# Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

### Triangular Hexagons

##### Age 7 to 11 Challenge Level:

Investigate these hexagons drawn from different sized equilateral triangles.

### Squareo'scope Determines the Kind of Triangle

##### Age 11 to 14

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

### 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.

### 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.

### Witch's Hat

##### Age 11 to 16 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

### 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?

### 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?

### Two by One

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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?

### All Wrapped Up

##### Age 7 to 11 Challenge Level:

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

### 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?

### 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"?

### 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 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?

##### 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?

### 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?

### 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?

##### 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?

### Round and Round the Circle

##### Age 7 to 11 Challenge Level:

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

### 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.

### 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?

### 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?

### 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?

### 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.

### 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.

### Tiling Into Slanted Rectangles

##### Age 7 to 11 Challenge Level:

A follow-up activity to Tiles in the Garden.

### 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.

### 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?

### Four Layers

##### Age 5 to 11 Challenge Level:

Can you create more models that follow these rules?

### More Pebbles

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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.

### 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.

### 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 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?

### 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?

### 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?

### 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?