Improving grades at GCSE through developing numeracy

With the reformed GCSE courses, there is an increasing requirement for students to demonstrate competency at using numerical skills. For some subjects these skills can be worth up to 15% of the overall grade. It is important to note that numerical skills are not just needed for Maths lessons. As part of Fulford School’s attempts to support students in developing these skills across relevant GCSE subjects, this booklet has been created to help students apply the skill of using and calculating percentages. This booklet can be used by parents / carers to support home learning, by 6th form mentors in form time or by students independently working through the questions. An answer booklet can be found on the Fulford School website. At the end of this booklet there is information about percentages, which has been taken from the Numeracy How to…Guide and should provide a useful reference point. If you would like further information about how students can be supported with developing their numeracy skills across the curriculum, then please contact Mr Hickling via the School Office.

Business- AQA The following questions are typical of those that would be asked in Unit 1.

Design and Technology - AQA The following questions are typical of those that would be asked in Paper 1. Question 1 You have been asked to redesign your chosen product to make it suitable for a child aged between 3 and 5 years old. The data in the table below shows the preferred colour scheme according to 250 children aged between 3 and 5 years old. Calculate the missing percentages. [2 marks]

Number of children Percentage of total

Pastel colours 55 22%

Primary colours 105

Fluorescent colours 50 20%

Subtle colours 30

Metallic colours 10 4%

Total

Food and Nutrition - AQA This course requires students to calculate and interpret percentage data, e.g. % carbohydrate in food and converting data into percentages in order to analyse and present information about nutrition.

Geography - AQA The following questions are typical of those that would be asked in Paper 3: Geographical Applications.

1. As part of your primary data collection, you carry out a questionnaire to find out about urban regeneration in Manchester. 14 out of 30 respondents stated that they “strongly agreed” that the regeneration was a success. Calculate what percentage of respondents “strongly agreed” that the regeneration was a success. (1 mark)

2. The number of bus routes in Nottingham increased from 24 in 2010 to 31 in 2016. Calculate the percentage change. (1 mark)

3. Which word has the same meaning as the 50th percentile? Clearly shade one circle. (1 mark) o Mean o Median o Mode o range

Maths - Edexcel The following questions are typical of those that would be asked in any maths paper or calculator only (CO).

1. Equivalence of fractions, percentages and decimals (also ratios). Arrange these is increasing order: 0.45 1/3 30% 2/5 33%

2. Finding percentages of amounts and finding percentage increase or decrease (CO).

Find 23% of 67 Increase 450 by 12.5%

3. Equivalence of recurring decimals.

Write 2/7 as a decimal. Write 0.34̇5̇ as a fraction in its simplest form.

4. Expressing one quantity as a percentage of another. A class of 32 has 12 boys. What percentage of the class are girls?

5. Reverse percentage calculations.

In a sale all items are reduced by 15%. A pair of shoes now costs £51, how much were they before the sale?

6. Repeated percentage (CO).

An investment of £150 increases by 2.5% each year, for 3 years.

PE - AQA The following questions are typical of those that would be asked in Paper 1. However, questions relating to percentages could also appear on Paper 2.

1. Joe has undertaken a six week fitness programme with the main aim of improving his

cardiovascular endurance.

What would be the upper and lower percentage heart rate zones he should be working in to ensure he

improves in his area of focus? Underline one answer.

40% - 50%

50% - 60%

60% - 70%

70% - 80%

2. Calculate Joe’s actual heart rate from the two zones if Joe is a 16 year old boy using the calculation

of:

Maximum Heart Rate – Age and then working out the two percentages.

3. Figure 7 shows Olympic doping cases by sport from 1968 to 2010.

Olympic doping cases by sport, 1968–2010

No. of doping cases reported

Weightlifting 36

Athletics (Track and Field) 28

Cross Country Skiing 12

Equestrian

8

Ice Hockey, Wrestling 6

Cycling 5

Biathlon, Modern Pentathlon, Volleyball 3

Baseball, Gymnastics, Judo, Rowing, Swimming, Shooting

3

Alpine Skiing, Basketball, Boxing, Canoeing, Sailing

1

Total

127

Using Figure 7, identify the activity with the greatest number of reported doping cases and calculate the percentage as a proportion of the total cases.

GCSE Science - AQA The following questions are typical of those that would be asked in AQA GCSE Trilogy and Separate Sciences.

Biology

1) Figure 3 shows the percentages of adults in the UK who have coronary heart disease.

Figure 3

Calculate the difference in the percentage of male and female adults aged 65 and over who have coronary heart disease.

................................................... % (1)

2) Several snails ate some lettuces.

The lettuces contained 11 000 kJ of energy.

Only 10% of this energy was transferred to the snails.

Calculate the energy transferred to the snails from the lettuces.

