DAWOOD PUBLIC SCHOOL COURSE OUTLINE FOR CLASS VI MATHEMATICS

Transcription

1 DAWOOD PUBLIC SCHOOL COURSE OUTLINE FOR CLASS VI MATHEMATICS Books: Sang, T.et al, 2008, New Syllabus Mathematics 1(6 th Edition), Singapore; Oxford University Press. Introduction: This syllabus designed to promote continuity, coherence and progression within the study of Mathematics. The syllabus builds on the knowledge, understanding and skills developed within the Key Stage of Study for Mathematics. This syllabus has been designed to meet the requirements of the GCSE regulations. It has been designed to be as free as possible from ethnic, gender, religious, political or other forms of bias. Syllabus Aims and Assessment Objectives: The syllabus demands understanding of basic mathematical concepts and their applications, together with an ability to show this by clear expression and careful reasoning. In the examination, importance will be attached to skills in algebraic manipulation and to numerical accuracy in calculations. Aims: The course should enable students to: Use the laws of arithmetic and inverse operations to simplify calculations with whole numbers and decimals. Manipulate numbers, algebraic expressions and equations, and apply routine algorithms. Understand everyday systems of measurement and use them to estimate, measure and calculate. Recognize and use spatial relationships in two and three dimensions. Draw accurate mathematical diagrams, graphs and constructions. Check results of calculations by using inverse operations. Estimate, approximate and check their working. Solve word problems involving whole numbers, percentages, decimals, money or measures: choose operations and mental or written methods appropriate to the numbers and context, including problems with more than one step. Assessment objectives: The examination tests the ability of students to: Recognize the appropriate mathematical procedures for a given situation. Perform calculations by suitable methods, with and without a calculating aid. Use the common systems of units. Estimate, approximate and use appropriate degrees of accuracy. Interpret, use and present information in written, graphical, diagrammatic and tabular forms. Use geometrical instruments. Recognize and apply spatial relationships in two and three dimensions. Recognize patterns and structures in a variety of situations and form and justify generalizations. Understand and use mathematical language and symbols and present mathematical arguments in a logical and clear fashion. Apply and interpret Mathematics in a variety of situations, including daily life. Formulate problems into mathematical terms, select, apply and communicate appropriate techniques of solution and interpret the solutions in terms of the problems. Units: SI units will be used in questions involving mass and measures: the use of the centimeter will continue. Monthly syllabus: MONTHS TOPICS DURATION Factors and Multiply 1.5 Weeks AUGUST Integers 2 Weeks

2 SEPTEMBER OCTOBER Math activity Calendar Rational Numbers Fundamental Algebra Math activity Calendar Fundamental Algebra Geometrical construction Basic Geometrical Concepts and Properties Math activity Calendar 2.5 Weeks 1.5 Weeks 0.5 Week 1.5 Weeks 2 Weeks NOVEMBER REVISION FOR MID TERM EXAMS Math activity Calendar DECEMBER MID TERM EXAMS JANUARY FEBRUARY MARCH APRIL Estimation and Approximation Perimeter and Area of Simple Geometrical Figures Math activity Calendar 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 Ratio, Rate and Speed Functions and graphs Reading of bar graphs and pictogram(ex#13a) Math activity Calendar (Contd)Reading of bar graphs and pictogram(ex#13a) REVISION FOR FINAL EXAMS Math activity Calendar 2 Weeks 2 Weeks 0.5 Week 1.5 Weeks 2 Weeks 1.5 Weeks 2 Weeks 0.5 Week 1 Week MAY FINAL TERM EXAMS Syllabus contents: AUGUST

3 CHAPTER # 1: Factors and multiples Page numbers: 3-25 CHAPTER # 2: Integers Page numbers: Month Theme or Topic Subject Content Factors and Multiples Chap No. 1 Pg No.( 3-25) 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.

4 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. 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.

5 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. SEPTEMBER CHAPTER # 3: Rational Numbers Page numbers: CHAPTER # 5: Fundamental Algebra Page numbers: 91-1 Month Theme or Topic Subject Content Rational Numbers Chap No.3 Pg No.(53-68) 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.

6 Fundamental Algebra Chap No.5 Pg No.( 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. 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:

7 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. Month Theme or Topic Subject Content OCTOBER CHAPTER # 5 (Contd.) Fundamental Algebra Page numbers: CHAPTER # 16: Geometrical Constructions Page numbers: CHAPTER # 14: Basic Geometrical Concepts and Properties Page numbers:

8 Contd. Fundamental Algebra Chap No.5 Pg No.( Geometrical Constructions Chap No.16 Pg No.( ) 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. Basic Geometrical Concepts and Properties Chap No.14 Pg No.( ) 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, alternate, 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: i. The radius, diameter and center of a circle. ii. The vertex, base and midpoint base of a triangle. Two-dimensional shapes (semi-circle/half circle, quarter-circle, triangle, parallelogram-rhombus.

9 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.

10 NOVEMBER (REVISION FOR MID TERM EXAMS) DECEMBER (MID TERM EXAMS) JANUARY CHAPTER # 4: Estimation and Approximation Page numbers: CHAPTER # 8: Perimeter and Area of Simple Geometrical Figures Page numbers: Month Theme or Topic Subject Content

11 Estimation and Approximation Chap No.4 Pg No.(71-88) 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. Perimeter and Area of Simple Geometrical Figures Chap No.8 Pg No.( ) Use and interpret vocabulary of triangles, circles, special quadrilaterals. Solve problems involving. i. The perimeter and area of a rectangle and triangle. ii. The circumference and area of a circle. iii. 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 = 9.57 = 9.6 (correct to 2 significant figures) not = = 9.5; 123 do not round off prematurely. The first significant figure of is 4, not 0 and thus , correct to two significant figures, and is and not The first two significant figures of are 2 and 0, not 2 and 1 and thus , correct to four significant figures, is 2.015, not , correct to three significant figures, is 4.40, not 4.4 ;( Note: Do not confuse number of decimal places with number of significant figures).

12 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 , give your answer as 6.33 or 6.327, not 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: CHAPTER # 7: Algebraic Equations & Simple Inequalities Page Numbers: Month Theme or Topic Subject Content

13 Volume and Surface Area Book 1, Chap No.9 Pg No.( ) Identify and convert a metric unit of volume into another metric unit such as 1 m 3 = liters, 1 liter = cm 3, etc. Draw the net of cuboids. State and use the formulae for finding the volume and surface area of cuboids. Algebraic Equations and Simple Inequalities Chap No.7 Pg No.( ) 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: i. Equal numbers may be added to or subtracted from each side. ii. 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.

14 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.

15 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

16 CHAPTER # 10 Ratio, Rate and Speed Page Numbers: MARCH CHAPTER # 12: Functions and Graphs Page Numbers: CHAPTER # 13 (Book 1): Statistics (Ex#13a) Page Numbers:

17 Month Theme or Topic Subject Content Ratio, Rate and Speed Book 1, Chap No. 10 Pg No.( ) Functions and Graphs Book 1, Chap No.12 Pg No.( ) Statistics Book 1, Chap No.13 Pg No.( ) 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. 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.

18 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.

19 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. APRIL (REVISION FOR FINAL EXAMS) MAY (FINAL EXAMS) Breadh 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 openended 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 Homework: 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 is approximately equal to

20 Operations a + b a b a b, ab, a.b a b, a, a/b b a divided by b a plus b a minus b a multiplied by b RESOURCE LIST Books: Sang, T.et al, 2008, New Syllabus Mathematics Work Book 1(6 th 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) 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) Book1 Websites: