Matched To The Pearson Edexcel ILowerSecondary Award And The UK .

A closer look at theStudent BookWhere students arehelped to masterfundamental knowledgeand skills over a seriesof lessons.A short formativeassessment wherestudents can checktheir understanding.Formative assessmentQuestions check onstudents’ progress andlearning and providea route to furtherguidance or extension.Provide guidancearound examples ofkey concepts withbar models, and otherpictorial representationswhere needed.Key pointsCheckMaster P54Explain key conceptsand definitions wherestudents need them.Strengthen P67Extend P71Test P75Writing expressions and formulae3 Check upLog how you did on yourStudent Progression Chart.14 Jack is paid 5 for each hour he babysits.Write a formula that connects the total amount he is paid, T, and thenumber of hours he babysits, x.Simplifying expressions4 Copy and complete these addition pyramids. Each brick is the sum ofthe two bricks below.aMasterCheck P65Strengthen P67Extend P71Key point2aExploreWhy do we ‘simplify’ in algebra?4y 1 72 2 2 23In the same way, you can writeb b b b3Q6 hintThink of a rod that is x cm long.a 2x2 3x2 u x2b 4a 2b2 3b2c 2b2 3b b2d 5x 2x2 7xe 8x4 x4f 12x2 3x3 – 2x37 Simplifya a bLike terms must have exactly thesame letters and powers. E.g 2x2and 3x3 are not like terms as thepowers of x are different.An algebraic expressione.g. 3x 2y, contains numbers andletters.Each part of an algebraic expressionis called a term.d m 2e x 5f q 7 pQ7a hintp q is written as pqSo x x x 3x8b48bmeans 8b 4. Work out 8 4.48 Simplifya 2b 5bdKey pointb 9a 3a12b4ec 3a 2a 3a9a2f36b129 Match the equivalent expressions.Like terms contain the same letter(or do not contain a letter).You simplify an expression bycollecting like terms.2xx x4x – 3x4x2x 2xQ3e hint9x 7 x uUnit 3 Equations, functions and formulae5430/09/2019 16:28a35 Expanda x(x 3) values.1 This is an addition pyramid. Work outthe missingd 2x(3x 1)Investigation5a 1 4bx x3x7xx3x 4xx22x 2x9x3b b(b 2)e 4t(10 2t)c 5(11 x)15 Write an algebraic expression fora a more than bb 3 more than a, multiplied by bc a multiplied by itselfd b divided by 5.Keypointc 10c 5cThe identity symbol (;) showsthat two expressions are alwaysequivalent.3 t at 2b ; 2b a.Forc example,Q11 hintc 2 x 2x 518 A square has sides a cm long.Write a formula for finding the area of the square, A, using the length ofthe side, a.Problem-solving19 How sure are you of your answers? Were you mostlyJust guessing6 aArea of rectangle length widthWorkthethisareaof a pyramid?rectangle with width 12 cm and length 7 cm.2 How many different possibilities canyou outfind foraddition5a 1 4b7 T 5BaaConfidentChallenge20 A pattern is made of squares and rectangles.Pattern 1abWorkout differentthe densityof a blockwithmass 20 kg and volume 4 m3.3 This is a multiplication pyramid. Howmanypossibilitiescan youfind?9 The approximate perimeter, P, of a semicircle can be3acalculated using the formula P a 2Work out the approximate perimeter when a 4 cm.aaWhat next? Use your results to decide whether to strengthen orextend your learning.What is the value of T when B 12?mass8 Density , where mass is in kg, volume is in m3 and density isvolumein kg/m3.3a 1 2bFeeling doubtfulaa17 A class has 30 students. A teacher buys sweets to share between them.Write a formula that connects the number of sweets each studentreceives, S, and the number of sweets the teacher buys, p.Test with some numerical values fora and b. 22c a(10 a)a16 A regular pentagon has 5 sides of equal length.Write a formula that connects the perimeter, P, to the length of one ofthe sides, a.f 7t 2tSubstitution3a 1 2b2aThe order of multiplication does not matter.8b 2b4When you put three rods together the total length is 3x cm.x3 5Simplifya4aaaa