Resources tagged with: Investigations

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Broad Topics > Mathematical Thinking > Investigations

Tiles on a Patio

Age 7 to 11 Challenge Level:

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

Making Squares

Age 7 to 11

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?

Triangular Hexagons

Age 7 to 11 Challenge Level:

Investigate these hexagons drawn from different sized equilateral triangles.

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?

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?

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?

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?

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?

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.

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?

Escher Tessellations

Age 7 to 11 Challenge Level:

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

Newspapers

Age 7 to 11 Challenge Level:

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?

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?

Tri.'s

Age 7 to 11 Challenge Level:

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

Two by One

Age 7 to 11 Challenge Level:

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

Opening Out

Age 5 to 11

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

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?

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.

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.

Triangle Relations

Age 7 to 11 Challenge Level:

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

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?

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?

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.

Triangle Shapes

Age 5 to 11 Challenge Level:

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

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?

Great Squares

Age 7 to 11 Challenge Level:

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

Tiling Into Slanted Rectangles

Age 7 to 11 Challenge Level:

A follow-up activity to Tiles in the Garden.

Extending Great Squares

Age 7 to 11 Challenge Level:

Explore one of these five pictures.

Eye View

Age 7 to 11 Challenge Level:

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

Tiles in the Garden

Age 7 to 11 Challenge Level:

How many tiles do we need to tile these patios?

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.

Four Layers

Age 5 to 11 Challenge Level:

Can you create more models that follow these rules?

How Tall?

Age 5 to 11 Challenge Level:

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

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?

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.

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.

Shaping It

Age 5 to 11 Challenge Level:

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.

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?

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?

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.

New House

Age 7 to 11 Challenge Level:

In this investigation, you must try to make houses using cubes. If the base must not spill over 4 squares and you have 7 cubes which stand for 7 rooms, what different designs can you come up with?

Building with Rods

Age 7 to 11 Challenge Level:

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

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"?

Experiencing Problem Solving

Age 5 to 11

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

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?

Sweets in a Box

Age 7 to 11 Challenge Level:

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Watch Your Feet

Age 7 to 11 Challenge Level:

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?

Room Doubling

Age 7 to 11 Challenge Level:

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

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?

It Figures

Age 7 to 11 Challenge Level:

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?