Resources tagged with: Visualising

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There are 255 results

Broad Topics > Thinking Mathematically > Visualising

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?

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?

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?

Brush Loads

Age 7 to 11
Challenge Level

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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.

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?

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?

Construct-o-straws

Age 7 to 11
Challenge Level

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

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?

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?

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?

More Pebbles

Age 7 to 11
Challenge Level

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

Move a Match

Age 7 to 11
Challenge Level

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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?

Redblue

Age 7 to 11
Challenge Level

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

Matchsticks

Age 7 to 11
Challenge Level

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

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?

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!

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?

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.

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?

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?

Quadrilaterals

Age 7 to 11
Challenge Level

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

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.

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.

Painting Possibilities

Age 7 to 11
Challenge Level

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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!

Nine-pin Triangles

Age 7 to 11
Challenge Level

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

Dodecamagic

Age 7 to 11
Challenge Level

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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?

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?

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?

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?

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?

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?

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?

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?

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.

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?

Folding, Cutting and Punching

Age 7 to 11
Challenge Level

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

28 - Upward and Onward

Age 7 to 11
Challenge Level

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

Folded Number Line

Age 7 to 11
Challenge Level

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

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?

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?

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?

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?

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?