Functional Skills

Mathematics: implications for teaching and learning

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Mathematics: Introduction

• The papers were divided into three tasks: tennis, offices and coffee shop

• Contexts were chosen to reflect the everyday use of mathematics

• Some questions were common to both Level 1 and Level 2 assessments

• The total mark for each paper was 60

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• Tasks required students to apply knowledge• Many tasks required students to choose the

method of solution and the operations needed to solve the problem

• In some tasks students were required to choose or interpret the data to use to solve the problem

• Students were expected to express their answers accurately

Mathematics: Introduction

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What students could do well: Level 1

Students were generally successful at:• interpreting data from simple tables and graphs• drawing scaled diagrams• writing a series of numbers in order• drawing lines of symmetry on simple geometric

shapes• measuring angles and length

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Students were generally successful at:• interpreting data from tables and graphs• interpreting information presented in unfamiliar

ways• working with equivalent fractions and percentages• using unfamiliar mathematical formulae given in

the question (see question 13)

What students could do well: Level 2

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Question Performance Statistics

The facility value of a question is one way of its measuring performance

– The facility value = the proportion of students who gained the marks

– A facility value of 1 means that all students got the question correct

– A facility value of 0.5 means that 50% of students gained the marks

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Question Performance Statistics

Facility values – Level 1

Question Facility Question Facility

1 0.83 9 0.79

2 0.49 10 0.44

3 0.72 11 0.28

4 0.54 12 0.79

5 0.36 13 0.62

6 0.48 14 0.63

7 0.43 15 0.25

8 0.49 16 0.67

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Question Performance Statistics

Facility values – Level 2Question Facility Question Facility

1 0.45 9 0.48

2 0.86 10 0.49

3 0.69 11 0.59

4 0.48 12 0.63

5 0.69 13 0.51

6 0.51 14 0.43

7 0.62 15 0.61

8 0.13 16 0.31

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Question Performance StatisticsCommon questions

Level 1 Level 2 Level 1 facility

Level 2 facility

Q6 Q6 0.48 0.51

Q7 Q7 0.43 0.62

Q11 Q9 0.28 0.48

Q6: About half of Level 1 and Level 2 students were able to work with ratios in the context of diluting drinks.

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Common questions

Level 1 Level 2 Level 1 facility

Level 2 facility

Q6 Q6 0.48 0.51

Q7 Q7 0.43 0.62

Q11 Q9 0.28 0.48

Q7: Less than half of Level 1 students could use data given in a simple table, work out a range and carry out a two-step calculation involving rectangular area. Almost two thirds of Level 2 students gained the marks in this question.

Question Performance Statistics

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Common questions

Level 1 Level 2 Level 1 facility

Level 2 facility

Q6 Q6 0.48 0.51

Q7 Q7 0.43 0.62

Q11 Q9 0.28 0.48

Q11/Q9: About half of Level 2 students were able to convert mm to metres and work with linear dimensions. Less than a third of Level 1 students gained the marks in this multi-step question.

Question Performance Statistics

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• Emphasise the importance of reading carefully• Encourage students to show the detailed steps • Give students opportunities to use mathematics

in everyday life• Make sure students have the correct equipment

for the assessment

How centres can help students improve their performance:

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• Emphasise the need for students to make sure they write numbers clearly

• Give students practice in interpreting answers shown on a calculator

• Give students practice in solving problems involving time, money, areas, ratios and large numbers

How centres can help students improve their performance:

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Examples of student responses

• text without boxes are comments or questions intended to prompt discussions

Student responses appear in boxes.

Extracts from the questions appear in boxes.

In the following exemplars:

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Level 1: Q2a

• what are the key skills required to get the answer 467 000?• what errors have students made in the following answers?• how could you help students avoid these errors?

470 191 467 190 467 291 500 000

468 191 467 470 000

The attendance for the first week of the 2006 Championshipwas 467,191.What is the number 467 191 rounded to the nearest thousand?

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Level 1: Q10a

• what understanding is required to get the answer 20%?

1.5%

• how could you help students who gave the following answers?

In an office, 1/5 of the workers are male. What percentage of the workers are male?

25%5% 75%

15%

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Level 1: Q7dThis is the plan of the office in Plymouth

What is the total cost of the rent for this office in Plymouth for a week? (rent is £97 per m ) [2 marks]

12 x 30 = 360

30 m

12 m

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£4074

This student has not followed through and so only scores one mark.

The correct answer is £34 920. Can you see how this student got this answer?

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Level 1: Q10b

For how long was this person at work on Wednesday?Give your answer in hours and minutes.

Mon Tue Wed Thu Fri Starting time 09 00 08 55 08 15 09 10 09 15 Finishing time 17 05 16 10 16 00 17 00 16 30

• What do students have to do to get the correct answer of 7 hours 45 minutes?

• What errors have students made in giving the following answers?

8 h 45 min 8 h 15 min 7 h 15 min 6 h 45 min

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Level 1: Q2a

Correct answer: 467 000

How would you mark these responses?

Level 1: Q10bCorrect answer: 7 hours 45 minutes

Do you agree with the marking of this response?

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Level 1: Q4a

The table shows the prize money won by the two finalists in the men’s finals of 2006 and 2007.

2006 2007

Winning finalist £655 000 £700 000

Losing finalist £327 000 £327 500

What was the total prize money won by the two finalists in 2007?

A common incorrect answer was £1 355 000. What error has been made here?

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Level 2: Q13aThe calculation required in this question was:

£6.20 x 5.5(hrs) x 6 (days) = £204.60

A common incorrect answer was £197.16, which results from using 5.3 instead of 5.5 and illustrates an error in calculating with time values.

Students also need practice in using the correct notation for money, for example common answers included:

£204.60p £204.6 £20.406 £20460

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Level 2: Q13bSometimes Sally works extra hours. Mabel pays Sally £6.20 plus half as much again for each extra hour.

What is Sally paid for each extra hour?

The correct calculation leads to the answer £9.30. A common error was to only calculate half of £6.20.

Students may have misread the question, possibly reading extra as the addition to the hourly rate.

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Level 2: Q2bHow do the number of aces served by male players compare with the number of aces served by female players?

It doubled.

These answers do not gain the mark. Why not?

The number of aces are bigger for female than for males.

In 5 matches Krajicek had 45 aces.

Males served more than twice as many.

Here is an example of a correct answer:

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Marking Exercise

Mark a Level 1 and a Level 2 paper.

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Students should:• read the question carefully• show the detailed steps to their calculations• write numbers clearly• use a calculator, ruler and protractor, where

appropriate• use the correct notation for money and time

Key points

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Key points

Centres should:• give students practice in interpreting answers

shown on a calculator• give students practice in solving problems

involving time and money, areas, ratios and in working with large numbers

• give students opportunities to use mathematics in everyday life via a variety of appropriate contexts

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Further support

• For further information please visit the Functional Skills website at:fspilot.recruitment@edexcel.org.uk

• Alternatively please email the Functional Skills inbox at:http://developments.edexcel.org.uk/fs/