#### The cube

Written with this little fancy three up in the air, the cube of a number is simply this number multiplied by itself twice. For example $2^3=2\times 2\times 2=8$. Compute the cube of the following numbers:

# Monomials & polynomials

Learning
8

#### Sum of the 10 first cubes

Look at these cubes, of size 1, 2, 3,... Suppose they are made of squares, all of the same unit height. How can you spread these squares on the plane? If you have 10 cubes, what is the area tiled by all these cubes?

# Monomials & polynomials

Modeling
8

#### The sum of the 10 first squares

Look at these pyramids. They are made of square pieces, all of the same height, which is the depth of each step. Hence their volume is the sum of the squares. You have six of them to make a cuboid. If there are ten stairs, what is the size of this cuboid made of the six pyramids?

# Monomials & polynomials

Modeling
8

#### The turning points

Now, let's turn our attention to the corners, the turning points, alternating bottom-left, top-left, top-right and bottom-right, beginning with 1, 2, 3, 5, 7...

# Operations with natural numbers

Reasoning
5

#### Equivalent expressions

Which of the following expressions is equivalent to 3k+6?

# Numbers & operations

Reasoning
8

#### From natural to algebraic language

Translate the following sentence in algebraic language: The square of an even number

# Numbers & operations

Training
8