MATHEMATICS. Teaching Objectives and Learning Outcomes (Form 2)

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2 MATHEMATICS Teaching Objectives and (Form 2) Directorate for Quality and Standards in Education Curriculum Management and elearning Department Malta 2012 Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

3 FORM 2 - Mathematics Number Unit code and title MTH 8.1 Factors, Multiples and Using a Calculator (Levels ) Objective 1 The teacher will teach the students to recognise and find common factors and multiples, up to three numbers. 8.1 recognise and find common factors and common multiples of three numbers. 7.3 find common factors and common multiples of two numbers. 7.2 find all the factors of given numbers up to 100 and list all the multiples of the numbers from 1 to find all the factors of given numbers up to 50 and list all the multiples of the numbers from 1 to 10. Objective 2 The teacher will teach the students to recognise prime numbers and write numbers as a product of their prime factors. 8.1 understand that prime numbers are the building blocks of all natural numbers and be able to check which numbers less than 100 are prime 7.3 understand the definition of a prime number and be able to identify and distinguish between factors and prime factors. 7.2 use prime numbers to write numbers as a product of prime factors. 7.1 identify all the prime numbers up to 50. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

4 Objective 3 The teacher will teach the students to find the least common multiple and highest common factor (up to three numbers) and solve simple problems using LCM and HCF. 8.1 solve simple problems involving the use of HCF. 7.3 solve simple problems involving the use of LCM. 7.2 find the HCF and LCM of two numbers. 7.1 find the LCM of two numbers. Objective 4 The teacher will teach the students to use the four rules for calculations with integers including the correct use of operations and the use of brackets. use the four rules for calculations including the correct use of operations and brackets. 7.3 use the four rules for calculations with integers including the correct use of operations and brackets. 7.2 use the correct order of the four basic rules with integers including the use of brackets for calculations involving up to three operations. 7.1 use the correct order of the four basic rules with integers for calculations involving two operations Objective 5 The teacher will teach the students to make efficient use of the basic functions on a calculator; including the fraction, bracket, square, cube, square root and cube root keys. 8.1 use the required key calculator functions in complex calculations involving fractions, brackets squares, cubes, square roots and cube roots. 7.3 make efficient use of the basic calculator functions in simple calculations involving fractions, brackets, squares, cubes and square roots. 7.2 make efficient use of the basic calculator functions in simple calculations involving fractions, brackets, squares and cubes. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

5 7.1 make efficient use of the basic calculator functions in simple calculations involving squares and cubes. FORM 2 - Mathematics Shape, Space and Measures Unit code and title MTH 8.2 Angles (Levels ) Objective 1 The teacher will teach the students to estimate the size of an angle and use a protractor to measure and draw angles up to 360. estimate, measure and draw angles up to estimate, measure and draw angles up to estimate and measure angles up to estimate angles up to 180. Objective 2 The teacher will teach the students to solve problems involving angles at a point, angles on a straight line and vertically opposite angles; solve problems involving parallel lines. 8.1 find missing angles in geometric diagrams by forming and solving algebraic equations. 7.3 solve simple problems involving angles at a point, angles on straight line, vertically opposite angles, and angles formed between parallel lines. 7.2 identify vertically opposite angles and angles formed between parallel lines in diagrams. 7.1 calculate missing angles using the facts that angles at a point add up to 360 and angles on a straight line are supplementary. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

6 Objective 3 The teacher will teach the students to find unknown angles in triangles and quadrilaterals. 8.1 find the interior angles in regular polygons. 7.3 work out missing angles in complex diagrams involving triangles and quadrilaterals. 7.2 understand that the angle sum of a quadrilateral is 360 and find missing angles. 7.1 find unknown angles in any type of triangle. Objective 4 The teacher will teach the students to understand a proof that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 8.1 write a general proof that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 7.3 understand a proof that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 7.2 find the value of an exterior angle of a triangle given the two interior opposite angles 7.1 know that an exterior and an interior angle of a triangle add up to 180. FORM 2 - Mathematics Number Unit code and title MTH 8.3 Fractions (Levels ) Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

