Unlock GCSE Maths
Secure your students’ mathematical knowledge with fully-updated and revised textbooks
Collins GCSE Maths 5th Edition
Refreshed and updated for today’s students, drawing on 25 years of knowledge and expertise. The programme maximises and secures knowledge needed for success in GCSE maths with high-quality practice and carefully refined pacing to support students’ progress.
Student Books
l Contextualise learning and promote career opportunities with features written and reviewed by the WISE (Women into Science and Engineering) Young Professionals’ Board
l Enhance exam preparation with new exam practice questions and worked exemplars to reflect the recent GCSE maths exams
l Help all students reach their potential with content reviewed and adjusted for greater accessibility as well as challenging content for Higher students
l Strengthen knowledge and deepen understanding with high-quality explanations and hundreds of worked examples
l Foster independence and self-reflection with answers at the back
l Practise reasoning, explaining and problem-solving using the facts and methods they have been taught
Statistics: Statistical diagrams and averages 3
This chapter is going to show you:
• how to draw and interpret pie charts
• how to draw and interpret line graphs
• how to solve problems that use averages
• how to calculate averages from frequency tables
• how to draw scatter diagrams and lines of best fit.
You should already know:
• how to calculate and use the mode, median and mean
• how to extract information from tables and diagrams.
Context and careers
A pioneer of presenting information visually was Florence Nightingale (1820–1910), who was very good at mathematics from an early age. In 1859, she was elected the first female member of the Royal Statistical Society. Florence developed a form of the pie chart, now known as the ‘Polar Area Diagram’ or the ‘Nightingale Rose Diagram’, which illustrated monthly patient deaths in military field hospitals. She called these diagrams ‘coxcombs’ and used them to present reports on the conditions of medical care in the Crimean War to Parliament and to civil servants who may not have fully understood traditional statistical reports.
Careers that use this maths
• Stockbrokers use line graphs to see patterns that help to reveal information about when or where to invest a client’s money.
• Market researchers use scatter diagrams to see the relationship between advertising methods and sales.
• Epidemiologists use statistical diagrams and averages to determine which groups of people may be at high risk of health issues.
3.1 Statistical representation
This section will show you how to:
• draw and interpret bar charts and pie charts
• draw and interpret line graphs.
Bar charts and pie charts
You are already familiar with bar charts in which the vertical axis represents frequency and the horizontal axis represents categorical data – the data you are considering.
The frequency table shows the average monthly rainfall over a six-month period.
The diagrams below show three different ways the data can be represented.
As a pictogram: As a bar chart:
You should also be able to recognise and use multiple or dual bar charts and composite bar charts, which can be used to compare two sets of related data as shown in the next example.
Teacher Packs
l Carefully structured lessons and thorough explanations of the mathematical facts, concepts, methods and strategies to ensure a smooth transition from KS3 to GCSE
l Save time and use the detailed, practical schemes of work to prepare and plan your lessons
l Extra support on more challenging topics
l Tackle common misconceptions head on and help students to make mathematical connections
Refreshed worked exemplars at the end of each chapter
Worked exemplars
1
a
320
b
b
New exam-style questions at the end of each chapter
Ready to progress?
I can draw and interpret pie charts.
I can draw and interpret line graphs.
I can calculate the mode, median, mean and range and decide which average to use.
I can calculate the mean from a frequency table.
I can estimate the mean from a grouped frequency table.
I can draw and interpret a scatter diagram.
I can draw a line of best fit on a scatter diagram.
Review questions
1 The pie chart gives information about the mathematics examination GCSE grades of some students.
Mathematics examination grades
a What grade was the mode?
b What fraction of the students obtained a grade 8?
24 of the students got grade 9.
i How many of the students got grade 6?
ii How many of the students took the examination?
This accurate pie chart gives information about the English examination grades for a different set of students.
English examination grades Grade 9
6
Measure the angle with a protractor.
= 360 ÷ 5 Use the value of 320 given in the question.
Lizzy says: “More students got a grade 8 in English than in mathematics.”
