Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

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?

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?

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.

Four Layers

Age 5 to 11 Challenge Level:

Can you create more models that follow these rules?

Two by One

Age 7 to 11 Challenge Level:

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

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?

Redblue

Age 7 to 11 Challenge Level:

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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.

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.

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?

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?

Triangular Hexagons

Age 7 to 11 Challenge Level:

Investigate these hexagons drawn from different sized equilateral triangles.

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.

Triple Cubes

Age 5 to 11 Challenge Level:

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

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.

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.

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.

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?

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?

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?

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?

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?

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?

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?

All Wrapped Up

Age 7 to 11 Challenge Level:

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

Triangle Pin-down

Age 7 to 11 Challenge Level:

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Move a Match

Age 7 to 11 Challenge Level:

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Triangle Relations

Age 7 to 11 Challenge Level:

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

Opening Out

Age 5 to 11

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

Tri.'s

Age 7 to 11 Challenge Level:

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

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?

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.

Three Sets of Cubes, Two Surfaces

Age 7 to 11 Challenge Level:

How many models can you find which obey these rules?

Squareo'scope Determines the Kind of Triangle

Age 11 to 14

A description of some experiments in which you can make discoveries about triangles.

Eye View

Age 7 to 11 Challenge Level:

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

More Pebbles

Age 7 to 11 Challenge Level:

Have a go at this 3D extension to the Pebbles problem.

Cubes

Age 7 to 11 Challenge Level:

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

Roll These Dice

Age 7 to 11 Challenge Level:

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

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?

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?

28 and It's Upward and Onward

Age 7 to 11 Challenge Level:

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

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?

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?

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.

Steps to the Podium

Age 7 to 14 Challenge Level:

It starts quite simple but great opportunities for number discoveries and patterns!

Experiencing Problem Solving

Age 5 to 11

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

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?

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?

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?

Extending Great Squares

Age 7 to 11 Challenge Level:

Explore one of these five pictures.