Resources tagged with: Visualising

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Broad Topics > Thinking Mathematically > Visualising

Three Squares

Age 5 to 11 Challenge Level:

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

Nine-pin Triangles

Age 7 to 11 Challenge Level:

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

Construct-o-straws

Age 7 to 11 Challenge Level:

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

Folding Flowers 1

Age 7 to 11 Challenge Level:

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

Counters

Age 7 to 11 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Folding, Cutting and Punching

Age 7 to 11 Challenge Level:

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

Diagrams

Age 7 to 11 Challenge Level:

A group activity using visualisation of squares and triangles.

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?

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!

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?

Knight's Swap

Age 7 to 11 Challenge Level:

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

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?

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 ...

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.

Tetrafit

Age 7 to 11 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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?

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?

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?

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?

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.

Taking Steps

Age 7 to 11 Challenge Level:

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

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?

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!

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.

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?

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?

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?

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.

Seeing Squares for Two

Age 5 to 11 Challenge Level:

Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

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?

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?

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?

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?

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.

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?

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?

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.

Turning Cogs

Age 7 to 11 Challenge Level:

What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.

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?

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.

Domino Numbers

Age 7 to 11 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

World of Tan 28 - Concentrating on Coordinates

Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outline of the playing piece?

World of Tan 24 - Clocks

Age 7 to 11 Challenge Level:

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

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?

Colour Wheels

Age 7 to 11 Challenge Level:

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

Right or Left?

Age 7 to 11 Challenge Level:

Which of these dice are right-handed and which are left-handed?

Tetrahedra Tester

Age 11 to 14 Challenge Level:

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?