Graphs+and+Algebra

** Direct Proportions **

Suppose you want to know the temperature of a room in degrees celcius. You only have a thermometer which tells you the temperature in fahrenheit. How would you find what the temperature in degrees celcius using this thermometer?

What if you wanted to measure the length of a path in metres but only had a tape measure measuring in feet and inches?

How would you find out what a bag of sweets costs in pounds if you bought them in on holiday in America using US dollars?

All these questions can be answered using a principle known as **Direct Proportionality**.

If the ratio between two variables (such as pounds and dollars) is always the same then these variables are said to be **Directly Proportional** to each other**. **

> what are they and what makes them directional proportional?
 * Look at the image to the right >>>>
 * How does it demonstrate direct proportionality?
 * Can you see any other physical examples around you,

Direct proportion problems can be solved by calculating the ratio between two variables... ** > You buy 6 kg so you pay £3. > If you buy 20 kg, you pay £10. **The cost of potatoes is DIRECTLY PROPORTIONAL to the amount of potatoes you buy**
 * __ Some worked examples: __** (//taken from ncetm//)**
 * Potatoes cost 50p per kilogram.
 * The ratio 6 : 3 is the same as the ratio 20 : 10, since they both simplify to 2 : 1. **

> There are 15 toffees in the box. > How many chocolates are there? > > In this problem, the ratio of the number of toffees to the number of chocolates is constant. > The solution can be modelled on a number line. 5 is multiplied by 3 to make 15 (i.e. scaled up by a factor of 3), so 2 must also be multiplied by 3 to get the answer of 6 chocolates. We could also think of this as finding a pair of equivalent fractions such that:
 * Direct proportion problems can sometimes be solved by scaling...**
 * In a box of sweets there are 5 toffees for every 2 chocolates.
 * The number of toffees in a box of sweets is DIRECTLY PROPORTIONAL to the number of chocolates. **

**Another approach is the unitary method, in which the value of one of the variables is reduced to 1....** > How much flour will a cake for 7 people need?6 people need 120 g flour. > 1 person needs 120 ÷ 6 = 20 g flour. > 7 people need 20 × 7 = 140 g flour. **The amount of flour needed to make a cake is DIRECTLY PROPORTIONAL to the amount of people the cake is made for.**
 * A cake recipe for 6 people needs 120 g flour.

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 * __Links and Resources__ **
 * 1) Lesson on Linear Equation Graphs (J Mills-Dadson) [|_Linear_Graph[1.pptx]]
 * 2) Linear Equations Card Sort [|Linear Equations Card Sort.pub]
 * 3) Algebra - Tables, Spreadsheets and Graphs[|Algebra.pptx]