LEARNING AREA 1 : NUMBERS AND OPERATIONS 1. W W12 5 Jan 13 Jan RATIONAL NUMBERS CONTENT LEARNING STANDARDS STANDARDS Recognise positive negative

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1 SEKOLAH MENENGAH (LAKI-LAKI) METHODIST JALAN HANG JEBAT, KUALA LUMPUR. KURIKULUM STANDARD SEKOLAH MENENGAH (KSSM) RANCANGAN PELAJARAN TAHUNAN 2017 MATEMATIK TINGKATAN 1 1

2 LEARNING AREA 1 : NUMBERS AND OPERATIONS 1. W W12 5 Jan 13 Jan RATIONAL NUMBERS CONTENT LEARNING STANDARDS STANDARDS Recognise positive negative numbers 1.1 Integers based on real-life situations Recognise describe integers Represent integers on number lines make connections between the values positions of the integers with respect to other integers on the number line. NOTES Relate to real-life situations such as left right, up down movement. VALUE Hardworking Curious Hardworking Compare arrange integers in order 1.2 Basic arithmetic operations involving integers Add subtract integers using number lines or other appropriate methods. Hence, make generalisation about addition subtraction of integers Multiply divide integers using various methods. Hence make generalisation about multiplication division of integers. 2 Other methods such as concrete Accurate materials (coloured chips), virtual manipulative materials GSP software. Systematical THINKING MAP Tree Map

3 Accurate Perform computations involving combined basic arithmetic operations of integers by following the order of operations Describe the laws of arithmetic operations which are Identity Law, Communicative Law, Associative Law Distributive Law. Carry out exploratory activities. Logic Perform efficient computations using the laws of basic arithmetic operations. Example of an efficient computation involving Distributive Law: = ( ) 25 = = Efficient computations may differ among pupils. Critical thinking Solve problems involving integers. W Positive negative 16 Jan fractions 24 Jan Represent positive negative fractions on number lines Compare arrange positive negative fractions in order Perform computations involving combined basic arithmetic operations of positive negative fractions by following the order of operations. Rational Accurate Hard working Critical thinking Solve problems involving positive negative fractions. 1.4 Positive negative decimals Represent positive negative decimals on number lines Compare arrange positive negative decimals in order Perform computations involving combined basic arithmetic operations of positive negative decimals by following the order of operations. 3 Creative Responsibiliyty

4 1.4.4 Solve problems involving positive negative decimals. W4 25 Jan 26 Jan 1.5 Rational numbers Recognise describe rational numbers Rational numbers are numbers that Logic can be written in fractional form, that is, p q are integers, q 0. Perform computations involving combined basic arithmetic operations of rational numbers by following the order of operations. Solve problems involving rational numbers. W5 29 Jan 31 Jan TAHUN BARU CHINA 4 Systematical Responsible Tree Map

5 2. FACTORS AND MULTIPLES W Factors, prime factors 2 Feb Highest 10 Feb Common Determine list the factors of whole numbers, hence make generalisation about factors. 5 Cooperate Bubble Map

6 Factor (HCF) 2.2 Multiples, common multiples Lowest Common Multiple (LCM) Determine list the prime factors of a whole number, hence express the number in the form of prime factorisation Explain determine the common factors of whole numbers. Also consider cases involving more than three whole numbers Determine the HCF of two three whole numbers. Use various methods including repeated division the use of prime factorisation Solve problems involving HCF Explain determine the common multiples of whole numbers. Double Bubble Map Also consider cases involving more Helpfulness Double Bubble than three whole numbers. Map Determine the LCM of two three whole numbers Solve problems involving LCM. Use various methods including repeated division the use of prime factorisation. Creative 6

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8 3. SQUARES, SQUARE ROOTS, CUBES AND CUBE ROOTS W7 13 Feb 17 Feb 3.1 Squares square roots Explain the meaning of squares perfect squares. Explore the formation of squares Sharing using various methods including the use of concrete materials. Bridge Map Determine whether a number is a perfect square. Perfect squares are 1, 4, 9,... Circle Map State the relationship between squares square roots. Relationship is stated based on the Perfection outcome of exploration. Focus Square roots of a number are in positive negative values Determine the square of a number with without using technological tools Determine the square roots of a number without using technological tools. Limit to: Camlness a) perfect squares Bridge Map b) fractions when the numerators denominators are perfect squares c) fractions that can be simplified such that the numerators denominators are perfect squares d) decimals that can be written in the form of the squares of other decimals. Tolerance Determine the square roots of a positive number using technological tools. 8

