oxford gcse maths for ocr sample teacher guide material

Advance Material

Contains 8 uncorrected sample pages from the Oxford GCSE

Maths for OCR 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

Teacher Guides

How does Oxford GCSE Maths for OCR support your teaching?Oxford GCSE Maths for OCR provides two Teacher Guides, Foundation and Higher, to match the two Student Books. These comprehensive teacher resources are full of practical and accessible lesson plans. They are designed to make teaching easier for the whole range of teacher experience and needs, including NQTs and non-specialists, and have a particular focus on the processes of the new GCSEs.

In addition, OxBox CD-ROMs offer a wealth of activities and resources that include a huge amount of teacher support and assessment material. This will help inspire your students and give you more time to actually teach by doing a huge amount of the hard work for you, as well as covering all aspects of the new GCSE. Therefore, in addition to sample material from the Teacher Guides, we have also included samples of related resources from the OxBox CD-ROMs to give you as full as possible an idea of just how much help we have to offer you and your school.

ContentsIntroduction page ....................................................................................................... page 3An introduction page at the beginning of each Teacher Guide shows how Oxford GCSE Maths for OCR 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 5-8The 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

21

5Formulae and equations

Objectives covered in this chapter are:

FA6.3 Use the conventions for coordinates in a planeFA6.3 Find the coordinates of the midpoint of a line

segment FA6.2 Distinguish between the words ‘equation’, ‘formula’

and ‘expression’FA8.1 Manipulate algebraic expressionsFA7.1 Substitute numbers into a formulaFA7.1 Change the subject of a formulaFA7.1 Derive a formulaFA8.2 Solve simple equations by using inverse operationsFA8.2 Solve linear equations with the unknown on

either side and including brackets

A7Formulae and equations

Useful ICT resourcesl Autograph A7.1 Coordinates and midpoints

l Animation A7.4 Substituting into formulae

l Starter A7.5 Formulae multi-choice

l Powerpoint A7.7 Solving linear equations

l Consolidation A7.8 Linear equations practice

l Chapter test A7 Formulae and equations

l Summative on-screen test A7 Formulae and equations

l Formative on-screen test A7 Formulae and equations

The spider diagram shows a variety of ways in which a linear equation can be transformed. By tackling this activity, students should begin to appreciate that there is not just one single unique way to correctly transform an equation; also, by transforming an equation correctly, the value of x stays the same.Encourage students to add to the spider diagram by thinking about the different types of operation that are used here: adding/ subtracting, and multiplying/ dividing.

RICH TASK COMMENTARY

Pre-requisite knowledge• Coordinatesinasinglequadrant• Orderofoperations(BIDMAS)• Recognitionofsquaredterms• Calculatingwithnegativeintegers

iii

Guide to this book

NUMBER ALGEBRA GEOMETRY DATA

UN

IT CU

NIT B

UN

IT A

A1 Integers and decimals

A2 Summary statistics

A3 Constructions

A4 Factors, mutiples and ratio

A5 Sequences

A6 Representing and interpreting

dataA7 Formulae and equations

A8 Constructions and pythagoras

B9 Fractions, decimals and percentages B10 Circles,

angles and lines

B11 Straight lines

B12 Transformations

B13 Bivariate data and time series

B14 Simultaneous equations and

inequalitiesB15 Surds and indices

B16 Vectors

B17 Percentages and proportional

changeB18 Circles

C19 Algebraic manipulation

C20 Surface area and volume

C21 Graphs

C22 Everyday arithmetic and

boundsC23 Trigonometry

C24 Graphs 2

C25 Study of chance

iii

Guide to this book

NUMBER ALGEBRA GEOMETRY DATA

UN

IT CU

NIT B

UN

IT A

A1 Integers and decimals

A2 Summary statistics

A3 Constructions

A4 Factors, mutiples and ratio

A5 Sequences

A6 Representing and interpreting

dataA7 Formulae and equations

A8 Constructions and pythagoras

B9 Fractions, decimals and percentages B10 Circles,

angles and lines

B11 Straight lines

B12 Transformations

B13 Bivariate data and time series

B14 Simultaneous equations and

inequalitiesB15 Surds and indices

B16 Vectors

B17 Percentages and proportional

changeB18 Circles

C19 Algebraic manipulation

C20 Surface area and volume

C21 Graphs

C22 Everyday arithmetic and

boundsC23 Trigonometry

C24 Graphs 2

C25 Study of chance

Advance Material • Uncorrected sample Introduction page from

Oxford GCSE Maths for OCR Foundation Teacher GuideAdvance Material • Uncorrected sample Chapter Introduction page from

