# Resources tagged with: Investigations

Filter by: Content type:
Age range:
Challenge level:

### There are 141 results

Broad Topics > Thinking Mathematically > Investigations

### Two on Five

##### Age 5 to 11Challenge 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?

### Train Carriages

##### Age 5 to 11Challenge Level

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

### Stairs

##### Age 5 to 11Challenge 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.

### Cubes Here and There

##### Age 7 to 11Challenge 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?

### Making Cuboids

##### Age 7 to 11Challenge 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?

### Newspapers

##### Age 7 to 11Challenge Level

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

### Polo Square

##### Age 7 to 11Challenge Level

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

### Calcunos

##### Age 7 to 11Challenge Level

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

### Bean Bags for Bernard's Bag

##### Age 7 to 11Challenge 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?

### It Figures

##### Age 7 to 11Challenge 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?

### Sweets in a Box

##### Age 7 to 11Challenge 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?

##### Age 7 to 11Challenge 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?

### Lost Books

##### Age 7 to 11Challenge Level

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

### New House

##### Age 7 to 11Challenge 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?

### Birthday Cake Candles

##### Age 7 to 11Challenge Level

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

### Sticks and Triangles

##### Age 7 to 11Challenge 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?

### Three Sets of Cubes, Two Surfaces

##### Age 7 to 11Challenge Level

How many models can you find which obey these rules?

### Polygonals

##### Age 7 to 11Challenge Level

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

### Crossing the Town Square

##### Age 7 to 11Challenge Level

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

### Building with Rods

##### Age 7 to 11Challenge Level

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

##### Age 7 to 11Challenge Level

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

### Room Doubling

##### Age 7 to 11Challenge Level

Investigate the different ways you could split up these rooms so that you have double the number.

### 3 Rings

##### Age 7 to 11Challenge Level

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

### Magazines

##### Age 7 to 11Challenge Level

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

### Halloween Investigation

##### Age 7 to 11Challenge Level

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

### Ice Cream

##### Age 7 to 11Challenge Level

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

### Street Party

##### Age 7 to 11Challenge Level

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

### My New Patio

##### Age 7 to 11Challenge Level

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

### Fencing Lambs

##### Age 7 to 11Challenge Level

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

### Hexpentas

##### Age 5 to 11Challenge Level

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

### Taking a Die for a Walk

##### Age 5 to 11Challenge 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.

##### Age 7 to 11Challenge Level

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

### Tri.'s

##### Age 7 to 11Challenge Level

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

### Sticky Triangles

##### Age 7 to 11Challenge Level

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

### Pebbles

##### Age 7 to 11Challenge Level

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

### Number Squares

##### Age 5 to 11Challenge Level

Start with four numbers at the corners of a square and put the total of two corners in the middle of that side. Keep going... Can you estimate what the size of the last four numbers will be?

### Cuboid-in-a-box

##### Age 7 to 11Challenge 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?

##### Age 7 to 11Challenge 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.

### Extending Great Squares

##### Age 7 to 11Challenge Level

Explore one of these five pictures.

### Triple Cubes

##### Age 5 to 11Challenge Level

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

### Egyptian Rope

##### Age 7 to 11Challenge 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?

### Tiling

##### Age 7 to 11Challenge Level

An investigation that gives you the opportunity to make and justify predictions.

### Calendar Patterns

##### Age 7 to 11Challenge Level

In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?

### Tiles on a Patio

##### Age 7 to 11Challenge Level

How many ways can you find of tiling the square patio, using square tiles of different sizes?

##### Age 7 to 11Challenge Level

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

##### Age 7 to 11Challenge 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.

### Consecutive Numbers

##### Age 7 to 14Challenge Level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

### Roll These Dice

##### Age 7 to 11Challenge 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?

### Four Layers

##### Age 5 to 11Challenge Level

Can you create more models that follow these rules?

### The Great Tiling Count

##### Age 7 to 11Challenge Level

Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.