Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

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.

Two on Five

Age 5 to 11
Challenge Level

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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?

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?

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"?

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?

Repeating Patterns

Age 5 to 7
Challenge Level

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

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.

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?

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?

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?

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.

All Wrapped Up

Age 7 to 11
Challenge Level

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

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?

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?

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.

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.

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?

Investigating Pascal's Triangle

Age 7 to 11
Challenge Level

In this investigation, we look at Pascal's Triangle in a slightly different way - rotated and with the top line of ones taken off.

Bean Bags for Bernard's Bag

Age 7 to 11
Challenge Level

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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?

Taking a Die for a Walk

Age 5 to 11
Challenge Level

Investigate the numbers that come up on a die as you roll it in the direction of north, south, east and west, without going over the path it's already made.

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?

Triangle Relations

Age 7 to 11
Challenge Level

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

Birthday Cake Candles

Age 7 to 11
Challenge Level

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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.

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?

Eye View

Age 7 to 11
Challenge Level

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

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.

Extending Great Squares

Age 7 to 11
Challenge Level

Explore one of these five pictures.

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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?

Stairs

Age 5 to 11
Challenge Level

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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.

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.

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?

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?

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?

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?

Cubes Here and There

Age 7 to 11
Challenge Level

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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?