Oxford GCSE Maths for Edexcel New 2010 Edition Teacher Guide sample material

Advance Material

Contains 8 uncorrected sample pages from the Oxford GCSE

Maths for Edexcel Teacher Guides, each providing over 250 pages

of practical teaching notes, plus samples of the teacher support

material available on the Assessment OxBox CD-ROM

K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 1 13/1/10 10:06:05

How does the new 2010 Edition of Oxford GCSE Maths for Edexcel support your teaching?Oxford GCSE Maths for Edexcel New 2010 Edition provides four levelled student books, making learning simpler and more strongly targeted, and therefore more successful for all of your students. There is a single student book for each of the four overlapping levels:

3 Foundation, covering grades GFE, with an extra booster section covering grades DC

3 Foundation Plus, covering grades EDC, with GF consolidation

3 Higher, covering grades DCB

3 Higher Plus, covering BAA*, with DC consolidation

There is a Homework Book and Teacher Guide specifically for each level. In addition, OxBox CD-ROMs offer a wealth of activities and resources, including a huge amount of teacher support and assessment material that will help inspire your students and give you more time to actually teach by doing do a huge amount of the hard work for you as well as covering all aspects of the new GCSE.

We have included just some sample material from the Teacher Guide and related resources from the OxBox CD-ROMs to give you an idea of just how much help we have to offer you and your school.

1


ContentsIntroduction page ....................................................................................................... page 3An introduction page at the beginning of each Teacher Guide shows how Oxford GCSE Maths for Edexcel New 2010 Edition is clearly structured into chapters that link closely to the four main curriculum strands, to help your medium term planning.

Chapter introduction ............................................................................................ page 4Each chapter is introduced with an engaging link to the real world and a commentary on the rich task designed to help deliver AO3, and teaching notes provide extra background to help make the most of this resource.

Lesson plans ............................................................................................................ pages 5–6The Teacher Guides provide thorough lesson plans linked to the material in the Student Books, with specification objectives clearly spelt out, and exercise commentary to provide focus on the new requirements.

Summary page ................................................................................................................ page 9The summary page provides answers to the exam questions appearing in the student book together with a commentary highlighting what examiners are looking for in an answer.

Case study teacher notes ...........................................................................page 10Teacher notes on the real-life case studies provided in the Student Books and OxBox CD-ROMs help make it easier to bring functional maths to life in the classroom.

Assessment resources ......................................................................pages 11–12A huge amount of resources are included in the Assessment OxBox for all your assessment needs, including both on-screen tests and tests that you can print out. On-screen tests, both formative and summative, provide intuitive assessment with a wealth of questions at all levels to help consolidate learning, with auto-marking, meaningful feedback to monitor progress, and on-screen diagnostic reports providing graded feedback for teachers.

Self-assessment checklist ..........................................................................page 13Self-assessment checklist shows how students are encouraged to monitor and improve their own progress.

Scheme of Work .........................................................................................................page 14Schemes of work are provided to match the lessons with GCSE objectives, allowing you to map out the term’s work quickly and easily

2


Finding your way around this book

N1 Integers and decimals

A1 Expressions

UN

IT 1

1

UN

IT 2

NUMBER ALGEBRA GEOMETRY DATA

N2 Integers calculations

N5 Powers, roots and primes

N6 Ratio and proportion

A2 Functions and graphs

A3 Sequences

A4 Formulae and real-life

graphs

N4 Fractions and decimals

A5 Equations

G2 Angles and 2-D shapes

G3 2-D and 3-D shapes

D1 Probability

G4 Transformations

G5 Further transformations

G6 Measuring and constructing

D2 Collecting data

D3 Displaying data

D4 Averages and range

D5 Further probability

PLUS SECTION C Booster

A6 Further equations

G7 Further geometry

N7 Decimal calculations

UN

IT 3

N3 Fractions and

percentages

1

4

7

11

21

18

14

10

12

15

17

20

23

13

16

2

19

22

24

25

3

5

6

8

G1 Measures, length and area

9

FDN_findingyourway_page.indd 3 30/12/09 15:07:46Advance Material • Uncorrected sample Introduction page from

Oxford GCSE Maths for Edexcel New 2010 Edition Foundation Teacher GuideAdvance Material • Uncorrected sample Chapter Introduction page from

Oxford GCSE Maths for Edexcel New 2010 Edition Higher Plus Teacher Guide3 4

The three unit structure is followed in the specification B (modular) book.

All books provide students with access to grade C level material



A1 Expressions

UNIT 1

1

UNIT 2

NUMBERALGEBRAGEOMETRY DATA


N5 Powers, roots and

primes



A3 Sequences


graphs


A5 Equations



D1 Probability

G4 Transformations



D2 Collecting data

D3 Displaying data





G7 Further geometry


UNIT 3

N3 Fractions and

percentages

1

4

7

11

21

18

14

10

12

15

17

20

23

13

16

2

19

22

24

25

3

5

6

8


9

FDN_findingyourway_page.indd 330/12/09 15:07:46




A1 Expressions

UN

IT 1

1

UN

IT 2

NUMBER ALGEBRA GEOMETRY DATA


N5 Powers, roots and primes



A3 Sequences


graphs


A5 Equations



D1 Probability

G4 Transformations



D2 Collecting data

D3 Displaying data





G7 Further geometry


UN

IT 3

N3 Fractions and

percentages

1

4

7

11

21

18

14

10

12

15

17

20

23

13

16

2

19

22

24

25

3

5

6

8


9

FDN_findingyourway_page.indd 3 30/12/09 15:07:46Advance Material • Uncorrected sample Introduction page from

Oxford GCSE Maths for Edexcel New 2010 Edition Foundation Teacher GuideAdvance Material • Uncorrected sample Chapter Introduction page from


The three unit structure is followed in the specification B (modular) book.