7 Objective 1 The teacher will teach the students to write a fraction that is equivalent to another fraction and change improper fractions to mixed numbers and vice-versa. 8.1 write a fraction that is equivalent to another fraction and change improper fractions to mixed numbers and vice-versa. 7.3 write a fraction that is equivalent to another fraction and change improper fractions to mixed numbers. 7.2 write a fraction that is equivalent to another fraction. 7.1 use equivalent fractions to compare/order fractions. Objective 2 Objective 3 The teacher will teach the students to add and/or subtract two fractions, including mixed numbers. 8.1 add and subtract mixed numbers in parts: first the wholes, then the fractions. 7.3 add and subtract mixed numbers by expressing them as improper fractions, using both equivalent fractions and L.C.M. 7.2 add and subtract two fractions (with different denominators) using equivalent fractions. 7.1 add and subtract two fractions with same denominators. The teacher will teach the students to arrange fractions in ascending/descending order; understand that the reciprocal of a number is its multiplicative inverse. 8.1 manipulate reciprocals as multiplicative inverses of fractions and whole numbers. 7.3 understand that multiplication and division are functions opposite to each other and that of each other, called reciprocals of each other. 7.2 arrange fractions (denominators having common multiples) in ascending/descending order using LCM. 7.1 arrange a set of fractions (with denominators 2, 5 or 10) on a number line from 0 to 1 (divided in tenths). 1 x and x are multiplicative inverses Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

8 Objective 4 The teacher will teach the students to multiply and divide one fraction by another fraction (excluding mixed numbers). 8.1 multiply and divide one fraction by another fraction without using the calculator; numerators and denominators may or may not be simplified. 7.3 multiply and divide one fraction by another fraction without using the calculator, numerators and denominators can be simplified. 7.2 multiply one fraction by another without the use of the calculator. 7.1 simplify fractions by cancelling. Objective 5 The teacher will teach the students to solve problems involving fractions. 8.1 solve problems in addition and subtraction involving mixed numbers, and multiplication and division involving fractions but not mixed numbers. 7.3 solve problems in finding fractions of any quantity. 7.2 solve simple problems in addition and subtraction of fractions with different denominators. 7.1 solve simple problems in addition and subtraction of fractions with common denominators. FORM 2 - Mathematics Number Unit code and title MTH 8.4 Decimals (Levels ) Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

9 Objective 1 The teacher will teach the students to recognise and use the symbols <, >, and to compare two quantities. Use the number line to illustrate simple cases of inequalities. 8.1 illustrate simple cases of inequalities on a number line. 7.3 recognise and use the symbols and for integers, decimals and fractions. 7.2 recognise and use the symbols < and > for integers and decimals. 7.1 compare integers and decimals and determine which is larger or smaller. Objective 2 The teacher will teach the students to read decimal numbers from number lines and scales; read and use scales in practical situations. 8.1 read multiple dials to get one reading. 7.3 read from scales such as speedometer, ampere meter, altimeter and air speed indicator. 7.2 read decimal numbers up to three places of decimals from number lines and scales. 7.1 read decimal numbers up to two places of decimals from scales measuring length, weight, capacity, speed and fuel gauge. Objective 3 The teacher will teach the students to arrange decimal numbers in order of size. 8.1 find a number between any two given decimal numbers. 7.3 arrange any set of decimal numbers in ascending and descending order. 7.2 arrange numbers in ascending and descending order up to 3 decimal places. 7.1 arrange numbers in ascending and descending order up to 2 decimal places. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

10 Objective 4 The teacher will teach the students to round numbers to a given number of decimal places and carry out rough estimates to check accuracy. 8.1 recognise the difference between decimal places and significant figures. 7.3 carry rough estimates to check accuracy. 7.2 round numbers to a given number of decimal places. 7.1 round numbers to one decimal place. Objective 5 The teacher will teach the students to change fractions into decimals and vice versa; recognise recurring and non-recurring decimals. 8.1 recognise that particular fractions have specific recurring decimal patterns. 7.3 change fractions to decimals. 7.2 change decimals, with a finite number of decimal places to fractions in their lowest terms. 7.1 change decimals with up to 3 decimal places to fractions in their lowest terms. FORM 2 - Mathematics Unit code and title Number MTH 8.5 Percentages Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

