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Resources tagged with Practical Activity similar to Opening Out:

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

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?

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.

Three Sets of Cubes, Two Surfaces

Stage: 2 Challenge Level:

How many models can you find which obey these rules?

Cover the Tray

Stage: 2 Challenge Level:

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

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.

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?

Two by One

Stage: 2 Challenge Level:

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

Tangram Tangle

Stage: 1 Challenge Level:

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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?

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?

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?

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?

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?

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?

Tri.'s

Stage: 2 Challenge Level:

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

Making Longer, Making Shorter

Stage: 1 Challenge Level:

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

How Many?

Stage: 1 Challenge Level:

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Dienes' Logiblocs

Stage: 1 Challenge Level:

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

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?

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?

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.

Repeating Patterns

Stage: 1 Challenge Level:

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Polydron

Stage: 2 Challenge Level:

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

A City of Towers

Stage: 1 Challenge Level:

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

Chairs and Tables

Stage: 1 Challenge Level:

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

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.

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?

Baked Bean Cans

Stage: 1 Challenge Level:

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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.

Tricky Triangles

Stage: 1 Challenge Level:

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Pairs of Numbers

Stage: 1 Challenge Level:

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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?

Escher Tessellations

Stage: 2 Challenge Level:

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

Four Layers

Stage: 1 and 2 Challenge Level:

Can you create more models that follow these rules?

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?

Little Man

Stage: 1 Challenge Level:

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

Triangle Relations

Stage: 2 Challenge Level:

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

Stage: 2 Challenge Level:

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

Making Maths: Birds from an Egg

Stage: 2 Challenge Level:

Can you make the birds from the egg tangram?

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.

Pyramid Numbers

Stage: 2 Challenge Level:

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

Halving

Stage: 1 Challenge Level:

These pictures show squares split into halves. Can you find other ways?

Seven Sticks

Stage: 1 Challenge Level:

Explore the triangles that can be made with seven sticks of the same length.

Three Fingers and a Loop of String

Stage: 1 Challenge Level:

Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.

Creating Cubes

Stage: 2 and 3 Challenge Level:

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.