Beaconhouse / Middle / Mathematics / Class 6 / Subject Guide / Suggested Scheme of Work
Term I
(15 Weeks)
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Term II
(15 Weeks)
● Square and cube roots
Orientation
● HCF and LCM
Number System
● Time and Average speed
Number Properties
● Algebraic expressions and factorization
Integer and Decimals
● Equations and Inequalities
Fractions and Percentages
● 2D and 3D shapes
Ratio, rate and Proportion
● Area and Volume
Sequence and Patterns
● Introduction to coordinate geometry
Lines and Angle Properties
● Measure of Central Tendency
Angle properties, bisectors and construction of polygons
● Introduction to Set Theory
Transformation*
● Probability*
Frequency distribution and statistical graphs*
* The highlighted sections/ topics in this document will not be covered in the academic year 2020-2021
Suggested
Time
0.5 week
Strand
Titles/ Topics
Orientation
1.5 weeks Numbers
Attainment Targets
Suggested Strategies
Suggested Vocabulary
Suggested Resources
Spend the week recapping on number work - counting, square numbers, fractions, looking at the 100 square grids
to look for number patterns through games and fun worksheets
● Generate a discussion
● Numeral
● Number lines
Understanding ● Read, write, order and
Number
compare whole number
with students on why and ● Numeric
marked in
● Natural numbers
Systems
including greater than
how man first felt the
positive &
1000000
need to have numbers in ● Whole numbers
negative numbers
● Know different types of
● Large
his life and what type of ● Integers
● Positive integers
Real Numbers’ subsets (
numbers do they see
thermometer or a
● Negative integers
Natural, Whole, Integers,
around them and the
picture of
● Even
Rational, Irrational
numbers they see in
thermometer that
● Odd
numbers)
Mathematics that they
is numbered
● Convert whole numbers
cannot see in real life (e.g ● Prime numbers
above and below
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into rational numbers
negative numbers) to be
Composite numbers
zero
● Recognize Rational and
● Rational numbers
● Abacus
able to categorize
● Decimal place
Irrational numbers
different kinds of numbers ● Irrational numbers
● With increasing degree of ● Use number cards with
● Less than
value chart
● Greater than
● Number line
challenge, understand and
various multi-digit
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use the concept of place
numbers (smaller and
value for any real numbers
greater than one million)
of any size
written on them and ask
Use number line to
students to read them and
illustrate the position of
compare their sizes
● Group discussion on the
any Real number
Use negative numbers in
pros and cons of rounding
context, and calculate
off amounts. When is it
intervals across zero
okay to round off? When
Use symbols <, >, =, =, ?,
is it not?
● Use number line for
= to compare and order
different types of real
ordering and comparing
numbers
real numbers
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Round any number to a
Investigate real life
required degree of
situations where
accuracy and significance
rounded/approximate
Use knowledge of
numbers are given and
rounding to give an
figure out possible
estimate to a calculation
original numbers
and uses it to check the
reasonableness of the
solution.
Suggested Online Resources:
http://www.softschools.com/math/classifying_numbers/ (classification of numbers/ number system using
Venn diagram)
http://www.math-play.com/rational-and-irrational-numbers-game/rational-and-irrational-numbersgame.html (differentiation of rational and irrational numbers)
● Reinforce application of
● Using multiplication grids
1 week
Number
Properties
divisibility tests for 2, 3, 4,
investigate patterns in
5 & 10 to identify the
multiplication tables to
numbers that are divisible
identify numbers that are
by the given numbers
divisible by the different
● Multiply multi– digit
tables
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Number line
Unit
Ten
Hundred
Thousand
Ten thousand
Hundred thousand
Million
Ten million
Hundred million
Tenth
Hundredth
thousandth
Large numbers
Ordering
Rounding
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Approximation
Significant number
Index numbers
Full form
Approximate
Place value
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marked in
tenths/hundredths
Decimal number
cards
Numbered cards
Base ten material
Thermometer
Weather chart
Number line
Fraction
wall/number line
Square and cube
root bingo cards
Fraction
dominoes
Online games
Calculator where
necessary
whole numbers by a multi- ●
digit whole number using
the formal written method
of long multiplication
● Divide multi-digit whole
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numbers by a 2-digit
whole number using the of
long division and short
division, interpreting
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remainders as whole
number remainders,
fractions, or by rounding,
as appropriate for the
context
● Multiply and divide whole
and decimal numbers by
multiples of 10 (up to
1000000000)
Display a number and have ●
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different groups run
different divisibility tests ●
on that number (Including ●
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division by 1 and 0)
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Online games on
multiplication and division ●
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of multi-digit whole
numbers
Use a number line with
place value headings and
moveable cards with single
digits on them to discuss
place value. Investigate
how the digits move in
relation to the decimal
point when multiplied or
divided by multiples of
ten.
● Cross curricular links:
Include contexts that lend
themselves to using large
numbers (such as
astronomical data or
demographic data) and
small numbers (e.g.
concept of microorganism)
divisible
digit
remainder
quotient
divisor
dividend
short division
long division
Suggested Online Resources:
http://www.mathplayground.com/index_multiplication_division.html (For multiplication and division of large numbers)
https://www.studyladder.com/games/activity/multiply-by-multiples-of-10-22221 (for multiplication with multiples of 10s)
● Quick mental tests on
● Whole numbers
1.5 weeks The Four Integers and ● Perform mental
● Integers
Operations
Decimals
calculations, including
mixed operation (e.g
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● Positive integers
mixed operations and
22/11x10, 50+60x5,
● Negative integers
integers <100
50/5+4x3 etc.
