Maths Workout - Algebra & Problem Solving

© Smart Interactive Ltd.87

Algebra & Problem Solving Topics

Topic Target 1 Target 2 Target 3 Target 4 Target 5

1 Writing Algebra 1Multiply a constant by avariable and a variable by avariable, e.g. 4xb=4b,3x4b=12b

Multiply 2 terms, e.g.3ax4b=12ba, c x c=c2

Express an addition orsubtraction phrase with asingle variable as anexpression

Express a multiplication ordivision phrase with asingle variable as anexpression

Express a single stagephrase with up to 2variables as an expression

2 Writing Algebra 2Express a 2-stage phrasewith a single variable as anexpression: multiply, addand subtract

Express a 2-stage phrasewith a single variable as anexpression: divide, add andsubtract

Express a 2-stage phrasewith 2 variables as anexpression

Express a 2-stage phrasewith up to 2 variables as anexpression (using brackets)

Express a 2-stage phrasewith up to 2 variables as anexpression (using algebraicbrackets and fractions)

3 Like Terms

Simplify an expression ofup to 3 single variableterms by collecting liketerms (positive answers)

Add and subtract integers:Revision prior to adding andsubtracting terms

Simplify an expression ofup to 3 single variableterms by collecting liketerms (pos and neganswers)

Simplify an expression ofup to 4 double variableterms by collecting liketerms

Simplify an expression ofup to 6 double variableterms by collecting liketerms

4 Expanding BracketsExpand brackets of theform 2(a+3), 3(2t-3):single variable

Expand brackets of theform 4a(2b-2), a(3a+2): upto 2 variables

Expand brackets of theform -(y–4),-4a(3b+2): upto 2 variables

Expand brackets of theform 4a(b-c), -3b(a+b-c):up to 4 variables

Expand brackets andsimplify an expression ofthe form 3(7x+2)+3x,-3a(7a+2)-3a(a+2)

5 Factorising

Identify the HCF of 2 or 3numbers

Identify the HCF of up to 3algebraic terms

Factorise an expression ofthe form 3t+6, 9ab-3b

Factorise an expression ofthe form ab2+6b, 3cd2–12dFactorise an expression ofthe form 15a2-3ac+9ab

Simplify an algebraicfraction by factorisation

6 Solving Equations 1Solve a simple equation byinspection: x+4=12, 2x=4,x/2=5

Complete the solution to asimple equation:2x+3x=10, 2x+1=7,x/2+3=5

Complete the solution to asimple equation:3(x+4)=15, 3(x+1)=x-8,3(x+1)=3(x-8)

Solve a simple equation ofthe form 2x+3x=10,2x+1=7

Solve a simple equation ofthe form x/2+3=5,3(x+4)=15, 3(x+1)=x-8,3(x+1)=-3(x-8)

7 Algebraic ModellingUse algebraic modelling tosolve a single-stageproblem

Use algebraic modelling tosolve a 2-stage problem

Use algebraic modelling tosolve a 2-stage problem

Use algebraic modelling tosolve a 3-stage problemincluding the use ofbrackets

Use algebraic modelling tosolve a 3-stage problemincluding the use ofbrackets

8 Substitution

Revise the order ofoperations

Find the value of anexpression by substitution;non-negative values

Find the value of anexpression by substitution;non-negative values

Find the value of anexpression by substitution;some negative values

Find the value of anexpression by substitution;extension

9 Formulae

Substitute into formulae;convert between Fahrenheitand Celsius; recognisecommon formulae

Use a formula in reversegiven the subject

Use a formula in reversegiven the subject

Solve a problem using aformula

Solve a problem using aformula

Construct a formula fromgiven information

10 Problem Solving TheoryIdentify the features of aproblem versus astraightforward question

Identify the abilities andqualities required to solve aproblem

Understand the 4-stageproblem solving process

Be aware of some usefulproblem solving strategies

Maths Workout - Algebra & Problem Solving

© Smart Interactive Ltd.88

Algebra & Problem Solving Topics

Topic Target 1 Target 2 Target 3 Target 4 Target 5

11 Spotting PatternsCopy a shape pattern Complete missing elements

in a pattern or sequence ofobjects

Extend a sequence ofshapes and extractinformation to form asimple number sequence

Extend a sequence ofshapes or a line pattern

Extend a sequence ofshapes

12 Problems & Puzzles 1Solve a space-fillingproblem: Pentominoes

Solve a matchstick puzzle Play SolitairePlay Lights OutSolve an anagram-stylenumber puzzle

Play Noughts & CrossesSolve the frog puzzleSolve the Queens problemPlay 4-in-a-Row

Solve a logic problem:Guess the Pegs

13 Language Tasks & Quizzes 1

Engage with Mathslanguage by matchingterms to their descriptions

Engage with Mathslanguage throughwordsearch puzzles

Engage with Mathslanguage throughcrossword puzzles

Engage with Mathslanguage by completingsentencesEngage with Mathslanguage through Hangman

