How to use this Teacher’s Resource

This Teacher’s Resource contains both general guidance and teaching notes that help you to deliver the content in our Cambridge Secondary Mathematics resources. This Teacher’s Resource contains both general guidance and teaching notes that help you to deliver the content in our Cambridge Lower Secondary Mathematics resources. Some of the material is provided as downloadable files, available on Cambridge GO. (For more information about how to access and use your digital resource, please see inside front cover.) See the Contents page for details of all the material available to you, both in this book and through Cambridge GO.

Teaching notes

This book provides teaching notes for each unit of the Learner’s Book and Workbook. Each set of teaching notes contains the following features to help you deliver the unit. The Unit plan summarises the topics covered in the unit, including the number of learning hours recommended for the topic, an outline of the learning content and the Cambridge resources that can be used to deliver the topic.

Topic

Introduction and 1.1 Factors, multiples and primes Approximate number of learning hours

Getting Started multiples.

10–15 minutes

3

Cross-unit resources Language worksheet 1: 1.1–1.4 Diagnostic check Outline of learning content

Understand factors, multiples, prime factors, highest common factors and lowest common End of unit 1 test Resources

Learner’s Book

Learner’s Book Section 1.1

Workbook Section 1.1

Additional teaching ideas Section 1.1

The Background knowledge feature explains prior knowledge required to access the unit and gives suggestions for addressing any gaps in your learners’ prior knowledge. Learners’ prior knowledge can be informally assessed through the Getting started feature in the Learner’s Book. BACKGROUND KNOWLEDGE

Before teaching unit 1, you may want to use diagnostic check activity to assess whether the learners are ready to begin Stage 8. This diagnostic check can assist you as the teacher to identify gaps in the learner's understanding which you can use to address before teaching this unit.

The Teaching skills focus feature covers a teaching skill and suggests how to implement it in the unit. TEACHING SKILLS FOCUS

Active learning It is important learners are given the chance to explore new mathematical situations for themselves so that they can look for patterns and make conjectures.

Reflecting the Learner’s Book, each unit consists of multiple sections. A section covers a learning topic. At the start of each section, the Learning plan table includes the learning objectives, learning intentions and success criteria that are covered in the section. It can be helpful to share learning intentions and success criteria with your learners at the start of a lesson so that they can begin to take responsibility for their own learning

LEARNING PLAN

Learning objective

8Ni.03 Learning intentions

Understand factors, multiples, prime factors, highest common factors and lowest common multiples. Success criteria

Use a factor tree to write a composite number over 100 as a product of prime numbers, e.g. 135 or 280.

There are often common misconceptions associated with particular learning topics. These are listed, along with suggestions for identifying evidence of the misconceptions in your class and suggestions for how to overcome them.

Misconception Learners sometimes put ‘1’ on one of the branches of a factor tree. How to identify Give them a number and ask ‘how can we start?’ So 20 could start with 2 and 10 or 4 and 5 but not with 1 and 20. How to overcome

Emphasise that they should not see 1 on any branch. Ask ‘what would happen if we did allow 1?’ (You would split 1 as 1 and 1; then split each of those as 1 and 1; it never stops!)

For each topic, there is a selection of starter ideas, main teaching ideas and plenary ideas. You can pick out individual ideas and mix and match them depending on the needs of your class. The activities include suggestions for how they can be differentiated or used for assessment. Homework ideas are also provided.

Starter idea

Prior knowledge (10 minutes) Resources: ‘Getting started’ questions in the Learner’s Book Description: Give the learners a few minutes to try the questions.

Main teaching idea

Factor trees (30 minutes) Learning intention: Investigating the properties of factor trees. Resources: Learner’s Book Exercise 1.1, Question 1

The Language support feature contains suggestions for how to support learners with English as an additional language. The vocabulary terms and definitions from the Learner’s Book are also collected here.

The Cross-curricular links feature provides suggestions for linking to other subject areas.