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Use vocabulary and
Choose set of counters in ● Less than
● Greater than
symbols related to addition
different colours to
● Number line
and subtraction,
represent positive and
● Decimal
multiplication and division
negative integers.
● Place value
of integers and decimal
Matching sets of both
numbers to describe and
colours represent zero. For ● Unit
● Ten
record number sentences.
example, blue chips
Order, add and subtract
represent negative integers, ● Hundred
● Thousand
(with or without number
while red chips represent
lines), multiply and divide
positive integers. To solve ● Ten thousand
positive and negative
the problem of (+3) + (–7), ● Hundred thousand
integers
set out three red chips and ● Million
Understand and use
seven blue ones. Physically ● Ten million
commutative and
match up pairs of red and ● Hundred million
associative and distributive
blue chips to equate them ● Tenth
● Hundredth
laws of the four operations
to zero, and remove the
● thousandth
in whole numbers – no
remaining chips. The
definitions
remaining four blue chips ● Large numbers
Identify the value of each
represent the solution, (–4). ● Ordering
● Number sentences
digit in decimal numbers ● Review the concept of
● Terminating
Differentiate between
multiplication by asking
● Non-terminating
terminating, recurring and
students how they can
non-recurring decimals
represent 4 x 2. Include a ● Recurring
Use the symbols > and < to
discussion of commutative ● Non-recurring
compare integers and
property, multiplication as ● Product
● Sum
decimals
repeated addition, and
● addition
Round places of decimal to
multiplication as groups.
the nearest whole number
Ask students whether they ● total
● subtraction
and up to 3 decimal place
can apply their
● difference
Multiply a decimal number
understanding of
with a whole number and a
multiplication of positive ● operation
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decimal number (up to 3
integers to model (–5) •
decimal places only).
(+3). Discuss their thinking ● calculation
Divide decimal numbers by
and bring in the definition ● multiplication
a whole number and by a
of commutative property, ● division
decimal number up to 3
so that the question can be ● divisor
decimal places(by
understood as (+3) x (–5)
converting decimals to
or three groups of –5. And
fractions and by direct
apply the knowledge for
division)
division of integers.
● Use BODMAS to solve
● Online math games on
numerical expressions
integer and decimal
involving integers and
addition, subtraction,
decimals
multiplication and division
● Solve word problems that ● Present the class with
call for addition,
scenarios requiring
subtraction, multiplication
addition, subtraction,
and division of any
multiplication and division
numbers in context of
by decimals, and ask
money, length and weight.
students to record their
estimates and the strategies
they used to arrive at
them
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dividend
Remainder
brackets
BODMAS
Suggested Online Resources:
http://www.sheppardsoftware.com/mathgames/fruitshoot/FS_Mixed_Integers.htm (For mixed operations on Integers)
http://www.math-play.com/decimal-math-games.html (for different games related to decimals including rounding, adding, subtracting, place value etc.)
http://www.sheppardsoftware.com/mathgames/decimals/CompareDecimals.htm (for comparing decimals)
● Ask students to use factor ● Prime numbers
1.5 weeks
Square and ● Recognize prime and
Cube Roots
composite numbers < 200
trees to identify prime and ● Composite numbers
● Calculate squares and
● Perfect square
composite numbers
● To develop concept of
● Perfect cube
cubes, square roots and
cube roots of larger
roots, tell students that a ● Square root
numbers
dance floor is square and ● Cube root
● Use calculator methods to
● Rounding
has an area of 81 m2 .
find squares and cubes,
What are its dimensions? ● Approximation
● Powers/index/exponent
square roots and cube roots. ● Explain why the v30 is
● Use knowledge of the
between 5 and 6 or 3v100 ● Inverse
● Rational roots
relationship between
is between 4 and 5.
● Online games on square
● Irrational roots
powers and roots to
evaluate whole number
and square roots, cubes and ● Prime number
● Composite numbers
powers of any appropriate
cube roots.
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● Prime factor
number, for example, 34 =
Online games on
81 and vice versa (e.g. 3v27
identification of square or ● Prime factorization
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= 3)
Understand that the square
root and cube root is the
inverse process of squaring
and cubing a number
respectively.
Estimate squares and square
roots to solve problems on
Square roots, cubes and
cube roots of small
numbers (e.g. 3v27, 3v8
and v64 etc.)
Describe principal roots and
tell if they are Rational of
Irrational (e.g. v4=2 is
rational number 3v2 or v3 =
decimal are irrational
numbers
Use approximation to the
nearest perfect square and
perfect cube numbers to
find square root and cube
roots of non-square and
non-cubic numbers (e.g.
v1000)
Use estimation to check
answers to calculations and
determine an appropriate
degree of accuracy in
context of a problem
cube root of a number
being a rational or
irrational number
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Suggested Online Resources:
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https://www.mathgames.com/skill/8.6-square-roots-of-perfect-squares (for practicing square root)
https://www.mathgames.com/skill/8.8-estimate-cube-roots (for estimating cube roots of non-perfect cube ●
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numbers)
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http://www.mathopolis.com/games/estimate-sqroot.php ( for estimating square roots of non-perfect
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square numbers)
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Factor tree
Index
Power
Exponent
Factor
Divisor
Multiple
Common factor
Common multiple
Common divisor
lowest (least) common
multiple(LCM)
Highest Common
Factor(HCF)
Greatest Common
Factor (GCD)
Numerator
Denominator
Rational number
Irrational numbers
Fraction
proper fraction
improper fraction
Mixed number
Equivalent fractions
Reciprocal
Cancellation
Integers
Reduce
Simplest form
common denominator
Quantities
Percentage
Relationship
Interest
Principal Amount
Time
Interest Rate
● Ask students to use Venn ●
LCM and HCF ● Recognize prime and
composite numbers < 200
diagram to find common ●
● Find common factors and
multiples and factors and ●
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common multiples of a set
eventually choose HCF
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of multi – digit numbers
and LCM from them.
