Students will be able to : Make links between rates and ratios, and direct proportion Simplify rates to solve problems

 What is an example of a rate? A ratio?  What do rates and ratios have in common?  What is a difference between a rate and a ratio?  Does working with rates rely on direct proportion? Why?  Does working with ratios rely on direct proportion? Why?

Jenny bought a 45 g bag of lollies at the movies for $2.70. a) How much would an 80 g bag of lollies cost? b) How many grams of lollies could be bought for 65c? Jenny bought a 45 g bag of lollies at the movies for $2.70. a)How much would an 80 g bag of lollies cost? b)How many grams of lollies could be bought for 65c?

 What are the two variables? (mass and cost) How do you know? (the units give that information)  Is this an example of direct proportion? (yes) How do you know? (as the amount of lollies bought increases, so too would the cost — and vice versa, in the same proportion — making it direct proportion)  What is the simplest cost per mass rate that we could write? ($2.70 ÷ 45 g = $0.06/g)  What is the simplest mass per cost rate that we could write? (45 g ÷ $2.70 = 16.7 g/$)  What other units could we use to understand this rate better? (e.g. 6c/g)  What do you need to consider about the units in order to answer part b) of the problem? (the units are not consistent — you need to use either c/g rate units or change the 65c into dollars to match the rate unit $/g)

 a)A4 lecture pads (140 pages) cost $2.65 and 10 A4 lecture pads (140 pages) cost $26.50  b)An electronic game costs $29.95 and three games cost $89.  c)White enamel paint at $42.80 for five litres and $32.20 for four litres.  d)Downloading a song costs $0.99 and downloading five songs costs $4.95.  e)A L water tank sells for $494 and a L tank sells for $599.  f)A six-pack of socks cost $10.94 and a three-pack costs $5.47.