Method Marks for GCSE Maths Calculations You have to show the working in maths calculations to get full marks. This page gives examples of how to write calculations in written questions and practises how to type the same calculations in online questions. Example1: add the numbers 6, 12 and 4. Write or type the calculation as 6+12+4. You should write the numbers in the order in which they were given, first 6, then 12 and then 4, because it helps both a human and an electronic marking system. Example2: multiply 6 by 3 and then divide the result by 2.You would probably write this, using a horizontal fraction bar, as $${\it{{6 \times 3} \over 2}}$$. The product 6×3 is the numerator. The product is divided by the denominator 2. You can write or type the calculation in one line, as 6×3 ⁄ 2. The horizontal bar has been replaced, in the above, with a slash bar to show division. This method of typing maths is called in-line maths because the numerator and denominator are typed on the same line.
Symbols for Maths Operators Use these symbols to type calculations:
More Info There are at least two symbols for multiplication and two for division. Alternative symbols are a complication for online tests and so only one symbol is supported. Reasons for the choice include the ease of use and the versatility of the symbol. For example, the slash / division sign is easier to type than the ÷ sign. It is used to represent division in calculations and in fractions, such as 1/3, meaning both 1 divided by 3 and one-third. Therefore, for division in online answers use the slash / division sign and not the ÷ sign. Example: for divide 15 by 3, type 15/3. 11/3 means both 11 divided by 3 and eleven-thirds. Do not confuse it with the fraction 1⅓ - some people type 1⅓ with a space, as in 1 1/3 but that can be confused with 11/3. For multiplication, as in multiply 15 by 3, type 15×3. Use the ordinary keyboard character x for the multiplication sign. Do not use the * symbol. The * is used in spreadsheets and other computer programs but it is used only by a minority in GCSE maths exams. A * for multiplication is not supported in these GCSE maths online tests. The use of the ^ symbol, as in 2^3 for 23 to represent an index (a power of), is widely accepted. The test questions rarely require you to type an index but it cannot be avoided completely. Test Your Skill - typing in-line maths calculations Use x for multiply and / for divide. Do not include any brackets. Click the Check button to submit. Click Reset for another try.
Typing calculations in-line is almost identical to using a scientific calculator. Example 3: divide 30 by 5 and then multiply the result by 3. Using a calculator you press these buttons: 30÷5×3=. That gives 6×3=18. To type the calculation on a keyboard, press these keys: 30 ⁄ 5x3. Notice that the / symbol has replaced the ÷ symbol for division. The keyboard x has replaced the × for multiplication. Example 4: divide 30 by the product 5 times 3. Using the bracket buttons on a scientific calculator you enter 30÷(5×3)=. Using a keyboard you type 30 ⁄ (5×3). From the BODMAS rule, the brackets mean:
30 ⁄ (5×3) = 30 ⁄ 15 = 2 or more simply 30 ⁄ (5×3) = 2. In a written answer you may prefer to use a horizontal fraction bar as in: $${\it{{30}\over 5 \times 3} = {{30}\over 15} =\small 2}$$ or just $${\it{{30}\over 5 \times 3} = \small 2}$$. In an online test you are not asked to show the full calculation, including the working out, in a single question. The full calculation, including the result of the calculation, would be divided into at least two smaller part questions: the Calculation part, for the method mark, and the Answer part, for the accuracy mark. In the example above, the answer to the Calculation part is the 30 ⁄ (5×3) bit. The answer to the Answer part is the result of the calculation, which is 2. Example 5: a slightly more complicated example. Calculate the average value of 6, 12 and 4. You add the numbers and divide the total by 3. You can write that as: $${\it{{6 + 12 + 4}\over 3}}$$ or (6+12+4) ⁄ 3 in a written question and (6+12+4) ⁄ 3 in an online question. Notice that the three numbers, 6, 12 and 4 are written in the same order as given. The brackets are important - they show that the total is divided by 3. Writing 6+12+4 ⁄ 3 without the brackets is not correct. Practice Quiz
The online Practice Quiz includes three questions, 6, 7 and 8, that practise typing simple maths calculations.
Typing even the most simple calculation needs practice. You have to follow the correct order of operations - the BODMAS rule. The
quiz contains some revision notes on BODMAS.
The Calculator Fraction Button This web page is about how to write calculations in a test or exam question. It is not about how to carry out the actual calculation. For example, to calculate the fraction two-thirds of 144, maybe you enter the two-thirds as a fraction - using the fraction button. To do the calculation you press these buttons 2F3x144= where F is the fraction button. The answer is 96. How would you explain your working to get the method mark. Assuming you were allowed to use a calculator, you cannot get the mark for just saying "I used the fraction button on the calculator". The chances are that the examiner wants to know that you understand the maths - and is not interested in whether you can press the correct buttons. The next section on Fraction Calculations explains how to write this type of fraction calculation. It also shows how to calculate fractions without using the fraction button. Fraction Calculations To calculate a ' fraction of ', such as two-thirds of 66, you multiply the fraction two-thirds and the 66.