● Online games on multiples, ●
(up to 4 digit numbers)
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● Find prime factors of any
factors, LCM and HCF
number using division and
factor tree methods
● Write prime factors in the
index/power notation
● Use LCM and HCF in
simple problem solving
Suggested Online Resources:
http://www.bbc.co.uk/education/guides/zp6p34j/test (for practising factors and multiples)
http://www.bbc.co.uk/bitesize/quiz/q65495764 (for practising LCM and HCF)
● Online game on rational
2 weeks
Fractions and ● Recognize Rational and
Percentages
Irrational numbers
and irrational numbers
● Convert whole numbers
● Have all students make up
into rational numbers
one multiple-choice
● Identify and convert
question to ask the class
between various forms of
and let them collect the
fractions (e.g. proper
data on to be able to
fractions, improper
calculate the fraction,
fractions, equivalent
decimal and percentage of
fractions, mixed number
students choosing a
etc.)
particular answer.
● Simplify fractions by
● Hold speed competitions to
cancelling all common
calculate different speeds.
factors and generate
Compare two given parts,
equivalent fractions.
convert them to
● Compare and order
percentages and check
fractions, including
which is larger?
● Compare, which is bigger
fractions > 1 , by
converting them into
20% of 50kg or 15% of
equivalent fractions or
70kg etc. to compare two
decimal notations
quantities by percentages
1 weeks
Annual
Equivalence
Quotient
Inverse Operation
Simplify
Product
Sum
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1 week
Ratio, Rate and ●
Proportion
Add, subtract, multiply and
divide simple and mixed
fractions by integers and
fractions, writing the
answer in its simplest form
Use BODMAS to solve
numerical expressions
involving fractions
Calculate simple
percentages of quantities
and vice versa, with and
without a calculator and
solve simple problems
involving percentages
Compare two quantities by
calculating their percentage
(simple cases)
Use the knowledge of
percentages to solve
problems related to simple
interest (simple cases)
Convert and use
equivalences between
simple fractions, decimals,
ratios and percentages,
including in different
contexts.
Solve word problems
related to fractions and
percentages in context of
money, length and weight.
Use the concept of fraction
to express quantities as
ratio (two or more) and
rate, simplifying where
appropriate to find
equivalent ratios (simple
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Online games on proper,
improper, equivalent
fractions
● Online games on
percentages
Online games on equivalent ●
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fractions
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Place a variety of the three
colours (e.g. blue, white, red) ●
of poker chips into beakers and ●
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ask students to compare the
Quantities
Fractions
Ratio
Rate
Unit
Equivalent ratios
● Ratio table
cases)
number of red chips to blue
Find the missing term in a chips or number of red chips to ● Unit rate
pair of equivalent ratios.
white chips etc. to develop the ● percentages
● Recognize and use common concept of two and three term
measure/units of rate
ratio. Also ask students to
● Convert and use
divide the chips in a given
equivalences between
ratio.
simple fractions, decimals, Give students examples from
ratios and percentages,
daily life to understand how
including in different
different quantities can be used
contexts.
together to form a rate (e.g.100
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km/h, 70 beats/min, $1.69/100
g, $9.50/kg)
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Suggested Online Resources:
http://mathsnacks.com/ratio-rumble.html (for developing the concept of ratios)
● Use letter symbols to
● Introduce students to a
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2 weeks Algebra
Algebraic
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Expressions and
represent unknown
relations game e.g.
Factorization
numbers.
Amanda puts a 3 into the ●
● Develop an understanding
function machine and gets ●
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of the algebraic terms
out a 7. The function
including like term,
machine continues to use ●
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variable, constant,
the same rule, but this
expression and equation
time, Amanda puts in a 6 ●
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and inequality
and gets out a 13. Now
● Multiply simple algebraic
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predict what the output
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expressions by positive and
will be if the input is 5.
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negative constants and a
Explain how you know
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variable
this. Use symbols or
● Simplify linear algebraic
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words to show three
expressions by collecting
different rules the function ●
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like terms (addition and
machine could be
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subtraction)
following at each step.
● Use knowledge of
Later introduce the concept ●
BODMAS to simplify
of changing number to be a ●
algebraic expressions
variable and fixed number ●
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involving brackets
to be a constant for
Constant
Variables
Coefficient
Term
Like term
Reciprocal
Power
Numerical expression
Algebraic expression
Operation
Monomial
Binomial
Polynomial
Linear expression
Equation
Linear equation
formula
Inequality
Linear Inequality
Simplify
Expand
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Variable and
number cards
● Algebra Tiles
● Function
machines
● Online games
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Factorize simple algebraic
students to be able to
expressions with numeric
define the simple algebraic ●
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and algebraic common
expression.
● Recall the concept of
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factors(by taking out
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common terms and by
factors of a numeral to
regrouping)
make students understand ●
the concept of factorization ●
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in algebra. Also, take
factorization as the inverse ●
process of multiplication ●
of an algebraic expression ●
with a number or a variable
or both.