The exam specification objectives covered by the chapter are summarised

The student book provides an open ended challenge which draws in many of the themes of the chapter

The mathematics covered is securely placed in a wider context

The OxBox provides resources to enliven lessons

Basic knowledge assumed from previous chapters or KS3 is clearly indicated


55

N3.5 Fraction of a quantity

Objectives

No Calculate a fraction of a given quantity

Useful resources

• Calculators

Starter

Ask students to each fill in a 33 grid with

numbers 201 .

Ask simple fractional questions (based primarily on

2

1 and 4

1 ), for example: 2

1 of 32, 4

1 of 40.

Students cross off answers as they appear in the

grid. The first to complete a row in any direction

wins.

Teaching notes

Reintroduce the class to the topic of fractions and

discuss expressing one quantity as a fraction of

another by asking questions about the class:

‘What fraction of the class is girls/have blue

eyes/brown hair?’ and so on.

Refer to the mental starter and discuss how to find

2

1 and4

1 of amounts. Extend to discuss how to find

3

1 of an amount, 8

1 of an amount.

Encourage students to generalise, using algebra: to

findn

1 of an amount, divide by n.

Discuss how to find 3

2 of 36.

Encourage students to say the calculation aloud to

reinforce the denominator as the size of the part, the

numerator as the number of parts.

Emphasise 3

2 means 2 lots of 3

1 .

Work through the calculation: divide by 3 to find3

1

then multiply by 2 to find 3

2 .

Generalise: divide by the denominator then multiply

by the numerator.

Discuss what ‘of’ means when finding a fraction of

something. Use a simple integer example, say ‘3 lots

of 4’ to link to multiplication.

Ensure students understand 3

2 of 36363

2= .

Plenary

Discuss fractional increases.

The value of a house increases by5

1 of its original

selling price in 2 years. It originally cost £200 000.

How much is it worth after 2 years?

Exercise commentary

Question 1 focuses on writing fractions in simplest

form and understanding the roles of numerator and

denominator in a fraction.

Question 2 focuses on finding unitary fractions of

amounts.

In question 3, students must express one number as

a fraction of another from a worded example. Recall

the link between fractions and the phrase ‘out of’.

Encourage students to first consider the total

number of parts before calculating the fraction in

each case.

Question 4 extends to calculating non-unitary

fractions of amounts. This is initially scaffolded to

remind students to first calculate the unitary fraction

before multiplying by the numerator.

In question 5, some students might want to convert

the fraction to a decimal to evaluate the question.

However, encourage students to follow the same

method used in question 4.

Simplification

Students could be given further examples of finding

unitary fractions that divide simply into the given

amount.

Extension

Students could be asked to work out fractions of

various quantities using a written method of long

division/multiplication rather than with a calculator.

Functional maths

Being able to work with fractions of amounts is an

important functional skill in many areas of real life.

Question 3 gives three examples of where this may

be necessary.

Problem solving

Pose a problem such as:

Tariq took 45 minutes to complete a job which pays

£8 per hour. How much is he paid?

Suzi is offered a choice – deal A, 5

4 of £20 or deal

B, 7

3 of £35. Which deal should she choose?

72

D4.6 Diagrams and charts 2

Objectives

Di Interpret a wide range of graphs and diagrams

and draw conclusions

Useful resources

• Mini-whiteboards

• Diagrams from student book

Starter

The time per day, in minutes, spent on a computer

by a group of boys and girls is summarised as:

Median

Inter-quartile

range

Boys 135 40

Girls 75 15

Ask students to discuss and explain this summary.

Teaching notes

Ask the students to work in twos or threes. Each

group will be allocated a chart showing data with an

explanation of its theme and source. Use the

diagrams on the left-hand page of the student book

spread (pictogram, bar chart, bar-line chart and

second pie chart). The group will then have about 10

minutes to discuss and record as much about it as

they can, including, where relevant, detail such as

range or mode and any conclusions or comments

about the data. Allocate the data appropriate to each

group. Give 2- and/or 1-minute warnings before

stopping groups. Allocate a different set of data to

each group and repeat.

Select some of the data groups for feedback and to

initiate discussion about the findings.

Plenary

Take one of the diagrams used in the introductory

activity, and ask specific questions about it.

Students should respond on whiteboards. Explore

how many worked on the data earlier. Did their

work in the lesson assist them in answering the

questions?

Repeat with a different set of data in order to

include more students in the ‘seen it before’

experience.

