S5 FIN 0 Rates
Stage 5 Mathematics Rates
Learning Intention
For students to understand how to use rates in a variety of situation and the importance of the unitary method
Success Criteria
Students will be successful when they can confidently convert rates where one variable is changing
Students who are capable will be able to work with multi-step conversions often where both units of measure are changing. This could also include rates being embedded within other rates.
Learning Notes
Example 1.
You know that 3 oranges cost $2.64. How much would you expect to pay for 7 oranges
3 oranges = $2.64. When using the unitary method it is always our goal to find what 1 unit costs. Therefore we divid both sides by 3.
1 orange = $0.68. Now we can easily find what 7 oranges costs, by multiplying both sides by 7
7 oranges = $4.76
Example 2.
You buy 4 kilograms of bananas for $6.48. You also know that on average there are 5 bananas in every kilogram. What is the most amount of bananas you can buy with $20?
1 kilogram = 5 bananas Therefore 4 kilograms = 20 bananas.
$6.48 = 20 bananas. We need to know how much we can buy for $20. It would be nice to know how much we can buy for $1. Divide both sides by 20
$1 = 3.08 bananas. To find how many we can but with $20 we multiply both sides by 20.
$20 = 61.7 bananas or 61 bananas
Syllabus Dot Points
NOTE - For stage 5 there is no associated dot point for rates in the finance section of the course. This is seen as an important pre-requisite for this topic.
Lesson Tasks
1. You know from the internet that the tallest sail of the opera house is 65 metres. In a photo that you have taken, this sail is 8.2cm. The smallest sail in your photo is only 2.2cm.
Steve says, "I can approximate the height of the smallest sail."
Michelle says, "I can calculate the exact height of the smallest sail."
Explain how each student might do these calculations
2. A photo on your computer is 22 centimetres wide by 14cm high. You are projecting this photo to a large TV. This TV has dimensions 112 centimetres wide and 80 centimetres high. You want to enlarge this photo as much as possible onto the TV. What would be the dimensions of this photo on the large TV.
3. Jess is the fastest runner in the school. She runs the 100 metres in a time that is usually between 12 and 13 seconds. Approximately what speed is she running in kilometres per hour. Explain how you calculated this speed.
1. A family photo is 12cm long by 9cm high. You wish to enlarge it and place it into a photo frame that is 60cm long and 30cm high. Explain why some of these enlargement factors would and/or would not be suitable.
An enlargement factor of 10
An enlargement factor of 5
An enlargement factor of 3
2. To make 12 small cheesecakes you need to use 250mls of cream cheese. If you were making 15 small cheesecakes how much cream cheese would you use.
3. A map has a scale where 1centimetre = 80 kilometres. The distance between Sydney and Brisbane on the map is 12.2 centimetres. The actual distance between the two cities is 925 kilometres. Explain why there is a difference between these two measurements.
Woolworths sell Special K for $4.80 for a 300 gram pack.
Coles sell Special K for $6.00 for a 500 gram pack
Aldi sell Special K as well. They sell a 750 gram pack. They wish their Special K to be better value than Woolworths but not as good as Coles. How much might they sell their Special K for?
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Ratio An Eco-System
A wild cat needs three birds per week to survive. Three birds will eat 10 caterpillars each per week. The 30 caterpillars will eat two small bushes every week.
- In the area that these animals live, the eco-system can support 500 small bushes being eaten per week. How many of each other animal can live within this eco-system?
- What if the eco-system could support 200 caterpillars? How much of each animal and plant would be in the eco-system?
The population of the area stabilises at 750 wildcats, 2250 birds, 7500 caterpillars and 500 bushes.
a) Describe what would happen to all the populations if a drought knocked out all but 10 bushes?
b) Describe what would happen to all the populations if a virus knocked out all but 5 of the big cats?
Discussion QuestionS5 FIN 1.1 Discussion
Check Your Understanding