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Transcript of 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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 2 13/1/10 10:06:07
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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 3 13/1/10 10:06:07
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
Finding your way around this book
N1 Integers and decimals
A1 Expressions
UNIT 1
1
UNIT 2
NUMBERALGEBRAGEOMETRY 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
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
G1 Measures, length and area
9
FDN_findingyourway_page.indd 330/12/09 15:07:46
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 4 13/1/10 10:06:07
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.
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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 5 13/1/10 10:06:12
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
Advance Material • Uncorrected sample lesson plan page from
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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 6 13/1/10 10:06:12
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
Advance Material • Uncorrected sample lesson plan page from
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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 7 13/1/10 10:06:13
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.
Advance Material • Uncorrected sample lesson plan page from
Oxford GCSE Maths for Edexcel New 2010 Edition Higher Teacher GuideAdvance Material • Uncorrected sample lesson plan page from
Oxford GCSE Maths for Edexcel New 2010 Edition Higher Plus Teacher Guide7 8
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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 8 13/1/10 10:06:13
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.
Advance Material • Uncorrected sample lesson plan page from
Oxford GCSE Maths for Edexcel New 2010 Edition Higher Teacher GuideAdvance Material • Uncorrected sample lesson plan page from
Oxford GCSE Maths for Edexcel New 2010 Edition Higher Plus Teacher Guide7 8
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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 9 13/1/10 10:06:14
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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 10 13/1/10 10:06:14
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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 11 13/1/10 10:06:14
© 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°
© Oxford University Press 2010
Chapter test Foundation Plus
Measures and Pythagoras G7
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)
© Oxford University Press 2010
Chapter test Foundation Plus
Measures and Pythagoras G7
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
Advance Material • Uncorrected sample screens from the
Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM11 12
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 12 13/1/10 10:06:15
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
Advance Material • Uncorrected sample screens from the
Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM
Advance Material • Uncorrected sample screens from the
Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM11 12
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 13 13/1/10 10:06:15
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 screens from the
Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM
Advance Material • Uncorrected sample screen from the
Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM13 14
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 14 13/1/10 10:06:16
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 screens from the
Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM
Advance Material • Uncorrected sample screen from the
Oxford GCSE Maths for Edexcel New 2010 Edition Assessment OxBox CD-ROM13 14
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
Nb Understand and use positive numbers and negative integers, both as positions and translations on a number line
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 Understand and use positive numbers and negative integers, both as positions and translations on a number line
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
SP m Write probabilities in words or fractions, decimals and percentages
SPm Mark events and/or probabilities on a probability scale of 0 to 1
SPp Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 1
SPp Use 1 − p as the probability of an event not occurring where p is the probability of the event occurring
SPp Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 1
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 Write probabilities in words or fractions, decimals and percentages
SP m Mark events and/or probabilities on a probability scale of 0 to 1
SPp Identify different mutually exclusive outcomes and know that the sum of the probabilities of all outcomes is 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
K37046_MATHS_GCSE.TG_BLAD_A4col_16pp.indd 15 13/1/10 10:06:16
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