Oxford GCSE Maths for OCR Higher Teacher Guide

Specification A 3 unit structure followed

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 OxBox provides resources to enliven lessons

Basic knowledge assumed from previous chapters or KS3 is clearly indicated

43

• Use ratio notation, including reduction to its

simplest form; know its various links to fraction

notation (FA4.1)

• Divide a quantity in a given ratio (FA4.2)

• Determine the original quantity by knowing

the size of one part of the divided quantity (FA4.2)

• Solve word problems about ratio, including using

informal strategies and the unitary method of

solution (FA4.2)

Introducing ratio

A4.3

3

Starter

Use a spider diagram display with a randomly drawn set of

24 black and 6 red dots in the centre. Ask students to suggest

equivalent ratios to put on the legs. Does one of the legs give the

ratio in its lowest terms? Which is it? (Add it to the diagram if it

is not there.)

Resources

Spider diagram for Smartboard or OHP

Plenary

The investigation of the Golden Ratio,

if not already done, could become a

mini-project involving mathematics,

history and art.

Teaching notes

Both the notation and concept of ratio have been

encountered before. It is worth emphasising that the

direction in which the ratio is written is determined by the

wording of the given information. The vocabulary of

simplest form and unitary form will need to be emphasised.

A couple of examples involving simplifying ratios and

using ratio in a practical money context could also be

attempted by the group.

The rich task in the text concerning the Fibonacci sequence

can be attempted in class or as homework and provides a

launching point for pupils if they have access to the

internet.

Exercise commentary

Question 1 The key phrase here is

‘simplest form’.

Question 2 The phrase ‘unitary form’

will need emphasising again.

Question 3 These questions all

involve applying ratios in simple

financial contexts.

Question 4 This substantial AO3

task may need some guidance from

the teacher to get the students

started. The idea of writing a two

digit number AB as 10A + B could be

introduced to more able students to

allow an attempt at mathematical

explanation. There are a lot of

patterns in this task and even those

who cannot get to a symbolic

explanation of what is going on can

derive benefit.

Advance Material • Uncorrected sample lesson plan page from

Oxford GCSE Maths for OCR Foundation Teacher Guide


Oxford GCSE Maths for OCR Foundation Teacher Guide

Lots of hints and ideas from experienced classroom teachers

Practical suggestions to help cater for less and more able students

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

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

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

Each lesson lists the objectives addressed

65

• Generate terms of a sequence using position-to-

term rules

• Generate common integer sequences (including

sequences of odd or even integers, squared integers,

powers of 2, powers of 10, triangular numbers) (HA7.2)

• Use linear expressions to describe the n th term of an

arithmetic sequence, justifying its form by referring

to the activity or context from which it was

generated (HA7.3)

Square and triangle numbers

A5.2

2

Starter

Starting with 100, go around the class asking students for the

next term in the sequence you describe, for example: Count

down in 7s, in square numbers, in steps of 0.95.

Plenary

There are a number of ideas in the

exercise that could be developed further

including the sigma notation. Students

could research a formula for the sum of

the square numbers and hence finish off

the rich task which began the section.

The method of summing arithmetic series

attributed to Gauss could be investigated

and some may be able to generalise the

approach for any arithmetic series.

Teaching notes

The rich task provides a good introduction to this section.

Encourage the class to look closely at how to get from one

term to the next and hopefully they will spot that a square

number is being added each time. It is unlikely that a general

formula will be forthcoming but the problem can be left for

the plenary session at this stage.

Exercise commentary

This is the famous handshake

investigation sometimes also

presented as the mystic rose puzzle.

Pupils should record results in a table

and look for a pattern in the numbers.

This should be clear given they

recently saw the triangle numbers.

The general term is easily adapted

from the triangle number formula.

Question 1 This provides a famous

number pattern that the sum of the

odd numbers gives square numbers.

Question 2 This AO3 investigation

will probably be helped if the students

list the square numbers they know on

their page. It is not unusual to have to

remind pupils that 1 is also a square

number. At some stage in the lesson

it would be good to collect together

their findings to fill in any gaps.

