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Dawood Public School Course Outline for Class VI
Mathematics 2014-15
Books:
Sang, T.et al, 2008, New Syllabus Mathematics 1(6th Edition), Singapore; Oxford University
Monthly Syllabus for the year 2014-15
MONTHS TOPICS DURATION
AUGUST Factors and Multiples Integers Math activity Calendar
1.5weeks 2weeks
SEPTEMBER Rational Numbers Fundamental Algebra Math activity Calendar
2.5 weeks 1.5 week
OCTOBER
Fundamental Algebra Geometrical construction Basic Geometrical Concepts
and Properties Math activity Calendar
0.5 week 1.5 weeks 2 weeks
NOVEMBER REVISION FOR MID TERM
EXAMS Math activity Calendar
DECEMBER MID TERM EXAMS
JANUARY
Estimation and Approximation Perimeter and Area of Simple
Geometrical Figures. Maths activity Calendar
2weeks 2 weeks
FEBRUARY
Length and area conversion Volume and surface area of
cube and cuboids(Ex#9a) Algebraic Equations and
Simple Inequalities(Ex#7a-7e) Math activity Calendar
0.5 week 1.5week 2weeks
MARCH
Ratio, Rate and Speed Functions and graphs Reading of bar graphs and
pictogram(Ex#13a) Math activity Calendar
1.5 weeks 2 weeks 0.5 week
APRIL
(Contd)Reading of bar graphs and pictogram(Ex#13a)
REVISION FOR FINAL EXAMS Math activity Calendar
1 week
MAY FINAL TERM EXAMS
2
Syllabus Content:
AUGUST
CHAPTER#1: Factors and multiples Page numbers: 3-25 CHAPTER#2: Integers Page numbers: 31-47
Month Theme or Topic Subject Content
AU
GU
ST
Factors and Multiples
Chap No. 1
Pg No.( 3-25)
Students should be able to:
Use the four operations for
calculations with whole numbers,
decimal fractions and vulgar (and
mixed) fractions, including correct
ordering of operations and use of
brackets.
Write down the factors of a whole
number.
Write down the multiples of a whole
number.
Distinguish a prime number from a
composite number.
Express a composite number as a
product of prime numbers using index
notations.
Find the HCF of two or more
numbers.
Find the LCM of two or more
numbers.
Find the squares and square roots of
numbers.
Find the cubes and cube roots of
numbers.
Estimate mentally the square roots
and cube roots of numbers which are
not perfect squares or cubes.
AU
GU
ST
Integers
Chap No. 2
Pg No.(31-47)
Use natural numbers, integers
(positive, negative and zero), prime
numbers, common factors and
common multiples, rational and
irrational numbers, real numbers;
Use negative numbers in practical
situations.
Represent integers and order them
using the number line.
Perform addition of integers.
Perform subtraction of integers.
Solve non-routine problems using
problem solving strategies such as
drawing a diagram, using trial and
error etc.
3
ATTAINABLE TARGETS Factors and multiples:
Apply and explain the use of prime factorizations, common factors, and common multiples in
problem situations.
Find and use the prime factorization of composite numbers. For example:
1 - Use the prime factorization to recognize the greatest common factor (GCF).
2 - Use the prime factorization to recognize the least common multiple (LCM).
3 - Apply the prime factorization to solve problems and explain solutions.
Integers:
Define negative numbers, origin, opposite numbers and integers
Construct a vertical and horizontal number line
Explain the difference between positive and negative numbers
Assign an integer to a specific situation.
Recognize and order integers.
Add, subtract, multiply and divide integers.
4
SEPTEMBER
CHAPTER#3: Rational Numbers Page numbers: 53-68
CHAPTER#5: Fundamental Algebra Page numbers: 91-106
Month Theme or Topic Subject Content
SEP
TEM
BER
Rational Numbers
Chap No.3
Pg No.(53-68)
Students should be able to:
Calculate squares, square roots,
cubes and cube roots of numbers.
Identify a rational number.
Order rational numbers on a number
line.
Perform addition and subtraction on
rational numbers.
Perform multiplication and division
on rational numbers.
Use the four basic operations on
numbers and brackets to simplify
rational numbers.
Solve word problems involving
rational numbers.
Represent recurring and terminating
decimals.
SEP
TEM
BER
Fundamental Algebra
Chap No.5
Pg No.(91-106
Students should be able to:
Use letters to express generalized
numbers.
Write down algebraic expressions
from given mathematical statements.
Evaluate algebraic expressions by
substitution.
