Resources tagged with: Visualising

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Broad Topics > Thinking Mathematically > Visualising

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?

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?

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?

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.

Shunting Puzzle

Age 7 to 11
Challenge Level

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

Single Track

Age 7 to 11
Challenge Level

What is the best way to shunt these carriages so that each train can continue its journey?

Waiting for Blast Off

Age 7 to 11
Challenge Level

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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.

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!

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?

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?

Nine-pin Triangles

Age 7 to 11
Challenge Level

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

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?

Quadrilaterals

Age 7 to 11
Challenge Level

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

Cuboid-in-a-box

Age 7 to 11
Challenge Level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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?

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?

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?

More Pebbles

Age 7 to 11
Challenge Level

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

Jigsaw Pieces

Age 7 to 11
Challenge Level

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Display Boards

Age 7 to 11
Challenge Level

Design an arrangement of display boards in the school hall which fits the requirements of different people.

Open Boxes

Age 7 to 11
Challenge Level

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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?

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.

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?

Square Corners

Age 7 to 11
Challenge Level

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

Four Triangles Puzzle

Age 5 to 11
Challenge Level

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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?

World of Tan 17 - Weather

Age 7 to 11
Challenge Level

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

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?

Counting Cards

Age 7 to 11
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?

Paw Prints

Age 7 to 11
Challenge Level

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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?

Folding, Cutting and Punching

Age 7 to 11
Challenge Level

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

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?

Triple Cubes

Age 5 to 11
Challenge Level

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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?

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?

Polygon Rings

Age 11 to 14
Challenge Level

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

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?

World of Tan 10 - Butterflies

Age 7 to 11
Challenge Level

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

Trace the Edges

Age 7 to 11
Challenge Level

On which of these shapes can you trace a path along all of its edges, without going over any edge twice?

How Would We Count?

Age 5 to 11
Challenge Level

An activity centred around observations of dots and how we visualise number arrangement patterns.

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.

World of Tan 16 - Time Flies

Age 7 to 11
Challenge Level

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

World of Tan 29 - the Telephone

Age 7 to 11
Challenge Level

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

Map Folding

Age 7 to 11
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?

World of Tan 8 - Sports Car

Age 7 to 11
Challenge Level

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

World of Tan 11 - the Past, Present and Future

Age 7 to 11
Challenge Level

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

World of Tan 27 - Sharing

Age 7 to 11
Challenge Level

Can you fit the tangram pieces into the outline of Little Fung at the table?