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#### Resources tagged with Investigations similar to Route Product:

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Broad Topics > Using, Applying and Reasoning about Mathematics > Investigations

### Polo Square

##### Stage: 2 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.

### Newspapers

##### Stage: 2 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

##### Stage: 2 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?

### Ice Cream

##### Stage: 2 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.

### Calcunos

##### Stage: 2 Challenge Level:

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

### It Figures

##### Stage: 2 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?

### Building with Rods

##### Stage: 2 Challenge Level:

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

### Cubes Here and There

##### Stage: 2 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?

### The Pied Piper of Hamelin

##### Stage: 2 Challenge Level:

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

### Watch Your Feet

##### Stage: 2 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?

### Street Party

##### Stage: 2 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.

### Room Doubling

##### Stage: 2 Challenge Level:

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

### 3 Rings

##### Stage: 2 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?

### Tri.'s

##### Stage: 2 Challenge Level:

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

### My New Patio

##### Stage: 2 Challenge Level:

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

### Tiles on a Patio

##### Stage: 2 Challenge Level:

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

### Stairs

##### Stage: 1 and 2 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.

### Egyptian Rope

##### Stage: 2 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?

### Bean Bags for Bernard's Bag

##### Stage: 2 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?

### Buying a Balloon

##### Stage: 2 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?

### Cuboid-in-a-box

##### Stage: 2 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?

### Two by One

##### Stage: 2 Challenge Level:

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

### Sweets in a Box

##### Stage: 2 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?

### New House

##### Stage: 2 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?

### Magazines

##### Stage: 2 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.

### Sticks and Triangles

##### Stage: 2 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

##### Stage: 2 Challenge Level:

How many models can you find which obey these rules?

### Two on Five

##### Stage: 1 and 2 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 Cuboids

##### Stage: 2 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?

### Train Carriages

##### Stage: 1 and 2 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?

### It's All about 64

##### Stage: 2 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.

### Sets of Numbers

##### Stage: 2 Challenge Level:

How many different sets of numbers with at least four members can you find in the numbers in this box?

### Follow the Numbers

##### Stage: 2 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.

### Making Squares

##### Stage: 2

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?

### It Was 2010!

##### Stage: 1 and 2 Challenge Level:

If the answer's 2010, what could the question be?

### Tiling

##### Stage: 2 Challenge Level:

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

### Making Boxes

##### Stage: 2 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?

### More Transformations on a Pegboard

##### Stage: 2 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.

### Plants

##### Stage: 1 and 2 Challenge Level:

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

### Magic Constants

##### Stage: 2 Challenge Level:

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

### Sending Cards

##### Stage: 2 Challenge 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?

### Abundant Numbers

##### Stage: 2 Challenge Level:

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

### Doplication

##### Stage: 2 Challenge Level:

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

### Hexpentas

##### Stage: 1 and 2 Challenge Level:

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

### Gran, How Old Are You?

##### Stage: 2 Challenge Level:

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

### Worms

##### Stage: 2 Challenge Level:

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?

### Little Boxes

##### Stage: 2 Challenge Level:

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

##### Stage: 2 Challenge 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.

### Escher Tessellations

##### Stage: 2 Challenge Level:

This practical investigation invites you to make tessellating shapes in a similar way to the artist Escher.

### Polygonals

##### Stage: 2 Challenge Level:

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