Exercise commentary

Students tend not to look carefully at or fully use

diagrams given in exam papers. Focusing on

‘information’ in an open way and not including

questions, encourages students to use eyes and

initiative, and to be a little more creative. This

strengthens observational skills.

All of the questions require students to answer

comprehension-style. Ensure they use full sentences

and explain their findings clearly (QWC.)

Simplification

Students could be given a writing frame for their

responses or work in groups with support and

discuss their answers carefully before committing

them to paper.

Extension

Students could be asked to design two data sets that

exhibit certain characteristics on comparison.

Functional maths

Displaying data in a useful way will help when it

comes to analysing it effectively. Charts displaying

real life data can be found in a wide variety of

different media such as newspapers and the internet.

The difficulty of interpreting data displayed in many

of these ways is often underestimated since many

sources try and ‘make’ the data fit their point of

view.

Problem solving

Similar problems to question 4 but without the

scaffolding, part c only, will provide a greater

challenge. Direct students to the example for a

method of solving the question.

Advance Material • Uncorrected sample lesson plan page from

Oxford GCSE Maths for Edexcel New 2010 Edition Foundation Teacher Guide


Oxford GCSE Maths for Edexcel New 2010 Edition Foundation Plus Teacher Guide5 6

Lots of hints and ideas from experienced classroom teachers

Practical suggestions to help cater for less and more able students


55

N3.5 Fraction of a quantity

Objectives

No Calculate a fraction of a given quantity

Useful resources

• Calculators

Starter

Ask students to each fill in a 33 grid with

numbers 201 .

Ask simple fractional questions (based primarily on

2

1 and 4

1 ), for example: 2

1 of 32, 4

1 of 40.

Students cross off answers as they appear in the

grid. The first to complete a row in any direction

wins.

Teaching notes

Reintroduce the class to the topic of fractions and

discuss expressing one quantity as a fraction of

another by asking questions about the class:

‘What fraction of the class is girls/have blue

eyes/brown hair?’ and so on.

Refer to the mental starter and discuss how to find

2

1 and4

1 of amounts. Extend to discuss how to find

3

1 of an amount, 8

1 of an amount.

Encourage students to generalise, using algebra: to

findn

1 of an amount, divide by n.

Discuss how to find 3

2 of 36.

Encourage students to say the calculation aloud to

reinforce the denominator as the size of the part, the

numerator as the number of parts.

Emphasise 3

2 means 2 lots of 3

1 .

Work through the calculation: divide by 3 to find3

1

then multiply by 2 to find 3

2 .

Generalise: divide by the denominator then multiply

by the numerator.

Discuss what ‘of’ means when finding a fraction of

something. Use a simple integer example, say ‘3 lots

of 4’ to link to multiplication.

Ensure students understand 3

2 of 36363

2= .

Plenary

Discuss fractional increases.

The value of a house increases by5

1 of its original

selling price in 2 years. It originally cost £200 000.

How much is it worth after 2 years?

Exercise commentary

Question 1 focuses on writing fractions in simplest

form and understanding the roles of numerator and

denominator in a fraction.

Question 2 focuses on finding unitary fractions of

amounts.

In question 3, students must express one number as

a fraction of another from a worded example. Recall

the link between fractions and the phrase ‘out of’.

Encourage students to first consider the total

number of parts before calculating the fraction in

each case.

Question 4 extends to calculating non-unitary

fractions of amounts. This is initially scaffolded to

remind students to first calculate the unitary fraction

before multiplying by the numerator.

In question 5, some students might want to convert

the fraction to a decimal to evaluate the question.

However, encourage students to follow the same

method used in question 4.

Simplification

Students could be given further examples of finding

unitary fractions that divide simply into the given

amount.

Extension

Students could be asked to work out fractions of

various quantities using a written method of long

division/multiplication rather than with a calculator.

Functional maths

Being able to work with fractions of amounts is an

important functional skill in many areas of real life.

Question 3 gives three examples of where this may

be necessary.

Problem solving

Pose a problem such as:

Tariq took 45 minutes to complete a job which pays

£8 per hour. How much is he paid?

Suzi is offered a choice – deal A, 5

4 of £20 or deal

B, 7

3 of £35. Which deal should she choose?

72

D4.6 Diagrams and charts 2

Objectives

Di Interpret a wide range of graphs and diagrams

and draw conclusions

Useful resources

• Mini-whiteboards

• Diagrams from student book

Starter

The time per day, in minutes, spent on a computer

by a group of boys and girls is summarised as:

Median

Inter-quartile

range

Boys 135 40

Girls 75 15

Ask students to discuss and explain this summary.

Teaching notes

Ask the students to work in twos or threes. Each

group will be allocated a chart showing data with an

explanation of its theme and source. Use the

diagrams on the left-hand page of the student book

spread (pictogram, bar chart, bar-line chart and

second pie chart). The group will then have about 10

minutes to discuss and record as much about it as

they can, including, where relevant, detail such as

range or mode and any conclusions or comments

about the data. Allocate the data appropriate to each

group. Give 2- and/or 1-minute warnings before

stopping groups. Allocate a different set of data to

each group and repeat.

Select some of the data groups for feedback and to

initiate discussion about the findings.

Plenary

Take one of the diagrams used in the introductory

activity, and ask specific questions about it.

