Maths - Differentiated Curriculum for Year 7 (08 0ct 09)

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    MATHEMATICS SCHEME OF WORK SPN-21 (INTERIM STAGE)DIFFERENTIATED CURRICULUM

    YEAR 7

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    1. FACTORS AND

    MULTIPLES (3weeks)

    1.1 Factors, Multiples,Prime Numbers,Prime Factorisationand Index notation(a) Factors(b) Multiples(c) Prime Numbers

    and PrimeFactorisation

    (d) Index Notation

    Review factors and multiples.

    Note that 1 is a factor ofevery number, and everynumber is a factor and amultiple of itself.

    List all the factors of a wholenumber.

    List some multiples of a wholenumber.

    Review prime numbers arenumbers that have only twofactors, 1 and itself. Note that 1is not a prime number.

    Show prime factorisation of anumber (suggestion: use shortdivision and factor treemethods).

    Introduce index notation andrepresent the primefactorisation of a number in

    index notation e.g. 23 3272 =

    .

    Review factors and multiples.

    Note that 1 is a factor ofevery number, and everynumber is a factor and amultiple of itself.

    List all the factors of a wholenumber.

    List some multiples of a wholenumber.

    Review prime numbers arenumbers that have only twofactors, 1 and itself. Note that 1is not a prime number.

    Show prime factorisation of anumber (suggestion: use shortdivision and factor treemethods).

    Introduce index notation andrepresent the primefactorisation of a number in

    index notation e.g. 23 3272 =

    .

    Explain the meaning of factorsand multiples.

    Note that 1 is a factor ofevery number, and everynumber is a factor and amultiple of itself.

    List all the factors of a wholenumber.

    List some multiples of a wholenumber.

    Explain that prime numbersare numbers that have only twofactors, 1 and itself. Note that 1is not a prime number.

    Show prime factorisation of anumber (suggestion: use shortdivision and factor treemethods).

    Introduce index notation andrepresent the primefactorisation of a number in

    index notation e.g. 23 3272 =.

    1.2 Highest CommonFactor

    (HCF)

    Review the method of findingHCF of two or three numbers(suggestion: use short division

    Review the method of findingHCF of two or three numbers(suggestion: use short division

    Review the method of findingHCF of two or three numbers(suggestion: use short division

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    method). method). method).

    1.3 Lowest CommonMultiple (LCM)

    Review the method of findingLCM of two or three numbers(suggestion: use short division

    method).

    Review the method of findingLCM of two or three numbers(suggestion: use short division

    method)

    Review the method of findingLCM of two or three numbers(suggestion: use short division

    method).

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    2. REAL NUMBERS(4 weeks)

    2.1 Idea of NegativeNumbers andNumber Line(a) Negative

    Numbers(b) Number Line

    Introduce the naturalnumbers 1, 2, 3, as positiveintegers, i.e. +1, +2, +3, foremphasis (read as positive one,positive two, positive three,etc).

    Explain the application fornegative numbers throughdaily examples.

    Introduce negative integersas opposites of positiveintegers, and as -1, -2, -3, (read as negative one, negativetwo, negative three, etc) andzero is neutral.

    Compare two integers bythe use of a number line anduse symbols < and > to showrelationship between the two

    Introduce the naturalnumbers 1, 2, 3, as positiveintegers, i.e. +1, +2, +3, foremphasis (read as positive one,positive two, positive three,etc).

    Explain the application fornegative numbers throughdaily examples.

    Introduce negative integersas opposites of positiveintegers, and as -1, -2, -3, (read as negative one, negativetwo, negative three, etc) andzero is neutral.

    Compare two integers bythe use of a number line anduse symbols < and > to showrelationship between the two

    Introduce the naturalnumbers 1, 2, 3, as positiveintegers, i.e. +1, +2, +3, foremphasis (read as positive one,positive two, positive three,etc).

    Explain the application fornegative numbers throughdaily examples.

    Introduce negative integersas opposites of positiveintegers, and as -1, -2, -3, (read as negative one, negativetwo, negative three, etc) andzero is neutral.

    Compare two integers by theuse of a number line and usesymbols < and > to showrelationship between the two

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    integers, e.g. -5 < 2 integers, e.g. -5 < 2 integers, e.g. -5 < 2

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    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    2.2 Addition andSubtraction ofIntegers(a) Addition(b) Subtraction

    Add and subtract negativeintegers concretely, pictoriallyand symbolically.

    Lead pupils to read negativenumbers and operations

    correctly, e.g. 4 (-1) (readas 4 minus negative 1).

    Guide students in performingsimple mental computationsuch as the following:- add mentally any pair of two-

    digit numbers using numberbond method, e.g. 7 + 5 = 7+ (3 + 2) = (7 + 3) + 2 = 10+ 2 = 12.

    - subtract mentally any pair oftwo-digit numbers e.g. 23 8= (23 3) 5 = 20 5 = 15,- add or subtract mentallyany pair of three-digitmultiples of 10, e.g. 360 +540 = (300 + 60) + (500 +40) = (300 + 500) + (60 +40) = 800 + 100 = 900.

    - find out what must beadded to any two-digitnumber to make a total of100, e.g. 47 + ? = 100;

    - subtract any two three-digitnumbers when the difference

    is less than 10 by roundingand compensating,e.g. 503 497.

    Add and subtract negativeintegers concretely, pictoriallyand symbolically.

    Lead pupils to read negativenumbers and operations

    correctly, e.g. 4 (-1) (readas 4 minus negative 1).

    Guide students in performingsimple mental computationsuch as the following:- add mentally any pair of two-

    digit numbers using numberbond method, e.g. 7 + 5 = 7+ (3 + 2) = (7 + 3) + 2 = 10+ 2 = 12.

    - subtract mentally any pair oftwo-digit numbers e.g. 23 8= (23 3) 5 = 20 5 = 15,- add or subtract mentallyany pair of three-digitmultiples of 10, e.g. 360 +540 = (300 + 60) + (500 +40) = (300 + 500) + (60 +40) = 800 + 100 = 900.