Question 3 This question introduces

the sigma notation for sum of and

may need a little further explanation

by the teacher, though this notation

could be met again in the plenary

session.

Question 4 This functional maths

task needs the use of the triangle

number formulae. Some may need

reminding to be consistent by

working in pounds or in pence.

• Use the conventions for coordinates in the plane; plot

points in all four quadrants

• Understand that one coordinate identifies a point on a

number line, two coordinates identify a point in a

plane using the terms ‘1D’ and ‘2D’

• Use axes and coordinates to specify points in all four

quadrants

• Locate points with given coordinates

• Find the coordinates of the midpoint of the line

segment AB, given points A and B, then

calculate the length AB. (FA6.3)

Coordinates of points

A7.9

9

Starter

Begin by chanting a sequence of numbers, starting from 6 and

going up in steps of 0.5. You could use a count stick or number

line. Repeat the activity going up in steps of 0.4.

Challenge students to individually record these sequences

(perhaps on a mini whiteboard) as quickly as possible, this time

going up in steps of 0.3, beginning at 4.1. Give students exactly

one minute for this activity, and then compare results.

Repeat with 0.3s but this time going back from 12.5.

Resources

Mini whiteboard

Plenary

Fractional/decimal coordinates can be

introduced as a simple extension.

The historical development of the system

of coordinates and why they are called

Cartesian coordinates can be

investigated.

Some students may wish to look at other

coordinate systems such as map

references or polar coordinates.

3-D coordinates could be investigated as

a precursor to later work.

Teaching notes

Students will have met the idea of plotting coordinates

before at least in the first quadrant. A quick test of plotting

points using AUTOGRAPH should both revise basic ideas

and indicate the knowledge base of the students. Extend the

axes into four quadrants and indicate how negative numbers

are interpreted in a pair of coordinates. Using

AUTOGRAPH get the students to come up individually and

plot specified points, perhaps to produce shapes. The order

(x, y) needs to be emphasised and that brackets need to be

drawn around the numbers. It is worth plotting points like

(0, 3) (–6, 0) etc since these can cause confusion.

It is worth highlighting the coordinates of the origin and the

vocabulary ‘origin’ as well.

Once they are familiar with the idea of plotting points then

set a task of finding the midpoint of a line segment joining

two points. They can investigate this and hopefully come up

with some conclusions on a general method. The results can

be collected together at a suitable point and the method

summarised and its use reinforced with a further example.

Exercise commentary

These questions can be done on

squared paper or on screen using

AUTOGRAPH.

Question 1 The coordinates need to

be enclosed in brackets and be in the

correct order.

Question 2 This problem solving

question does require calculation of

the coordinates of the mid-points and

not just observation from the

coordinates-axes.

Question 3 This question involves

more calculation of mid-points, which

could be done by drawing or

calculation.

Question 4 This question requires

knowledge of the properties of the

diagonals of some quadrilaterals or

can be solved by plotting the points

on axes scaled in tens.

Question 5 This question can be

answered by reasoning alone or by

plotting and observation.

Question 6 This problem needs

considerable thought but is probably

best solved by drawing at this level.

Some revision of quadrilaterals may

be required for some.


Oxford GCSE Maths for OCR Higher Teacher GuideAdvance Material • Uncorrected sample lesson plan page from

Oxford GCSE Maths for OCR Higher Teacher Guide

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

Suggestions for how to incorporate software packages into your teaching

Extension activities to put topics into cultural and historical context

Questions needing A03 problem solving skills are clearly highlighted

7 8

Common misconceptions highlighted

10 Business Case study

A6.1Business Case study

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.

Useful resourcesBusiness worksheet FoundationBalance sheet templateAnnie’s cards cash flow tableAnnie’s cards breakeven graphPowerPoint 3.2, Excel spreadsheet 4

Objectivesl Use calculators effectively and efficientlyl Discuss, plot and interpret graphs modelling real situationsl Use formulae from mathematics and other subjects

Aiml To introduce students to some of the ways that mathematics

can be used in business;l To express the importance of mathematics in financial

situations.

ExtensionStudents 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.