Simplify algebraic expressions
involving +, −, x, ÷ and power of an
algebraic term.
Simplify algebraic expressions
involving brackets.
Perform addition and subtraction of
algebraic expressions.
Simplify simple algebraic fractions.
Factorization of simple algebraic
expressions.
Factorization of simple algebraic
expressions by grouping.
Use four operations for calculation of
algebraic equations.
5
ATTAINABLE TARGETS Rational Numbers:
Construct and use a large number line to develop an understanding of rational numbers.
Determine if a number is rational or irrational, order rational and irrational numbers on a number line and locate square roots on a number line.
Know the meaning of square roots, find the square root of a perfect square and approximate the square root of a non perfect square to the nearest whole number.
Fundamental Algebra:
Determine if a polynomial is written as a product of linear factors.
Write a quadratic polynomial as a product of linear factors with real and complex roots.
Write a cubic polynomial as a product of linear factors with real and complex roots
6
OCTOBER
CHAPTER #5 (Contd.) Fundamental Algebra Page numbers: 91-106 CHAPTER #16: Geometrical Constructions Page numbers: 383-396 CHAPTER#14: Basic Geometrical Concepts and Properties Page numbers: 333-350
Month Theme or Topic Subject Content
OC
TOB
ER
Contd. Fundamental Algebra
Chap No.5
Pg No.(91-106
Geometrical Constructions
Chap No.16
Pg No.(381-399)
Students should be able to:
Measure lines and angles;
Construct simple geometrical figures
from given data, angle bisectors and
perpendicular bisectors using
protractors or set squares as necessary;
Read and make scale drawings.
(Where it is necessary to construct a
triangle given the three sides, ruler and
compasses only must be used.)
Construct a triangle from given data
using a pair of compasses, a ruler and/or
a protractor.
Construct a quadrilateral from given
data using a pair of compasses, a ruler
and/or a protractor.
7
OC
TOB
ER
Basic Geometrical Concepts
and Properties
Chap No.14
Pg No.(331-353)
Students should be able to:
Measure a given angle with a
protractor.
Identify (a) acute, (b) obtuse, and (c)
reflex angles.
Find the complement and supplement
of a given angle.
Construct a given angle with a ruler
and a protractor.
Find unknown angles using the
properties of:
(a) Angles at a point, (b) Vertically
opposite angles, (c) Adjacent angles
on a straight line.
Find unknown angles using the
properties of:
(a) Corresponding, (b) alternate, (c)
interior angles for two parallel lines
cut by a transversal.
Use and interpret the geometrical
terms: point, line, plane, parallel,
perpendicular, right angle, acute,
obtuse and reflex angles, interior and
exterior angles, regular and irregular
polygons, pentagons,
ATTAINABLE TARGETS
Geometrical Construction:
Given a circular cutout students be able to construct and identify:
the radius, diameter and center of a circle;
the vertex, base and midpoint base of a triangle;
Two-dimensional shapes (semi-circle/half circle, quarter-circle, triangle, parallelogram-rhombus.
Apply loci to spatial problems involving shapes and paths; use straight edge and compasses to
produce standard constructions including the midpoint and perpendicular bisector of a line
segment, the perpendicular from a point to a line, and the bisector of an angle.
Basic Geometrical Concepts and Properties:
Describe and identify basic geometry ideas including line segments, rays, lines, parallel lines, perpendicular lines, and midpoint. Students will describe attribute of angles and measure angles.
Describe, identify and visualize parallel and perpendicular edges or faces; use these properties to classify 2-D shapes.
Use correctly the vocabulary, notation and labeling conventions for lines, angles and shapes
8
NOVEMBER Revision for Mid Term Exams
DECEMBER Mid Term Exams
JANUARY CHAPTER#4: Estimation and Approximation Page numbers: 73-86
9
CHAPTER#8: Perimeter and Area of Simple Geometrical Figures Page numbers: 169-188
Month Theme or Topic Subject Content
JAN
UA
RY
Estimation and Approximation
Chap No.4
Pg No.(71-88)
Students should be able to:
Make an estimate of the value of a
given problem involving sum,
difference, product, quotient, square
and square root, cube and cube root
of numbers.
Round off a number to the required
degree of accuracy.
State the rules for writing significant
figures.
Make estimates of numbers,
quantities and lengths, give
approximations to specified numbers
of significant figures and decimal
places and round off answers to
reasonable accuracy in the context of
a given problem.
JAN
UA
RY
Perimeter and Area of Simple
Geometrical Figures
Chap No.8
Pg No.(169-188)
Students should be able to:
Use and interpret vocabulary of
triangles, circles, special
quadrilaterals;
Solve problems involving
the perimeter and area of a rectangle
and triangle,
the circumference and area of a
circle,
the area of a parallelogram and a
trapezium,
Calculate the area of complex figures
involving triangles, rectangles,
parallelograms, trapeziums, circles
etc.
ATTAINABLE TARGETS: Estimation and Approximation:
Understand how to measure and estimate lengths.
Understand the difference between measuring and estimating;.
Become more aware of linear measurements in the world and communicate better about the significance of these measurements.
Points to be noted:
It should remind that:
not to do rounding off before the end of the calculation if they are asked to give the answer in a rounded form. e.g. 6.34 + 3.23 = 9.57 = 9.6 (correct to 2 significant figures) not 6 . 3 4 + 3 . 2 3 = 6.3 + 3.2 = 9.5; 123 do not round off prematurely
10
that the first significant figure of 0.04218 is 4, not 0 and thus 0.04218, correct to two significant figures, is 0.042 and not 0.04;
that the first two significant figures of 2.01479 are 2 and 0, not 2 and 1 and thus 2.01479, correct to four significant figures, is 2.015, not 2.0148;
that 4.398, correct to three significant figures, is 4.40, not 4.4;(Note: Do not confuse number of decimal places with number of significant figures.)
to do rounding off at the very end of the calculation and work to one more significant figure than you are required to give. For example, use four significant figures until the end of your calculations if the final answer is to be given to three significant figures;
not to give an answer to too many decimal places or significant figures. For example, if your calculator shows 6.326579438, give your answer as 6.33 or 6.327, not 6.326579438;
Perimeter and Area of Simple Geometrical Figures:
Perimeter: Given a polygon, the lengths of whose sides are given or can be determined, calculate the
perimeter. Given a rectangular grid, create a figure with a specified perimeter. Given a figure on a rectangular grid, create a figure having different dimensions but the same
perimeter. Area: Given a figure on a rectangular grid, find the area. Given a rectangular grid, create a figure with a specified area. Given a figure on a rectangular grid, create a different figure with the same area.
FEBRUARY CHAPTER#9: Volume and surface area (Ex#9a) Page numbers: 189-190 CHAPTER#7: Algebraic Equations & Simple Inequalities Page Numbers: 139-166
Month Theme or Topic Subject Content
11
FEB
RU
AR
Y
Volume and Surface Area
Book 1, Chap No.9
Pg No.(189-190)
Students should be able to:
Identify and convert a metric unit of
volume into another metric unit such
as:
1 m3 = 1 000 litres,
1 litre = 1 000 cm3, etc.
Draw the net of a cuboid.
State and use the formulae for finding
the volume and surface area of
cuboids.
FEB
RU
AR
Y
Algebraic Equations and Simple
Inequalities
Chap No.7
Pg No.(137-165)
Students should be able to:
Solve simple linear equations in one
unknown;
Solve fractional equations with
numerical and linear algebraic
denominators;
Solve simple algebraic equations by
inspection.
State the rules for solving algebraic
equations:
(a) equal numbers may be added to or
subtracted from each side,
(b) Each side may be multiplied or
divided by equal numbers except
zero.
Use the above rules to solve simple
algebraic equations.
Use the rules to solve algebraic
equations involving fractions and
decimals.
Find the value of an unknown in a
formula by substitution.
Construct simple formulae from given
word
Expressions.
Express word expressions by algebraic
methods.
ATTAINABLE TARGETS Volume and Surface Area:
Calculate the area of right-angled triangles given the lengths of the two perpendicular sides, and the
volume and surface area of cubes and cuboids.
Calculate unknown side if two sides and volume is given;
Calculate surface area using formula of cube, cuboids and prism.
12
Algebraic Equations and Simple Inequalities:
Demonstrate an understanding of vocabulary used in algebraic thinking.
Discover general expressions using variables to represent number patterns.
Write and solve single-step equations using variables. Points to be noted: The concept of transferring a term from one side of an equation to another side and changing the signs could be introduced after students have enough practice with adding or subtracting equal numbers from both sides of an equation and multiplying or dividing each side of an equation by equal numbers. This is an area where many errors frequently occur. Common Errors Made By Students
13
MARCH CHAPTER#10 Ratio, Rate and Speed Page Numbers: 225-246 CHAPTER# 12: Functions and Graphs
14
Page Numbers: 269-288 CHAPTER# 13(Book 1): Statistics (Ex#13a) Page Numbers: 291-324
Month Theme or Topic Subject Content
MA
RC
H
Ratio, Rate and Speed
Book 1, Chap No. 10
Pg No.(225-246)
Students should be able to:
Demonstrate an understanding of the
elementary ideas and notation of
ratio, direct and inverse proportion
and common measures of rate;
Divide a quantity in a given ratio;
Use scales in practical situations,
calculate average speed;
Express direct and inverse proportion
use this form of expression to find
unknown quantities.