    - find out what must be addedto any two-digit number tomake a total of 100, e.g. 47

    + ? = 100;- subtract any two three-digitnumbers when the difference

    is less than 10 by roundingand compensating,e.g. 503 497.

    Add and subtract negativeintegers concretely, pictoriallyand symbolically.

    Lead pupils to read negativenumbers and operations

    correctly, e.g. 4 (-1) (readas 4 minus negative 1).

    Guide students in performingsimple mental computationsuch as the following:- add mentally any pair of two-

    digit numbers using numberbond method, e.g. 7 + 5 = 7+ (3 + 2) = (7 + 3) + 2 = 10+ 2 = 12.

    - subtract mentally any pair oftwo-digit numbers e.g. 23 8= (23 3) 5 = 20 5 = 15,- add or subtract mentallyany pair of three-digitmultiples of 10, e.g. 360 +540 = (300 + 60) + (500 +40) = (300 + 500) + (60 +40) = 800 + 100 = 900.

    - find out what must be addedto any two-digit number tomake a total of 100, e.g. 47

    + ? = 100;- subtract any two three-digitnumbers when the difference

    is less than 10 by roundingand compensating, e.g. 503 497.

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    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    2.3 Multiplication,Division andCombinedOperations ofIntegers(a) Multiplication(b) Division(c) Combined

    Operations ofIntegers

    Establish the rules for themultiplication of integers anddivision of integers.

    Discuss useful strategies forcalculations especially mentalcalculations:

    - double and findcorresponding halves fornumbers from 1 to 50;

    - multiply by 5 (multiply by 10and take half);- multiply by 25 (multiple by100 and divide by 4);

    - multiply any two or threedigit numbers by 10 anddivide any multiples of 100by 10 or 100.

    Review and revise rules ofcombined operations in termsof order of operations.

    Evaluate expression (with orwithout brackets) involving thecombined operations (use smallnumbers only).

    Establish the rules for themultiplication of integers anddivision of integers.

    Discuss useful strategies forcalculations especially mentalcalculations:

    - double and findcorresponding halves fornumbers from 1 to 50;

    - multiply by 5 (multiply by 10and take half);- multiply by 25 (multiple by100 and divide by 4);

    - multiply any two or threedigit numbers by 10 anddivide any multiples of 100by 10 or 100.

    Review and revise rules ofcombined operations in termsof order of operations.

    Evaluate expression (with orwithout brackets) involving thecombined operations (use smallnumbers only).

    Establish the rules for themultiplication of integers anddivision of integers.

    Discuss useful strategies forcalculations especially mentalcalculations:

    - double and findcorresponding halves fornumbers from 1 to 50;

    - multiply by 5 (multiply by 10and take half);- multiply by 25 (multiple by100 and divide by 4);

    - multiply any two or threedigit numbers by 10 anddivide any multiples of 100by 10 or 100.

    Review and revise rules ofcombined operations in termsof order of operations.

    Evaluate expression (with orwithout brackets) involving thecombined operations (use smallnumbers only).

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    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    2.4 Fractions(a) Types of

    Fractions(b) Addition and

    Subtraction(c) Multiplication

    and Division

    Identify equivalentfractions and obtain a fractionwhich is equivalent to a givenone.

    Reduce a fraction to its lowestterms.

    Convert an improper fraction to amixed

    number and vice versa

    Add, subtract, multiply anddivide fractions concretely,pictorially and symbolically.

    Give examples of reciprocals

    and note that 1=a

    b

    b

    aand

    that 0 has no reciprocal.

    Perform simple mentalcomputation involving fractionssuch as the following:

    + ; 1 3

    1; +

    3

    1; 4

    ; 3 13

    2.

    Identify equivalentfractions and obtain a fractionwhich is equivalent to a givenone.

    Reduce a fraction to its lowestterms.

    Convert an improper fraction to amixed

    number and vice versa

    Add, subtract, multiply anddivide fractions concretely,pictorially and symbolically.

    Give examples of reciprocals

    and note that 1=a

    b

    b

    aand

    that 0 has no reciprocal.

    Perform simple mentalcomputation involving fractionssuch as the following:

    + ; 1 3

    1; +

    3

    1; 4

    ; 3 13

    2.

    Identify equivalentfractions and obtain a fractionwhich is equivalent to a givenone.

    Reduce a fraction to its lowestterms.

    Convert an improper fraction to amixed

    number and vice versa

    Add, subtract, multiply anddivide fractions concretely,pictorially and symbolically.

    Give examples of reciprocals

    and note that 1=a

    b

    b

    aand

    that 0 has no reciprocal.

    Perform simple mentalcomputation involving fractionssuch as the following:

    + ; 1 3

    1; +

    3

    1; 4

    ; 3 13

    2.

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    2.5 Decimals and Use ofCalculator(a) Fractions and

    Decimals(b) Addition and

    Subtraction(c) Multiplicationand

    Division

    Convert a fraction into adecimal and

    vice-versa.

    Give examples of recurringdecimals.

    Arrange numbers in ascendingor

    descending order. Add, subtract, multiply and

    dividedecimals.

    Use a calculator to carry outoperations.

    Convert a fraction into adecimal and

    vice-versa.

    Give examples of recurringdecimals.

    Arrange numbers in ascendingor

    descending order. Add, subtract, multiply and

    dividedecimals.

    Use a calculator to carry outoperations.

    Convert a fraction into adecimal and

    vice-versa.

    Give examples of recurringdecimals.

    Arrange numbers in ascendingor

    descending order. Add, subtract, multiply and

    dividedecimals.

    Use a calculator to carry outoperations.

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    2.6 Squares, SquareRoots, Cubes andCube Roots(a) Squares and

    Square Roots

    Find squares of numbers(whole numbers, integers,fractions and decimals) andnote that the square of anynumber including negativenumbers is always positive.

    Find square roots ofnumbers by prime factorisationand note that square root of anegative number does notexist.

    Remind students that squareroot of a positive integer yieldsonly a positive square root.

    In general the square roots

    of a is a. The symbol

    Find squares of numbers(whole numbers, integers,fractions and decimals) andnote that the square of anynumber including negativenumbers is always positive.

