Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

Lawn Border

Age 5 to 11
Challenge 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?

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?

Fencing Lambs

Age 7 to 11
Challenge Level

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

Tea Cups

Age 7 to 14
Challenge Level

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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.

Extending Great Squares

Age 7 to 11
Challenge Level

Explore one of these five pictures.

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?

Tiling

Age 7 to 11
Challenge Level

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

Consecutive Numbers

Age 7 to 14
Challenge Level

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

Pebbles

Age 7 to 11
Challenge 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?

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?

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?

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?

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?

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?

It's All about 64

Age 7 to 11
Challenge 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.

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.

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?

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?

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"?

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?

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?

Tri.'s

Age 7 to 11
Challenge Level

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

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?

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.

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?

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?

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?

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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.

Tiles in the Garden

Age 7 to 11
Challenge Level

How many tiles do we need to tile these patios?

Building with Rods

Age 7 to 11
Challenge Level

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

Building with Longer Rods

Age 7 to 14
Challenge Level

A challenging activity focusing on finding all possible ways of stacking rods.

Tiling Into Slanted Rectangles

Age 7 to 11
Challenge Level

A follow-up activity to Tiles in the Garden.

Polo Square

Age 7 to 11
Challenge Level

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

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.

Train Carriages

Age 5 to 11
Challenge 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?

Teddy Town

Age 5 to 14
Challenge Level

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

The Great Tiling Count

Age 7 to 11
Challenge 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.

Magazines

Age 7 to 11
Challenge 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.

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?

Street Party

Age 7 to 11
Challenge 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.

Tables Without Tens

Age 7 to 11
Challenge Level

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

Buying a Balloon

Age 7 to 11
Challenge 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?

Lost Books

Age 7 to 11
Challenge 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?

Halloween Investigation

Age 7 to 11
Challenge 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?

Counting on Letters

Age 11 to 14
Challenge Level

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

3 Rings

Age 7 to 11
Challenge 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?

Ice Cream

Age 7 to 11
Challenge 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.

Newspapers

Age 7 to 11
Challenge 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?