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Resources tagged with Investigations similar to From One Shape to Another:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Using, Applying and Reasoning about Mathematics > Investigations

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Lawn Border

Stage: 1 and 2 Challenge Level: Challenge Level:1

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

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Making Squares

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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Fencing Lambs

Stage: 2 Challenge Level: Challenge Level:1

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

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Great Squares

Stage: 2 and 3 Challenge Level: Challenge Level:1

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Tiles in the Garden

Stage: 2 Challenge Level: Challenge Level:1

How many tiles do we need to tile these patios?

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Pebbles

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Shaping It

Stage: 1 and 2 Challenge Level: Challenge Level:1

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

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Cutting it Out

Stage: 1 and 2 Challenge Level: Challenge Level:1

I cut this square into two different shapes. What can you say about the relationship between them?

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Tiles on a Patio

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How many ways can you find of tiling the square patio, using square tiles of different sizes?

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Tessellating Triangles

Stage: 2 Challenge Level: Challenge Level:1

Can you make these equilateral triangles fit together to cover the paper without any gaps between them? Can you tessellate isosceles triangles?

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My New Patio

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

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Tiling Into Slanted Rectangles

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A follow-up activity to Tiles in the Garden.

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Fencing

Stage: 2 Challenge Level: Challenge Level:1

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

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Experiencing Problem Solving

Stage: 1 and 2

Bernard Bagnall looks at what 'problem solving' might really mean in the context of primary classrooms.

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Opening Out

Stage: 1 and 2

Bernard Bagnall describes how to get more out of some favourite NRICH investigations.

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Marvellous Matrix

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Follow the directions for circling numbers in the matrix. Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice?

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Two Squared

Stage: 2 Challenge Level: Challenge Level:1

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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More Transformations on a Pegboard

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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Newspapers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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Count the Digits

Stage: 1 and 2 Challenge Level: Challenge Level:1

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

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It Was 2010!

Stage: 1 and 2 Challenge Level: Challenge Level:1

If the answer's 2010, what could the question be?

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The Big Cheese

Stage: 2 Challenge Level: Challenge Level:1

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

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It Must Be 2000

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Here are many ideas for you to investigate - all linked with the number 2000.

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Alien Counting

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.

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Taking a Die for a Walk

Stage: 1 and 2 Challenge Level: Challenge Level:2 Challenge Level:2

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

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Fit These Shapes

Stage: 1 and 2 Challenge Level: Challenge Level:1

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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Tiling

Stage: 2 Challenge Level: Challenge Level:1

An investigation that gives you the opportunity to make and justify predictions.

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Making Boxes

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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Gran, How Old Are You?

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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Follow the Numbers

Stage: 2 Challenge Level: Challenge Level:1

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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Calcunos

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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Ip Dip

Stage: 1 and 2 Challenge Level: Challenge Level:1

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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Polygonals

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

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Street Party

Stage: 2 Challenge Level: Challenge Level:1

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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Triangle Relations

Stage: 2 Challenge Level: Challenge Level:1

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

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Extending Great Squares

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore one of these five pictures.

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Ice Cream

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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Two by One

Stage: 2 Challenge Level: Challenge Level:1

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

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The Great Tiling Count

Stage: 2 Challenge Level: Challenge Level:1

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.

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3 Rings

Stage: 2 Challenge Level: Challenge Level:1

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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Sticky Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

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Cubes

Stage: 1 and 2 Challenge Level: Challenge Level:1

Investigate the number of faces you can see when you arrange three cubes in different ways.

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Number Squares

Stage: 1 and 2 Challenge Level: Challenge Level:1

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

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Are You a Smart Shopper?

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?

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Halloween Investigation

Stage: 2 Challenge Level: Challenge Level:1

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

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Sending and Receiving Cards

Stage: 2 Challenge Level: Challenge Level:1

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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All Wrapped Up

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the largest cuboid you can wrap in an A3 sheet of paper?

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Triangular Hexagons

Stage: 2 Challenge Level: Challenge Level:1

Investigate these hexagons drawn from different sized equilateral triangles.

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Birds in the Garden

Stage: 1 and 2 Challenge Level: Challenge Level:1

This activity asks you to collect information about the birds you see in the garden. Are there patterns in the data or do the birds seem to visit randomly?

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Tessellating Transformations

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you find out how the 6-triangle shape is transformed in these tessellations? Will the tessellations go on for ever? Why or why not?