Materials for the lesson

Rulers and children’s bags & backpacks.

Teacher’s Bell.

Layout of the classroom

The desks are in their normal position.

We assume that the children in the classroom are 20

(If there is an even number, there is no problem; if it is a single number then the teacher takes part in the count.

1^st Phase

The teacher asks the children to bring their bags/ backpacks in front of the black-board.

One student can count: He/she finds them 20.

The teacher tells the children to stand next to their bags/ backpacks.

If all the children have a backpack, and if the backpacks are 20 then the students are 20.

By name, the teacher tells 10 children to take their bags and carry them to the back of the classroom.

We repeat:

How many children are in the classroom: 20

How many children are in front: 10 (we count them)

So how many are at the back: ………….. (also 10 = half)
If all children have one bag / backpack and if the children at the back of the class are 10.

Then how many bags/ backpacks are in front? (10)

And how many children? (Also 10).

2^nd Phase

Surfaces: Length
(We suppose that the black-board of the class is 2 meters, and that the rulers in our pencil-cases are 20 cm).

John and Anna want to draw one table (furniture) each on the board that is one meter long.

How do we divide the board in half to fit both tables? Let’s measure the table.

The teacher tells the children to get their rulers.

The teacher says to one student to keep his/her ruler at the edge of the board. To another student, to place his/hers ruler next to the other ruler.  Next to the second, another students places a  ruler etc etc.
So, with 5 children, we have 1 meter, with 10 children we have 2 meters. The rest of the children are at their desks discussing with the teacher about the length of the board.

3d Phase

 If the whole board is 10 children=10 rulers. Then how much is the half board? (5 children=5 rulers).
How many children have to take their rulers and leave, so as to find the half of the board? (5 children). We do that and we draw a line to the point where the 5^th child’s ruler ends.
So, now John has half of the black-board to draw his table and Anna the other half and they can draw their tables.
The teacher can continue (if the level of knowledge o the mathematics allows it) with the centimeters of the ruler:
If every ruler is 20 cm and the board is 2 meters, then we have 10 rulers. How much is the half of the board? (100 cm=1m).

4^th Phase

Conclusion: (as explained in the book) To find the half, we have to know the whole. And the opposite. The creative lesson can be done with other even-sized objects too: markers, books, gums and whatever else the Teacher’s imagination dictates.