9 3.1.7 Estimate (i) the square of a number, (ii) the square roots of a number. Discuss the ways to improve the estimation until the best estimation is obtained; whether in the form of a range, a whole number or to a stated accuracy Make generalisation about multiplication involving: (i) square roots of the same numbers, (ii) square roots of different numbers. Generalisations are made based on the outcome of explorations. 20 Feb 24 Feb 3.2 Cubes cube roots Courage Confidence Pose solve problems involving squares square roots. W8 Effort Explain the meaning of cubes perfect cubes. Explore the formation of cubes using Balance various methods including the use of concrete materials Determine whether a number is a perfect cube. Perfect cubes are 1, 8, 27, State the relationship between cubes cube roots. Relationship is stated based on the Courage outcome of exploration. Trust Determine the cube of a number with without using technological tools Determine the cube root of a number without using technological tools. Limit to: a) fractions when the numerators denominators are perfect cubes. b) fractions that can be simplified such that the numerators denominators are perfect cubes. c) decimals that can be written in the form of the cubes of other decimals. Patient Self 9 Circle Map Bridge Map

10 3.2.6 Determine the cube root of a number using technological tools. awareness Discuss the ways to improve the estimation until the best estimation is obtained; whether in the form of a range, a whole number or to a stated accuracy Estimate (i) the cube of a number, (ii) the cube root of a number. Thrift Solve problems involving cubes cube roots Perform computations involving addition, subtraction, multiplication, division the combination of these operations on squares, square roots, cubes cube roots. 10

11 LEARNING AREA 2 : RELATIONSHIP AND ALGEBRA 4. RATIOS, RATES AND PROPORTIONS Represent the relation between three W9 4.1 Ratios quantities in the form of a : b : c. 27 Feb Identify determine the equivalent 3 Mac ratios in numerical, geometrical or daily situation contexts. Rational Examples of equivalent ratios in geometrical context: 1:2 4.2 Rates 2: Express ratios of two three quantities in simplest form. Including those involving fractions decimals Determine the between ratios rates. Carry out exploratory activities. relationship Volunteering Involve various situations such as speed, acceleration, pressure density. Involve conversion of units. Rate is a special case of ratio that involves two measurements of different units. 4.3 Proportions W10 6 Mac 10 Mac Determine the relationship between ratios proportions Determine an unknown value in a Use various methods including cross multiplication unitary method. proportion. 4.4 Ratios, rates proportions Carry out exploratory activities. Involve real-life situations. Determine the ratio of three quantities, given two or more ratios of two quantities. Determine the ratio or the related value given (i) the ratio of two quantities the value of one quantity. (ii) the ratio of three quantities 11 Involve real-life situations Teamwork Tidiness Bridge Map

12 the value of one quantity. W13 27 Mac 31 Mac W Mac 17 Mac W Mac 24 Mac 4.5 Relationship between ratios, rates proportions with percentages, fractions decimals Determine the value related to a rate Solve problems involving ratios, rates proportions, including making estimations. Thankfulness Determine the relationship between Carry out exploratory activities. percentages ratios Determine the percentage of a quantity by applying the concept of proportions Solve problems involving relationship between ratios, rates proportions with percentages, fractions decimals. Involve various situations. UJIAN SELARAS 2017 CUTI PERTENGAHAN PENGGAL 1 12 Sincerity Obedience

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14 ALGEBRAIC EXPRESSIONS 5. W 14 3 Apr 7 Apr W Apr 21 Apr 5.1 Variables algebraic expressions 5.2 Algebraic expressions involving basic arithmetic operations Letters as variables. Use letters to represent quantities with unknown values. Hence, state whether the value of the variable varies or fixed, with justification. Will Power Involve real-life situations Derive algebraic expressions based on arithmetic expressions that represent a situation Determine the values of algebraic expressions given the values of variables make connection with appropriate situations Identify the terms in an algebraic expression. Hence, state the possible coefficients for the algebraic terms. Tree Map Identify like unlike terms. Bubble Map Add subtract two or more algebraic expressions Make generalisation about repeated multiplication of algebraic expressions Multiply divide expressions with one term. Patience algebraic 14 Correlate repeated multiplication with the power of two or more.

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16 6. W17 24 Apr 28 Apr W 18 2 May 5 May LINEAR EQUATIONS Linear equations in one variable Carry out exploratory activities involving algebraic expressions algebraic equations. Identify linear equations in one variable describe the characteristics of the equations Form linear equations in one variable based on a statement or a situation, vice-versa Solve linear variable Solve problems involving equations in one variable. equations in one Use various methods such as trial Passion Circle map Responsibility improvement, backtracking, applying the understing of equality concept. linear Identify linear equations in two 6.2 Linear equations in variables describe the characteristics two variables of the equations. Hardwork State the general form of linear equations in two variables, which is ax + by = c. Understing Tree Map Bubble Map Form linear equations in two variables based on a statement or a situation, vice-versa Determine explain possible solutions of linear equations in two variables Represent graphically the linear equations in two variables. Accountability Including cases of (x, y) when (i) x is fixed y varies, (ii) x varies y is fixed. Involve all quadrants of the Cartesian system. 16 Honesty