Thinking and Working Mathematically skills are woven throughout the questions in the Learner’s Book and Workbook. These questions, indicated by , incorporate specific characteristics that encourage mathematical thinking. The teaching notes for each unit identify all of these questions and their characteristics. The Guidance on selected Thinking and Working Mathematically questions section then looks at one of the questions in detail and provides more guidance about developing the skill that it supports Additional teaching notes are provided for the six NRICH projects in the Learner’s Book, to help you make the most of them. LANGUAGE SUPPORT

Factor tree: a method of finding prime factors HCF: an abbreviation for highest common factor

CROSS-CURRICULAR LINKS

Many of the key words in this unit and in the Learner’s Book will be used in different types of businesses, in economics, engineering and science.

Guidance on selected Thinking and working mathematically questions

Specialising and generalising

Learner’s Book Exercise 1.4, Question 15

For part a of Question 15, learners need to do more than say ‘yes’ or ‘they are the same’. The best answer will be to write (52)3 as the product of three terms (52 ×52 × 52) giving 56 and then do something similar with (53)2 .

Digital resources to download

This Teacher’s Resource includes a range of digital materials that you can download from Cambridge GO. (For more information about how to access and use your digital resource, please see inside front cover.) This icon indicates material that is available from Cambridge GO. Helpful documents for planning include: • Letter for parents – Introducing the Cambridge Primary and Lower Secondary resources: a template letter for parents, introducing the Cambridge Primary Mathematics resources. • Lesson plan template: a Word document that you can use for planning your lessons. Examples of completed lesson plans are also provided. • Curriculum framework correlation: a table showing how the Cambridge Primary Mathematics resources map to the Cambridge Primary Mathematics curriculum framework. • Scheme of work: a suggested scheme of work that you can use to plan teaching throughout the year. Each unit includes: • Language worksheets: these worksheets provide language support and can be particularly helpful for learners with English as an additional language. Answers sheets are provided. • Resource sheets: these include templates and any other materials that support activities described in the teaching notes. • End-of-unit tests: these provide quick checks of the learner’s understanding of the concepts covered in the unit. Answers are provided. Advice on using these tests formatively is given in the

Assessment for Learning section of this Teacher's Resource. Additionally, the Teacher’s Resource includes: • Diagnostic check and answers: a test to use at the beginning of the year to discover the level that learners are working at. The results of this test can inform your planning. • Mid-year test and answers: a test to use after learners have studied half the units in the Learner’s

Book. You can use this test to check whether there are areas that you need to go over again. • End-of-year test and answers: a test to use after learners have studied all units in the Learner’s

Book. You can use this test to check whether there are areas that you need to go over again, and to help inform your planning for the next year. • Answers to Learner’s Book questions