● Online games on
factorization and
simplifications of algebraic
expressions
Suggested online resources:
https://www.khanacademy.org/math/algebra/one-variable-linear-inequalities/alg1inequalities/e/inequalities_on_a_number_line (Tutorial --- Use of number lines for algebraic inequalities)
● Use the example of
2 weeks
Equations and ● Solve basic linear
Inequalities
equations in single
function machines once
variable (using balancing
again to help students
and inverse operation
understand how to form an
methods)
equation e.g. a girl owns
● Begin to use conventional
three horses. She purchases
linear algebra to construct
more horses at an auction;
and solve simple linear
consequently, she now has
equations in given
more horses. Look for
situations (single variable
some quantity that acts like
only)
a term number, in that it
● Change the subject of a
can change in a step-byformula and use
step fashion. That number
substitution method to
will be represented by the
calculate values of
x-variable. The girl may
unknown variables (simple
buy 1, or 2, or 3, or 4, or . .
cases)
. horses. In this case, the x-
Evaluate
Factorize
Common factor
Numeric
Algebraic
Regrouping
BODMAS
Inverse operation
Subject of a formula
Substitute
Number line
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Develop an understanding
of the use of <,> and =
signs in algebraic numbers
● Use number line to
illustrate basic algebraic
inequalities in single
variable (without solution
e.g. x=3, x= -4.5, x= ½)
variable will be the number
of horses she buys. Next,
identify what is the term
value. The term value
depends on the term
number. The number of
horses she ends up with
depends on how many she
buys, so the term value
will be the number of
horses she ends up with.
Then, consider the
presence of a constant or a
numerical coefficient. If
there is a quantity to start
with, or one to remove at
the end, there will be a
constant to add or subtract.
If a variable is being
multiplied or divided, there
will be a numerical
coefficient to connect to
the variable. In this
example, the girl starts
with three horses. She has
three horses no matter how
many she buys. These
three horses are
represented by the constant
+ 3. Hence Put the pieces
together in the relation to
form an equation.
● Ask the class to list all the
values of x that make x>3
true to make them
understand the importance
of number line to illustrate
inequalities and intervals
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Online games on linear
equations and linear
inequalities in one variable
Suggested Online Resources:
http://www.mathplayground.com/SaveTheZogs/SaveTheZogs.html (linear equation)
http://www.mathplayground.com/AlgebraEquations.html (solving a linear equation)
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Sequence and ● Recognise simple patterns ● Ask students to share
Patterns
in different number
patterns they have seen, or ●
sequences (both increasing
present them with samples ●
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and decreasing)
of patterns. Ask them to
● Generate sequences from
describe the patterns. Ask ●
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practical contexts and
whether there are other
describe the nth term in
ways to represent the same
simple cases.
pattern. Review pattern● Use the nth term to
related vocabulary as
generate a sequence.
opportunity arises during
the discussion.
● Introduce students to a
relations game e.g.
Amanda puts a 3 into the
function machine and gets
out a 7. The function
machine continues to use
the same rule, but this
time, Amanda puts in a 6
and gets out a 13. Now
predict what the output
will be if the input is 5.
Explain how you know
this. Use symbols or
words to show three
different rules the function
machine could be
following at each step.
Later introduce the concept
of changing number to be a
variable and fixed number
Pattern
Sequence
Rule
Increasing sequences
Decreasing sequences
Formula
to be a constant for
students to be able to
define the nth (algebraic
expression) term.
● Online games on
Sequences, patterns and
nth term
Suggested Online Resources:
http://www.scootle.edu.au/ec/viewing/L1922/index.html (to generate sequences from practical context)
https://mathsframe.co.uk/en/resources/resource/42/sequences (for sequences)
https://www.funbrain.com/games/number-cracker-game (to find a missing number in given sequence)
http://www.kidport.com/Grade7/TAL/Patterns.htm (Higher order number pattern)
1.5 weeks
Space,
2-D and 3D ● Classify different types of ● Provide students with or
Shape and
shapes
polygons and polyhedra
have them bring in a
Measure
(pyramids, cubes and
multitude of 2-D shapes
prisms)
and classify them
● Differentiate between
according to the number of
regular and irregular
lines of symmetry, and
polygons
rotational symmetry with
● Differentiate between
the angle and order of
convex and concave
rotation.
● Use graph paper and ask
polygons
● Identify and illustrate all
students to draw a shape
lines of symmetry in a wide
and to cut it along a line of
range of 2D shapes and
symmetry. Students
applies this understanding
exchange their drawing
to complete a range of
with another student who
symmetrical patterns
will complete the 2-D
● Rotate objects using
shape. Students should
rotational symmetry and
approach this by counting
describe order of rotational
the spaces from the
symmetry of different 2D
vertices to the line of
shapes
symmetry in order to place
● Identify and recognize
each of the mirrored
planes of symmetry of 3D
vertices and complete the
shapes
shape.
● Uses mathematical
● Identify different 2D
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2-dimensional figure
3-dimensional solid
Polygon
Ployhedra
Regular polygon
Irregular polygons
Concave polygons
Convex polygons
Equilateral polygons
Equiangular polygons
Triangles
Quadrilateral
Equilateral triangle
Isosceles Triangle
Scalene triangle
Right triangle
Obtuse angled triangle
Square
Parallelogram
Rectangle
Rhombus
Kite
trapezium
Pentagon
Hexagon
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ruler
set square
protractor
pencils
pair of compasses
squared paper
nets of shapes
2-D shape cutouts
3-D Solids
set square
pair of compasses
protractor
ruler
tracing paper
scissors
empty cardboard
boxed and tins
● Calculator where
necessary
● Unit cards
● Calculator where
necessary
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language to describe the
properties of a range of
common 2D shapes and 3D ●
objects including side, face,
edge, corner, base and
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angle.