    Find square roots ofnumbers by prime factorisationand note that square root of anegative number does notexist.

    Remind students that squareroot of a positive integer yieldsonly a positive square root.

    In general the square roots

    of a is a. The symbol

    Find squares of numbers(whole numbers, integers,fractions and decimals) andnote that the square of anynumber including negativenumbers is always positive.

    Find square roots ofnumbers by prime factorisationand note that square root of anegative number does notexist.

    Remind students that squareroot of a positive integer yieldsonly a positive square root.

    In general the square roots

    of a is a. The symbol

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    (b) Cubes andCube Roots

    denotes the positive squareroot of a number and the

    symbol - denotes the negativesquare root of a number.

    Find the cubes of positiveand negative numbers.

    Find the cube roots ofpositive and negative numbersby prime factorisation.

    denotes the positive squareroot of a number and the

    symbol - denotes the negativesquare root of a number.

    Find the cubes of positiveand negative numbers.

    Find the cube roots ofpositive and negative numbersby prime factorisation.

    denotes the positive squareroot of a number and the

    symbol - denotes the negativesquare root of a number.

    Find the cubes of positiveand negative numbers.

    Find the cube roots ofpositive and negative numbersby prime factorisation.

    3. APPROXIMATIONAND ESTIMATION(1 week)

    3.1 Approximation(a) Place Value(b) Decimal

    Places

    (c) SignificantFigures

    Round off numbers to agiven place value.

    Round off numbers to agiven number of decimal

    places. Round off numbers to agiven number of significantfigures.

    Round off numbers to agiven place value.

    Round off numbers to agiven number of decimal

    places. Round off numbers to agiven number of significantfigures.

    Round off numbers to agiven place value.

    Round off numbers to agiven number of decimal

    places. Round off numbers to agiven number of significantfigures.

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    3.2 Estimation Estimate, compute and

    verify the sum, difference,product and quotient of realnumbers.

    Use a calculator to evaluatearithmetic expressions andround off to a given number ofdecimal places or significant

    Estimate, compute and

    verify the sum, difference,product and quotient of realnumbers.

    Use a calculator to evaluatearithmetic expressions andround off to a given number ofdecimal places or significant

    -

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    figures. figures.

    4. MEASURES ANDMONEY (2 weeks)

    4.1 The SI units Give a global view of the SIunit.

    Give the meaning of prefixes(e.g. kilo, hector, etc) and theusage of symbols (e.g. k, h, etc).Use concrete objects wheneverpossible in introducing eachconcept.

    Give a global view of the SIunit.

    Give the meaning of prefixes(e.g. kilo, hector, etc) and theusage of symbols (e.g. k, h, etc).Use concrete objects wheneverpossible in introducing eachconcept.

    Give a global view of the SIunit.

    Give the meaning of prefixes(e.g. kilo, hector, etc) and theusage of symbols (e.g. k, h, etc).Use concrete objects wheneverpossible in introducing eachconcept.

    4.2 Length Convert from one unit oflength to another.

    Select the appropriate unit

    of length for measuring a givendistance.

    Solve problems involvinglengths.

    Convert from one unit oflength to another.

    Select the appropriate unit

    of length for measuring a givendistance.

    Solve simple problemsinvolving lengths.

    Convert from one unit oflength to another.

    Select the appropriate unit

    of length for measuring a givendistance.

    Solve simple problemsinvolving lengths.

    4.3 Mass Convert from one unit ofmass to another.

    Select the appropriate unitof mass (e.g. g, kg, and tonne)for measuring the mass of agiven object.

    Solve problems involving

    mass.

    Convert from one unit ofmass to another.

    Select the appropriate unitof mass (e.g. g, kg, and tonne)for measuring the mass of agiven object.

    Solve simple problems

    involving mass.

    Convert from one unit ofmass to another.

    Select the appropriate unitof mass (e.g. g, kg, and tonne)for measuring the mass of agiven object.

    Solve simple problemsinvolving mass.

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    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    4.4 Volume andCapacity

    Explain the meaning ofvolume and capacity.

    Solve problems involvingvolume and capacity.

    Explain the meaning ofvolume and capacity.

    Solve simple problemsinvolving volume and capacity.

    Explain the meaning ofvolume and capacity.

    Solve simple problemsinvolving volume and capacity.

    4.5 Time Including the24-hour clocknotation

    Revise units of time andcommon time notation (12-hourclock).

    Convert between hours,minutes and seconds and findthe sum and difference of times.

    Introduce the 24-hour clocknotation and conversion betweenthe two notations.

    Solve problems on time andinterpret timetables.

    Revise units of time andcommon time notation (12-hourclock).

    Convert between hours,minutes and seconds and findthe sum and difference of times.

    Introduce the 24-hour clocknotation and conversion betweenthe two notations.

    Solve simple problems ontime and interpret timetables.

    Revise units of time andcommon time notation (12-hourclock).

    Convert between hours,minutes and seconds and findthe sum and difference of times.

    Introduce the 24-hour clocknotation and conversion betweenthe two notations.

    Solve simple problems ontime and interpret timetables.

    4.6 Money IncludingLocal Currency andDenominations

    Revise local currencydenominations.

    Express money in dollars ($)and cents (c).

    Solve everyday problems onmoney, e.g. shopping, etc.

    Revise local currencydenominations.

    Express money in dollars ($)and cents (c).

    Solve everyday problems onmoney, e.g. shopping, etc.

    Revise local currencydenominations.

    Express money in dollars ($)and cents (c).

    Solve everyday problems onmoney, e.g. shopping, etc.

    5. ALGEBRA 1 (3weeks)

    5.1 Representation ofUnknowns UsingSymbols and Letters

    Explain the meaning of an

    unknown.

    Represent an unknown by asymbol or a letter.

    Explain the meaning of an

    unknown.

    Represent an unknown by asymbol or a letter.

    Explain the meaning of an

    unknown.

    Represent an unknown by asymbol or a letter.

    5.2 AlgebraicExpressions

    Give some examples ofalgebraic expressions.

    Give some examples ofalgebraic expressions.

    Give some examples ofalgebraic expressions.

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    Explain the meaning ofvariables, terms and coefficients.

    Identify the various terms

    e.g. constant term, x-term, 2x -

    term, xy-term, etc.

    Explain the meaning of liketerms and unlike terms

    Explain the meaning ofvariables, terms and coefficients.

    Identify the various terms

    e.g. constant term, x-term, 2x -

    term, xy-term, etc.

    Explain the meaning of liketerms and unlike terms

    Explain the meaning ofvariables, terms and coefficients.

    Identify the various terms

    e.g. constant term, x-term, 2x -

    term, xy-term, etc.

    Explain the meaning of liketerms and unlike terms

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    5.3 Interpretation ofAlgebraic Notations

    Illustrate the notations andinterpret them:a + a = 2a ; a b = a + (-b)

    a b = ab or ba

    a 2 = 2a (Emphasis that a2

    is inappropriate)2aaa = (Emphasis that a x a

    2a)aa1 =

    b

    aba =

    2

    a2a = or a

    2

    1

    a (b + c) = a(b + c) [Removal

    of brackets will be done in Yr 8]

    Illustrate the notations andinterpret them:a + a = 2a ; a b = a + (-b)

    a b = ab or ba

    a 2 = 2a (Emphasis that a2

    is inappropriate)2aaa = (Emphasis that a x a

    2a)aa1 =

    b

    aba =

    2

    a2a = or a

    2

    1

    a (b + c) = a(b + c) [Removal

    of brackets will be done in Yr 8]

    Illustrate the notations andinterpret them:a + a = 2a ; a b = a + (-b)

    a b = ab or ba

    a 2 = 2a (Emphasis that a2

    is inappropriate)2aaa = (Emphasis that a x a

    2a)aa1 =

    b

    aba =

    2

    a2a = or a

    2

    1

    a (b + c) = a(b + c) [Removal

    of brackets will be done in Yr 8]

    5.4 Evaluation ofAlgebraic

    Expressions

    Evaluate an algebraicexpression by substituting given

    values of variables.

    Evaluate an algebraicexpression by substituting given

    values of variables.

    Evaluate an algebraicexpression by substituting given

    values of variables.

    5.5 Simplification ofAlgebraic

    Expressions(a) Addition and

    Collect and simplifyliketerms in algebraic expressionsinvolving addition andsubtraction (emphasise the

    Collect and simplifyliketerms in algebraic expressionsinvolving addition andsubtraction (emphasise the

    Collect and simplifyliketerms in algebraic expressionsinvolving addition andsubtraction (emphasise the

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    Subtraction(b) Multiplication

    andDivision

    importance of taking therespective sign along whencollecting like terms in theexpression

    e.g. +a + 2b + 3a - b )

    Simplify algebraicexpressions involvingmultiplication and division.

    importance of taking therespective sign along whencollecting like terms in theexpression

    e.g. +a + 2b + 3a - b )

    Simplify algebraicexpressions involvingmultiplication and division.

    importance of taking therespective sign along whencollecting like terms in theexpression

    e.g. +a + 2b + 3a - b )

    Simplify algebraicexpressions involvingmultiplication and division.

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    5.6 Solving LinearEquations

    Distinguish betweenexpressions and equations.Explain the terms equation andsolution of an equation.

    Use the balance conceptto explain the effect whentransferring terms and whensplitting terms.

    Generalise the ideas onoperations that:(i) when terms are transferred,there is a change in sign e.g.

    a) x + 2 = 6, then x = 6 2,

    b) x 2 = 6, then x = 6 + 2,

    (ii) when terms are split, there isno change in sign e.g.

    d)2

    6x6,2x == = 3

    Distinguish betweenexpressions and equations.Explain the terms equation andsolution of an equation.

    Use the balance conceptto explain the effect whentransferring terms and whensplitting terms.

    Generalise the ideas onoperations that:(i) when terms are transferred,there is a change in sign e.g.

    a) x + 2 = 6, then x = 6 2,

    b) x 2 = 6, then x = 6 + 2,

    (ii) when terms are split, there isno change in sign e.g.

    d)2

    6x6,2x == = 3

    Distinguish betweenexpressions and equations.Explain the terms equation andsolution of an equation.

    Use the balance conceptto explain the effect whentransferring terms and whensplitting terms.

    Generalise the ideas onoperations that:(i) when terms are transferred,there is a change in sign e.g.

    a) x + 2 = 6, then x = 6 2,

    b) x 2 = 6, then x = 6 + 2,

    (ii) when terms are split, there isno change in sign e.g.

    d)2

    6x6,2x == = 3

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    e) 3=

    ==

    2

    6x6,2x

    Explain thetechnique of solving linearequations, stressing on puttingthe unknown terms on one sideand constant terms on the other.Caution on common mistakes:

    48

    2x2,

    4

    2====x etc.

    Includeequations with simple singlefractions which can be reduced

    to linear equations e.g. 54

    x=

    (equations involving bracketsand fractional equations will bedone in Year 8).

    Showstudents how to identify key

    words and extract theinformation given in wordproblems, then translate theminto mathematical statements,and finally solve the equationsobtained.

    e) 3=

    ==

    2

    6x6,2x

    Explain thetechnique of solving linearequations, stressing on puttingthe unknown terms on one sideand constant terms on the other.Caution on common mistakes:

    48

    2x2,

    4

    2====x etc.

    Includeequations with simple singlefractions which can be reduced

    to linear equations e.g. 54

    x=

    (equations involving bracketsand fractional equations will bedone in Year 8).

    Showstudents how to identify key

    words and extract theinformation given in wordproblems, then translate theminto mathematical statements,and finally solve the equationsobtained.

    e) 3=

    ==

    2

    6x6,2x

    Explain thetechnique of solving linearequations, stressing on puttingthe unknown terms on one sideand constant terms on the other.Caution on common mistakes:

    48

    2x2,

    4

    2====x etc.

    Includeequations with simple singlefractions which can be reduced

    to linear equations e.g. 54

    x=

    (equations involving bracketsand fractional equations will bedone in Year 8).

    Showstudents how to identify key

    words and extract theinformation given in wordproblems, then translate theminto mathematical statements,and finally solve the equationsobtained.

