## Todas as tarefas

#### Castillo de naipes

En un concurso me mandan construir un castillo de naipes... como el de la figura...
¿Cuántas cartas necesito para que el piso alcance los 50 pisos? Esperemos que no se caiga.

# Sequences

Modeling

8

#### Let's walk it!

Choose the program that will walk Scratch the cat along the spirale of integers! (see the first hint for a reminder)

# Unassigned

Modeling

5

#### 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