# Resources tagged with: Investigations

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### There are 141 results

Broad Topics > Thinking Mathematically > Investigations

### 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?

### 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?

### 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?

### Triangular Hexagons

##### Age 7 to 11Challenge Level

Investigate these hexagons drawn from different sized equilateral triangles.

### Shaping It

##### Age 5 to 11Challenge 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.

### Triangle Relations

##### Age 7 to 11Challenge Level

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

### Triangle Shapes

##### Age 5 to 11Challenge Level

This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.

### Cutting Corners

##### Age 7 to 11Challenge 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?

### Two by One

##### Age 7 to 11Challenge Level

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

### Cutting it Out

##### Age 5 to 11Challenge Level

I cut this square into two different shapes. What can you say about the relationship between them?

### Lawn Border

##### Age 5 to 11Challenge Level

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

### Fit These Shapes

##### Age 5 to 11Challenge 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?

### 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.

### Great Squares

##### Age 7 to 11Challenge Level

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

### More Transformations on a Pegboard

##### Age 7 to 11Challenge 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 Transformations

##### Age 7 to 11Challenge 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?

### How Tall?

##### Age 5 to 11Challenge Level

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

### Tiling Into Slanted Rectangles

##### Age 7 to 11Challenge Level

A follow-up activity to Tiles in the Garden.

### Making Boxes

##### Age 7 to 11Challenge Level

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

### Tiles in the Garden

##### Age 7 to 11Challenge Level

How many tiles do we need to tile these patios?

### 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.

### Fencing

##### Age 7 to 11Challenge Level

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

### Extending Great Squares

##### Age 7 to 11Challenge Level

Explore one of these five pictures.

##### 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?

### 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?

### Are You a Smart Shopper?

##### Age 7 to 11Challenge Level

In my local town there are three supermarkets which each has a special deal on some products. If you bought all your shopping in one shop, where would be the cheapest?

### 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?

### 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?

##### 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.

### Tessellating Triangles

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

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

### 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?

### 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?

### Investigating Pascal's Triangle

##### Age 7 to 11Challenge 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.

### 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?

### 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?

### All Wrapped Up

##### Age 7 to 11Challenge Level

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

### Experiencing Problem Solving

##### Age 5 to 11

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

### Sending and Receiving Cards

##### Age 7 to 11Challenge 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?

### Building with Rods

##### Age 7 to 11Challenge Level

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

### Eye View

##### Age 7 to 11Challenge Level

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

### The Domesday Project

##### Age 7 to 11Challenge Level

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

### Polygonals

##### Age 7 to 11Challenge Level

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

### Three Sets of Cubes, Two Surfaces

##### Age 7 to 11Challenge Level

How many models can you find which obey these rules?

### Four Layers

##### Age 5 to 11Challenge Level

Can you create more models that follow these rules?

### Count the Digits

##### Age 5 to 11Challenge Level

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

### 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.

### 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.

### More Pebbles

##### Age 7 to 11Challenge Level

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

### The Numbers Give the Design

##### Age 7 to 11Challenge Level

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.