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    6. INTRODUCTION TOGEOMETRY (2

    weeks)

    6.1 Points, Lines and Discuss the concepts of a point,

    a line and a plane

    Discuss the concepts of a point,a line and a plane

    Discuss the concepts of a point,a line and a plane

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    Planes Look for physical examples ofpoint, line and plane

    Name a point, a line segmentand a plane by using letters

    Recognise the differencebetween a line and a linesegment

    Draw and measure line

    segments

    Look for physical examples ofpoint, line and plane

    Name a point, a line segmentand a plane by using letters

    Recognise the differencebetween a line and a linesegment

    Draw and measure line

    segments

    Look for physical examples ofpoint, line and plane

    Name a point, a line segmentand a plane by using letters

    Recognise the differencebetween a line and a linesegment

    Draw and measure line

    segments

    6.2 Angles(a) Acute angles(b) Right angles(c) Obtuse angles(d) Reflex angles

    Explain and show that an angleis a measure of turn. Recogniseangles at points of intersection,arms and vertices.

    Illustrate the use of theprotractor to measure a givenangle in degree ( ).

    Lead students to draw angles ofgiven magnitude.

    Recognise angles in terms ofquarter-turn, half-turn and full-turn.

    Recognise the different types ofangles: acute, right, obtuse andreflex.

    Use the proper symbols innaming angles: eg.

    CBAorABC ,

    for right angle, , etc

    Explain and show that an angleis a measure of turn. Recogniseangles at points of intersection,arms and vertices.

    Illustrate the use of theprotractor to measure a givenangle in degree ( ).

    Lead students to draw angles ofgiven magnitude.

    Recognise angles in terms ofquarter-turn, half-turn and full-turn.

    Recognise the different types ofangles: acute, right, obtuse andreflex.

    Use the proper symbols innaming angles: eg.

    CBAorABC ,

    for right angle, , etc

    Explain and show that an angleis a measure of turn. Recogniseangles at points of intersection,arms and vertices.

    Illustrate the use of theprotractor to measure a givenangle in degree ( ).

    Lead students to draw angles ofgiven magnitude.

    Recognise angles in terms ofquarter-turn, half-turn and full-turn.

    Recognise the different types ofangles: acute, right, obtuse andreflex.

    Use the proper symbols innaming angles: eg.

    CBAorABC ,

    for right angle, , etc

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    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    6.3 Properties ofAngles

    (a) Complementaryangles

    (b) Supplementary

    angles(c) Adjacent angles

    on astraight line

    (d) Angles at a point(e) Vertically

    oppositeangles

    Investigate the followingproperties: complementary andsupplementary angles, adjacentangles on a straight line, anglesat a point and vertically opposite

    angles. Derive the relationships in each

    group of angles mentioned eg.Sum of all angles at a point is360, etc.

    Find the complementary or thesupplementary angle for a givenangle

    Find the value of angles in adiagram by applying the above-mentioned properties.

    Investigate the followingproperties: complementary andsupplementary angles, adjacentangles on a straight line, anglesat a point and vertically opposite

    angles. Derive the relationships in each

    group of angles mentioned eg.Sum of all angles at a point is360, etc.

    Find the complementary or thesupplementary angle for a givenangle

    Find the value of angles in adiagram by applying the above-mentioned properties.

    Investigate the followingproperties: complementary andsupplementary angles, adjacentangles on a straight line, anglesat a point and vertically opposite

    angles. Derive the relationships in each

    group of angles mentioned eg.Sum of all angles at a point is360, etc.

    Find the complementary or thesupplementary angle for a givenangle

    Find the value of angles in adiagram by applying the above-mentioned properties.

    6.4 Parallel Lines andPerpendicular Lines

    Recognise parallel, non-paralleland perpendicular lines indiagrams and use the symbols

    // and where appropriate.

    Introduce a transversal crossing two lines (the two linesmay not be parallel)and nameangles formed: correspondingangles, alternate angles andinterior angles on the same sideof the transversal.

    Investigate the properties ofthese angles in the case of a pairof parallel lines.

    Find unknown angles indiagrams by applying theproperties in 6.3 and 6.4.

    Recognise parallel, non-paralleland perpendicular lines indiagrams and use the symbols

    // and where appropriate.

    Introduce a transversal crossing two lines (the two linesmay not be parallel)and nameangles formed: correspondingangles, alternate angles andinterior angles on the same sideof the transversal.

    Investigate the properties ofthese angles in the case of a pairof parallel lines.

    Find unknown angles indiagrams by applying theproperties in 6.3 and 6.4.

    Recognise parallel, non-paralleland perpendicular lines indiagrams and use the symbols

    // and where appropriate.

    Introduce a transversal crossing two lines (the two linesmay not be parallel)and nameangles formed: correspondingangles, alternate angles andinterior angles on the same sideof the transversal.

    Investigate the properties ofthese angles in the case of a pairof parallel lines.

    Find unknown angles indiagrams by applying theproperties in 6.3 and 6.4.

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    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    7. POLYGONS (3weeks)

    7.1 Types of Polygons

    State a polygon as a closedplane figure with three or morestraight edges.

    Name the different polygons upto the decagon.

    Recognise regular and irregularpolygons.

    State a polygon as a closedplane figure with three or morestraight edges.

    Name the different polygons upto the decagon.

    Recognise regular and irregularpolygons.

    State a polygon as a closedplane figure with three or morestraight edges.

    Name the different polygons upto the decagon.

    Recognise regular and irregularpolygons.

    7.2 Triangles(a) Types ofTriangles

    (b) Angle Propertiesof

    Triangles:(i) Interior Angles(ii) Exterior Angles

    Name and classify trianglesaccording to sides (scalene,isosceles and equilateraltriangles) or angles (acute-angled triangles, right-angledtriangles and obtuse-angledtriangles).

    Investigate angle properties oftriangles:

    Angle sum of a triangle = 180oexterior angle = sum of two

    oppositeinteriorangles.

