Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

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.

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?

Halving

Age 5 to 7
Challenge Level

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

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.

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?

Repeating Patterns

Age 5 to 7
Challenge Level

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

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?

Four Layers

Age 5 to 11
Challenge Level

Can you create more models that follow these rules?

All Wrapped Up

Age 7 to 11
Challenge Level

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

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.

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.

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?

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?

Triangle Relations

Age 7 to 11
Challenge Level

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

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?

Tri.'s

Age 7 to 11
Challenge Level

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

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?

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?

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?

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?

Two by One

Age 7 to 11
Challenge Level

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

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?

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?

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?

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.

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?

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?

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.

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?

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?

Cubes

Age 7 to 11
Challenge Level

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

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?

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?

Great Squares

Age 7 to 11
Challenge Level

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

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.

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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.

Seven Sticks

Age 5 to 7
Challenge Level

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

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?

28 - Upward and Onward

Age 7 to 11
Challenge Level

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

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.

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?

Experiencing Problem Solving

Age 5 to 11

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

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.

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?

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?

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.