y y yb x x11 In between which pairs of expressionsd 2 r rcan ryou 5writee ;?5r ra a bub a12yg y 7hb a bub a6c ab u ba4 Simplifyd a bub aa x2 3x2b x x2 x28a23b 2b 3 b 2 b 3 2 b b 6b2b3 Simplify by collecting like terms.a 2x 4x 2 6x ub 2b 6c 3cc 6y 2y 8 3bd 4y 2 3ye 9x 3 3y 7xf 9a 7b 2a 5Discussion Are the two expressions 3x 2y and 2y 3x equivalent?Write letters in alphabetical order.Write numbers before letters.a 2 2 a 2ab t t bc p p p y ySimplifya 3b 2bx2 Simplifya n nb y y y y yc 2a 3ad 5b 6be 5a 3af 8b 3bg 7y 2y 3yDiscussion Why is x x x x the same as 4x?Key pointWorked exampleWarm upKey pointSimplify x x xM03 Equations, Functions and Formula v4.indd 54106 Simplifyb 2 2 2Topic links: Order of operations, Indices2x 1 322xc m m m mFluencyWrite these additions asmultiplications: 5 5 5 9 9 9 9 9 10 10 18 18 18 18 18Worked example3x7b t t tExercise 3.1x3x5xa b b Simplify expressions by collecting like terms.xa3b5 SimplifyYou will learn to:1 Write using index notation.a 3 3 3 3c 5 5 5 5 5 5cTest P753.1 Simplifying algebraic expressionsWhy learn this?Algebra is a language that people in everycountry in the world can understand. It doesn’tneed to be translated into Japanese, Spanishor any other language.b1 Expanda 3(x 4)b 2(a w)10 Copy and complete these multiplication pyramids.Each brick is the product oftwo bricks below.2 theSimplifya x xabc b 4x 7xd 4t te 7x 2b 5xPattern 2Pattern 3aa10 Use the formula b 10t – c to work out the value of b whena t 3, c 512 Explore Why do we ‘simplify’bint algebra? 1, c 7Is it easier to explore this questionc t now4, c that 2you have completed thelesson?d t 3, c 4What further information do you need to be able to answer this?11 Work out the value of the expression ab 2c when a 2, b 5, c 9.13 Reflect In algebra, letters are used to represent values we do not12theWhattheyouvalueof donex2 whenx 7?know. This lesson may befirst istimehavealgebra.Choose A, B or C to complete each statement.In this lesson, I did.A wellB okC not very wellSo far, I think algebra is.A easyB okC difficultWhen I think about65 the next lesson,I feel.A confident B okC unsureIf you answeredmostly As and Bs, did your experience surpriseM03 Equations, Functions and Formula v4.indd 65-66you? Why?If you answered mostly Cs, then look back at the questions youfound most difficult. Ask a friend or your teacher to explain them toyou. Then answer the statements above again.ExploreEquations, functions and formulaeWrite and simplify an algebraic expression for the area ofa Pattern 1b Pattern 2c Pattern 3d Pattern 10e Pattern n.21 Find a value of x so thata x2 is equal to 2xb x2 is equal to x3.22 a b 2 and a – b 6.a and b are whole numbers. What are the values of a and b?Reflect313 Mia has x stamps. Write expressions for the number of stamps eachperson has.a Carl has 7 fewer than Mia.b Onick has 12 times as many as Mia.c Mehmet has half as many as Mia.ReflectOutlines lesson objectivesand the fundamentalknowledge and skills thatstudents will master toboost confidence.ConfidenceCheckWorked examplesLesson opener8MasterUnit 3 Equations, functions and formulae6630/09/2019 16:28Reflect22x55Year 7, Section 3.1M03 Equations, Functions and Formula v4.indd 55-56Unit 3 Equations, functions and formulae5630/09/2019 16:28Warm upHints and tipsLessons begin with accessiblequestions designed to recap priorknowledge, and develop students’mathematical fluency in the factsand skills they will soon be using.Guide students to helpbuild problem-solvingstrategies throughoutthe course.Enables students to understand theirown confidence levels with a topic sothey can make the decision whetherto ‘strengthen’ or ‘extend’ knowledge.9