Identify 2D shapes within
3D objects and recognises
3D objects from 2D
drawings.
Describes 2D shapes and
3D objects using specific
vocabulary including face,
edge, vertex, angle,
diagonal, radius, diameter
and circumference
Demonstrate understanding
of the relationship between
3D objects and their nets.
Identify similar and
congruent 2D shapes and
3D objects
Use mathematical language
to describe the properties of
regular and irregular,
convex and concave 2D
shapes and 3D objects.
shapes and 3D objects in ●
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their environment
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Online games on
recognition of congruent ●
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and similar shapes
Online games on linear and ●
rotational symmetry in 2D ●
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shapes and planes of
●
symmetry in 3D objects
Suggested Online Resources:
https://www.youtube.com/watch?v=sWgHtiTSywc (differentiation between convex and concave
polygons)
http://study.com/academy/lesson/concave-convex-polygons-definition-examples.html (Tutorial on
differentiation between convex and concave polygons)
https://illuminations.nctm.org/activity.aspx?id=3544 (relationship between 3D objects and their nets)
http://www.hbschool.com/activity/elab2004/gr3/21.html (lines of symmetry)
● Know use and convert
● Provide pictures of many
1.5 weeks
Area and
Volume
among km, m, cm and mm,
regular triangles, squares
kg and g, liters and mili
and rectangles, with the
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Heptagon
Octagon
Nonagon
decagon
solid
faces
vertices
edges
Cube/cuboid
prism
pyramid
cylinder
circle
circumference
diameter
radius/radii
sector
chord
arc
concentric
eccentric
pi (p)
polyhedra
Angle
diagonal
Area
Surface Area
Perimeter
Squared units
Net
Volume
Cubic units
Space
Capacity
Mass
Length
Altitude
Right Prism
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liters, and vice versa
Use mathematical language
to describe the properties of
regular and irregular 2D
shapes and 3D objects.
Illustrate and name parts of
circles, including radius,
diameter and
circumference, semi circle,
quadrant and know that the
diameter is twice the radius
of a circle.
●
Identify chord, arc and
sector in a circle
By applying appropriate
formulae, calculate the
areas and perimeters of
triangles, squares,
rectangles, and circles.
Calculate the perimeter and
area of simple compound
shapes made with the above ●
mentioned 2D shapes only
(only whole shape).
Understand the meaning of
prisms and right prisms.
Describe 2D shapes and 3D
●
objects using specific
vocabulary including face,
edge, angle, diagonal,
radius, diameter and
●
circumference and apply
this knowledge to
demonstrate understanding
of the relationship between
3D objects and their nets
(including triangular
prisms, cube, cuboids and
●
measure of one side
provided for each. Have ●
students explore to find the ●
most efficient method for ●
finding the perimeters of ●
●
each. Lead students to
discover that “side + side + ●
side + side…” is inefficient ●
when multiplication can be ●
used instead. Repeat the ●
activity with rectangles and ●
●
squares.
Use exploratory activities ●
to find the value of p. Give ●
students circles of different ●
sizes and thread/string to ●
●
calculate the perimeter.
Compare the answer with ●
the answers calculated by ●
the formula and discuss the ●
●
error in the answer
●
Provide paper copies of
nets for students who are ●
having difficulty
visualizing the parts of a 3- ●
D object, for them to cut ●
and fold or use Polydrons. ●
Use a variety of different ●
●
shapes of boxes and
containers for cutting and ●
calculating surface area. ●
Generate a discussions on ●
●
volume, using informal
●
measurement methods,
●
such as linking cubes.
●
Show and discuss the
centimetre cube. Explain ●
that just as square units are ●
Polydron
Triangular prism
Rectangular prism
Right cylinder
Pipe
Right Pyramid
Cone
sphere
lines
segments
rays
parallel
perpendicular
intersecting lines
angles
set square
measure
acute
obtuse
reflex
opposite angles
alternate angles
vertically opposite
angles
adjacent angles
corresponding angles
Triangles
Quadrilateral
Protractor
Standard ruler
Compass
Angle bisector
Line bisector
SSS
SAS
AAS
Symmetry
Rotation
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●
cylinders)
Calculate the surface area
and volume of simple right
prisms with basic 2D
shaped bases (including
triangular, square,
rectangular bases)
Calculate the surface area
and volume of a right
Cylinder
Calculate volume of fluid in
the aforementioned 3D
●
solids
Calculate the missing
dimension from the given
area/perimeter/surface
area/volume of
aforementioned shapes and
solids. (simple cases)
Use concepts of area,
perimeter, surface area and
volume in problem solving
(simple cases)
Approximate areas and
perimeters, surface areas
and volumes of shapes and
objects with non-integer
dimensions
Use metric units length,
mass, capacity for
estimation and calculations.