    Use the angle properties ofequilateral and isosceles triangleto find unknown angles in

    Name and classify trianglesaccording to sides (scalene,isosceles and equilateraltriangles) or angles (acute-angled triangles, right-angledtriangles and obtuse-angledtriangles).

    Investigate angle properties oftriangles:

    Angle sum of a triangle = 180oexterior angle = sum of two

    oppositeinteriorangles.

    Use the angle properties ofequilateral and isosceles triangleto find unknown angles in

    Name and classify trianglesaccording to sides (scalene,isosceles and equilateraltriangles) or angles (acute-angled triangles, right-angledtriangles and obtuse-angledtriangles).

    Investigate angle properties oftriangles:

    Angle sum of a triangle = 180oexterior angle = sum of two

    oppositeinteriorangles.

    Use the angle properties ofequilateral and isosceles triangleto find unknown angles in

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    triangles. triangles. triangles.

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    7.3 Quadrilaterals(a) Types of

    quadrilaterals

    (b) Angleproperties ofquadrilaterals

    Understand a quadrilateral as afour-sided closed figure.

    Recognise the followingquadrilaterals: parallelogram,

    rectangle, square, rhombus, kiteand trapezium.

    Investigate the properties ofthese quadrilaterals with respectto sides, angles and diagonals.Discuss relationships amongparallelogram, rectangle, square

    Understand a quadrilateral as afour-sided closed figure.

    Recognise the followingquadrilaterals: parallelogram,

    rectangle, square, rhombus, kiteand trapezium.

    Investigate the properties ofthese quadrilaterals with respectto sides, angles and diagonals.Discuss relationships amongparallelogram, rectangle, square

    Understand a quadrilateral as afour-sided closed figure.

    Recognise the followingquadrilaterals: parallelogram,

    rectangle, square, rhombus, kiteand trapezium.

    Investigate the properties ofthese quadrilaterals with respectto sides, angles and diagonals.Discuss relationships amongparallelogram, rectangle, square

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    and rhombus.

    Investigate the angle property ofquadrilateral:Angle sum of a quadrilateral =360o

    Use these properties to findunknown angle in a givenquadrilateral.

    and rhombus.

    Investigate the angle property ofquadrilateral:Angle sum of a quadrilateral =360o

    Use these properties to findunknown angle in a givenquadrilateral.

    and rhombus.

    Investigate the angle property ofquadrilateral:Angle sum of a quadrilateral =360o

    Use these properties to findunknown angle in a givenquadrilateral.

    7.4 Angle Properties ofPolygons

    Investigate angle properties ofpolygons:For regular or irregular polygons:

    a. sum of interior angles of an

    n-gon = 0180)2( n

    b. sum of exterior angles of apolygon = 360

    c. int. + ext. = 180o

    For regular polygons:

    d.

    =.

    360

    0

    extn or

    next

    0360

    . =

    e.n

    n0

    180)2(.int

    =

    Use these properties to solverelated problems.

    WILL BE DONE AFTER YEAR 8 WILL BE DONE AFTER YEAR 8

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

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    7.5 GeometricalConstructions

    Construct an angle, an anglebisectors, perpendiculars linesperpendicular bisectors andparallel lines.

    Demonstrate the proper use ofthe instruments for eachconstruction.

    Construct a triangle, given: threesides; two angles and the sidebetween them; two sides and anincluded angle; two sides and anon-included angle, including theambiguous case. An example ofan ambiguous case: Construct a

    ABC given thatBCandcmABA 58,35 ===

    ).

    [ two possible triangles:

    1ABC and 2ABC ]

    Construct a quadrilateral basedon given data.

    Construct an angle, an anglebisectors, perpendiculars linesperpendicular bisectors andparallel lines.

    Demonstrate the proper use ofthe instruments for eachconstruction.

    Construct a triangle, given: threesides; two angles and the sidebetween them; two sides and anincluded angle; two sides and anon-included angle, including theambiguous case. An example ofan ambiguous case: Construct a

    ABC given thatBCandcmABA 58,35 ===

    ).

    [ two possible triangles:

    1ABC and 2ABC ]

    Construct a quadrilateral basedon given data.

    WILL BE DONE AFTER YEAR 8

    Differentiated Curriculum SPN-21 Year 7 Page 19 of27

    C1A C2

    B

    5 cm

    8 cm

    5 cm35

    C1A C2

    B

    5 cm

    8 cm

    5 cm35

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    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    8. PERIMETER ANDAREA (3 weeks)

    8.1 Idea of Perimeter Understand perimeter as the

    distance around a shape or

    figure.

    Understand perimeter as thedistance around a shape or

    figure.

    Understand perimeter as thedistance around a shape or

    figure.

    8.2 Perimeter ofPolygons

    Find the perimeter of afigure by adding the lengths ofall the sides or by measuring thedistance around the figure byusing a string or a measuringtape.

    Find the perimeter of apolygon by adding the lengths ofall the sides emphasise the useof the same unit of length.

    Find the perimeter of apolygon by formulae (forrectangles, squares and regularpolygons).

    Solve problems onperimeters of plane figures.

    Find the perimeter of afigure by adding the lengths ofall the sides or by measuring thedistance around the figure byusing a string or a measuringtape.

    Find the perimeter of apolygon by adding the lengths ofall the sides emphasise the useof the same unit of length.

    Find the perimeter of apolygon by formulae (forrectangles, squares and regularpolygons).

    Solve problems onperimeters of plane figures.

    Find the perimeter of afigure by adding the lengths of allthe sides or by measuring thedistance around the figure byusing a string or a measuringtape.

    Find the perimeter of atriangle, square and rectangle byadding the lengths of all thesides emphasise the use of thesame unit of length.

    Find the perimeter of atriangle, square and rectangle byformulae.

    Solve problems onperimeters of triangle, squareand rectangle.

    8.3 Circumference ofCircle

    Name the parts of a circle:centre, radius, diameter,

    semicircle and circumference. Draw a circle with a given

    radius (or diameter).

    Investigate the ratio

    diameter

    ncecircumfereand introduce

    Name the parts of a circle:centre, radius, diameter,

    semicircle and circumference. Draw a circle with a given

    radius (or diameter).

