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 = 2SPREADSHEET

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 = 1.5SPREADSHEET

Other examples of direct Other examples of direct proportionalityproportionality 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 THE RULE OF THREE (Direct)(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

TAPS

INVERSE

People Sweets24 2

12 46 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 THE RULE OF THREE (Inverse)(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 problemNow it’s noon. It’s boiling.The pool is empty!

So, we want to fill it.

At the poolAt the poolTwo 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, the At 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.