used to measure area and
surface area, cubic units
are used to measure
volume. Have students
bring in small boxes of
various shapes and sizes
and use centimetre cubes
to determine the volume of
each box and provide
students with relevant
contexts for determining
volume
Use online games on
calculation of perimeters,
areas and volumes
Suggested online resources:
https://mathsframe.co.uk/en/resources/resource/86/convert_g_to_kg (Online Games & Activities)
https://www.studyladder.com/games/activity/converting-between-units-of-mass-grams-and-kilograms27995 (Problems & Activities)
http://www.onlinemathlearning.com/parts-of-circle.html (Parts of a circle)
http://www.hoodamath.com/mobile/games/tronix.html (Online Games & Activities)
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Similar
Congruent
Plane
Planes of symmetry
Kilometer
Meter
Centimeter
Millimeter
Kilograms
Grams
Liters
Mili-liters
1.5 weeks
Lines and
Angles
Properties
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Estimate angles to the
nearest 10 and 100 degrees
Differentiate among lines,
rays and line segments
Differentiate between
Parallel and Perpendicular
lines
Identify, construct acute,
obtuse and reflex angles
using a protractor and use
the vocabulary to describe
and classify a range of
angles within shapes in the
environment
Uses informal methods to
estimate, measure and
describe the size of angles
in relation to a right angle.
Understand identify
between interior and
exterior angles of polygons
Knows that complementary
angles add up to 90 degrees
and supplementary angles
add up to 180 degrees and
uses this knowledge to
calculate missing angles
Understand and use the
angle properties of angles
on a point, adjacent angles
on a line, vertically
opposite angles, alternate
angles, corresponding
angles and interior angles
between parallel lines to
calculate unknown angles
in simple problems.
●
Have students investigate
angles in various shapes,
using the corner of a piece
of paper as a reference for
right angle. Does it fit the
angle of the shape or is
the angle greater/less than
the corner of the paper?
● Have students identify
angles in a variety of real
life contexts (e.g., angles
formed by the two hands
of a clock, by the
intersection of two roads,
and by the blades of
scissors or hedge clippers
etc.)
● Have students represent
parallel or perpendicular
lines, or to make a variety
of angles, including a
right angle, vertically
opposite angles on a
straight line etc.,
concretely using items
like toothpicks or straws
● Online games on angle
properties of parallel and
perpendicular lines
Suggested Online Resources:
https://www.khanacademy.org/math/basic-geo/basic-geo-lines/linesrays/e/recognizing_rays_lines_and_line_segments (for practice)
http://www.cpalms.org/Public/PreviewResourceAssessment/Preview/68848 (Questions Eliciting
Thinking)
http://www.transum.org/Software/SW/Starter_of_the_day/Similar.asp?ID_Topic=3 (A complete resource
including activities, videos and worksheets for teaching Angles& Lines and Angles)
http://study.com/academy/lesson/interior-and-exterior-angles-of-triangles.html (Video for teachers)
● Know how to name
● Use paper folding activity
1.5 weeks
Angle
properties,
polygons and their angles
to explain the concept of
bisectors and
mathematically (e.g using
perpendicular and line
construction of
different notation such as
bisectors
● Have students arrange two
Polygons
<ABC or <A etc.)
● Using a standard ruler and
straws, or two toothpicks:
compass, draw angle and ● parallel to one another;
● intersecting;
line bisectors to divide
● perpendicular at an end
angles and lines
● Understand the terms SSS,
point of one straw;
SAS and ASA in triangles ● perpendicular at endpoints
● Use a ruler and protractor to
of each straw;
●
construct a triangle given
one straw perpendicular to
two sides and the included
the other straw and
angle (SAS) or two angles
bisecting;
● one straw perpendicular to
and the included side
(ASA) or three sides (SSS)
the other straw, but not at
● Draw angle and line
its end points and not
bisectors to divide angles
bisecting;
● one straw bisecting the
and sides of triangles
● Understand and use the sum
other straw but not
of all angles properties of
perpendicular;
triangles and quadrilaterals ● each straw bisecting the
to calculate missing
other straw but not
angle(s) in triangles and
perpendicular;
● one straw bisected by the
quadrilateral (simple
questions only)
other straw and
perpendicular;
● each straw bisecting the
other straw and
perpendicular.
● Have students write the
upper case letters of the
alphabet that only use line
segments. Have them find
examples of bisectors of
segments, perpendicular
segments, and
perpendicular bisectors
● Have the student draw a
triangle of any type and
label its angles 1, 2, 3. Cut
it out. Then have the
student tear off the three
angles and place the three
vertices together to form a
180° angle. Have students
measure and record the
three angles and
investigate the sum of the
angles. Use the same
activity for investigation
on sum of the interior
angles of a quadrilateral.
Suggested online resources:
https://www.khanacademy.org/math/geometry/hs-geo-foundations/hs-geo-polygons/v/sum-of-interior-angles-of-a-polygon (for teachers’ exposition)
http://www.onlinemathlearning.com/congruent-triangles.html (Resource to explain SSS, SAS and ASA in triangles including explanations, practice sheets &
activities)
http://www.helpingwithmath.com/by_subject/geometry/geo_missing_angles_8g5.htm (worksheets )
● Convert between 12 hour
● Online game on
● second
● Analog Wall
1 week
Time and
● minute
Average Speed
clock and 24 hour clock
conversion of times
Clock
● Use real life situations to ● hour
● Digital Clock
and vice versa
● With a degree of
● analogue
● Calculator
calculate arrival time,
● digital
complexity, give the time
journey time and
where
●
that is earlier than or later
departure time.
12- hour
necessary
● 24 – hour
than a particular point in
●
●
●
●
time, calculate the
difference between two
times and find start or end
times for a given time
interval on the same day
Know and calculate arrival
time, departure time and
journey time in a given
situation on the same day
Differentiate between
uniform and average speed
Understand the
relationship between
speed, distance and time.