Students should respond on whiteboards. Explore

how many worked on the data earlier. Did their

work in the lesson assist them in answering the

questions?

Repeat with a different set of data in order to

include more students in the ‘seen it before’

experience.

Exercise commentary

Students tend not to look carefully at or fully use

diagrams given in exam papers. Focusing on

‘information’ in an open way and not including

questions, encourages students to use eyes and

initiative, and to be a little more creative. This

strengthens observational skills.

All of the questions require students to answer

comprehension-style. Ensure they use full sentences

and explain their findings clearly (QWC.)

Simplification

Students could be given a writing frame for their

responses or work in groups with support and

discuss their answers carefully before committing

them to paper.

Extension

Students could be asked to design two data sets that

exhibit certain characteristics on comparison.

Functional maths

Displaying data in a useful way will help when it

comes to analysing it effectively. Charts displaying

real life data can be found in a wide variety of

different media such as newspapers and the internet.

The difficulty of interpreting data displayed in many

of these ways is often underestimated since many

sources try and ‘make’ the data fit their point of

view.

Problem solving

Similar problems to question 4 but without the

scaffolding, part c only, will provide a greater

challenge. Direct students to the example for a

method of solving the question.


Oxford GCSE Maths for Edexcel New 2010 Edition Foundation Teacher Guide


Oxford GCSE Maths for Edexcel New 2010 Edition Foundation Plus Teacher Guide5 6

Questions needing A03 problem solving skills are clearly highlighted

Opportunities to practice Quality of Written Communications are clearly highlighted


51

A1.1 Straight line graphs

Objectives

Al Recognise and plot equations that correspond

to straight-line graphs in the coordinate plane,

including finding gradients.

Useful resources

• 2mm graph paper

• Graph plotting tool

Starter

Which integers between 10 and 10 are neither even

nor prime? (Note, negatives can be odd or even in

exactly the same way as positive numbers. 0 is even,

1 is not prime, so the list is –9, 7, 5, 3, 1, 1, 9.)

What answers can you make by adding two of these

numbers? For example, –1 + 9 = 8

Teaching notes

Imagine you have a rule for changing one number

into another number.

Starting number 2 – 1 end number.

Call the starting number x and the end number y.

You can write this rule as y = 2x 1.

Think of some possible starting numbers (x) and the

matching y numbers. Ask students to give a variety

of examples: decimal, fraction, negative, standard

form. How can you show a picture of the possible

results?

Draw a set of axes from 10 to 10 in the x and y

directions. Give students these instructions:

Select a set of values to use for x and complete a

table.

Plot points. Extend line through points. Label the

line.

Go around the class and check graphs. Explain that

equations like y = 2x – 1 are called linear equations.

Discuss the example in the student book, which

relates to an implicit equation.

Plenary

Discuss question 6 or How could you draw the line

for 8x 4000y = 0?

Rearrange to 8x = 4000y x = 500y.

Mark an x-axis scale in units of 500.

x 0 500 1000

y 0 1 2

Exercise commentary

Question 1 should be done without trying to draw

the graphs.

y = 7 and x = –2 may cause problems because there

is only one algebraic term. Students may need

reminding of lines parallel to the axes.

Question 2 is routine practice while questions 3 and

6 are practical examples of using straight-line

graphs.

If students calculate the values of y wrongly, or

label the axes incorrectly, they will not be able to

draw straight lines in questions 2, 3 and 5. In

question 4 students should not draw the graph.

Question 6 could be used in the plenary session as a

starting point for a discussion on the intersection of

lines.

Simplification

Ensure students are comfortable with plotting

straight-line graphs from a table of values before

attempting the rest of the exercise. Further practice

may be necessary to supplement question 2.

Extension

Ask the students to plot the graph (using a table of

values) of y = x2 (or another simple quadratic.)

Functional maths

The use of graphs to model real-life situations is

common (questions 3 and 6 give two possible

situations.) Further examples such as exchange rate

conversions could also be given.

Problem solving

Question 6 uses the principle of straight-line graphs

to solve a practical (and relevant?) problem.

165

G5.3 Solving problems using the sine and cosine l

Objectives

Gh Use the sine and cosine rules to solve 2-D and

3-D problems

Useful resources

• Calculators

Starter

My watch was showing the correct time at 13:20. As

the battery ran down it lost 1 min in the first 5 min,

then 2 min in the next 10 min, then 4 min in the next

15 min, 8 min in the next 20 min and so on. Explain

why the watch will stop before the real time is

15:15.

(In the time between 14:45 and 15:15 the watch

needs to lose 32 minutes: it can’t lose 32 minutes in

30 minutes.).

Teaching notes

Recap the sine and cosine rules, and focus on the

conditions for using each rule. These are outlined in

the student book. Emphasise the importance of

sketching and labelling a diagram.

The first example refers to bearings, which you will

need to recap. The example also uses basic angle

facts. Ask students why the cosine rule is used

rather than the sine rule.

The second example uses both the sine rule and the

cosine rule, but it also uses alternate angles. Discuss

rounding errors that might occur if the value for PR

is rounded off before finding the value of QR.

Plenary

An isosceles triangle has equal sides 7 m and base

angles 55°. What is the length of the other side?