• Answers to Workbook questions • Glossary

CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: END-OF-UNIT 1 TEST

Name ___________________________________ Date _____________

CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: END-OF-YEAR TEST MARK SCHEME Cambridge Lower Secondary Mathematics 8 – Byrd, Byrd & Pearce © Cambridge University Press 2021 1 Stage 8 End-of-year test Mark Scheme This test and its sample answers have been written by the authors. Cambridge International may award marks differently. B marks: marks awarded for answers, independent of method. M marks: marks awarded for using a correct method. A marks: marks awarded for a correct answer that must come from a correct method. Q Answer Mark Comment 1a −5 B1 1b 1 B1 1c 9 B1 1d 6 and −6 B1 2 A correct factor tree for 540 M1 22 × 33 × 5 A1 In any order. 3 y = 4x − 7 and 14 1 4 y x= + B1 Only these two chosen. 4a 4 × 2.5 = 10 and 10 × 5.8 M1 58 A1 4b 6.8 × (10 − 0.1) M1 Accept 68 − 0.68. 67.32 A1 5a 215° B1 5b 215 − 180 (= 35) M1 Accept equivalent methods. e.g. 360 − 215 = 145 and 180 − 145 (= 35). 035° A1 CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: UNIT 14 VOCABULARY Cambridge Lower Secondary Mathematics 8 – Byrd, Byrd & Pearce © Cambridge University Press 2021 1 Name ___________________________________ Date _____________ Language worksheet 1: 14.1–14.3 1 Fill in the labels on the diagrams. Use the words in the box. The first question has been done for you. column vector line segment midpoint bearing 2 Read the definitions. Put the letters in the correct order. The first question has been done for you. a tengcunor congruent synonym for identical in shape and size b snarttlea _________ transform a shape by moving each part of the shape the same distance in the same direction c jobtec _________ a shape before a transformation d megia _________ a shape after a transformation award marks differently. marks: marks awarded for answers, independent of me marks: marks awarded for using a correct method. marks: marks awarded for a correct answer that must A correct factor tree for 540 4 1 Name ___________________________________ Date _: 14.1 Cambridge Lower Secondary Mathematics 8 – Byrd, Byrd & Pearce © Cambridge University Press 2021 1 Stage 8 End-of-Unit 1 Test This test and its sample answers have been written by the authors. Cambridge International may award marks differently. 1 Work out a −3 × −5 ____________________________________________________________________________ [1] b −32 ÷ 4 ____________________________________________________________________________ [1] c −2 × (1 + −8) ____________________________________________________________________________ [1] 2 a Find the highest common factor of 24 and 32. __________________________________ [1] b Find the lowest common multiple of 6 and 9. __________________________________ [1] 3 Find the prime factors of 44. ___________________________________________________ [1] 4 a Using a tree diagram, or otherwise, write 200 as a product of prime factors. ____________________________________________________________________________ [2] ____________________________________________________________________________ _________________________ ________________________________ ____________________________ _______________________________ a product of prime factors. Cambridge Lower Secondary Mathematics 8 – Byrd, Byr Fill in the labels on the diagrams. Use the words i The first question has been done for you. column vector line segment midpoint Read the definitions. Put the letters in the correc synonym for identical in shape and size snarttlea _________ transform a shape by moving eac distance in the same direction jobtec _________ a shape before a transformation megia _________ a shape after a transformation CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: END-OF-YEAR TEST Cambridge Lower Secondary Mathematics 8 – Byrd, Byrd & Pearce © Cambridge University Press 2021 4 11 The probability of a coloured spinner landing on red is 2 5 . Work out the probability of the spinner not landing on red. ____________________________________________________________________________ ____________________________________________________________________________ [2] 12 a Complete the table of values for y = 3x − 5. x −1 0 1 2 3 y [2] b On the coordinate grid, draw the graph of y = 3x − 5 for 1 3 x − ≤ ≤ . [2] c If the line y = 3x − 5 is continued, would the point (12, 30) lie on the line? Tick the correct box. Yes No Show your working. _________________________________________________________________________ _________________________________________________________________________ [2] Cambridge Lower Secondary Mathematics 8 – Byrd, Byrd & Pearce © Cambridge University Press 2021 In any order. B1 Only these two chosen. M1 A1 M1 Accept 68 − 0.68. A1 B1 M1 180 − 145 (= 35). A1 _________________________ [2] [2] x − ≤ ≤ − 5 is continued, would the point (12, 30) lie on the line? Tick the correct box. Yes No _________________________________________________________________________ _________________________________________________________________________ CAMBRIDGE LOWER SECONDARY MATHEMATICS 8: END-OF-YEAR TEST 8 The diagram shows points A and M on a coordinate grid. a Write down the vector that translates point A to point M.           [1] b M is the midpoint of the line segment AB. Work out the coordinates of point B. B(___, ___) _________________________________________________________________________ _________________________________________________________________________ [2] 9 A rectangle has a length of 3x cm and a width of x + 2 cm. a Write an expression, using brackets, for the area of the rectangle. _________________________________________________________________________ [1] b Expand the brackets in your expression in part a. _________________________________________________________________________ [1] c When x = 7, work out the area of the rectangle. _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ [2] 10 Insert the correct symbol, < or >, between each pair of fractions. a 7 7 34 33 b 11 13 27 27

Cambridge Lower Secondary Mathematics 8 – Byrd, Byrd & Pearce © Cambridge University Press 2021 [2]

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