Resources tagged with: Investigations

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Broad Topics > Thinking Mathematically > Investigations

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"?

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.

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?

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.

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.

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?

Extending Great Squares

Age 7 to 11
Challenge Level

Explore one of these five pictures.

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?

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.

Move a Match

Age 7 to 11
Challenge Level

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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?

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?

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.

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.

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.

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?

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.

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?

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?

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?

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?

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?

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?

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.

Tri.'s

Age 7 to 11
Challenge Level

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

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?

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?

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.

More Pebbles

Age 7 to 11
Challenge Level

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

Follow the Numbers

Age 7 to 11
Challenge 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.

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.

Three Sets of Cubes, Two Surfaces

Age 7 to 11
Challenge Level

How many models can you find which obey these rules?

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.

Building with Rods

Age 7 to 11
Challenge Level

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

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.

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?

Little Boxes

Age 7 to 11
Challenge Level

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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.

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.

Number Squares

Age 5 to 11
Challenge 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?

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?

Calendar Patterns

Age 7 to 11
Challenge 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?

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?

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?

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?

Triangular Hexagons

Age 7 to 11
Challenge Level

Investigate these hexagons drawn from different sized equilateral triangles.

Exploring Wild & Wonderful Number Patterns

Age 7 to 11
Challenge Level

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.