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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
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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.
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