**Mathematics 3** ESO – Unit 4 PROPORTIONALITY extra activities

**1 –** Watch the video on “Proportional Relationships” and answer:

- a) When are two quantities said to be “directly proportional”?
- b) What is the ratio in Karl’s recipe?
- c) How do we draw line that represents a direct proportion?
- d) Why any line that represents a direct proportion goes through the origin?
- e) Write the ratio, the table and draw the graph for this relationship: when x=3 y=2 ; when x=6 y=4 ; when x=15 y=10 and check that the line goes through the origin.

**2 –** Watch the video on “Solving Indirect Proportion Math Problems” and answer:

- a) When is a proportion “inverse”?
- b) Boyle’s Law says that when the pressure on a gas increases, its volume decreases, P
_{1}V_{1}= P_{2}V_{2 }. What type of proportion is Boyle’s Law? Why? - c) A piston at 3 atmospheres has a volume of 2 litres. What will be the volume if the pressure increases to 12 atm?
- d) A balloon at 1.1 atm has a volume of 4 l. What volume will occupy the air inside the balloon if it goes out (1 atm)?

**3 –** Watch the video on “Proportions” and answer:

- a) When are two fractions “equivalent”?
- b) What is a ratio?
- c) What is a proportion?
- d) Two ratios to be equivalent if they have the same _______ and the same _______ .
- e) What are proportions good for?
- f) How do we use “cross multiplying” to find the “unknown number”?
- g) Mary reads one book in three days, in how many days does she read 4 books?
- h) Bob reads 2 books in 1 week, in how many days does he read 5 books?
- i) The scale in a map says 2 cm in the map is 15 km in reality. How far in reality are two points that in the map are at a distance of 6.2 cm?