StrengthenA closer look at theStudent BookWhere students who areyet to develop a solidunderstanding and/ordon’t feel confident,can strengthentheir learning.Problem-solvingReal life mathsexamples putlearning into context.Clearly signposted questionsenable students to recognise thatthey need to try different strategies.Master P54Check P65ExtendStrengthen P67Visual remindersSupport students withscaffolded guidancewhere they need it most.Support learning andprovide a different wayof looking at a problem.5 A triangle has side length n cm.The second side is 5 less than double this length.The third side is twice the length of the second side.Write an expression for the perimeter of the triangle. Simplify yourexpression as much as possible.3 ExtendYou will:StrengthenCheck P65 Strengthen your understanding with practice.Simplifying expressionsQ1 hintDraw bars to help.pppttt3t10y2yQ2i hint4242224iv a3e a3a3a3a3a3av a5a 2w 3w 08 Simplify these. Which is the ‘odd one out’?d n 29 Copy and complete.Q9a hintx67M03 Equations, Functions and Formula v4.indd 67-68c1bc2a1bc1a2b2b 1 a2b2bb222b1 a10 This is part of a spreadsheet a shop usesto calculate wages.c1a1bc1acc–aa2b2a2b1Aa What value will be calculated in cell D2?2 Mrs Badri3 Mr Guptab What expressions should be written in4 Mrs Alamcells D3 and D4 to calculate the wages5of Mr Gupta and Mrs Alam?6c The value in cell B4 is changed to 19. What value will show in cell D4?d The expression in C5 calculates the meannumber of hours worked.What is this value?e What does the expression in cell B5 calculate?y-coordinate13BPay per hour8715 (B2 B3 B4)/3CDNumber of hours Pay25 B2 * C21715 (C2 C3 C4)/3Key pointIn spreadsheets * is used insteadof .Unit 3 Equations, functions and formulae71b b( b 2) m(m 1 1)c d(3 d) m31M03 Equations, Functions and Formula v4.indd 71-727230/09/2019 16:28d r(r 1) Q9d hintCheck P65Master P54Strengthen P67Extend P713 Unit testiii m m m22211 Simplify by collecting like terms.x13333a t2 t2 3t ut2 ub p3 p pc 3x x2 2xTestDraw the arrows.ii x3 x3xx54m3ma m(m 1) 10 a Complete the pattern.t t 2tt2 t2 2t2t3 t3 2t3t4 t4 ub Simplify by collecting like terms.i p2 p24Q4a hint3b–aWork out several pairs of coordinates and plot them on a coordinategrid. Join them with a line. What do you notice? Design your ownfunction machine and generate coordinates. Plot them and join themwith a line. What do you notice?1 To convert between hours and minutes use the formulaminutes number of hours 60Work out the number of minutes in 7 hours.iv 2x2 3x2x13Q4 hintStart with x 0.13e 9n 11n 99 When a 2 and b 4 all but one of these expressions have thesame value.Which is the ‘odd one out’?y-coordinatex-coordinate8c–b4 Problem-solving Jasmin is working out coordinates using a rule.She takes the x-coordinate and puts it into the function machine toget a y-coordinate:x-coordinate7f t(10 t) 44 Copy and complete.a 2(x 3) u x ub 3(x 4) (x 4) (x 4) (x 4) u uc 4(b 2)d 5(t 3) u t u 3 ut ue 3(6 a)f 2(r 3) u r u 3g 6(10 b)xc2a2bb Company 2 uses the formula C 0.1M 0.01T.Work out the bill for each of the customers if they used this company.c Which company should each customer use?7 Copy and complete.6e m(m 3) 43 4 iii a2d a3a3a3a31b Write the algebraic expressions in the magic square so that all therows, columns and diagonals sum to 3c.c 2 n3yNumbers, e.g. 7, can only be addedto other numbers. 