Set a third of the class to solve the problem using

each of the following methods: sine rule, cosine

rule, splitting it up into two right-angled triangles.

Discuss which method students prefer.

(8.03 m to 3 significant figures.)

Exercise commentary

The questions are problems involving the sine and

cosine rules. Encourage students to always draw and

label a diagram, and to fill in any unknowns that

they work out. Discourage rounding off

intermediate calculations.

Questions 1 and 2 relate to bearings, and require

students to draw a diagram from a written

description. Similarly questions 7, 8 and 9 require a

diagram to be drawn.

Many of the problems are multi-stage so encourage

students to communicate their methods clearly and

concisely (QWC.)

Simplification

Students may need further routine practice at

applying the sine and cosine rules without context.

They may also struggle with the bearings questions

and these could be avoided. Avoid questions 7 to 9.

Extension

Students should be comfortable working through the

problems in questions 7 to 9. Further examples of

this geometrical nature can be given as appropriate.

Functional maths

Working with bearings, especially when the

triangles are non-right-angled, is important in

navigation and map reading. It is unusual to use the

sine and cosine rules formally but it is useful if

accurate information is needed.

Problem solving

Questions 7 to 9 are examples of geometrical

problem solving using the ideas covered here.


Oxford GCSE Maths for Edexcel New 2010 Edition Higher Teacher GuideAdvance Material • Uncorrected sample lesson plan page from


Hints for what to highlight, what to look out for, etc.

Real-life applications and further instances to cover A02 are highlighted

Each lesson lists the objectives addressed


51

A1.1 Straight line graphs

Objectives

Al Recognise and plot equations that correspond

to straight-line graphs in the coordinate plane,

including finding gradients.

Useful resources

• 2mm graph paper

• Graph plotting tool

Starter

Which integers between 10 and 10 are neither even

nor prime? (Note, negatives can be odd or even in

exactly the same way as positive numbers. 0 is even,

1 is not prime, so the list is –9, 7, 5, 3, 1, 1, 9.)

What answers can you make by adding two of these

numbers? For example, –1 + 9 = 8

Teaching notes

Imagine you have a rule for changing one number

into another number.

Starting number 2 – 1 end number.

Call the starting number x and the end number y.

You can write this rule as y = 2x 1.

Think of some possible starting numbers (x) and the

matching y numbers. Ask students to give a variety

of examples: decimal, fraction, negative, standard

form. How can you show a picture of the possible

results?

Draw a set of axes from 10 to 10 in the x and y

directions. Give students these instructions:

Select a set of values to use for x and complete a

table.

Plot points. Extend line through points. Label the

line.

Go around the class and check graphs. Explain that

equations like y = 2x – 1 are called linear equations.

Discuss the example in the student book, which

relates to an implicit equation.

Plenary

Discuss question 6 or How could you draw the line

for 8x 4000y = 0?

Rearrange to 8x = 4000y x = 500y.

Mark an x-axis scale in units of 500.

x 0 500 1000

y 0 1 2

Exercise commentary

Question 1 should be done without trying to draw

the graphs.

y = 7 and x = –2 may cause problems because there

is only one algebraic term. Students may need

reminding of lines parallel to the axes.

Question 2 is routine practice while questions 3 and

6 are practical examples of using straight-line

graphs.

If students calculate the values of y wrongly, or

label the axes incorrectly, they will not be able to

draw straight lines in questions 2, 3 and 5. In

question 4 students should not draw the graph.

Question 6 could be used in the plenary session as a

starting point for a discussion on the intersection of

lines.

Simplification

Ensure students are comfortable with plotting

straight-line graphs from a table of values before

attempting the rest of the exercise. Further practice

may be necessary to supplement question 2.

Extension

Ask the students to plot the graph (using a table of

values) of y = x2 (or another simple quadratic.)

Functional maths

The use of graphs to model real-life situations is

common (questions 3 and 6 give two possible

situations.) Further examples such as exchange rate

conversions could also be given.

Problem solving

Question 6 uses the principle of straight-line graphs

to solve a practical (and relevant?) problem.

165

G5.3 Solving problems using the sine and cosine l

Objectives

Gh Use the sine and cosine rules to solve 2-D and

3-D problems

Useful resources

• Calculators

Starter

My watch was showing the correct time at 13:20. As

the battery ran down it lost 1 min in the first 5 min,

then 2 min in the next 10 min, then 4 min in the next

15 min, 8 min in the next 20 min and so on. Explain

why the watch will stop before the real time is

15:15.

(In the time between 14:45 and 15:15 the watch

needs to lose 32 minutes: it can’t lose 32 minutes in

30 minutes.).

Teaching notes

Recap the sine and cosine rules, and focus on the

conditions for using each rule. These are outlined in

the student book. Emphasise the importance of

sketching and labelling a diagram.

The first example refers to bearings, which you will

need to recap. The example also uses basic angle

facts. Ask students why the cosine rule is used

rather than the sine rule.

The second example uses both the sine rule and the

cosine rule, but it also uses alternate angles. Discuss

rounding errors that might occur if the value for PR

is rounded off before finding the value of QR.

Plenary

An isosceles triangle has equal sides 7 m and base

angles 55°. What is the length of the other side?