17 W 19 8 May 12 May W May25 May W May11 Jun 6.3 Simultaneous linear equations in two variables Form simultaneous linear equations based on daily situations. Hence, represent graphically the simultaneous linear equations in two variables explain the meaning of simultaneous linear equations. Use software to explore cases involving lines that are: (i) Intersecting (unique solution) (ii) Parallel (no solution) (iii) Overlapping (infinite solutions) Creativity Solve simultaneous linear equations in two variables using various methods. Involve graphical algebraic methods (substitution, elimination) Reliability Solve problems involving simultaneous linear equations in two variables. Use technological tools to explore check the answers. PEPERIKSAAN PERTENGAHAN TAHUN 2017 CUTI PERTENGAHAN TAHUN 17

18 7. W 24 LINEAR INEQUALITIES 7.1 Inequalities Jun 16 Jun Compare the values of numbers, describe inequality hence, form algebraic inequality. Use number lines to represent inequality relations, >, <,. Respect Tree Map Perfection Circle Map Involve negative numbers. Make generalisation about inequality related to (i) the converse transitive properties, additive multiplicative inverse, (ii) basic arithmetic operations. Carry out exploratory activities. Converse property if a < b, then b > a. Transitive property if a < b < c, then a < c. Additive inverse if a < b, then -a > -b. Multiplicative inverse if a < b, then. Basic arithmetic operations: when additions, subtractions, multiplications or divisions performed on both sides. W Jun 22 Jun 7.2 Linear inequalities in one variable W Jun 28 Jun Form linear inequalities based on daily life situations, viceversa. Solve problems involving inequalities in one variable. Solve simultaneous inequalities in one variable. Self respect linear Number lines can be used to solve problems. linear CUTI HARI RAYA PUASA 18

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20 LEARNING AREA 3 : MEASUREMENT AND GEOMETRY 8. LINES AND ANGLES W Jun 7 Jul 8.1 Lines angles Determine explain the congruency of line segments angles Estimate measure the size of line segments angles, explain how the estimation is obtained Recognise, compare explain the properties of angles on a straight line, reflex angles, one whole turn angles Describe the properties of complementary angles, supplementary angles conjugate angles Solve problems involving complementary angles, supplementary angles conjugate angles Construct (i) line segments, (ii) perpendicular bisectors of line segments, (iii) perpendicular line to a straight line, (iv) parallel lines explain the rationale of construction steps Construct angles angle bisectors, Use the angle of 60 as the first explain the rationale of example for construction using construction steps. compasses straightedge tool only. Focus 20 Tree Map Carry out exploratory activities. Use a) compasses straight edge tool only, b) any geometrical tools, c) geometry software for constructions. Sharing Tidiness Tidiness Tree Map Circle Map

21 W Jul 14 Jul 8.2 Angles related to intersecting lines Identify, explain draw vertically opposite angles adjacent angles at intersecting lines, including perpendicular lines Determine the values of angles related to intersecting lines, given the values of other angles Solve problems involving angles related to intersecting lines. 8.3 Angles related to parallel lines transversals Creativity Recognise, explain draw parallel lines transversals. Helpfulness Recognise, explain draw corresponding angles, alternate angles interior angles. W Jul 21 Jul Determine whether two straight lines are parallel based on the properties of angles related to transversals Determine the values of angles related to parallel lines transversals, given the values of other angles Recognise represent angles of elevation angles of depression in real-life situations Solve problems involving angles related to parallel lines transversals. Intentions 21 Include angles of elevation angles of depression. Curious

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23 9. BASIC POLYGONS W Polygons 24 Jul 28 Jul 9.2 Properties of triangles the interior exterior angles of triangles W Jul 4 Aug 9.3 Properties of quadrilateral s the interior exterior angles of quadrilateral s State the relationship between the number of sides, vertices diagonals of polygons Draw polygons, label vertices of polygons name the polygons based on the labeled vertices Recognise list geometric properties of various types of triangles. Hence classify triangles based on geometric properties. Carry out exploratory activities. Confidence Bridge Map Geometric properties include the number of axes of symmetry. Perfection Bubble Map Brace Map Involve various methods of exploration such as the use of dynamic software Make verify conjectures about Use various methods including the (i) the sum of interior angles, use of dynamic software. (ii) the sum of interior angle adjacent exterior angle, (iii) the relation between exterior angle the sum of the opposite interior angles of a triangle Solve problems involving triangles Describe the geometric properties of various types of quadrilaterals. Hence classify quadrilaterals based on the geometric properties Honesty Honesty Geometric properties include the number of axes of symmetry. Involve various exploratory methods such as the use of dynamic software. Make verify the conjectures about Use various methods including the (i) the sum of interior angles of a use of dynamic software. quadrilateral, (ii) the sum of interior angle 23 Courage Will Power Bubble Map Brace Map