3 2c a3a3a3a3aHow many times is a multiplied byitself?b n nAdd the y terms first.Q3 hintii a6a n nQ2e hint3 (2 4)i a4b a3ad 8m 3m t2t3 Expand 3(2 4)a a3a3ac 3b 5b tt2a Work out the cost of bills for each of these customers.Customer A: 10 minutes of calls, 1000 textsCustomer B: 300 minutes of calls, 20 textsCustomer C: 1000 minutes of callsQ6 hintQ7 hintCall the unknown number ‘x’ andconstruct an algebraic expression.8 In a magic square the diagonals, rows and columns all sum to thesame total.a Write the numbers 1–9 in the magic square (using each numberonly once) so that all the diagonals, rows and columns sum to 15.Three numbers have been written for you.3 Finance Company 1 uses the formula C 0.05M 0.02T for calculatingthe cost of a mobile phone bill, where M number of minutes of calls,T is the number of texts and C is in dollars.b 4a 2a Q2a hint2 Simplifya 2t 3tb 5g 7gc 10y 3yd 5p pe 10y 2b 3yf 6m n 5mg 4a 3b ah 3q 2b 3bi 4t 7 2tj 4y 8 2 3y210 cm6 Match each expression on a blue card to one on a yellow card.1 Copy and complete.a p p p upb m m m m umc d dd t t t t t7 A magician uses this number trick: Think of a number. Add 3.Multiply it by 2. Subtract double the number you first thought of.The number you have is 6.Explain the trick.2 A cube has edges of length 10 cm.5 Write the missing numbers.a 6 6 6 6ub 5 5 5 5 5uc 11 11 11uYou will:a1bba Work out the area of one of the square faces.b The cube is painted. Work out the total area that is painted.Another cube has edges of length x.c Write an algebraic expression for the area of one of the faces.d Write an algebraic expression for the total area of all the faces.3 Strengthen4a 1 4b3a 1 b1 A square has sides of length x. Write and simplify an expression for itsa perimeterb areaTest P75Extend P716 In the pyramid, each brickis the sum of the two bricks below.Work out the missing expressions.Q5 hintSketch and label the triangle.Q11 hint2 The formula for calculating the perimeter of a shape, P, is P 2a 3b.Work out the value of P when a 5 and b 7.You can only add terms with thesame letters and powers.cfor converting centimetres, c, to metres, m.100Work out the value of m when c 325.3 Use the formula m Unit 3 Equations, functions and formulae68n(n 3)4 Use the formula D to work out the value of D when n 4.230/09/2019 16:285 Expanda 3(x 4)b 5(x 7)c 7(10 x)6 Write an expression fora 2 less than yb 5 times mc y divided by 10d x more than y.7 Angela is paid 10 more than Imogen.Write a formula connecting the amount Angela is paid, A, and the amountImogen is paid, I.8 Write an expression fora b multiplied by itselfb double bc a divided by b.9 Work out the value of these expressions when p 3, q 6.a 2(p 3)b 5(2p q)10 Simplify by collecting like terms.a x 2xb 6x 2y – 3xLog how you did on yourStudent Progression Chart.11 When a 5, b 11 and c 9 work out the value ofa 4a 2cb 20 3ac 10c 2b a12 Use the formula z 2m a to work out the value of z whena m 3, a 5b m 1, a 7Unit test13 Simplifya r r r r rb 2 y 7 y yc 3y yd 3m 5me 18x 314 Simplify by collecting like terms.a 3r3 10r3b 12x 3x2 – 5x15 Expanda x(x 7)b r(r 5)c 2b(b 5)d 3b(2b 4)Monitoring progress16 Find the value of each expression when b 2 and m 9.a b3b b2 mb 2mc2d m2 b2e 3(m b)Provides a quick assessmentthat covers everything learnedin the unit, making it easyto see where students areChallengeprogressingor where additional17 Are there any values of x that make these pairs of expressionsequal?a 2x and 2xsupport might be needed.b 6x 3 and 3x 623x2xandc23d 2(3x 5) and 2(3x 5)18 Reflect Look back at the work you have done in this unit. Find a questionthat you could not answer immediately, but that you worked hard at, and thenanswered correctly.How do you feel when you find it difficult to answer a maths question?Write down the strategies you use to help you when you have difficulty.How do you feel when you eventually understand and get the correct answer?ReflectMaster P54Where students whohave performed wellin the ‘Check up’ andfeel confident canbuild on and deepentheir mathematicalunderstanding.Test P75 Extend your understanding with problem-solving.HintsExtendFinancec 10 12y 7 14y7510M03 Equations, Functions and Formula v4.indd 75-76Unit 3 Equations, functions and formulae7630/09/2019 16:2811