Calculate times in terms of the 12-
hour and 24-hour clock;
Read clocks, dials and timetables.
Apply the results:
(a) Average speed = Distance
travelled/Time taken,
(b) Distance travelled = Average speed x
Time taken,
(c) Time taken = Distance
travelled/Average speed, to calculate
average speed, distance travelled and
time taken respectively.
Convert speed in km/h to m/s and
vice versa.
MA
RC
H
Functions and Graphs Book 1, Chap No.12 Pg No.(269-288)
Statistics
Book 1, Chap No.13
Pg No.(291-324)
Students should be able to:
Demonstrate familiarity with Cartesian
coordinates in two dimensions.
Calculate the gradient of a straight line
from the coordinates of two points on it;
Interpret and obtain the equation of a
straight line graph in the form
y = mx + c.
Collect, classify and tabulate statistical
data; read, interpret and draw simple
inferences from tables and statistical
diagrams.
ATTAINABLE TARGETS Ratio, Rate and Speed:
Demonstrate their understanding of the concept of a ratio by using ratio language to describe relationships between quantities.
Choose appropriate units of measure and use ratios to convert within and between measurement systems to solve problems.
15
Functions and Graphs:
Generate coordinate pairs that satisfy a simple linear rule;
Plot the graphs of simple linear functions, where y is given explicitly in terms of x, on paper;
Recognize straight-line graphs parallel to the x-axis or y-axis
Statistics:
Organize data
Describe data
Read and interpret displays of data
Construct appropriate displays of data, pictogram, bar chart, line graph.
Justify the choice of display used for given data
State common pupil errors in data representation
Illustrate methods to misrepresent data
Use appropriate project work in the classroom to assist the pupils in their learning of data
representation
16
APRIL
REVISION FOR FINAL EXAMS
MAY
FINAL EXAMS
Breadth of Study:
During the key stage, students should be taught the knowledge, skills and understanding through:
(a) Activities that ensure they become familiar with, and confident using, standard procedures for the
range of calculations appropriate to this level of study;
(b) Solving familiar and unfamiliar problems in a range of numerical, algebraic and graphical contexts
and in open-ended and closed form;
(c) Using standard notations for decimals, fractions, percentages, ratio and indices;
(d) Activities that show how algebra, as an extension of number using symbols, gives precise form to
mathematical relationships and calculations;
(e) Activities in which they progress from using definitions and short chains of reasoning to
understanding and formulating proofs in algebra and geometry;
(f) A sequence of practical activities that address increasingly demanding statistical problems in which
they draw inferences from data and consider the uses of statistics in society;
Assessment and Home Work
Students will be assessed by taking test of each and every chapter. Home Work shall be given on a daily
basis.
Mathematical Notations:
The list which follows summarizes the notation used
Mathematical Symbols
= is equal to
≠ is not equal to
≡ is identical to or is congruent to
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≈ is approximately equal to
Operations
a + b a plus b
a – b a minus b
a × b, ab, a.b a multiplied by b
a ÷ b, a, a/b a divided by b
b
Resource List
Books:
Sang, T.et al, 2008, New Syllabus Mathematics Work Book 1(6th Edition), Singapore; Oxford University Press Bostock, L, S Chandler, A Shepherd, E Smith ST(P) Mathematics Books 1A to 5A
(Stanley Thornes)
Book 1A
Book 1B
Buckwell, Geoff Mastering Mathematics (Macmillan Education Ltd) 0 333 62049 6
Collins, J, Warren, T and C J Cox Steps in Understanding Mathematics (John Murray) Book 1
Book 2
National Mathematics Project (NMP) Mathematics for Secondary Schools Red Track Books 1 to 5
(Longman Singapore Publishers Pte Ltd)
Book 1
Book 2
Cox, C J and D Bell Understanding Mathematics Books 1–5 (John Murray) Book 1
Websites:
www.nrich.com
www.hoddereducation.com
www.collinseducation.com
www.pearsonschoolsandfecolleges.co.uk
www.hoddereducation.com
www.lettsandlonsdale.com
www.counton.org
www.math.com
www.maths-help.co.uk
www.mathsnet.net