El lenguage de gráficos, presentación para alumnos de primer curso de la ESO. The language of graphs presentation for students of the first year.

1. The language of graphs
Mathematics. 1st Year Secondary Education

2. You know…
 Cartesian coordinate system
x-axis: horizontal
y-axis: vertical
Origin: point (o,o)
 To plot points on a graph
P (3,5): “ordered pair”
(3 units to the right, and 5 units up)
 To plot the graph of a function
y = 2x + 1

3. “You have to be able to understand the
qualitative meaning
of a graph”
“Let’s practice together…”

4. Hamilton Alonso Vettel
Podiums
World Championships
Podiums
WorldChampionships
A
H
V
“Who has more Podiums?”
“Who has won more World Championships?”
H: Hamilton A: Alonso V: Vettel

5. Hamilton Alonso Vettel
Podiums
World Championships
Podiums
WorldChampionships
A
H
V
“Who has more Podiums?” ALONSO
“Who has won more World Championships?” VETTEL
H: Hamilton A: Alonso V: Vettel

6. Hamilton Alonso Vettel
Podiums 56 95 64
World Championships 1 2 4
Podiums
WorldChampionships
A
H
V
“Who has more Podiums?” ALONSO
“Who has won more World Championships?” VETTEL
H: Hamilton A: Alonso V: Vettel

7. 1. The Bus Stop Queue
Point 7 represents…

8. 1. The Bus Stop Queue
Point 7 represents Gavin
“He is the shortest and youngest person”
7

9. 1. The Bus Stop Queue
Point 6 represents…
7

10. 1. The Bus Stop Queue
Point 6 represents Cathy
“She is taller than Gavin but shorter than the rest of
the people”
7
6

11. 1. The Bus Stop Queue
Points 2 and 5 represent…
7
6

12. 1. The Bus Stop Queue
Points 2 and 5 represent Alice or Errol
“They are the tallest”
Point 2 represents…
7
6

13. 1. The Bus Stop Queue
Points 2 and 5 represent Alice or Errol
“They are the tallest”
Point 2 represents Alice
“She is one of the tallest and older than Errol”
So point 5 represents…
7
62

14. 1. The Bus Stop Queue
Points 2 and 5 represent Alice or Errol
“They are the tallest”
Point 2 represents Alice
“She is one of the tallest and older than Errol”
So point 5 represents Errol
“He is one of the tallest and younger than Alice”
7
62 5

15. 1. The Bus Stop Queue
Point 3 represents…
7
62 5

16. 1. The Bus Stop Queue
Point 3 represents Freda
“She is shorter than Alice and Errol but taller than
the rest of the people”
7
62 25

17. 1. The Bus Stop Queue
Points 1 and 4 represent…
7
62 5 2

18. 1. The Bus Stop Queue
Points 1 and 4 represent Brendaor Dennis
“They have the same height”
Point 1 represents…
7
62 5 2

19. 1. The Bus Stop Queue
Points 1 and 4 represent Brenda or Dennis
“They have the same height”
Point 1 represents Dennis
“He is older than Brenda”
So point 4 represents…
7
62 5 21

20. 1. The Bus Stop Queue
Points 1 and 4 represent Brenda or Dennis
“They have the same height”
Point 1 represents Dennis
“He is older than Brenda”
So point 4 represents Brenda
“She is younger than Dennis”
7
62 5 214

21. 1. The Bus Stop Queue
7
62 5 214

22. 2. Planes
A (Dusty) B (Siddeley)

23. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B

24. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive than airplane A

25. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The older airplane is cheaper

26. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The older airplane is cheaper

27. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The older airplane is cheaper
 The faster airplane is smaller

28. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The older airplane is cheaper
 The faster airplane is smaller

29. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The older airplane is cheaper
 The faster airplane is smaller
 The larger airplane is older

30. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The older airplane is cheaper
 The faster airplane is smaller
 The larger airplane is older

31. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The older airplane is cheaper
 The faster airplane is smaller
 The larger airplane is older
 The cheaper airplane carries fewer passengers

32. 2. Planes
A (Dusty) B (Siddeley)
 Airplane A is older than airplane B
 Airplane B is more expensive tan airplane A
 The older airplane is cheaper
 The faster airplane is smaller
 The larger airplane is older
 The cheaper airplane carries fewer passengers

33. 2. Planes
A (Dusty) B (Siddeley)

34. 3. Which Graph?
The 100 metres race.
The men's world record is
9.58 seconds, set by Usain Bolt
0,00
2,00
4,00
6,00
8,00
10,00
12,00
0 50 100 150SPEED
DISTANCE
GRAPH 3
0
2
4
6
8
10
12
0 50 100 150
SPEED
DISTANCE
GRAPH 1
0
2
4
6
8
10
12
0 50 100 150
SPEED
DISTANCE
GRAPH 2

35. 0,00
2,00
4,00
6,00
8,00
10,00
12,00
0 20 40 60 80 100 120 140
SPEED
DISTANCE
GRAPH 3
3. Which Graph?

36. To sum up…
Graphsare very useful to draw conclusionsfrom different set of data
and to find if there is a correlation between them.
http://www.nytimes.com/interactive/2012/08/05/sports/olympics/the-100-meter-dash-one-race-every-medalist-ever.html?_r=0

37. The language of graphs
Mathematics. 1st Year Secondary Education