Resources tagged with: Visualising

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Broad Topics > Thinking Mathematically > Visualising

Midpoint Triangle

Age 7 to 11 Challenge Level:

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

Sponge Sections

Age 7 to 11 Challenge Level:

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

Jomista Mat

Age 7 to 11 Challenge Level:

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

Let Us Reflect

Age 7 to 11 Challenge Level:

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Construct-o-straws

Age 7 to 11 Challenge Level:

Make a cube out of straws and have a go at this practical challenge.

Reef and Granny

Age 7 to 11 Challenge Level:

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

Matchsticks

Age 7 to 11 Challenge Level:

Reasoning about the number of matches needed to build squares that share their sides.

Hexagon Transformations

Age 7 to 11 Challenge Level:

Can you cut a regular hexagon into two pieces to make a parallelogram? Try cutting it into three pieces to make a rhombus!

Pyramid Numbers

Age 7 to 11 Challenge Level:

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

Triangular Faces

Age 7 to 11 Challenge Level:

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

Regular Rings 2

Age 7 to 11 Challenge Level:

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

Regular Rings 1

Age 7 to 11 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?

Folding Flowers 2

Age 7 to 11 Challenge Level:

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

Folding Flowers 1

Age 7 to 11 Challenge Level:

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

Move Those Halves

Age 7 to 11 Challenge Level:

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

Making Maths: Rolypoly

Age 5 to 11 Challenge Level:

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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!

Folding, Cutting and Punching

Age 7 to 11 Challenge Level:

Exploring and predicting folding, cutting and punching holes and making spirals.

Fractional Triangles

Age 7 to 11 Challenge Level:

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

Green Cube, Yellow Cube

Age 7 to 11 Challenge Level:

How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?

Dicey

Age 7 to 11 Challenge Level:

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

Shape Mapping

Age 7 to 11 Challenge Level:

What is the relationship between these first two shapes? Which shape relates to the third one in the same way? Can you explain why?

More Building with Cubes

Age 7 to 11 Challenge Level:

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

Wrapping Presents

Age 7 to 11 Challenge Level:

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

Peg Rotation

Age 7 to 11 Challenge Level:

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

A Puzzling Cube

Age 7 to 11 Challenge Level:

Here are the six faces of a cube - in no particular order. Here are three views of the cube. Can you deduce where the faces are in relation to each other and record them on the net of this cube?

Twice as Big?

Age 7 to 11 Challenge Level:

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

Diagrams

Age 7 to 11 Challenge Level:

A group activity using visualisation of squares and triangles.

Putting Two and Two Together

Age 7 to 11 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?

Little Boxes

Age 7 to 11 Challenge Level:

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

Holes

Age 5 to 11 Challenge Level:

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

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?

A Square in a Circle

Age 7 to 11 Challenge Level:

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

Purposeful Paper Folding

Age 5 to 11

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

Square Surprise

Age 5 to 11 Challenge Level:

Why do you think that the red player chose that particular dot in this game of Seeing Squares?

Square to L

Age 7 to 11 Challenge Level:

Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.

Painted Faces

Age 7 to 11 Challenge Level:

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

Music to My Ears

Age 7 to 11 Challenge Level:

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

Tetrahedron Faces

Age 7 to 11 Challenge Level:

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

Flip

Age 7 to 11 Challenge Level:

Can you picture where this letter "F" will be on the grid if you flip it in these different ways?

Cube Drilling

Age 7 to 11 Challenge Level:

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

Two Squared

Age 7 to 11 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?

Child's Play

Age 7 to 11 Challenge Level:

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

More Pebbles

Age 7 to 11 Challenge Level:

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

28 and It's Upward and Onward

Age 7 to 11 Challenge Level:

Can you find ways of joining cubes together so that 28 faces are visible?

World of Tan 22 - an Appealing Stroll

Age 7 to 11 Challenge Level:

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

Hexpentas

Age 5 to 11 Challenge Level:

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

World of Tan 26 - Old Chestnut

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?

Picture a Pyramid ...

Age 7 to 11 Challenge Level:

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Dramatic Mathematics

Age 5 to 11

This article for teachers describes a project which explores the power of storytelling to convey concepts and ideas to children.