Solve simple problems
involving time and average
speed
Suggested Online Resources:
http://www.onlinemathlearning.com/average-speed-problems.html (average speed word problems)
http://www.homeschoolmath.net/worksheets/speed_time_distance.php (lessons, activities & worksheets)
https://www.texasgateway.org/resource/average-speed (practice sheets)
1 weeks
Introduction to ● Understand in a coordinate ● Play the game of
Coordinate
point (a,b), “a” is the xBattleships in four
Geometry
coordinate and “b” is the yquadrants by placing
coordinate
submarines carriers and
● Plot and Locate points in
destroyers in different
the four quadrants
quadrants on different
● Use knowledge of function
points and then take turns
machines to understand and
in asking the destroyers to
formulate basic linear
destroy a particular ship
functions
by calling out the point at
● Plot and compare the
which the ship is located
graphs of linear functions
in that moment. or play
(e.g. Y = c, x =a and y = mx
Treasure Hunt to find a
+ c) and observe the pattern
selected coordinate from
in the coordinate points that
"closer" or "further away"
form these linear
responses.
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Arrival time
Departure time
Journey time
Distance
Speed
Uniform speed
Average speed
Ordinate
Abscissa
Point
Coordinates
Location
Quadrant
Function machine
Rule
Formula
Linear
Origin
Horizontal
Vertical
X-axis
Y-axis
translation
●
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●
Graph papers
Rulers
Pencils
Protractor
functions
●
Use the knowledge of
function machines to
remind students the
concept of input and
output numbers and
develop the concept of
input as the x-coordinate
and output as the ycoordinate.
● Use online resources to
draw lines and observe
the changes in them as the
points are changed and
vice versa
Suggested Online Resources:
https://www.engageny.org/sites/default/files/downloadable-resources/math-g6-m3-topic-c-lesson-15-teacher.pdf (lesson plan with complete resources)
https://www.khanacademy.org/math/basic-geo/basic-geo-coord-plane/coordinate-plane-4-quad/v/the-coordinate-plane (Teachers’ exposition)
https://www.mathplayground.com/functionmachine.html (Games & Videos can be used as starter activity)
● Demonstrate
● Distribute to each student
0.5 week
Transformation
(2D shapes)
understanding of
a sheet of graph paper, a
transformation by
pair of scissors. Have
reflecting 2D shapes in
students cut out a 2-D
a given line on four
shape and draw a
quadrant grid (simple
vertical/horizontal line on
cases)
the graph paper. To model
a set of successive
reflections, have students
do a few reflections
downward or upward and
a few to the left or right.
After each reflection,
students will be asked the
following questions: a) In
which direction did the 2D shape move? b) What
changed? c) What
remained the same?
●
Online games on
reflection of 2D shapes in
different lines of
reflection
Suggested Online Resources:
https://www.khanacademy.org/math/geometry-home/transformations ( for understanding transformation by reflecting)
https://mathsframe.co.uk/en/resources/resource/153/coordinates--reasoning-about-position-and-shapes ( transformation)
● Collect and record data,
● coordinates
1.5
Handling
Frequency
1. Have a class discussion
● quadrant
weeks
Data
Distribution
choosing an appropriate
about first-hand and
● x-axis
and Statistical
method (by surveys,
second-hand data, the
● y-axis
Graphs
interviews,
differences between
● vertices
measurement and
continuous and discrete
● positive
electronic means)
data and when to use
● Differentiate between
● negative
each type.
● horizontal
discrete and continuous
2. Ask students to look up
● vertical
data
the
● Construct and interpret
● origin
hockey/cricket/football
● data
frequency tables for
scores for a favourite
● ungrouped data
discrete data only
team over the course of
● Construct, compare and
● grouped data
10 games and then
● sector
interpret of bar
create a line graph with
● Fraction
graphs(vertical,
the ordered pairs (game
● proportion
horizontal, multiple
number, number of
● angle
(upto 3 bars), line
goals scored by
● data
graphs and pictogram
favourite team). Have
● degrees
for discrete data only
them create a second
● Calculate sector angles
● survey
graph with the ordered
● interview
from a given data set
pairs (game number,
● discrete data
and construct and
goals scored by
● continuous data
interpret pie charts
opposing team) and
● Selects and justify most
● frequency
then compare the two
● frequency table
appropriate graph(s) for
graphs.
● bar graph
a given data set and
3. Set up groups that
● multiple bar graph
draw simple
collect, arrange and
● sectional bar graph
conclusions based on
display different kinds
● histogram
the shape of graphs.
of data through
● line graph
different methods
●
●
●
●
●
Ruler
Protractor
compass
Graph paper
Calculator
where
necessary
including
questionnaires,
experiments, databases,
electronic media. Ask
students to construct
frequency tables from
that data and choose
the most appropriate
graph to represent
it.The groups may give
a presentation at the
end of their data
collection.
4. Examine many realworld pictographs, bar,
double bar, and line
graphs gathered from
newspapers,
magazines, and other
print media. Discuss
why the choice of
format is appropriate in
each case. Ask students
questions that can be
answered through
careful analysis of the
graph.
5. Link the concept of
fraction and ratio with
the calculation of area
of sectors for a pie
charts
●
●
●
●
pictogram
pie chart
questionnaire
tally bars
Suggested Online Resources
http://shodor.org/interactivate/activities/CircleGraph/ ( for Pie chart)
http://study.com/academy/lesson/interpreting-pie-charts-and-bar-graphs.html ( for bar and pie chart along with quiz)
http://www.scholastic.com/browse/unitplan.jsp?id=273 ( for bar graph)
● Calculate mean,
● For quantitative data
● data
1 week
Measure of
Central
Tendency
median, mode and
range for any
ungrouped data.
