Resources tagged with: Investigations

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There are 147 results

Broad Topics > Thinking Mathematically > Investigations

Halving

Age 5 to 7
Challenge Level

These pictures show squares split into halves. Can you find other ways?

Cutting it Out

Age 5 to 11
Challenge Level

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

Repeating Patterns

Age 5 to 7
Challenge Level

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

Baked Bean Cans

Age 5 to 7
Challenge Level

Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?

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.

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?

Seven Sticks

Age 5 to 7
Challenge Level

Explore the triangles that can be made with seven sticks of the same length.

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?

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?

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?

Triangle Relations

Age 7 to 11
Challenge Level

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

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?

Great Squares

Age 7 to 11
Challenge Level

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

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.

2 Rings

Age 5 to 7
Challenge Level

The red ring is inside the blue ring in this picture. Can you rearrange the rings in different ways? Perhaps you can overlap them or put one outside another?

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?

Two by One

Age 7 to 11
Challenge Level

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

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?

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?

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.

Let's Investigate Triangles

Age 5 to 7
Challenge Level

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Colouring Triangles

Age 5 to 7
Challenge Level

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

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.

Opening Out

Age 5 to 11

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

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?

Bracelets

Age 7 to 11
Challenge Level

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Tri.'s

Age 7 to 11
Challenge Level

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

Sort the Street

Age 5 to 7
Challenge Level

Sort the houses in my street into different groups. Can you do it in any other ways?

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?

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.

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.

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?

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?

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.

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.

Tiles in the Garden

Age 7 to 11
Challenge Level

How many tiles do we need to tile these patios?

Eye View

Age 7 to 11
Challenge Level

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

Extending Great Squares

Age 7 to 11
Challenge Level

Explore one of these five pictures.

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.

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?

Experiencing Problem Solving

Age 5 to 11

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

Four Layers

Age 5 to 11
Challenge Level

Can you create more models that follow these rules?

Tiling Into Slanted Rectangles

Age 7 to 11
Challenge Level

A follow-up activity to Tiles in the Garden.

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?

Triangular Hexagons

Age 7 to 11
Challenge Level

Investigate these hexagons drawn from different sized equilateral triangles.

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?

Olympic Rings

Age 5 to 7
Challenge Level

This problem is intended to get children to look really hard at something they will see many times in the next few months.

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?

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?

Hexpentas

Age 5 to 11
Challenge Level

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