Set a third of the class to solve the problem using

each of the following methods: sine rule, cosine

rule, splitting it up into two right-angled triangles.

Discuss which method students prefer.

(8.03 m to 3 significant figures.)

Exercise commentary

The questions are problems involving the sine and

cosine rules. Encourage students to always draw and

label a diagram, and to fill in any unknowns that

they work out. Discourage rounding off

intermediate calculations.

Questions 1 and 2 relate to bearings, and require

students to draw a diagram from a written

description. Similarly questions 7, 8 and 9 require a

diagram to be drawn.

Many of the problems are multi-stage so encourage

students to communicate their methods clearly and

concisely (QWC.)

Simplification

Students may need further routine practice at

applying the sine and cosine rules without context.

They may also struggle with the bearings questions

and these could be avoided. Avoid questions 7 to 9.

Extension

Students should be comfortable working through the

problems in questions 7 to 9. Further examples of

this geometrical nature can be given as appropriate.

Functional maths

Working with bearings, especially when the

triangles are non-right-angled, is important in

navigation and map reading. It is unusual to use the

sine and cosine rules formally but it is useful if

accurate information is needed.

Problem solving

Questions 7 to 9 are examples of geometrical

problem solving using the ideas covered here.


Oxford GCSE Maths for Edexcel New 2010 Edition Higher Teacher GuideAdvance Material • Uncorrected sample lesson plan page from


A quick, punchy activity to get students thinking and in the mood to learn

Suggestions for how to summarise the lesson and draw out its main themes


98

A2 Assessment

Answers

1 a 2a + 6b (2)

b x(x – 6) (2)

c 3x – 2x3

(2)

d 4x(3y + x) (2)

2 a m5

(1)

b n4

(1)

3 a a3

(1)

b 15x – 10 (1)

c 3y2 + 12y (2)

d 5x – 2 (2)

e x2 + x – 12 (2)

4 a k =15 (2)

b y = –7 (2)

5 a C = 90 + 0.5m (2)

b 300 miles (3)

Mark scheme/commentary

1 a 4a – 2a + 5b + b = 2a + 6b

b x(x – 6) = x2 – 6x

c x(3 – 2x2) = x 3 – x 2x

2

= 3x – 2x3

d The common factors can be x, 2, 4, 2x or 4x,

but the expression must be completely

factorised.

2 a Add the indices, 2 + 3 = 5

b Add the indices, 1 + 5 = 6, then subtract the

indices, 6 – 2 = 4.

3 a Add the indices, 1 + 1 + 1 = 3

b 5(3x – 2) = 5 3x – 5 2

= 15x – 10

c 3y(y + 4) = 3y y + 3y 4

= 3y2 + 12y

d 2(x – 4) + 3(x + 2) = 2 x – 2 4 + 3 x

+ 3 2

= 2x – 8 + 3x + 6

= 5x – 2

e 4 –3 = –12

4 + –3 = 1

4 a 50 = 4k – 10

60 = 4k

k = 60 ÷ 4 = 15

b y = 4n – 3d

= 4 2 – 3 5

= 8 – 15

= –7

5 a 50p = £0.50

b 240 = 90 + 0.5m

240 – 90 = 0.5m

150 = 0.5m

m = 150 ÷ 0.5

= 300

A02

177

CS Functional maths 7: Business

Aim

• To introduce students to some of the ways that mathematics can be used in business

• To express the importance of mathematics in financial situations

Useful resources

• Business worksheet Foundation

• Balance sheet template

• Annie’s cards cash flow table

• Annie’s cards breakeven graph

• Business PowerPoint

• Business spreadsheet

Teaching notes

Ask if any of the students’ families have their own business. Show the balance sheet template and invite

volunteers to explain what it means to the rest of the class.

Introduce the scenario of Annie’s cards as outlined in the student book and ask students to complete the

cash flow data (ensure that they understand the information!) They could then work through the example,

including the further questions at the bottom of the page. If students have ICT access, this is an ideal

opportunity to show the benefits of using a spreadsheet.

Ask students if they know what ‘breakeven’ means. Discuss why it is important for a business to know

their ‘breakeven’ point, and talk students through the method for creating a ‘breakeven chart’ in the case

study. Ensure that they understand how the lines relate to the data. Also, discuss the gradient and y-

intercept of each line, linking these values to the data.

Students could then use the questions below the graph to create their own ‘breakeven charts’ for the

scenarios described. This is a good opportunity to reinforce how to draw straight line graphs.

This case study is also good for introducing or reinforcing formulae – you could ask how many formulae

are presented on the case study pages.

Students may be unfamiliar with the term ‘direct proportion’ as this is outside the GCSE Foundation

specification, although it is referred to in the student book.

Extension

Students could apply the information in this case study to a business of their own that they could invent.

Examples:

- tuck shop at school;

- selling hand-made t-shirts.

Encourage students to think about the costs involved.

They could use the breakeven analysis to determine if their business would make a profit or a loss.