9Summary

Exam-style question commentary

A7Summary

Worked solution Commentary

1) Solve a) 5x=30 b) y+8=25 c) 2z – 3 = 21

1) a) 5x = 30 5x ÷ 5 = 30 ÷ 5 x = 6

check: 5 x 6 = 30 ✓

b) y+8 = 25 y+8 - 8= 25 – 8 y = 17 check: 17+8=25 ✓

c) 2z – 3 = 21 2z -3 + 3 = 21 + 3 2z = 24 2z ÷ 2 = 24 ÷ 2 z = 12 check: 2 x 12 -3 = 24 – 3 = 21 ✓

1) a) Students often quickly identify the inverse operation as ÷ 5. However they may think that they have to ÷ 5 twice, once for the 5 and once for the x. It may help to write the working in the form of fractions to be cancelled.

b) Some students may subtract 25 from 8 (the wrong order is also common with division). Some students may find rules such as ‘swap side, swap sign’ helpful.

c) A common error with two-operation equations is undoing the operations in the wrong order. Encourage students to ‘read’ an equation in terms of what is happening to the unknown – then reverse the operations. Function machines can help but should be weaned off before students tackle two-sided equations.

2) A rectangle has an area of 12x + 24. What might its length and width be? Give two different possible answers.

Area of a rectangle = length x width12x + 24 = 2(6x+12)

One possible answer is length = 2, width = 6x + 1212x + 24 = 12(x+2)

Another possibility is length = 12, width = x+2

2) This is an AO3-type problem, with no unique correct answer.

Students should recall the formula for the area of a rectangle fairly easily. They may however need encouragement in the tricky step of realising that they need to factorise.

This will be a newly-learned skill, and students may not realise that there is more than one way to factorise.

Those more confident with expanding may prefer to use a trial-and-error method by guessing the dimensions and multiplying – remind them that they will need to expand using brackets.

Case studies provide realistic and relevant scenarios in which to develop and practice AO3 problem solving skills and functional maths

109

Advance Material • Uncorrected sample Summary page

Oxford GCSE Maths for OCR Higher Teacher GuideAdvance Material • Uncorrected sample Case Study teacher notes page from

Oxford GCSE Maths for OCR Foundation Teacher Guide (referring to pages 354-355 of Foundation Student Book)

13

5 e maximum temperature, in °C, for each month is shown in the table.

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

6.4 6.7 9.3 11.8 15.7 18.3 20.8 20.6 17.3 13.3 9.2 7.2

Draw a line graph to show the maximum temperatures.

6 e height of water, in centimetres, in a harbour is measured at 3-hour intervals.

Time

Height (cm)

00:00 03:00 06:00 09:00 12:00 15:00 18:00 21:00 24:00

18 20 5 19 8 28 10 15 26

Draw a line graph to show the heights.

Consolidation Oxford GCSE Maths for OCR Foundation

Bivariate data and time series

3 © Oxford University Press 2010

13

3 Decide whether the lines are good lines of best fit. Explain your decision. a

1 Decide whether the lines are good lines of best fit. Explain your decision.

a b c

d e

2 Use the line of best fit to estimate

a the price of the crop, if there are 200 bugs

b the number of bugs, if the crop costs £2.50.

© Oxford University Press 2006

D5.5 More scatter graphs

Extra Practice 2 GCSE MathsFoundation Plus

£1 £3 £40 £2 £5 £60

500

400

300

200

100

Price of crop

Nu

mbe

r of

bugs

1601OP_Foundation-Plus_02 18/9/06 11:44 am Page 129

b


a b c

d e







£1 £3 £40 £2 £5 £60

500

400

300

200

100

Price of crop

Nu

mbe

r of

bugs


c


a b c

d e







£1 £3 £40 £2 £5 £60

500

400

300

200

100

Price of crop

Nu

mbe

r of

bugs


d


a b c

d e







£1 £3 £40 £2 £5 £60

500

400

300

200

100

Price of crop

Nu

mbe

r of

bugs


e


a b c

d e







£1 £3 £40 £2 £5 £60

500

400

300

200

100

Price of crop

Nu

mbe

r of

bugs


4 Use the line of best fit to estimate a the price of the crop, if there are 200 bugs b the number of bugs, if the crop costs £2.50.


a b c

d e







£1 £3 £40 £2 £5 £60

500

400

300

200

100

Price of crop

Nu

mbe

r o

f bu

gs





13

1 A bus company keeps a record of the number of items of lost property and the number of ‘reminder’ signs on all the buses, for each month of a year.

