Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

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?

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.

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?

Halving

Age 5 to 7
Challenge Level

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

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.

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.

All Wrapped Up

Age 7 to 11
Challenge Level

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

Repeating Patterns

Age 5 to 7
Challenge Level

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

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?

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?

Turning

Age 5 to 7
Challenge Level

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

Colouring Triangles

Age 5 to 7
Challenge Level

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

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?

28 - Upward and Onward

Age 7 to 11
Challenge Level

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

Teddy Town

Age 5 to 14
Challenge Level

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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 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.

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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.

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.

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?

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?

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.

Cubes

Age 7 to 11
Challenge Level

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

Four Layers

Age 5 to 11
Challenge Level

Can you create more models that follow these rules?

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?

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.

More Pebbles

Age 7 to 11
Challenge Level

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

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?

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?

Two by One

Age 7 to 11
Challenge Level

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

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?

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.

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?

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?

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?

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"?

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?

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?

Extending Great Squares

Age 7 to 11
Challenge Level

Explore one of these five pictures.

Tiling Into Slanted Rectangles

Age 7 to 11
Challenge Level

A follow-up activity to Tiles in the Garden.

Building with Longer Rods

Age 7 to 14
Challenge Level

A challenging activity focusing on finding all possible ways of stacking rods.

Building with Rods

Age 7 to 11
Challenge Level

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

Tiles in the Garden

Age 7 to 11
Challenge Level

How many tiles do we need to tile these patios?

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.

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?

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.

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.