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Resources tagged with Practical Activity similar to Counting Counters:

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

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Counting Counters

Age 7 to 11 Challenge Level:

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

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Cuisenaire Rods

Age 7 to 11 Challenge Level:

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

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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?

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Two on Five

Age 5 to 11 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?

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Dice Stairs

Age 7 to 11 Challenge Level:

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

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Four Colours

Age 5 to 11 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.

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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?

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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?

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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?

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Making Cuboids

Age 7 to 11 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?

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Sticks and Triangles

Age 7 to 11 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?

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Two by One

Age 7 to 11 Challenge Level:

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

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Shaping Up

Age 7 to 11 Challenge Level:

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

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Tri.'s

Age 7 to 11 Challenge Level:

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

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Cereal Packets

Age 7 to 11 Challenge Level:

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

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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?

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Egyptian Rope

Age 7 to 11 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?

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Three Sets of Cubes, Two Surfaces

Age 7 to 11 Challenge Level:

How many models can you find which obey these rules?

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Order the Changes

Age 7 to 11 Challenge Level:

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

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Cover the Tray

Age 7 to 11 Challenge Level:

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

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Creating Cubes

Age 7 to 11 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.

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Seven Flipped

Age 7 to 11 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.

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Cunning Card Trick

Age 11 to 14 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

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Counter Ideas

Age 7 to 11 Challenge Level:

Here are some ideas to try in the classroom for using counters to investigate number patterns.

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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?

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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.

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Rolling Triangle

Age 11 to 14 Challenge Level:

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

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Marbles

Age 11 to 14 Challenge Level:

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

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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 ...

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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?

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Fencing

Age 7 to 11 Challenge Level:

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

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Double Your Popcorn, Double Your Pleasure

Age 7 to 11 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.

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Cutting Corners

Age 7 to 11 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?

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Sea Defences

Age 7 to 14 Challenge Level:

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

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Four Layers

Age 5 to 11 Challenge Level:

Can you create more models that follow these rules?

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Fit These Shapes

Age 5 to 11 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?

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The Numbers Give the Design

Age 7 to 11 Challenge Level:

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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It's a Fence!

Age 5 to 11 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.

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Back to the Practical?

Age 7 to 14

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

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Matchsticks

Age 7 to 11 Challenge Level:

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

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Sort Them Out (2)

Age 7 to 11 Challenge Level:

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

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Construct-o-straws

Age 7 to 11 Challenge Level:

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

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Folding, Cutting and Punching

Age 7 to 11 Challenge Level:

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

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Triangle Relations

Age 7 to 11 Challenge Level:

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

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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?

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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?

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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?

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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?

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Building Patterns

Age 7 to 11 Challenge Level:

Can you deduce the pattern that has been used to lay out these bottle tops?

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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?