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Broad Topics > Using, Applying and Reasoning about Mathematics > Practical Activity

Cover the Tray

Stage: 2 Challenge Level:

These practical challenges are all about making a 'tray' and covering it with paper.

Seven Flipped

Stage: 2 Challenge Level:

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Sticks and Triangles

Stage: 2 Challenge Level:

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Tri.'s

Stage: 2 Challenge Level:

How many triangles can you make on the 3 by 3 pegboard?

Two by One

Stage: 2 Challenge Level:

An activity making various patterns with 2 x 1 rectangular tiles.

Two on Five

Stage: 1 and 2 Challenge Level:

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Putting Two and Two Together

Stage: 2 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?

Three Sets of Cubes, Two Surfaces

Stage: 2 Challenge Level:

How many models can you find which obey these rules?

Map Folding

Stage: 2 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?

Egyptian Rope

Stage: 2 Challenge Level:

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Cuboid-in-a-box

Stage: 2 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?

Cereal Packets

Stage: 2 Challenge Level:

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

Making Cuboids

Stage: 2 Challenge Level:

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Escher Tessellations

Stage: 2 Challenge Level:

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

Stage: 1 and 2 Challenge Level:

Our 2008 Advent Calendar has a 'Making Maths' activity for every day in the run-up to Christmas.

Stage: 2 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.

Four Colours

Stage: 1 and 2 Challenge Level:

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Shaping Up

Stage: 2 Challenge Level:

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

Dice Stairs

Stage: 2 Challenge Level:

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

Two Squared

Stage: 2 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?

Little Boxes

Stage: 2 Challenge Level:

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

Cutting Corners

Stage: 2 Challenge Level:

Can you make the most extraordinary, the most amazing, the most unusual patterns/designs from these triangles which are made in a special way?

Fit These Shapes

Stage: 1 and 2 Challenge Level:

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

Order the Changes

Stage: 2 Challenge Level:

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

Stage: 2 Challenge Level:

NRICH December 2006 advent calendar - a new tangram for each day in the run-up to Christmas.

Square Corners

Stage: 2 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?

Fencing

Stage: 2 Challenge Level:

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

Square Tangram

Stage: 2 Challenge Level:

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

Music to My Ears

Stage: 2 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?

Triangle Relations

Stage: 2 Challenge Level:

What do these two triangles have in common? How are they related?

How Tall?

Stage: 1 and 2 Challenge Level:

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Four Layers

Stage: 1 and 2 Challenge Level:

Can you create more models that follow these rules?

Making Maths: Happy Families

Stage: 1 and 2 Challenge Level:

Here is a version of the game 'Happy Families' for you to make and play.

Making Maths: Birds from an Egg

Stage: 2 Challenge Level:

Can you make the birds from the egg tangram?

It's a Fence!

Stage: 1 and 2 Challenge Level:

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

Polydron

Stage: 2 Challenge Level:

This activity investigates how you might make squares and pentominoes from Polydron.

Sort Them Out (2)

Stage: 2 Challenge Level:

Can you each work out the number on your card? What do you notice? How could you sort the cards?

Stage: 2 Challenge Level:

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Car Journey

Stage: 2 Challenge Level:

This practical activity involves measuring length/distance.

Counting Counters

Stage: 2 Challenge Level:

Take a counter and surround it by a ring of other counters that MUST touch two others. How many are needed?

A Patchwork Piece

Stage: 2 Challenge Level:

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

Triangle Shapes

Stage: 1 and 2 Challenge Level:

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

Making Maths: Stars

Stage: 2 Challenge Level:

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

World of Tan 26 - Old Chestnut

Stage: 2 Challenge Level:

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

World of Tan 25 - Pentominoes

Stage: 2 Challenge Level:

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

World of Tan 24 - Clocks

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of these clocks?

World of Tan 22 - an Appealing Stroll

Stage: 2 Challenge Level:

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

World of Tan 27 - Sharing

Stage: 2 Challenge Level:

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

World of Tan 28 - Concentrating on Coordinates

Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming playing the board game?