Number of ‘reminder’ signs

Number of lost property items

25 15 55 20 50 0 45 30 5 35 10 40

18 20 5 19 8 28 10 15 26 11 24 14

a Draw a scatter graph to show this information. Use 2 cm to represent 10 signs on the horizontal axis. Use 2 cm to represent 10 items on the vertical axis.

b State the type of correlation shown by the graph. c Copy and complete these sentences: e more ‘reminder’ signs that are used, the _____ items of property are lost. e fewer ‘reminder’ signs that are used, the _____ items of property are lost.

2 e instances of vandalism and the number of letters to a local newspaper each month are shown.

Instances of vandalism

Number of letters

38 23 13 50 8 36 45 20 31 43 5 25

12 13 9 15 8 14 15 10 9 13 7 12

a Draw a scatter graph to show the information. Use 2 cm to represent 10 instances of vandalism on the horizontal axis. Use 2 cm to represent 10 letters of vandalism on the vertical axis.

b State the type of correlation shown by the graph. c Describe in words any relationship between the instances of vandalism and the

number of letters.




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

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 OCR Assessment OxBox CD-ROMAdvance Material • Uncorrected sample screens from the

Oxford GCSE Maths for OCR Assessment OxBox CD-ROM 1211

Self assessment checklist Oxford GCSE Maths for OCR Foundation Integers and decimals


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. A1.1 p4–5 Understand place value and order positive numbers

A1.1 p4–5 Multiply and divide by powers of 10

A1.2 p6–7 Represent numbers as positions and transitions on a number line

A1.2 p6–7 Read measurements and information from scales, dials and timetables

A1.3 p8–9 Order temperatures and position them on a number line

A1.3 p8–9 Calculate changes in temperature

A1.4 p10–11 Order negative numbers and position them on a number line

A1.4 p10–11 Add, subtract and multiply with negative numbers

1

Advance Material • Uncorrected sample screens from the

Oxford GCSE Maths for OCR Assessment OxBox CD-ROMAdvance Material • Uncorrect sample screen Scheme of Work from the

Oxford GCSE Maths for OCR Assessment OxBox CD-ROM 1413

* By giving us your e-mail address you are agreeing to us sending you e-mails about relevant Oxford University Press products and offers. This includes the e-newsletter.

Your e-mail address won’t be passed onto third parties outside Oxford University Press.

All prices and dates are subject to change without notice. K37051

Photocopiable

Evaluation Form

Got a question?

Visit our website

Oxford University Press, Educational Supply Section, Saxon Way West, FREEPOST NH 2357, Corby, NN18 9BR, UK

Phone 01536 741068, Fax 01865 313472, [email protected], www.OxfordSecondary.co.uk

What now?It’s easy to see more Oxford GCSE Maths for OCR resources on approval/inspection.

Simply fill in the Photocopiable Evaluation Form to request the components you would like to evaluate, photocopy it, and send it back to us using the FREEPOST address provided below. To place a firm order, contact our Customer Services team on 01536 741068.

Please send me the following titles on inspection/approval:

Contact our friendly Customer Service team on 01536 741068 or e-mail [email protected] for up-to-date information or to arrange a no-obligation appointment with your local Educational Consultant.

Visit OxfordSecondary.co.uk/OCRmaths to download sample material, view OxBox screenshots and sign up to our e-newsletter which is packed full of the latest news, special offers, discounts and FREE resources.

Account number (if known)

Name

Job title

School/College

Address

Postcode

Tel

LA Date

Signature

E-mail*

Title ISBN Price Evaluate (3)

Foundation Teacher Guide 978 019 912728 3 £75.00

Higher Teacher Guide 978 019 912729 0 £75.00

Interactive OxBox CD-ROM 978 019 913932 3 £400.00 + VAT

Assessment OxBox CD-ROM 978 019 912730 6 £300.00 + VAT

Foundation Practice Book 978 019 913930 9 £6.50

Higher Practice Book 978 019 913931 6 £6.50

3 The two Oxford GCSE Maths for OCR Teacher Guides match the two Student Books, Foundation and Higher.

3 There is also a huge amount of extra teacher support material in the Oxford GCSE Maths for OCR OxBox CD-ROMs, order your evaluation copies on 30 days free approval.

3 In official partnership with OCR we offer a highly achievable route to success with OCR’s flexible new Specification A, developed with teachers for teachers.

Evaluate both of the Oxford GCSE Maths for OCR Teacher Guides

oxford gcse maths for ocr sample teacher guide material

Documents