1

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.

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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.

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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

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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.

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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

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NOVEMBER Revision for Mid Term Exams

DECEMBER Mid Term Exams

JANUARY CHAPTER#4: Estimation and Approximation Page numbers: 73-86

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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

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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.

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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.

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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

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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