    Investigate the ratio

    diameter

    ncecircumfereand introduce

    Name the parts of a circle:centre, radius, diameter,

    semicircle and circumference. Draw a circle with a given

    radius (or diameter).

    Investigate the ratio

    diameter

    ncecircumfereand introduce

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    the constant . Use the formulaC = d or C = 2r to solveproblems on circumference ofcircles.

    Solve problems involvingcircumference of a circle,semicircle and quadrants.

    the constant . Use the formulaC = d or C = 2r to solveproblems on circumference ofcircles.

    Solve problems involvingcircumference of a circle,semicircle and quadrants.

    the constant . Use the formulaC = d or C = 2r to solveproblems on circumference ofcircles.

    Solve problems involvingcircumference of a circle andsemi-circle.

    Content CoverageEXTENDED CORE

    Could do (100%) Should do (80%) Must do (60%)

    8.4 Area of a Rectangle,Square,Parallelogram,Triangle andTrapezium.

    Understand area as ameasure of the amount of planesurface.

    State that area is measuredin square units and the common

    units for area are mm2, cm2, m2,km2 and hectare, ha(100m x100m). (Read as squaremillimetres, square centimetresand so on).

    Convert from one area unit toanother.

    Use formulae to find theareas of rectangles and squares.

    Show the formula (base xheight) for the area of parallelogram by a practical

    activity and use the formula tosolve problems on areas ofparallelograms.

    Show the formula (2

    1x base

    x height) for the area of atriangle by dissecting a

    Understand area as ameasure of the amount of planesurface.

    State that area is measured

    in square units and the commonunits for area are mm2, cm2, m2,km2 and hectare, ha(100m x100m). (Read as squaremillimetres, square centimetresand so on).

    Convert from one area unit toanother.

    Use formulae to find theareas of triangles, rectangles,

    squares, parallelogram, andtrapezium.

    Apply the above formulae to findareas of composite figuresinvolving squares, rectangles ortriangles.

    Understand area as ameasure of the amount of planesurface.

    State that area is measured

    in square units and the commonunits for area are mm2, cm2, m2,km2 and hectare, ha(100m x100m). (Read as squaremillimetres, square centimetresand so on).

    Use formulae to find theareas of triangles, rectangles,squares, and parallelogram.

    Apply the above formulae to

    find areas of simple compositefigures involving squares,rectangles or triangles.

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    parallelogram or a rectangle anduse the formula to solveproblems on areas of triangles.

    Show the formula

    ( )

    + hba2

    1by dissecting a

    trapezium into two triangles anduse the formula to solve

    problems on areas of trapeziums.

    Apply the above formulae tofind areas of composite figures.

    8.5 Area of a Circle Introduce the formula for area ofa circle and apply the formula tosolve problems on areas ofcircles and composite figureswith circle parts (i.e. Quadrants,semicircles and full circles).

    Introduce the formula for area ofa circle and apply the formula tosolve problems on areas ofcircles and composite figureswith circle parts (i.e. Quadrants,semicircles and full circles).

    Introduce the formula for area ofa circle and apply the formula tosolve problems on areas ofcircles and composite figureswith circle parts (i.e. semicirclesand full circles).

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    9. RATIO, RATE ANDPROPORTION(3weeks)

    9.1 Ratio Lead students to understand

    the idea of ratio and emphasisethat quantities involved in a ratiomust be expressed in the same

    unit. Emphasise that each ratio

    number represents a value.

    Compare two quantities in

    the form of a : b orb

    aor three

    quantities in the form a : b : c.

    Lead students to understandthe idea of ratio and emphasisethat quantities involved in a ratiomust be expressed in the same

    unit. Emphasise that each ratio

    number represents a value.

    Compare two quantities in

    the form of a : b orb

    aor three

    quantities in the form a : b : c.

    Lead students to understandthe idea of ratio and emphasisethat quantities involved in a ratiomust be expressed in the same

    unit. Emphasise that each ratio

    number represents a value.

    Compare two quantities in

    the form of a : b orb

    aor three

    quantities in the form a : b : c.

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    Determine equivalent ratiosand simplify ratios to theirsimplest forms.

    Divide a quantity in a givenratio.

    Solve word problemsinvolving ratios.

    Determine equivalent ratiosand simplify ratios to theirsimplest forms.

    Divide a quantity in a givenratio.

    Solve word problemsinvolving ratios.

    Determine equivalent ratiosand simplify ratios to theirsimplest forms.

    Divide a quantity in a givenratio.

    Solve word problemsinvolving ratios.

    9.2Rate Explain rate and per byusing daily examples e.g.telephone charges, speed, andwages.

    Show actual notes or pictureof foreign currencies.

    Introduce the idea ofexchange rate and giveexamples regarding conversionfrom one currency to another.

    Interpret straight line graphsof rates e.g. price and speed.

    Introduce formula of speedand use the formula to solveproblems related to speed,distance and time,

    Speed =Time

    Distance.

    Solve problems related torate.

    Explain rate and per byusing daily examples e.g.telephone charges, speed, andwages.

    Show actual notes or pictureof foreign currencies.

    Introduce the idea ofexchange rate and giveexamples regarding conversionfrom one currency to another.

    Interpret straight line graphsof rates e.g. price and speed.

    Introduce formula of speedand use the formula to solveproblems related to speed,distance and time,

    Speed =Time

    Distance.

    Solve problems related torate.

    Explain rate and per byusing daily examples e.g.telephone charges, speed, andwages.

    Show actual notes or pictureof foreign currencies.

    Introduce the idea ofexchange rate and giveexamples regarding conversionfrom one currency to another.

    Interpret straight line graphsof rates e.g. price and speed.

    Introduce formula of speedand use the formula to solveproblems related to speed,distance and time,

    Speed =Time

    Distance.

    Solve problems related torate.

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    9.3 Proportion asEquality of TwoRatios

    (a) Direct Proportion

    Define proportion as astatement expressing the equalityof two ratios and give numericalexamples of proportion.

    Define proportion as astatement expressing the equalityof two ratios and give numericalexamples of proportion.

    Define proportion as astatement expressing the equalityof two ratios and give numericalexamples of proportion.