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Energy = ................................................................ kJ (1)

Chemistry

1) The percentage atom economy for a reaction is calculated using:

The equation for the reaction of copper carbonate and sulfuric acid is:

CuCO3 + H2SO4 → CuSO4 + H2O + CO2

Relative formula masses: CuCO3 = 123.5; H2SO4 = 98.0; CuSO4 = 159.5

Calculate the percentage atom economy for making copper sulfate from copper carbonate.

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Atom economy = ........................................... % (3)

2) Stainless steel is an alloy of iron, chromium and nickel. The diagram below represents the particles in stainless steel.

Particle diagram of stainless steal

Use the diagram to complete the percentages of metals in this stainless steel.

The first one has been done for you.

Element Percentage (%)

Iron, Fe 72

Chromium, Cr

Nickel, Ni

(2)

Physics

1. When the total energy input to the solar cells is 200 joules, the useful energy output from the solar cells to the batteries is 50 joules.

Calculate the efficiency of the solar cells.

........................................................................................................................

........................................................................................................................

........................................................................................................................

Efficiency = ...................................................... (2)

2. Burning 1 kg of wood transfers 15 MJ of energy to the stove. The stove then transfers 13.5 MJ of energy to the room.

Calculate the efficiency of the stove.

Show clearly how you work out your answer.

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Efficiency =................................................. (2)

Percentages are related to all subjects and students should be able to consider the following: What % of my final grade is Paper 1 worth? If I got 14 out of 20 in a test, what % and grade have I got? If I got 59% on an exam out of 88 marks and the grade

boundary was 65% for a grade 7, how many more marks would I need to achieve a 7?

40% of the marks for Paper 2 Section B are for AO3, how should this affect how I prepare for the exam compared with Paper 1 where 80% of the marks are for AO1 and AO2?

If my exam is two hours long and is marked out of 90, how long should I spend on a 20 mark essay?

Numeracy: How to… Guide: Percentages

% and pie charts

Grade A B C D E

Frequency 7 11 6 4 2

To calculate the percentage, of students who achieved a grade A, you should divide the value by the total i.e. 7 30. Then multiply the answer by 100 to get 23.33%. Percentage data can then easily be used to create a pie chart i.e. 23.33 100. Then multiply by 360 to get to 840. Percentages and rounding:

Once a percentage calculation has been made, it may be necessary to round the figure to the nearest whole number or to one or two decimal places. Decimal places are counted from the decimal point:

The number has four decimal places, while has two decimal places. To round a number to a given number of decimal places, look at the number in the next decimal place: If it's less than , round down . If it's or more, round up.

To help students remember whether to round up or down, some students at primary school learn the phrase “1 to 4 drop to the floor. 5 to 9 climb the vine”. Example 27/32 on a test is 84.37%, which can be rounded down to 84%. 23/32 on a test is 71.875%.

71.875% rounded to the nearest whole

number

71.875% rounded to 1 decimal place

71.875% rounded to 2 decimal places

72 71.9 71.88

Converting percentages, decimals and fractions

Percentage Decimal Fraction

100 1 1

75 0.75 ¾

66.66 0.66 2/3

50 0.5 ½

40 0.4 2/5

33.33 0.33 1/3

25 0.25 ¼

20 0.2 1/5

10 0.1 1/10

5 0.05 1/20

1 0.01 1/100

Source: Help your kids with Maths, DK

Calculating % change e.g. interest. If £400 is borrowed for 3 years at an interest rate of 5% pa (pa means per annum, or each year). Interest for one year = 5% of £400 = (5/100) × 400 = £20. Interest for 3 years = £20 × 3 = £60. To calculate the percentage increase: First: work out the difference (increase) between the two numbers you are comparing. Increase = New Number - Original Number Then: divide the increase by the original number and multiply the answer by 100. % increase = Increase ÷ Original Number × 100. If your answer is a negative number then this is a percentage decrease. Example 1 Population in 1990 of city A = 250,000 and by 2000 = 280,000. To work out the population increase: 280,000-250,000 = 30,000 30,000 / 250,000 x 100 = 12% increase over the 10 years (mean average annual growth is 1.2%) Example 2 If country B has a population that grows at 4.8% per year and its population is 20 million in 2010, what will be the population by 2015 if it continues to increase at the same rate? One method is to work out that 1% of 20 million is (200,000) and then multiply by 4.8 to get 960,000. Then add this on to the original population to make 20,960,000 after one year and then repeat. Another method is knowing that multiplying by 1.048 is the same as increasing the original value by 4.8%. Therefore over five years: 20,000,000 x 1.0485 = 25,283,454. The 5 can be changed to however many years you wish to calculate. To calculate percentage decrease: First: work out the difference (decrease) between the two numbers you are comparing. Decrease = Original Number - New Number Then: divide the decrease by the original number and multiply the answer by 100. % Decrease = Decrease ÷ Original Number × 100 If your answer is a negative number then this is a percentage increase. % of or %off 10% of £50 is £5, whereas 10% off £50 is £45.