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Maths
&
Cooking
Paella recipe for six people:
200 grammes of squid
300 grammes of prawns
½ kilo of clams
¼ kilo of crabs
¼ kilo of mussels
600 grammes of rice
2 ½ cups of water
2 ripe tomatoes
2 cloves of garlic
1 small onion
Parsley
1 green pepper
Saffron
800 grammes of chicken
Salt
Ingredients For six people For twelve people Division
squid 200 grammes 400 grammes 400:200 = 2
prawns 300 grammes 600 grammes 600:300 =2
clams ½ kilo 1 kilo 1 : ½ = 2
crabs ¼ kilo ½ kilo ½ : ¼ =2
mussels ¼ kilo ½ kilo ½ : ¼ =2
rice 600 grammes 1200 grammes 1200:600 = 2
cups of water 2 ½ 5 5 : 2 ½ = 2
12 people : 6 people = 2
SPREADSHEET
Ingredients For six people For nine people
squid 200 grammes 200 *1.5=300grammes
prawns 300 grammes 300*1.5=450 grammes
clams ½ =0.5 0.5*1.5=0.75 =3/4 kilo
crabs ¼ =0.25 0.25*1.5=0.375 =3/8 kilo
mussels ¼ =0.25 0.25*1.5=0.375 =3/8 kilo
rice 600 grammes 600*1.5=900 grammes
cups of water 2 ½=2.5 2.5*1.5=3.75
9 people : 6 people = 1.5
SPREADSHEET
Other examples of direct proportionalityOther examples of direct proportionality
 If an object travels at a constant speed, then the
distance traveled is proportional to the time spent
traveling, with the speed being the constant of
proportionality.
 On a map drawn to scale, the distance between any
two points on the map is proportional to the distance
between the two locations that the points represent,
with the constant of proportionality being the scale of
the map.
THE RULE OF THREE (Direct)THE RULE OF THREE (Direct)
 First, write the titles of
the two magnitudes
 Second, place the
quantities you know in
their correspondent
column
 Third, write an x for the
unknown quantity.
 Last, multiply in cross,
make equal the terms,
and find the x.
6
4 0,5 kilo
x
TAPSINVERSE
People Sweets
24 2
12 4
6 8
Number of sweets in the bag= 48
Inverse ProportionalityInverse Proportionality
Inverse ProportionalityInverse Proportionality
Some examples:
Magnitude A Magnitude B Proportionality
constant
speed time spent traveling distance of the
journey
number of people
working
number of working
days
working days for an
only worker
price of sweets number of sweets I
can buy
my money
Inverse ProportionalityInverse Proportionality
(24 very small prawns in the paella)(24 very small prawns in the paella)
For four people
For six people
For seven people
Six prawns for each
one
Four prawns for each
one
Three prawns and a
half for each one
(aproximately)
THE RULE OF THREE (Inverse)THE RULE OF THREE (Inverse)
 First, write the titles of
the two magnitudes
 Second, place the
quantities you know in
their correspondent
column
 Third, write an x for the
unknown quantity.
 Last, multiply in line,
make equal the terms,
and find the x.
4 6
x8
A summertime problemA summertime problem
Now it’s noon. It’s boiling.
The pool is empty!
So, we want to fill it.
At the poolAt the pool
Two taps
Tap A fills the pool in 3 hours
3 hours
Tap B fills the pool in 6 hours
6 hours
At the pool (and after, theAt the pool (and after, the
paella)paella)
So, if in an hour, we fill a half of the pool, it’s evident
that we will need two hours to fill completly the
pool.
Solution: 2 hours later, at 2 P.M.

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Departamento de matemáticas regla de 3

  • 1.
  • 3. Paella recipe for six people: 200 grammes of squid 300 grammes of prawns ½ kilo of clams
  • 4. ¼ kilo of crabs ¼ kilo of mussels 600 grammes of rice 2 ½ cups of water
  • 5. 2 ripe tomatoes 2 cloves of garlic 1 small onion Parsley
  • 6. 1 green pepper Saffron 800 grammes of chicken Salt
  • 7. Ingredients For six people For twelve people Division squid 200 grammes 400 grammes 400:200 = 2 prawns 300 grammes 600 grammes 600:300 =2 clams ½ kilo 1 kilo 1 : ½ = 2 crabs ¼ kilo ½ kilo ½ : ¼ =2 mussels ¼ kilo ½ kilo ½ : ¼ =2 rice 600 grammes 1200 grammes 1200:600 = 2 cups of water 2 ½ 5 5 : 2 ½ = 2 12 people : 6 people = 2 SPREADSHEET
  • 8. Ingredients For six people For nine people squid 200 grammes 200 *1.5=300grammes prawns 300 grammes 300*1.5=450 grammes clams ½ =0.5 0.5*1.5=0.75 =3/4 kilo crabs ¼ =0.25 0.25*1.5=0.375 =3/8 kilo mussels ¼ =0.25 0.25*1.5=0.375 =3/8 kilo rice 600 grammes 600*1.5=900 grammes cups of water 2 ½=2.5 2.5*1.5=3.75 9 people : 6 people = 1.5 SPREADSHEET
  • 9. Other examples of direct proportionalityOther examples of direct proportionality  If an object travels at a constant speed, then the distance traveled is proportional to the time spent traveling, with the speed being the constant of proportionality.  On a map drawn to scale, the distance between any two points on the map is proportional to the distance between the two locations that the points represent, with the constant of proportionality being the scale of the map.
  • 10. THE RULE OF THREE (Direct)THE RULE OF THREE (Direct)  First, write the titles of the two magnitudes  Second, place the quantities you know in their correspondent column  Third, write an x for the unknown quantity.  Last, multiply in cross, make equal the terms, and find the x. 6 4 0,5 kilo x TAPSINVERSE
  • 11. People Sweets 24 2 12 4 6 8 Number of sweets in the bag= 48 Inverse ProportionalityInverse Proportionality
  • 12. Inverse ProportionalityInverse Proportionality Some examples: Magnitude A Magnitude B Proportionality constant speed time spent traveling distance of the journey number of people working number of working days working days for an only worker price of sweets number of sweets I can buy my money
  • 13. Inverse ProportionalityInverse Proportionality (24 very small prawns in the paella)(24 very small prawns in the paella) For four people For six people For seven people Six prawns for each one Four prawns for each one Three prawns and a half for each one (aproximately)
  • 14. THE RULE OF THREE (Inverse)THE RULE OF THREE (Inverse)  First, write the titles of the two magnitudes  Second, place the quantities you know in their correspondent column  Third, write an x for the unknown quantity.  Last, multiply in line, make equal the terms, and find the x. 4 6 x8
  • 15. A summertime problemA summertime problem Now it’s noon. It’s boiling. The pool is empty! So, we want to fill it.
  • 16. At the poolAt the pool Two taps Tap A fills the pool in 3 hours 3 hours Tap B fills the pool in 6 hours 6 hours
  • 17. At the pool (and after, theAt the pool (and after, the paella)paella) So, if in an hour, we fill a half of the pool, it’s evident that we will need two hours to fill completly the pool. Solution: 2 hours later, at 2 P.M.

Editor's Notes

  1. It may not be 24 prawns in a quarter kilo, but less.