11 Objective 1 The teacher will teach the students to change percentages to fractions and decimals and vice-versa. 8.1 change mixed numbers to percentages and decimals and vice versa. 7.3 change fractions and decimals to percentages without the use of calculator. 7.2 change percentages to fractions and decimals without the use of calculator. 7.1 change percentages to fractions and decimals and vice versa using calculator when necessary. Objective 2 The teacher will teach the students to express one quantity as a percentage of another. 8.1 solve complex problems involving a quantity as a percentage of another. 7.3 solve simple problems involving a quantity as a percentage of another. 7.2 express one quantity as a percentage of another by calculation and/or spreadsheet software. 7.1 express one quantity as a percentage of another. Objective 3 The teacher will teach the students to work out the percentage of a quantity. 8.1 solve problems which involve finding the percentage of a quantity, where the percentage is a mixed number. 7.3 solve problems which involve finding the percentage of a quantity, using integral values. 7.2 work out more complex examples which involve finding the percentage of a quantity. 7.1 work out the percentage of a quantity where the percentage and/or the quantity is a multiple of 5. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

12 Objective 4 The teacher will teach the students to work out the percentage increase and decrease. 8.1 solve problems which involve percentage increase/decrease where the percentage is a mixed number. 7.3 solve problems which involve percentage increase/decrease using integral values. 7.2 work out the new amount after a percentage increase/decrease. 7.1 work out the percentage increase/decrease of a quantity. FORM 2 - Mathematics Shape, Space and Measures Unit code and title MTH 8.6 Area and Volume (Levels ) Objective 1 The teacher will teach the students to use the formula to find the area of a triangle; derive & use the formula to find the area of a parallelogram. 8.1 derive the formula A = ½bh for the area of a triangle. 7.3 derive the formula A = bh for the area of a parallelogram. 7.2 use the formulae to find the area of a parallelogram and a triangle. 7.1 work out the area of a triangle given the area of a rectangle or parallelogram. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

13 Objective 2 The teacher will teach the students to calculate the area of compound shapes. 8.1 find the area of compound shapes formed of squares/rectangles and triangles which need not be right-angled, using formulae. 7.3 find the area of compound shapes which can be split into right-angled triangles and squares/rectangles, using formulae. 7.2 find the area of compound shapes which can be split into squares/rectangles, using formulae. 7.1 find the area of compound shapes which can be split into right-angled triangles and squares/rectangles by counting squares. Objective 3 The teacher will teach the students to work out the surface area of a cube and cuboid. 8.1 derive the formulae for the surface area of a cube, A = 6l 2 and a cuboid, A = 2(lb+lw+bw) 7.3 find: the side of a cube given the surface area; a side of a cuboid given the surface area and the other two sides. 7.2 use the formulae to find the surface area of a cuboid. 7.1 use the formulae to find the surface area of a cube. Objective 4 The teacher will teach the students to find the volume of compound shapes involving cubes and cuboids. 8.1 find the volume of compound shapes involving more than 2 components (cubes/cuboids). 7.3 find the volume of compound shapes involving 2 components (cubes/cuboids). 7.2 identify the dimensions of the components (cubes/cuboids) of a compound shape. 7.1 identify the components (cubes/cuboids) making up a compound shape. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

14 Objective 5 The teacher will teach the students to understand that the prism is a solid with uniform cross-section; find the volume of a prism using V= area of cross-section length. 8.1 derive the formula: V= area of cross-section length. 7.3 find the length of a prism given the volume and cross-sectional area. 7.2 find the volume of a prism where the cross section is a triangle or a parallelogram. 7.1 find the volume of a prism where the cross section is a square or a rectangle. FORM 2 - Mathematics Shape, Space and Measures Unit code and title MTH 8.7 Triangles and Quadrilaterals (Levels ) Objective 1 The teacher will teach the students to classify triangles and quadrilaterals by identifying their geometric properties through line and/or rotational symmetry. 8.1 classify triangles and quadrilaterals by identifying their geometric properties through line and rotational symmetry. 7.3 classify triangles and distinguish between square, rectangle, rhombus and parallelogram by identifying some geometric properties including line or rotational symmetry. 7.2 distinguish between isosceles, equilateral and scalene triangles and between a square and a rectangle using their geometric properties. 7.1 classify triangles and quadrilaterals according to number of sides, length of sides, right angles and size of angles. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

