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

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Christmas Presents

Age 7 to 11 Challenge Level:

We need to wrap up this cube-shaped present, remembering that we can have no overlaps. What shapes can you find to use?

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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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Cubes

Age 7 to 11 Challenge Level:

How many faces can you see when you arrange these three cubes in different ways?

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All Wrapped Up

Age 7 to 11 Challenge Level:

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

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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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Sticky Triangles

Age 7 to 11 Challenge Level:

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

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Fencing Lambs

Age 7 to 11 Challenge Level:

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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Taking a Die for a Walk

Age 5 to 11 Challenge Level:

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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It Must Be 2000

Age 7 to 11 Challenge Level:

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

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The Big Cheese

Age 7 to 11 Challenge Level:

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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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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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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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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Are You a Smart Shopper?

Age 7 to 11 Challenge Level:

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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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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Tessellating Transformations

Age 7 to 11 Challenge Level:

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?

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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.

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Count the Digits

Age 5 to 11 Challenge Level:

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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Four Layers

Age 5 to 11 Challenge Level:

Can you create more models that follow these rules?

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Extending Great Squares

Age 7 to 11 Challenge Level:

Explore one of these five pictures.

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Polygonals

Age 7 to 11 Challenge Level:

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

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Eye View

Age 7 to 11 Challenge Level:

Why does the tower look a different size in each of these pictures?

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Tiling Into Slanted Rectangles

Age 7 to 11 Challenge Level:

A follow-up activity to Tiles in the Garden.

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Exploring Number Patterns You Make

Age 7 to 11 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? What do you think is happening to the numbers?

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Sending and Receiving Cards

Age 7 to 11 Challenge Level:

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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Opening Out

Age 5 to 11

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

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More Transformations on a Pegboard

Age 7 to 11 Challenge Level:

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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Lawn Border

Age 5 to 11 Challenge Level:

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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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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Lost Books

Age 7 to 11 Challenge Level:

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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The Great Tiling Count

Age 7 to 11 Challenge Level:

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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Crossing the Town Square

Age 7 to 11 Challenge Level:

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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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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Calcunos

Age 7 to 11 Challenge Level:

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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Halloween Investigation

Age 7 to 11 Challenge Level:

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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The Domesday Project

Age 7 to 11 Challenge Level:

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

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Tiles in the Garden

Age 7 to 11 Challenge Level:

How many tiles do we need to tile these patios?

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Become Maths Detectives

Age 7 to 11 Challenge Level:

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

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Ice Cream

Age 7 to 11 Challenge Level:

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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My New Patio

Age 7 to 11 Challenge Level:

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

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Magic Constants

Age 7 to 11 Challenge Level:

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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Street Party

Age 7 to 11 Challenge Level:

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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Making Boxes

Age 7 to 11 Challenge Level:

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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Train Carriages

Age 5 to 11 Challenge Level:

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

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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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Tessellating Triangles

Age 7 to 11 Challenge Level:

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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3 Rings

Age 7 to 11 Challenge Level:

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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Pebbles

Age 7 to 11 Challenge Level:

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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Great Squares

Age 7 to 11 Challenge Level:

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

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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?