Advance Material • Uncorrected sample Summary page

Oxford GCSE Maths for Edexcel New 2010 Edition Higher Teacher GuideAdvance Material • Uncorrected sample Case Study teacher notes page from

Oxford GCSE Maths for Edexcel New 2010 Edition Foundation Plus Teacher Guide (referring to pages 354-355 of Foundation Plus Student Book)

9 10

Details of what examiners are looking for in order to award marks


98

A2 Assessment

Answers

1 a 2a + 6b (2)

b x(x – 6) (2)

c 3x – 2x3

(2)

d 4x(3y + x) (2)

2 a m5

(1)

b n4

(1)

3 a a3

(1)

b 15x – 10 (1)

c 3y2 + 12y (2)

d 5x – 2 (2)

e x2 + x – 12 (2)

4 a k =15 (2)

b y = –7 (2)

5 a C = 90 + 0.5m (2)

b 300 miles (3)

Mark scheme/commentary

1 a 4a – 2a + 5b + b = 2a + 6b

b x(x – 6) = x2 – 6x

c x(3 – 2x2) = x 3 – x 2x

2

= 3x – 2x3

d The common factors can be x, 2, 4, 2x or 4x,

but the expression must be completely

factorised.

2 a Add the indices, 2 + 3 = 5

b Add the indices, 1 + 5 = 6, then subtract the

indices, 6 – 2 = 4.

3 a Add the indices, 1 + 1 + 1 = 3

b 5(3x – 2) = 5 3x – 5 2

= 15x – 10

c 3y(y + 4) = 3y y + 3y 4

= 3y2 + 12y

d 2(x – 4) + 3(x + 2) = 2 x – 2 4 + 3 x

+ 3 2

= 2x – 8 + 3x + 6

= 5x – 2

e 4 –3 = –12

4 + –3 = 1

4 a 50 = 4k – 10

60 = 4k

k = 60 ÷ 4 = 15

b y = 4n – 3d

= 4 2 – 3 5

= 8 – 15

= –7

5 a 50p = £0.50

b 240 = 90 + 0.5m

240 – 90 = 0.5m

150 = 0.5m

m = 150 ÷ 0.5

= 300

A02

177

CS Functional maths 7: Business

Aim

• To introduce students to some of the ways that mathematics can be used in business

• To express the importance of mathematics in financial situations

Useful resources

• Business worksheet Foundation

• Balance sheet template

• Annie’s cards cash flow table

• Annie’s cards breakeven graph

• Business PowerPoint

• Business spreadsheet

Teaching notes

Ask if any of the students’ families have their own business. Show the balance sheet template and invite

volunteers to explain what it means to the rest of the class.

Introduce the scenario of Annie’s cards as outlined in the student book and ask students to complete the

cash flow data (ensure that they understand the information!) They could then work through the example,

including the further questions at the bottom of the page. If students have ICT access, this is an ideal

opportunity to show the benefits of using a spreadsheet.

Ask students if they know what ‘breakeven’ means. Discuss why it is important for a business to know

their ‘breakeven’ point, and talk students through the method for creating a ‘breakeven chart’ in the case

study. Ensure that they understand how the lines relate to the data. Also, discuss the gradient and y-

intercept of each line, linking these values to the data.

Students could then use the questions below the graph to create their own ‘breakeven charts’ for the

scenarios described. This is a good opportunity to reinforce how to draw straight line graphs.

This case study is also good for introducing or reinforcing formulae – you could ask how many formulae

are presented on the case study pages.

Students may be unfamiliar with the term ‘direct proportion’ as this is outside the GCSE Foundation

specification, although it is referred to in the student book.

Extension

Students could apply the information in this case study to a business of their own that they could invent.

Examples:

- tuck shop at school;

- selling hand-made t-shirts.

Encourage students to think about the costs involved.

They could use the breakeven analysis to determine if their business would make a profit or a loss.

Advance Material • Uncorrected sample Summary page

Oxford GCSE Maths for Edexcel New 2010 Edition Higher Teacher GuideAdvance Material • Uncorrected sample Case Study teacher notes page from

Oxford GCSE Maths for Edexcel New 2010 Edition Foundation Plus Teacher Guide (referring to pages 354-355 of Foundation Plus Student Book)

9 10

Case studies provide realistic and relevant scenarios in which to develop and practice problem solving skills


© Oxford University Press 2010

Chapter test Foundation Plus

Measures and Pythagoras G7

3 a

Calculate the length of AB correct to 3 significant figures.

……………… (3 marks)

b A triangle has lengths of 6 cm, 9 cm and 11 cm.

Prove that it does not contain a right angle.

(3 marks)

AC = 8.2 cm

BC = 6.3 cm

Angle ABC = 90°




2 A car travels 20 km in 10 minutes and uses 1.2 litres of fuel.

a i Work out its average speed in kilometres per hour.

……………… (1 mark)

ii Work out its average speed in metres per second.

……………… (1 mark)

b Work out its fuel consumption in litres per 100 km.

………………….. (1 mark)




You may use a calculator.

1 This cylinder is 6 cm high and has a radius of 3 cm.

a Work out the volume of the cylinder.

……………… (3 marks)

b The cylinder in part a is filled with water, which is then

poured into the rectangular tank shown here.

Work out the depth of the water. Give your answer

correct to 3 significant figures.

