Writing numbers

Rogério Lourenço

1997 - Ciências Sociais - UFRJ

2000 - Comunicação, Imagem e Informação - UFF  

2001- 2008 - Empresa Municipal de Multimeios - MULTIRIO

2010  - Gramática Gerativa e Estudos de Cognição Museu Nacional -UFRJ

2010 - Rede Nacional de Pesquisa

2015  - Doutorado em Linguística - UFRJ

2017  - Laboratório de Estudo do discurso Imagem e Som - Museu Nacional - UFRJ

The image of mathematics

Language & Mathematics

The test

Osvaldo bought a cheese with a equilateral triangle shape.

He wants to equally divide the cheese among his four cousins and himself. 

Make a draw indicating how he can make the division.

A triangular cheese

( OBEMP 2011 / questão 97)

The answer

To divide a cheese in 5 equal parts is sufficient to divide it in 5k equal parts and give  k parts to each one. 

One way to do this partition is shown on the figure, where the cheeses was partitioned on 25 = 5 × 5 triangles.

Portuguese          Mathematics

•     1    Triangle 
•     ÷  Division   
•     4   Cousins + 1

• Cheese ( equilateral divisor )
• To divide  ( verb ) 
• Cousins ( N dividend ) & Oswaldo

languages

grammar                                              notation

Steps

• resources (similar initiatives)
• technologies (available)  
• MVP (prototype)

resources

 grammar, MathML, Parsing, Regex...

prototype

MVP:

basic operations

 ( + )   ( - )   ( × )   ( ÷ )

Pedro plays with a square checked board 4 x 6  and with pieces from types A, B andC.

Explain why it is not possible to cover the board with type B pieces.

discourse & mathematics

Pedro plays with a square checked board 4 x 6  and with pieces from types A, B andC.

The answer counts the squares on the pieces and cover the board with the c type piece as shown in the picture.

discourse & mathematics

Manipulate

the

DOM

Global attributes

• Conditional processing attributes »
• Core attributes »
• Graphical event attributes »
• Presentation attributes »
• class
• style
• externalResourcesRequired
• transform

<text>

the number line

2 

“All regular hexagons can be divided into 6  equilateral triangles (6-2) - 180=720 / 6=120 ✗ 120/2=60.

So if the equilateral triangles above are equals to the sid hexagon´s side, the equilateral triangles from hexagon, have the same side of the equilateral triangles from the hexagon, have the same side from equilateral triangles from the pictures, and consequently, the same area.

Therefore  the hexagon has the area: 6 x 1cm   = 6 cm  ”

ANSWER 1

2 

2 

ANSWER 2

“6 cm. As the hexagon is regular, it can be divided into equilateral triangles  in the following way.

Each triangle has área 1 cm , since they are congruent to the other (all sides from all figures have the same size, and the triangles sides from the hexagon  have the  same side from the hexagon, having also the same side).

For 6 triangles, the área is 6 x 1 cm   = 6 cm  ”

2 

2 

2 

2 

ANSWER 3

“We know one regular hexagon can be divided into 6 equilateral triangules with same side of the side of the hexagon, as drawn in the figure.

As the triangles that form the hexagon have the same side from others making the dodecagon, ( equalling the hexagon) then all  will have the same area: 1 cm.

As each hexagon is formed by 6 triangles, it will be igual to 6.1= 6 cm  . ”

2 

2 

ANSWER 4

“The regular hexagon can be divided into 6 equilateal triangles. As each triangle has área of 1 cm  , the hexagon has 6 cm  .”

2 

2 

ANSWER 5

” If all have the same side measures , it is enough to divide  the hexagon into six triangles.

If the area of the triangle is 1 cm  , multiply  by 6 (number of triangles from the hexagon) and we will have área of 6 cm   pertaining  to the hexágono. “

2 

2 

ANSWER 6

“If we connect a edge to opposite side, we will see the line will be the  bisector of two angles, then each angle will have 60°,

if we do that to all edges we will have 6 congruent equilateral triangles.

As the área of the others is 1 cm  , the hexago area will be 6.1= 6 cm  ”

2 

2 

(1) To infer the square having the same side of each side of the equilateral triangle 

(2) verify the picutre is composed by one of sides of the square .

The conclusion , in this case,  is  (6 x 1 cm = 6 cm  ).

To observe the picutre... the answers use the graphical resource.

2 

2 

http://www.mdpi.com/2227-9709/4/3/28/htm

motivation