● Compare, choose and
justify the appropriate
measures of central
tendency (mean, mode,
median) for a given set
of data
collected in the
previous unit, Ask
students to choose and
calculate appropriate
measure of central
tendency and explain
why it is the most
suitable average for the
given data.
● Data collected on
heights and weights of
various students in the
school could be used to
show average height of
students in class, even
give information on
height by gender.
● Use online games on
measures of central
tendency
●
●
●
●
●
●
●
●
●
Grouped data
Ungrouped data
Discrete data
Continuous data
median
mode
mean
range
average
Suggested Online Resources:
https://www.pbslearningmedia.org/resource/ea4d290e-7d88-43b6-b50f-5f3355df5e49/ea4d290e-7d88-43b6-b50f-5f3355df5e49/#.WSaPqNwlHIU (mean,
median and mode)
https://www.brainpop.com/math/probability/meanmedianmodeandrange/ ( mean, mode and median)
http://www.shodor.org/interactivate/lessons/IntroStatistics/ (introduction to statistics)
● Understand the meaning
● Use the example of
● Set
1.5 weeks
Introduction to
● Element
Set Theory
of the terms “set” and
collective nouns (e.g. a
● Equal sets
“elements of a set”
flock of birds, a fish of
● Describe and write
● Finite sets
school, a pack of
● Infinite sets
mathematically if an
wolves, a hive of bees)
● Natural numbers
object/number is an
to develop the basic
● Whole numbers
element of a set
understanding of a set
● Differentiate between
● Integers
(i.e. it is a
● Rational numbers
finite and infinite set
collection/group of like
● Describe and list
● Irrational numbers
items)
●
● Proper set
elements of a set from a
Use the knowledge of
● Improper set
simple descriptive
infinite and finite
●
●
●
●
set(e.g. set of first 5
positive even numbers)
Understand, describe
and write the universal
set, subsets ( both
proper and improper),
an empty set, equal sets,
disjoint sets and
overlapping sets
Describe in words and
write number of
elements in a set
mathematically
Find union and
intersection between
two sets
Show relationships
between sets using
Venn diagram (with 1
universal set and two
subsets)
sequences to introduce
infinite/finite sets
● Generate a discussion
on numbers system to
deepen the knowledge
of basic set theory
● Online games on set
theory and Venn
diagram
Suggested Online Resources:
http://www.math-only-math.com/types-of-sets.html (for sets)
https://www.youtube.com/watch?v=LOcHPWi3X2I&feature=youtu.be (sets game)
http://www.math-only-math.com/disjoint-of-sets-using-Venn-diagram.html (all type of sets)
● Understand the meaning
● Ask students to roll a
1 week
Probability
of the terms outcome,
die, toss a coin and
event, sample space,
spin a spinner to list all
mutually exclusive
possible outcomes of
events, equally likely
the experiment
● Make a connection
events, impossible
outcomes, favorable
with set theory to make
outcome.
sample space set of all
● Use the knowledge of
possible outcomes of
sets theory to list all
different experiments
●
element of sample space
Use two spinners (one
and its subsets of a
divided in equal sectors
●
●
●
●
Empty set
Universal set
Overlapping sets
Venn diagram
●
●
●
●
Event
outcome
Experiment
Mutually exclusive
event
Equally likely
events
Impossible events
Favorable outcomes
Sample space
probability
probability scale
●
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●
●
●
●
●
●
Dice
Coins
Bag of colored
balls
A pack of 52
cards
Numbered
spinners
Numbered
cards
Calculator
where
●
●
●
●
●
single event experiment
( a die, a coin,
numbered cards, a bag
of balls, a spinner , a
pack of 52 cards etc.)
Understand what it
means for an event to be
“mutually exclusive
event”
Use the knowledge of
set theory to write
number of elements in
sample space and its
subsets mathematically
Find and justify
probabilities in single
event experiments
Calculate and check that
the total probability of
all the mutually
exclusive outcomes of
an experiment is 1.
Use the knowledge of
probability in simple
problem solving.
and the other divided in
unequal sectors) to
develop the concept of
equally likely events.
Have students explore
situations for which
outcomes are equally
likely (e.g equal
numbers of different
coloured balls in a bag
etc.)
● Link the concept of
fractions to explain
students the idea of
probability of an event.
Also, sum of all parts
of a fraction makes a
whole = sum of all
probabilities of an
experiment is 1
● Ensure students acquire
an understanding that
probability can be
represented in multiple
forms (e.g. fraction,
decimal, ratio, and
percentage. One means
of accomplishing this
understanding is by
specifying a particular
form for the answer.
● Give questions,
occasionally, for which
different groups are
given the same
problem but each group
is asked to present the
answer in a different
●
●
●
●
poor chance
even chance
certain
impossible
necessary
form. When the class
discusses the results in
a large group, students
should observe the
variation in the answers
and discuss or account
for the differences.
Through such
experiences, students
should come to the
realization that the
various forms are
alternative
representations of the
same value.
● Online games on
probability
Suggested Online Resources:
http://www.mathgoodies.com/lessons/vol6/sample_spaces.html (probability)
https://www.youtube.com/watch?v=4IQpe3J-2AU (teacher’s resource)
https://www.youtube.com/watch?v=mhlc7peGlGg (teacher’s resource)