2 ⁄ 3 of 66 means
2 ⁄ 3 × 66
This is really no different from working out the cost of 2 items at £66 each. To calculate for ' 2 of ' you multiply by 2. The cost is 2 × 66. For ' 2 ⁄ 3 of ' you multiply by 2 ⁄ 3. The cost is 2 ⁄ 3 × 66. In your pre-GSCE days when you learned basic numeracy, you were probably taught to first calculate one-third and then multiply by 2 for two-thirds. You did something like this:
The method above is exactly right when you first learn fractions - but it is not the way to do it now. In a GCSE exam, to save time, you should try to combine those two lines of working into a single calculation. After all, you only get 1 mark for showing the working. Ask yourself - can you do the calculation and get the correct answer without showing the working in two stages? You are now beyond the learning stage and so should be happy to write the calculation in one step, as either: $${2 \over 3}$$ × 66 or 2⁄3 × 66 or 2 ⁄ 3 × 66 or $${{2 \times 66}\over 3}$$ or 2×66 ⁄ 3 or 66 ⁄ 3×2 You should be able to see that the above alternatives are all equivalent. The last one, 66 ⁄ 3×2 is possibly how you would do the calculation on a calculator, assumimg you do not use the fraction button. If you use the one-third method then you would press these calculator buttons for one-third: 66÷3. Then, for two-thirds you multiply by 2. The complete calculation on a calculator is 66÷3×2=. If you want a recommendation, the simplest way to write the working in a written exam is 2 ⁄ 3×66 In an online test, where you type your answer, the expected answer is 2 ⁄ 3×66, although variations such as 2×66 ⁄ 3 and 66 ⁄ 3×2 are also acceptable. In the calculation part of an online test question, you are not expected to include the answer. Do not enter 2 ⁄ 3×66=44, just enter 2 ⁄ 3×66. In a written exam it is sensible to show the working followed by the answer, as in 2 ⁄ 3×66=44 or 2÷3×66=44. Percentage Calculations A percentage is really a fraction, as in 20%, which is the same as the fraction 20 ⁄ 100. Calculating a 'percentage of' is the same as calculating a 'fraction of'. Example: calculate 20% of 66 20% of 66 = 20 ⁄ 100×66 = 20×0.66 = 2×6.6 = 13.2 The working out above is detailed and you can probably spot some short cuts. 20% can be written as: 20 ⁄ 100 or 2 ⁄ 10 or the decimal 0.2 The calculation can be simplified to: 20% of 66 = 2 ⁄ 10×66 = 2×6.6 = 13.2 Just writing 20 ⁄ 100×66 or 2 ⁄ 10×66 will get the method mark. Of course, you could use alternatives, such as 66 ⁄ 100×20 or 66 ⁄ 10×2. An Example Exam Question An item in a sale is reduced by 25% of the normal price, £80. Calculate the price reduction. The question is worth 2 marks, 1 mark for the method and 1 mark for the answer. Questions about price reductions and price increases always cause confusion. To avoid confusion, this question means that there is 25% off the normal price. Some students wrongly interpret that to mean the sale price is only 25% of the normal price. In fact the sale price is 100%-25% or 75% of the normal price. In the written exam you can explain the calculation 'in words'. Remember that often there is just one method mark for the calculation and your explanation of the method does not have to be detailed to get that mark. Acceptable explanations are: 1% of 80 is 80÷100. 25% is 25×80÷100=20 or 25% is one-quarter of 80 = 80/4 = 20 or Even simpler, you could just write: 25% is 25 ⁄ 100×80=20. All three answers above get the 'method' mark for the explanation/working and the 'accuracy' mark for a correct answer. The three methods are explained clearly and so would also get any additional mark for quality of communication. The last method 25 ⁄ 100×80=20 is concise and uses a correctly written calculation. It saves time in the exam and shows good understanding of maths calculations. An online marking system does not understand explanations written 'in words'. Apart from the last method 25 ⁄ 100×80 it is impossible for online marking to grade the above answers. To provide the opportunity for maximum marks in an online test, questions similar to this example question are divided into two parts, with 1 mark for each part. The first part deals with the method used to calculate the answer, as follows. Calculation Part (1 method mark) Calculation: price reduction = 25x80/100 £
Answer Part (1 mark) Answer: price reduction = 20 £
The calculation box shows a correct answer: 25×80 ⁄ 100. Note that it was not written as 25×80 ⁄ 100= with an equal sign at the end. The = sign is entered when using a calculator simply to tell the calculator to carry out the calculation. In the calculation part of a test question you are showing just the method used in the calculation. If the question is not asking you how to do the calculation using a calculator, do not include the = sign. You can see that for online marking of calculations, your answer has to be precise. You may not like that but there are a few benefits. An answer such as 25×80 ⁄ 100 is much more concise than an answer 'in words'. It is quicker to write because it is written in the language of mathematics. Using that language will improve the quality of your answers. Other possible calculation answers are: 25 ⁄ 100×80, (25 ⁄ 100)×80, 80 ⁄ 100×25 Notice that the brackets in (25 ⁄ 100)×80 are not needed, although they do avoid ambiguity. Without the brackets you may think that 25 ⁄ 100×80 means divide 25 by the product 100×80. The BODMAS rule does not help because, although the D is before the M in BODMAS, division and multiplication are equal in the rule. When there is doubt then it is accepted that the first operation, division or multiplication, is carried out first. Therefore, 25 ⁄ 100×80 means divide 25 by 100 because 25 ⁄ 100 is written first. Then you multiply the result by 80. © Edu-Sol.co.uk 2007-2012
|