A focus on STEMA closer look at the WorkbookSTEM lessons focus on key science, technology, engineering andmaths skills to give students the aspiration, knowledge and skills tothrive and succeed into STEM-related careers.The write-in student workbooks offer extra practice of key content along withstudent support, confidence checkers and progression charts, giving students thechance to reflect on their progress and take ownership of their work.Check P65Strengthen P67Extend P712.1Test P756 t represents a number. Write and simplify an expression fora 2 more than triple the numberb 5 less than double the numberc 4 more than double the numberd the number added to itselfe the number subtract 5f the number multiplied by itselfg the number divided by 3h 3 divided by the number.3.2 Writing algebraic expressionsYou will learn to: Write expressions using four operations.‘Triple’ means 3.1Why learn this?Computers are programmed using a computeralgebra system (CAS).a InputmOutput32ExploreThink of a number. Double it. Add 10. Divide by 2.Subtract your original number. Try this with differentnumbers. What answer do you get? Why?bm is multiplied by 2 then 3 is added.InputxOutput2243x 23To show that the whole expression isdivided by 3 draw a long division line.2 Simplifya y yd 4b 2bb 3x – 4x 2x2b b b b16ce 4c 3x 5 2x 4i 12 1 12 12, 2 6 12, 3 4 12. Factors are 1, 2, 3, 4, 6, 12ii 18 1 18, 2 iii 25A prime factor is a factorof a number that is also aprime number.i 2, 3ii7 Write an expression for the output of each function machine.Q3a hintc 4 2nb 1b4 Haruto is m years old. Write expressions for the ages of each of thesepeople.a Laila is 4 times as old as Haruto.b Maggie is 5 years older than Haruto.b4413c3535dbbbbbb123Problem-solving Simon finds all the factors of a number. This is his list.1, 2, 3, 4,,, 8, 10, 12,,, 20, 24,,, 48,, 80, 120, 240What are the missing numbers?4d What is the highest common factor (HCF) of 6 and 15?8 A rectangle has width b. The length is 5 more than the height.Q5a hintTry it with numbers. How would youwrite 5 more than 3?QR codes give studentsdirect access to workedexample videos on theirphones or tabletsproviding crucial supportfor tricky questions.Workedexamplee Find the HCF of each of these pairs of numbers.i 8 and 20bii 9 and 27a Write an expression for the length.b Write and simplify an expression for the perimeter.c Calculate the perimeter of the rectangle when b 10 cm.9 Explore Think of a number. Double it. Add 10. Halve it. Take away youroriginal number. Try this with different numbers. What answer do you get?Why?Is it easier to explore this question now that you have completed thelesson?What further information do you need to be able to answer this?5Year 7, Section 3.2M03 Equations, Functions and Formula v4.indd 57-58c Write down the common multiples of 4 and 8 that are in both lists.Check2Worked examplesSTEM questionshighlight importantlinks to using science inreal life.Provide guidance around examplesof key concepts with images,bar models, and other pictorialrepresentations where needed.STEM The diagram shows two cogs.The larger cog has 10 teeth and the smaller cog has 6 teeth.The cogs start to turn with the black dots next to each other.What is the smallest number of turns each cog must makebefore the black dots are next to each other again?5830/09/2019 16:28STEMThe lowest commonmultiple (LCM) of twonumbers is the smallestnumber that is a multipleof both numbers.d What is the lowest common multiple (LCM) of 4 and 8?6Unit 3 Equations, functions and formulaea List the first 8 multiples of 4.b List the first 8 multiples of 8.10 Reflect This lesson suggested bar modelling and function machines tohelp you with writing expressions. Did they help you? How?Did you