Welcome to the circus! I'm the ringmaster.

Your job is to help me direct the acrobats to form square-shaped towers.

How do you make a square tower? Show me

Your job is to help me direct the acrobats to form square-shaped towers.

How do you make a square tower? Show me

Enter a number:
Go

**two-person**base.

How many acrobats are needed to do this? Enter the total number of acrobats you need in the space.

You need to create a square shape with two acrobats in the base layer. So how many do you need in total? Try again

You need to create a square shape with two acrobats in the base layer. So how many do you need in total? Try again

To create a square shape based on two acrobats, you need two layers.

Two acrobats in the base times two layers is four acrobats: 2 x 2 = 4. OK

You need to create a square shape with two acrobats in the base layer. So how many do you need in total? Try again

You need to create a square shape with two acrobats in the base layer. So how many do you need in total? Try again

To create a square shape based on two acrobats, you need two layers.

Two acrobats in the base times two layers is four acrobats: 2 x 2 = 4. OK

Acrobats in base
Acrobats in tower

Count the number of acrobats in the base and enter this number in the top row.

Enter the number of acrobats in the whole tower in the bottom row. Try again

Number of acrobats in square tower
Number of acrobats in base
Acrobats in tower

Enter a number:
Go

**three-person**base.

How many acrobats are needed to do this? Enter the total number you need in the space.

You need to create a square shape with two acrobats in the base layer. So how many do you need in total? Try again

You need to create a square shape with two acrobats in the base layer. So how many do you need in total? Try again

To create a square shape based on three acrobats, you need three layers.

Three acrobats in the base times three layers is nine acrobats: 3 x 3 = 9. OK

Count the number of acrobats in the base and enter this number in the top row.

Enter the number of acrobats in the whole tower in the bottom row. Try again

Acrobats in base
Acrobats in tower

Acrobats in tower
Number of acrobats in square tower
Number of acrobats in base

The pattern relates to square numbers. These are numbers that are made by multiplying a number by itself, such as 2 x 2 = 4 and 3 x 3 = 9. We can write 3 x 3 as 3

^{2}and we call it '3 squared'. OK

Enter a number:
Go

Acrobats in base
Acrobats in tower

Acrobats in tower
Number of acrobats in square tower
Number of acrobats in base

**four-person**base.

You need to create a square shape with two acrobats in the base layer. So how many do you need in total? Try again

You need to create a square shape with two acrobats in the base layer. So how many do you need in total? Try again

To create a square shape based on three acrobats, you need four layers.

Four acrobats in the base times four layers is sixteen acrobats: 4 x 4 = 16. OK

Count the number of acrobats in the base and enter this number in the top row.

Enter the number of acrobats in the whole tower in the bottom row. Try again

There are five acrobats in the base. To create a square shape, the number in the base and the number of layers must be the same. So you need five layers in the tower.

To find the answer, multiply 5 x 5: you need 25 acrobats. OK

There are seven acrobats in the base. To create a square shape, the number in the base and the number of layers must be the same. So you need seven layers in the tower.

To find the answer, multiply 7 x 7: you need 49 acrobats. OK

There are 2 500 acrobats in the tower. To create a square shape, the number in the base and the number of layers must be the same. So you need to find the number you can multiply by itself to make 2 500.

Since 50 x 50 = 2 500, there must be 50 acrobats in the base and 50 layers in the tower. OK

For help, look at the pattern in the table and on the graph. OK

This curve shape occurs because the total number of acrobats does not increase by an equal amount each time an acrobat is added to the base. OK

Notice that when you plot squared numbers in a sequence, the graph curves sharply upwards. OK

Choose the correct answer for each of the questions that follow. OK

Question 1
In any square tower, the number in the base is:
A
double the number of layers
B
larger than the number of layers
C
the same as the number of layers
D
smaller than the number of layers

The answer is (C). In a square tower, the number in the base is always the same as the number of layers, no matter how large or small the tower. OK

The answer is (D). We work out the total by multiplying the number in the base by the number of layers.

In a square tower, these numbers are always the same, so you multiply the number by itself. OK

In a square tower, the number in the base is always the same as the number of layers, no matter how large or small the tower. OK

Question 2
Which of the below best describes the pattern in the table and on the graph?

The total number of acrobats in any square tower is: A the number in the base + the number of layers B the number in the base x 2 C the number in the base ÷ the number of layers D the number in the base x the number of layers

The total number of acrobats in any square tower is: A the number in the base + the number of layers B the number in the base x 2 C the number in the base ÷ the number of layers D the number in the base x the number of layers