Spotlight on Direct- Inverse Proportion Problems.pptx

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1. Spotlight on Direct & Inverse Proportion Problems

2. Skills you will need You will need to be able to multiply and divide work logically through a step by step solution know the difference between direct and inverse proportion © WJEC CBAC Ltd.

3. Two quantities are in direct proportion if, to find one quantity, you always multiply the other quantity by a fixed value. The cost of the apples = The number of apples  40p So the number of apples and the cost of the apples are in direct proportion. Understanding Check Direct proportion: 7 apples cost £ 2.80 How much do 12 of the same apples cost? © WJEC CBAC Ltd. Number of apples Cost 7 £2.80 1 40p 12 480p  7  12 = 280p = £4.80  7  12

4. Two quantities are in inverse proportion if, an increase (or decrease) in one quantity results in a decrease (or increase) in the other. Notice that, when the two quantities are multiplied together the result is always the same number. The number of workers  The number of hours = 6 So the number of workers and the number of hours are in inverse proportion. Understanding Check Inverse proportion: It would take 3 workers 2 hours to dig a hole. How long would it have taken 4 workers to dig the same-sized hole? © WJEC CBAC Ltd. Number of workers Number of hours 3 2 1 6 4 1.5  3  3  4  4

5. Autumn Series 2017, C1F Q23 & C1H Q9 © WJEC CBAC Ltd. What the examiner said Those who were most successful gave clear statements in steps rather than trying to attempt a single calculation. Many candidates stated that fewer workers would take less time rather than more time, confusing direct and inverse proportion. Some candidates may have improved their solution if their setting out had been less haphazard and confused. The use of a table to keep track of values is advocated in the solution to this type of question.

6. Common misunderstanding: 4 workers take 3 hours, so 1 worker would take ¾ hour. Is this correct? No! This is the common wrong answer! 1 worker will take more time than 4 workers to do the work, not less time. The number of workers and the number of hours are in inverse proportion. Does that mean that the whole question is about inverse proportion? No! This question also involves direct proportion as 1 worker will load less goods than 4 workers, not more in that time. So it is really important to keep a clear record of what you are doing at each step! Autumn Series 2017, C1F Q23 & C1H Q9 © WJEC CBAC Ltd.

7. Model answer: Step 1: Set up a table. Step 2: Work through a line at a time. Take care when choosing whether to  or  ! Autumn Series 2017, C1F Q23 & C1H Q9 © WJEC CBAC Ltd. Number of workers Number of tonnes Number of hours 4 5 3 1 5 12 1 10 24 6 10 4  4  4  2  2  6  6 Step 3: Write down the answer. Answer: 4 hours

8. Autumn Series 2017, C1F Q23 & C1H Q9 © WJEC CBAC Ltd. What the examiner said Some candidates were able to state a sensible assumption that they had needed to make when answering part (a). Many candidates made assumptions based on workers working at the same rate. This was not allowed as this information had been given in part (a). Not all candidates commented on how their answer to part (a) would have changed if their assumption had not been correct. These candidates may have benefited from rereading the question.

9. Autumn Series 2017, C1F Q23 & C1H Q9 © WJEC CBAC Ltd. Assumption examples The goods being loaded are not heavier. or The vehicles used are the same type. with the impact of the assumption: If the goods are heavier, then they may take more time to load. If the vehicles used are smaller, the goods may not all fit in one vehicle so the load time may be longer.

10. Number of people Number of days Length of verge 3 6 X 1 18 X 1 36 2X 9 4 2X Model answer: Step 1: Set up a table. Step 2: Work through a line at a time. Take care when choosing whether to  or  ! Summer Series 2017, C2F Q28 & C2H Q8 © WJEC CBAC Ltd.  3  3  2  2  9  9 Step 3: Write down the answer. Answer: 4 days

11. Summer Series 2017, C2F Q28 & C2H Q8 © WJEC CBAC Ltd. Assumption examples All the people work at the same rate, or The width of the grass verge is the same as before. or The grass is outside and the weather has not changed.

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