24 adjacent exterior angle of a quadrilateral, (iii) the relationship between the opposite angles in a parallelogram Solve problems quadrilaterals. involving Solve problems involving the combinations of triangles quadrilaterals. 24 Responsibility

25 10. PERIMETER AND AREA W Perimeter 7 Aug 11 Aug Various shapes including those involving straight lines curves Obedience Estimate the area of various shapes using various methods. Including the use of 1 unit 1 unit grid paper. Patience Derive the formulae of the area of triangles, parallelograms, kites trapeziums based on the area of rectangles. Carry out exploratory activities involving concrete materials or the use of dynamic software Determine the perimeter of various shapes when the side lengths are given or need to be measured Estimate the perimeter of various shapes, then evaluate the accuracy of estimation by comparing with the measured value Solve problems involving perimeter Area of triangles, parallelogra ms, kites trapeziums Hard working Solve problems involving areas of triangles, parallelograms, kites, trapeziums the combinations of these shapes. W Aug 18 Aug 10.3 Relationship Make verify the conjecture between about the relationship between perimeter perimeter area. area Solve problems involving perimeter area of triangles, rectangles, squares, parallelograms, kites, trapeziums the combinations of these shapes. Cooperation 25 Tree Map Bridge Map

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27 LEARNING AREA 4 : DISCRETE MATHEMATICS 11. INTRODUCTION TO SET W Set 21 Aug 25 Aug Explain the meaning of set. Carry out sorting classifying activities including those involving real-life situations Describe sets using: (i) description, (ii) listing, (iii) set builder notation. Including empty set its symbols, { }. Courtesy Circle Map Involve the use of set notation. Example of set builder notation: A = {x: x 10, x is even number} Identify whether an object is an element of a set represent the relation using symbol Determine the number of elements of a set represent the number of elements using symbol. Introduce the symbols. Introduce the symbol n(a). Focus Introduce the symbols for universal set ( ), complement of a set (A ) subset ( ). Rationality Compare explain whether two or more sets are equal hence, make generalisation about the equality of sets Venn diagrams, universal sets, complemen t of a set subsets Identify describe universal sets complement of a set Represent (i) the relation of a set universal set, (ii) complement of a set through Venn diagrams. 27 Brace Map

28 W 36 4 Sept 6 Sept Concentration Brace Map Identify describe subsets of a set Represent diagrams. subsets the possible using Venn Represent the relations between sets, subsets, universal sets complement of a set using Venn diagrams. W Aug 1 Sept CUTI PERTENGAHAN PENGGAL 2 28

29 LEARNING AREA 5 : STATISTICS AND PROBABILITY 12. DATA HANDLING W Sept 20 Sept Generate statistical questions Use statistical inquiry approach for 12.1 Data collect relevant data. collection, this topic. organization Statistical Inquiry representation 1. Posing / formulating real life process, problems interpretation 2. Planning collecting data of data 3. Organising data representation 4. Displaying / representing data 5. Analysing data 6. Interpretation conclusion 7. Communicating results Systematical Tree Map Statistical questions : questions that can be answered by collecting data where there will be variability in that data. Involve real life situations. Collect data using various methods such as interview, survey, experiment observation Classify data as categorical or numerical construct frequency tables. Numerical data : discrete or continuous Construct data representation for ungrouped data justify the appropriateness of a data representation. Data representation including various types of bar charts, pie chart, line graph, dot plot stem--leaf plot. Use various methods to construct data representations including the use of software. 29 Volunteering Brace Map

30 Convert a data representation to other suitable data representations with justification Interpret various data representations including making inferences or predictions Discuss the importance of representing data ethically in order to avoid confusion. 30 Focus Involve histograms frequency polygons. Tree Map

31 LEARNING AREA : MEASUREMENT AND GEOMETRY 13. THE PYTHAGORAS THEOREM W 3839/40 21 Sept 4 Oct 13.1 The Pythagoras Theorem Identify define the hypotenuse of a right-angled triangle. Effort Determine the relationship between the sides of right-angled triangle. Hence, explain the Pythagoras Theorem by referring to the relationship. Bridge Map Carry out exploratory activities by involving various methods including the use of dynamic software Determine the length of the unknown Determine the length of sides by applying the Pythagoras Theorem. side of (i) a right-angled triangle. (ii) combined geometric shapes. Courage Solve problems involving the Pythagoras Theorem The converse of Pythagoras Theorem Determine whether a triangle is a right-angled triangle give justification based on the converse of the Pythagoras Theorem. Understing Tree Map Solve problems involving the converse of the Pythagoras Theorem. 31

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