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    (b) Inverse orIndirect

    Proportion

    Explain direct proportion asthe equality of two ratios anddiscuss examples familiar tostudents.

    Solve problems on directproportion.

    Explain inverse proportionby providing real-life examples.

    Solve problems on inverseproportion.

    Explain direct proportion asthe equality of two ratios anddiscuss examples familiar tostudents.

    Solve problems on directproportion.

    Explain inverse proportionby providing real-life examples.

    Solve problems on inverseproportion.

    Explain direct proportion asthe equality of two ratios anddiscuss examples familiar tostudents.

    Solve problems on directproportion.

    Explain inverse proportionby providing real-life examples.

    Solve problems on inverseproportion.

    9.4 Scale Drawing

    Explain what a scale is and thepurpose of using a scaledrawing.

    Draw and interpret simple scaledrawings.

    Use scale drawings to solveproblems (find the unknownlength from the diagram).

    Explain what a scale is and thepurpose of using a scaledrawing.

    Draw and interpret simple scaledrawings.

    Use scale drawings to solveproblems (find the unknownlength from the diagram).

    -

    10. PERCENTAGE(2 weeks)

    10.1 ExpressingPercentage as aFraction or Decimal

    Illustrate the meaning ofpercent as parts of a hundredusing the 100-square grid.

    Express a percentage as adecimal or a fraction in its lowestterms.

    Illustrate the meaning ofpercent as parts of a hundredusing the 100-square grid.

    Express a percentage as adecimal or a fraction in its lowestterms.

    Illustrate the meaning ofpercent as parts of a hundredusing the 100-square grid.

    Express a percentage as adecimal or a fraction in its lowestterms.

    10.2 Expressing

    Fraction andDecimal as aPercentage

    Convert any fraction or decimal

    to percentage. Emphasize the rule: To express

    a fraction or decimal as apercentage, simply multiply it by100%.

    Convert any fraction or decimal

    to percentage. Emphasize the rule: To express

    a fraction or decimal as apercentage, simply multiply it by100%.

    Convert any fraction or decimal

    to percentage. Emphasize the rule: To express

    a fraction or decimal as apercentage, simply multiply it by100%.

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    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    10.3 Expressing OneQuantity as aPercentage ofAnother

    Express the ratio of a quantityp, to another quantity, q, in the

    form of a fractionq

    p, where p

    and q are quantities with thesame unit.

    Express the above fraction as a

    percentage, i.e.q

    p%100 .

    Express the ratio of a quantityp, to another quantity, q, in the

    form of a fractionq

    p, where p

    and q are quantities with thesame unit.

    Express the above fraction as a

    percentage, i.e.q

    p%100 .

    Express the ratio of a quantityp, to another quantity, q, in the

    form of a fractionq

    p, where p

    and q are quantities with thesame unit.

    Express the above fraction as a

    percentage, i.e.q

    p%100 .

    10.4 Calculating theValue of a GivenPercentage of aGiven Quantity

    Find a given percentage of aquantity.

    Find a number given thepercentage; rapidly compute 5%,10%, 25%, 50% and 75% of aquantity.

    Use percentage to compare twoquantities, including percentagesgreater than 100%.

    Find a given percentage of aquantity.

    Find a number given thepercentage; rapidly compute 5%,10%, 25%, 50% and 75% of aquantity.

    Use percentage to compare twoquantities, including percentagesgreater than 100%.

    Find a given percentage of aquantity.

    Find a number given thepercentage; rapidly compute 5%,10%, 25%, 50% and 75% of aquantity.

    Use percentage to compare twoquantities, including percentagesgreater than 100%.

    10.5 Finding

    percentageincrease ordecrease

    Explain the meaning of

    percentage increase andpercentage decrease.

    Find percentage increase ordecrease of a given quantity.

    Explain the meaning of

    percentage increase andpercentage decrease.

    Find percentage increase ordecrease of a given quantity.

    Explain the meaning of

    percentage increase andpercentage decrease.

    Find percentage increase ordecrease of a given quantity.

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    10.6 Problemsinvolvingpercentages

    Solve simple problems relatedto percentages.

    Solve simple problems relatedto percentages.

    Solve simple problems related topercentages. (Exclude calculationsinvolving reverse percentages, e.g.finding the cost price given theselling price and the percentageprofit)

    Content Coverage Could do (100%) Should do (80%) Must do (60%)

    11. STATISTICS (2weeks)

    11.1 Data CollectionMethod, Classifyingand Tabulating Data

    Carry out activities thatinvolve different methods of datacollection:- observation and measurement,- interviews,- survey including the use ofquestionnaires.

    Classify and tabulate datacollected to form a frequencytable (explain the uses of tallymarks in counting).

    Carry out activities thatinvolve different methods of datacollection:- observation and measurement,- interviews,- survey including the use ofquestionnaires.

    Classify and tabulate datacollected to form a frequencytable (explain the uses of tallymarks in counting).

    Carry out activities thatinvolve different methods of datacollection:- observation and measurement,- interviews,- survey including the use ofquestionnaires.

    Classify and tabulate datacollected to form a frequencytable (explain the uses of tallymarks in counting).

    11.2 Constructionand

    Interpretation ofTables, Bar

    Charts,

    Introduce each of thefollowing types of representationof statistical data and thetechniques and the principlesinvolved in its construction:

    Introduce each of thefollowing types of representationof statistical data and thetechniques and the principlesinvolved in its construction:

    Introduce each of thefollowing types of representationof statistical data and thetechniques and the principlesinvolved in its construction:

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    Pictographs, LineGraphs, Pie

    Charts

    - pictographs,- bar charts,- line graphs,

    - pie charts.

    Read and interpret statisticalgraphs including interpretingtables and drawings.

    - pictographs,- bar charts,- line graphs,

    - pie charts.

    Read and interpret statisticalgraphs including interpretingtables and drawings.

    - pictographs,- bar charts,- line graphs,

    - pie charts.

    Read and interpret statisticalgraphs including interpretingtables and drawings.

    Differentiated Curriculum SPN-21 Year 7 Page 27 of27