use any other methods? Explain the method(s) you used.Topic links: Order of operations, GraphsQR codesThe highest common factor (HCF)of two numbers is the largestnumber.a Write down all the factors of 6.c Write down all the factors of 15.45Q3e hintFinding half is the same as dividingby 2.f Ruth is 3 years younger than 5 times Haruto’s age.x multiplied by yx more than 2 times yy multiplied by itself7 less than y multiplied by itself2 more than 20 divided by x.217b Write down all the factors of 15.e Rashid is 5 years older than twice Haruto’s age.bdfhj332d Iman is half the age of Haruto.5 Write an algebraic expression fora y more than xc y less than xe 3 times y add 4 times xg 4 times x multiplied by itselfi x divided by yaQ3d hintc Ami is 6 years younger than Haruto.12a Write down all the factors ofiii23 John collects coins. He has b coins. Write an expression for how manyhe has when there area 2 moreb 4 fewerc 17 mored 5 times as manye half as many.572b Write down all of the prime factors of each number in part a.ExploreWarm upExercise 3.21 Simplifya 2x 3x 5xGuided questionswith partially workedsolutions help studentsstructure their answers.13m 2 3 2m 3A prime number has exactlytwo factors: 1 and itself.Circle the prime numbers.ReflectConfidenceWrite an expression for each function machine.Here is a list of numbers.1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14,15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25GuidedWorked exampleFluencyWork out: 32 53 14Factors, primes and multiplesMasterQ6a Literacy hintGuidedMasterTick each box as yourconfidence in thistopic improves.International Maths Practice Book Colour V5 spreads.indd 2Need extra help? Go to page 18 and tickthe boxes next to Q1–3. Then have a go atthem once you’ve finished 2.1–2.6.8/29/19 11:22 AM13

Progression to International GCSEMaths Progress International offers a seamlesstransition for progression into Pearson EdexcelInternational GCSE Mathematics (9-1) and beyond.TeachingResourcesInteractive front-of-classteaching resources thatboost engagement andinspire students.AssessmentTrack students’ progressfrom 11–16. It will saveyou time and give youconfidence in your datato plan appropriateintervention.PlanningComplete support forplanning and teachingwith detailed teachingnotes, planning guidesand lesson ideas.Find out son Edexcel International GCSE (9–1)qualifications are comparable to the UKGCSE, with appropriate international contentand assessment that will enable successfulprogression for learners.We have a range of resources available to helpyou prepare your students for success in PearsonEdexcel’s world class qualifications.Student ResourcesHundreds of auto-markedactivities for students touse in lessons or athome to build ontheir learning andpractice.Maths Progress International is also fully matched to the Pearson Edexcel iLowerSecondary award, part of the iProgress family. From Primary through to Secondary,iProgress delivers a consistent and high-quality educational experience for students aged5 to 19, by providing globally recognised qualifications and curriculum-matched resourcesat each school stage.Based on the UK curriculum but designed with a global outlook, iProgress is a learningjourney for your students from Pearson Edexcel, and includes iPrimary, iLowerSecondary,International GCSE (IG) and International A Level (IAL).1415

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Edexcel iLowerSecondary Award and the UK National Curriculum. That's why the Maths Progress programme was, and is, specifically founded on key . This course is built around a pedagogy based on leading mathematics educational research and best practice from teachers in the UK. The result is an innovative learning structure