Quizzes: Puzzles andproblems differentiatedfrom 1 to 7

14 Sequences 1

Enter missing terms in asequence with a commondifference

Enter missing terms in asequence with a commondifference

Enter missing terms in asequence with next termrule of the form: Un+1=3Un+1, 3(Un+1), Un/3+1,(Un+1)/3

Enter missing terms in asequence with amiscellaneous next termrule, including a Fibonaccisequence

Enter missing terms in asequence with amiscellaneous next termrule, including a Fibonaccisequence

15 Sequences 2Use the nth term rule togenerate a sequence

Identify the nth term rule ofa sequence with a commondifference

Use the nth term rule togenerate a sequence

Identify the nth term ruleof a quadratic sequenceusing differences

Identify the nth term rule ofa quadratic sequence usingdifferences

16 Solving Equations 2 Solve an equation with upto 1 bracket on each side

Solve an equation with upto 3 brackets on each side

Solve an equation withfractions

Solve a problem usingalgebraic modelling

Solve an equation by trialand improvement

17 Straight Lines 1

Read and plot coordinatesin all 4 quadrants

Read and plot coordinatesin all 4 quadrants

Draw a straight line bycalculating and plottingpoints

Calculate the gradient of astraight line between twopoints

Calculate the equation of astraight line by calculatingthe gradient and identifyingthe y-interceptKnow y=mx+c

18 Straight Lines 2Calculate the equation of astraight line

Rearrange an equation tothe form y=mx+c to findthe gradient and intercept

Find the midpoint between2 points the length of a linesegment

Calculate the length of aline segment

Solve problems withparallel and perpendicularlines

19 Simultaneous Equations

Solve a pair ofsimultaneous equationsgraphically

Solve a pair ofsimultaneous equations byelimination: adding orsubtracting leads directly tosolution

Solve a pair ofsimultaneous equations byelimination: multiply oneequation

Solve a pair ofsimultaneous equations byelimination: multiply bothequations

Solve a pair ofsimultaneous equations bysubstitutionSolve a pair ofsimultaneous equations: 1linear; 1 quadratic

20 Change the subject of aFormula

Change the subject of aformula: 1 or moreoperations required

Change the subject of aformula: 2 or moreoperations required

Change the subject of aformula: 3 or moreoperations required

Change the subject of aformula involving squaresand square roots

Change the subject of aformula: 3 or moreoperations requiredincluding factorisation

21 Quadratics 1Draw a quadratic bycalculating and plottingpoints

Draw a quadratic bycalculating and plottingpoints

Identify the intersectionpoints of a quadratic and astraight line

Identify the intersectionpoints of a quadratic and astraight line

Multiply out a factorisedquadratic expression

Maths Workout - Algebra & Problem Solving

© Smart Interactive Ltd.89

Algebra & Problem Solving Topics

Topic Target 1 Target 2 Target 3 Target 4 Target 5

22 Quadratics 2

Factorise a quadraticexpression

Solve a quadratic equationMultiply out and factoriseusing the difference of 2squares

Solve a quadratic equationby rearranging andfactorisingSolve problems involvingquadraticsSolve a quadratic equationwith non-unit x2 coefficient

Solve a quadratic equationby completing the square

Solve a quadratic equationusing the quadratic formulaSolve further problems

23 Indices 2

Know and apply the rules ofindices to numericalexpressions

Know and apply the rules ofindices to algebraicexpressions

Know and apply the rules ofindices to numerical andalgebraic expressions

Convert between fractionalindices and surds, andevaluate expressionsSolve equations involvingindices

Evaluate and simplifyexpressions in index formSolve equations involvingindices

24 Algebraic FractionsSimplify an algebraic fraction Simplify an algebraic

fractionMultiply and divide, addand subtract algebraicfractions

Add and subtract algebraicfractions

25 InequalitiesWrite and interpret aninequality and represent iton a number line

Write and interpret acombined inequality andrepresent it on a numberline

Solve an inequalityalgebraically

Solve an inequality withfractions algebraically

26 Proportion 2Solve a direct proportionquestion using a constantof proportionality

Solve a direct proportionquestion using a constantof proportionality

Solve an inverse proportionquestion using a constantof proportionality

Solve an inverse proportionquestion using a constantof proportionality

27 Problems & Puzzles 2

Solve a spatial puzzle:Gridlock

Solve Tile Slide, Towers ofHanoiPlay a sequence memorygame

Solve a nonogram puzzle Solve a logic problem basedon sequencing

Solve a logic problem basedon information handling

28 Problems & Puzzles 3 – Coming2014

29 Language Tasks & Quizzes 2Engage with Mathslanguage by matchingterms to their descriptions

Engage with Mathslanguage throughwordsearch puzzles

Engage with Mathslanguage throughcrossword puzzles

Engage with Mathslanguage by completingsentences

Quizzes: Puzzle &problems; Differentiatedfrom 1 to 7