……………… (3 marks)

Print out tests available on the Asessment OxBox for paper-based testing

Advance Material • Uncorrected sample screens from the

Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM


Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM11 12


13 9C Interactive Self testGCSEMathsFor Edexcel

13 9C Interactive Chapter testGCSEMathsFor Edexcel

Formative screen test from the Assessment OxBox

Summative screen test from the Assessment OxBox






Self assessment checklist Oxford GCSE Maths for Edexcel

1 © Oxford University Press 2010

G7 25 Further geometry Foundation

Name:

You can use this sheet to help you track your progress.

I can do

it.

I’m almost there.

I need a bit more

help. G7.1 p398–399 Grade D Understand congruence

G7.2 p400–401 Grade D Find exterior angles in triangles and quadrilaterals

G7.2 p400–401 Grade D Know the names of general polygons

G7.2 p400–401 Grade D Understand that regular polygons have equal sides and equal angles

G7.3 p402–403 Grade D Use the vocabulary associated with circles

G7.3 p402–403 Grade D Calculate the circumference and area of a circle

G7.4 p404–405 Grade F/E Use nets to construct cuboids from given information

G7.4 p404–405 Grade F/E Use 2-D representations of 3-D shapes



Advance Material • Uncorrected sample screen from the



Self assessment checklist Oxford GCSE Maths for Edexcel

1 © Oxford University Press 2010

G7 25 Further geometry Foundation

Name:

You can use this sheet to help you track your progress.

I can do

it.

I’m almost there.

I need a bit more

help. G7.1 p398–399 Grade D Understand congruence

G7.2 p400–401 Grade D Find exterior angles in triangles and quadrilaterals

G7.2 p400–401 Grade D Know the names of general polygons

G7.2 p400–401 Grade D Understand that regular polygons have equal sides and equal angles

G7.3 p402–403 Grade D Use the vocabulary associated with circles

G7.3 p402–403 Grade D Calculate the circumference and area of a circle

G7.4 p404–405 Grade F/E Use nets to construct cuboids from given information

G7.4 p404–405 Grade F/E Use 2-D representations of 3-D shapes



Advance Material • Uncorrected sample screen from the


Chapter Ref Spread

1. Integers and decimals (N1)

N1.1 Place value

N1.2 Reading scales

N1.3 Adding and subtracting negative numbers

N1.4 Multiplying and dividing negative numbers

N1.5 Rounding

2. Probability (D1)

D1.1 Probability

D1.2 Probability scale

D1.3 Mutually exclusive outcomes

D1.4 Two-way tables 1

D1.5 Expected frequency

D1.6 Relative frequency

D1.7 Two events

D1.8 Two events again

D1.9

3. Decimal calculations (N2)

N2.1 Mental addition and subtraction

N2.2 Written addition and subtraction

N2.3 Mental multiplication and division

Nb Order integers, decimals and fractions

Nb Understand and use positive numbers and negative integers, both as positions and translations on a number line

Nj Identify the value of digits in a decimal

Nj Understand place value

Na Multiply and divide any number by powers of 10


GMo“Interpret scales on a range of measuring instruments – seconds, minutes, hours, days, weeks, months and years– mm, cm, m, km, ml, cl, l, mg, g, kg, tonnes, °C”

GMo Use correct notation for time, 12- and 24-hour clock

GMo Work out time intervals

Na Add, subtract, multiply and divide negative numbers


Nb Order integers, decimals and fractions

Na Add, subtract, multiply and divide negative numbers

Na Multiply and divide by any negative number

Nu Round to the nearest integer and to a given number of significant figures

Nu Estimate answers to calculations including use of rounding

Gmo Recognise the inaccuracy of measurements

SPo List all outcomes for single events systematically

SPm Distinguish between events which are; impossible, unlikely, even chance, likely, and certain to occur

SP m Write probabilities in words or fractions, decimals and percentages

SP n Find the probability of an event happening using theoretical probability

SPp Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 1


SPm Mark events and/or probabilities on a probability scale of 0 to 1


SPp Use 1 − p as the probability of an event not occurring where p is the probability of the event occurring


SPp Add simple probabilities

SPf Design and use two-way tables for discrete and grouped data

SPp Find a missing probability from a list or table

SPn Find the probability of an event happening using theoretical probability

SPn Estimate the number of times an event will occur, given the probability and the number of trials

SPn Find the probability of an event happening using relative frequency

SPs Compare experimental data and theoretical probabilities

SPt Compare relative frequencies from samples of different sizes

SPo List all outcomes for two successive events systematically

SPo List all outcomes for two successive events systematically

SPo Use and draw sample space diagrams


SP m Mark events and/or probabilities on a probability scale of 0 to 1


SPp Use 1 − p as the probability of an event not occurring where p is the probability of the event occurring

SPn Estimate the number of times an event will occur, given the probability and the number of trials

Na Add and subtract mentally numbers with up to two decimal places

Na Add, subtract, multiply and divide whole numbers, negative numbers integers, fractions and decimals and numbers in index form

Na Add, subtract, multiply and divide whole numbers, negative numbers integers, fractions and decimals and numbers in index form

Nq Multiply and divide numbers using the commutative, associative, and distributive laws and factorisation where possible, or place value adjustments


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