Explain why Lizzy could be wrong.
Support for GCSE Maths
Practice Books for fluency
l Designed to support students in achieving Assessment Objective AO1 – using and applying standard techniques
l Build students’ confidence with hundreds of differentiated practice questions
l Easily identify topics for further practice, intervention, prior knowledge recall and revision and retrieval
l Challenge your most able students with plenty of ambitious questions
l Ideal for use both in the classroom or as a homework resource
Skills Books for reasoning and problem solving
l Designed to support students in achieving Assessment Objectives AO2 and AO3: reason, interpret and communicate mathematically; and solve problems
l Improve literacy, thinking skills and investigative strategies by providing opportunities for students to tackle problems within and outside mathematics
l Build confidence in tackling longer questions in class and provide further practice at home
l Encourage students to think and analyse their work with questions designed to encourage independence
Workbooks
Write-in workbooks with plenty of additional practice to support students to reach their full potential.
l Ideal for both classroom and home learning
l Targeted practice at exactly the right level to help every student with recovery
l Designed to build skills and boost confidence with lots of exam-style questions
Digital support available
l Unlimited access for teachers and students to the full Student Book
l Prior knowledge quizzes for each chapter
l Additional retrieval quizzes
l Worked solution videos for exam-style questions
l Easy to use for front-of-class teaching or access at home on computers, tablets and smartphones
Talk to your local rep for a free demo, pricing information or any further questions.
25 years of Collins GCSE Maths
Celebrating 25 years in print, the fifth edition of this classic and beloved GCSE Maths textbook has been updated for today’s students.
First published in 1997, the Collins GCSE Maths programme have been tested in classrooms across the UK and carefully refined over time by a highly experienced team of expert authors: Kevin Evans, Keith Gordon, Trevor Senior, Brian Speed and Michael Kent.
Meet the 5th edition author team
Kath Hipkiss is currently a Trust Lead for maths with over 22 years’ teaching experience as a Head of Department, AST and Lead Practitioner. She has worked as an ELE with a keen interest in metacognition. In addition to this, she has been a GCSE and A level examiner for 15 years with multiple exam boards and has authored a number of books and teacher guides.
Michael Kent has 30 years’ experience teaching secondary maths, 12 of them also leading a successful department. He co-authored the most recent editions of Collins GCSE Maths Student Books.
Anne Stothers MBA is a secondary maths consultant with over 30 years’ teaching and leadership experience. She is an examiner for multiple exam boards and a conference speaker. She has authored books and created video content for several organisations and she specialises in CPD creation and delivery.
Chris Pearce has an MA in maths and over 30 years’ teaching experience at secondary level from KS3 to A level. Previously an education advisor and examiner, he is now a full-time author and has written many bestselling KS3 and KS4 materials for Collins.
Working with WISE
WISE (Women into Science and Engineering) are leaders in creating positive cultural change in the STEM industry, driving gender equality and diversity. We have worked with the WISE Young Professionals’ Board to feature a broad range of inspiring and real-life careers in the unit openers. Find out more about WISE wisecampaign.org.uk and try their My Skills My Life quiz with your class.
NEW AQA GCSE Maths
Foundation Student Book, 5th edition
978-0-00-864733-9 £22.99
NEW AQA GCSE Maths
Higher Student Book, 5th edition 978-0-00-864732-2 £22.99
Foundation Teacher Pack
Higher Teacher Pack
Foundation Student Book, 1 year Collins Hub subscription
Foundation Student Book, Homework and Tests, 3 year Collins Hub subscription
Higher Student Book, 1 year Collins Hub subscription
Higher Student Book, 3 year Collins Hub subscription
978-0-00-811392-6 £115.00
978-0-00-811391-9 £115.00
Grade 5–7 Workbook
Achieve Grade 7–9 Workbook
978-0-00-871062-0 £700.00 +VAT
978-0-00-871047-7 £250.00 +VAT
978-0-00-871048-4 £700.00 +VAT
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