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, P1V1 = P2V2 . 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?