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

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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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2010: A Year of Investigations

Stage: 1, 2 and 3

This article for teachers suggests ideas for activities built around 10 and 2010.

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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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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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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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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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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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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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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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Tea Cups

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

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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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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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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How Tall?

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

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

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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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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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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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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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Cuboid-in-a-box

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

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

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?

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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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Watch Your Feet

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

I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?

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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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Double Your Popcorn, Double Your Pleasure

Stage: 2 Challenge Level: Challenge Level:1

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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Bean Bags for Bernard's Bag

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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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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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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Room Doubling

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

Investigate the different ways you could split up these rooms so that you have double the number.

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The Pied Piper of Hamelin

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

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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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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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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Two on Five

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

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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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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Sticks and Triangles

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

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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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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3 Sets of Cubes, 2 Surfaces

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

How many models can you find which obey these rules?

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Four Layers

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

Can you create more models that follow these rules?

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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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The Domesday Project

Stage: 2 Challenge Level: Challenge Level:1

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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Eye View

Stage: 2 Challenge Level: Challenge Level:1

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

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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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Building with Rods

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

In how many ways can you stack these rods, following the rules?

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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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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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Triple Cubes

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

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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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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28 and It's Upward and Onward

Stage: 2 Challenge Level: Challenge Level:1

Can you find ways of joining cubes together so that 28 faces are visible?

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Hexpentas

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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Cubes Here and There

Stage: 2 Challenge Level: Challenge Level:1

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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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?