenge Level:

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?

Eight Hidden Squares

Age 7 to 14 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?

Baravelle

Age 7 to 16 Challenge Level:

What can you see? What do you notice? What questions can you ask?

Polygon Rings

Age 11 to 14 Challenge Level:

Join pentagons together edge to edge. Will they form a ring?

Dissect

Age 11 to 14 Challenge Level:

What is the minimum number of squares a 13 by 13 square can be dissected into?

Semi-regular Tessellations

Age 11 to 16 Challenge Level:

Semi-regular tessellations combine two or more different regular polygons to fill the plane. Can you find all the semi-regular tessellations?

Square Coordinates

Age 11 to 14 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?

Ten Hidden Squares

Age 7 to 14 Challenge Level:

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

Polygon Pictures

Age 11 to 14 Challenge Level:

Can you work out how these polygon pictures were drawn, and use that to figure out their angles?

Shady Symmetry

Age 11 to 14 Challenge Level:

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

Tessellating Hexagons

Age 11 to 14 Challenge Level:

Which hexagons tessellate?

LOGO Challenge - Circles as Animals

Age 11 to 16 Challenge Level:

See if you can anticipate successive 'generations' of the two animals shown here.

Getting an Angle

Age 11 to 14 Challenge Level:

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Stringy Quads

Age 7 to 11 Challenge Level:

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

World of Tan 17 - Weather

Age 7 to 11 Challenge Level:

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

Concrete Wheel

Age 11 to 14 Challenge Level:

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

World of Tan 3 - Mah Ling

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of Mah Ling?

World of Tan 21 - Almost There Now

Age 7 to 11 Challenge Level:

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

World of Tan 25 - Pentominoes

Age 7 to 11 Challenge Level:

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

Three Squares

Age 5 to 11 Challenge Level:

What is the greatest number of squares you can make by overlapping three squares?

Troublesome Dice

Age 11 to 14 Challenge Level:

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

World of Tan 19 - A Circular Problem

Age 7 to 11 Challenge Level:

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

3D Stacks

Age 7 to 14 Challenge Level:

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

Peg Rotation

Age 7 to 11 Challenge Level:

Can you work out what kind of rotation produced this pattern of pegs in our pegboard?

World of Tan 10 - Butterflies

Age 7 to 11 Challenge Level:

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

Isosceles Triangles

Age 11 to 14 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?

Convex Polygons

Age 11 to 14 Challenge Level:

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

Keep Your Distance

Age 11 to 14 Challenge Level:

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

Tetra Square

Age 11 to 14 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.

Endless Noughts and Crosses

Age 7 to 11 Challenge Level:

An extension of noughts and crosses in which the grid is enlarged and the length of the winning line can to altered to 3, 4 or 5.

Rolling Triangle

Age 11 to 14 Challenge Level:

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

Put Yourself in a Box

Age 7 to 11 Challenge Level:

A game for 2 players. Given a board of dots in a grid pattern, players take turns drawing a line by connecting 2 adjacent dots. Your goal is to complete more squares than your opponent.

Weighty Problem

Age 11 to 14 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. . . .

Linkage

Age 11 to 14 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?

On the Edge

Age 11 to 14 Challenge Level:

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

Framed

Age 11 to 14 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. . . .

Square It

Age 11 to 16 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Zooming in on the Squares

Age 7 to 14

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?

John's Train Is on Time

Age 11 to 14 Challenge Level:

A train leaves on time. After it has gone 8 miles (at 33mph) the driver looks at his watch and sees that the hour hand is exactly over the minute hand. When did the train leave the station?

Coordinate Patterns

Age 11 to 14 Challenge Level:

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

The Development of Spatial and Geometric Thinking: the Importance of Instruction.

Age 5 to 11

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

Squares, Squares and More Squares

Age 11 to 14 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?

Seeing Squares

Age 5 to 11 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

Pattern Power

Age 5 to 14

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

Route to Infinity

Age 11 to 14 Challenge Level:

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

World of Tan 13 - A Storm in a Tea Cup

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the convex shapes?

Counter Roundup

Age 7 to 11 Challenge Level:

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.

Inside Seven Squares

Age 7 to 11 Challenge Level:

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?