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Escola Sadako
Barcelona

Age:
11 - 12 years old

Aims:
To present exponentiation as a new operation.
To represent it with materials
To understand the meaning of expressions such as "squared" or "cubed"
To memorize the first 20 squares
To investigate other squares

Materials:
 Bottle tops, Cuisenaire rods, a calculator

Vocabulary:
 Base, exponent, repeated multiplication, squared, cubed, raised to the power of …

Introductcion:
 The teacher introduces the exponentiation as a way to abbreviate a multiplication where the same factor is repeated. She suggests a few examples, and students make calculations both with pencil and paper and sometimes with the calculator.

Main part:
The teacher presents the calculation of powers with exponent 2 with Cuisenaire rods (for example, in order to represent 8 raised to 2 it is necessary to represent 8x8 (8 times 8) and this can be done with 8 rods of length 8).

When students represent just the first ten numbers raised to the second, they write down their mathematical representation and the result.

After observing that all have a squared shape, the term "eight squared" makes sense to indicate " 8 raise to 2". It is the same for powers with the exponent 3. They built cubes with the rods.

Round up:
The teacher suggests memorizing the first 20 squares. To help them make a table on the blackboard and observe that they know the top ten numbers so the task is not so difficult.

Observacions:
To reinforce the memorization of the first perfect square, the teacher will suggest for the next class a research project: Find the decomposition of all numbers (up to 200) as the sum of squares.