15 Objective 2 The teacher will teach the students to identify tessellating shapes and cover a given area with tessellating shapes. 8.1 create tessellating shapes and use it to cover a given area, such as tiling a room. 7.3 draw tessellating shape and select the appropriate arrangement to cover a given area, such as tiling a room. 7.2 identify shapes that need to be rotated to tessellate and be able to continue a pattern with such shapes. 7.1 identify shapes that need to be rotated to tessellate. Objective 3 The teacher will teach the students to make accurate drawings of triangles. 8.1 make accurate drawings of triangles given (a) the length of the three sides using ruler and compasses; (b) the length of one side and two angles using ruler and compasses and/or protractor; and (c) two sides and the included angle using ruler and compasses and/or protractor. 7.3 make accurate drawings of triangles given (a) the length of the three sides using ruler and compasses only; (b) the length of one side and two angles using ruler and protractor; and (c) two sides and the included angle using ruler and protractor. 7.2 make accurate drawings of triangles given (a) the length of one side and two angles using ruler and protractor; and (b) two sides and the included angle using ruler and protractor. 7.1 make an accurate drawing of triangles given two sides and the included angle using ruler and protractor. Objective 4 The teacher will teach the students to draw simple scale drawings from given data and interpret scale drawings. 8.1 draw scale drawings from given data and use scale drawings to find actual distances and areas. 7.3 draw simple scale drawings from given data and interpret scale drawings. 7.2 draw and interpret simple scale drawings, that is, involving positive integer lengths and ratios. 7.1 draw and interpret scale drawings using a ratio of 1cm to represent 1m and/or 1 km. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

16 Objective 5 The teacher will teach the students to draw scale drawings to solve problems involving angles of elevation and depression. 8.1 draw scale drawings to solve complex problems involving angles of elevation and depression. 7.3 draw scale drawings to solve simple problems involving angles of elevation and depression. 7.2 draw a scale drawing to solve a simple problem involving an unknown height (e.g.: finding the height of a tree). 7.1 solve a simple problem from a given scale drawing involving angles of elevation. FORM 2 - Mathematics Shape, Space and Measures Unit code and title MTH 8.8 Constructions (Levels ) Objective 1 The teacher will teach the students to use ruler and compasses only to construct a perpendicular at a point on a line. 8.1 use ruler and compasses only to construct a perpendicular at a point on a line and will be able to give adequate verbal justifications why the procedure works 7.3 use ruler and compasses only to construct a perpendicular at a point on a line. 7.2 use ruler and protractor to construct a perpendicular at a point on a line. 7.1 use ruler only to make a reasonable accurate sketch of a perpendicular at a point on a line. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

17 Objective 2 The teacher will teach the students to use ruler and compasses only to construct a perpendicular from a point to a line. 8.1 use ruler and compasses only to construct a perpendicular from a point to a line and will be able to give adequate verbal justifications why the procedure works. 7.3 use ruler and compasses only to construct a perpendicular from a point to a line. 7.2 use ruler and protractor only to construct a perpendicular from a point to a line. 7.1 use ruler only to make a reasonable accurate sketch of a perpendicular from a point to a line. Objective 3 The teacher will teach the students to use ruler and compasses only to construct the perpendicular bisector of a line segment. 8.1 use ruler and compasses only to construct the perpendicular bisector of a line segment and will be able to give adequate verbal justifications why the procedure works. 7.3 use ruler and compasses only to construct the perpendicular bisector of a line segment. 7.2 use ruler and protractor only to construct the perpendicular bisector of a line segment. 7.1 use ruler only to make a reasonable accurate sketch of the perpendicular bisector of a line segment. Objective 4 The teacher will teach the students to use ruler and compasses only to construct the bisector of an angle. 8.1 use ruler and compasses only to construct the bisector of an angle and will be able to give adequate verbal justifications why the procedure works. 7.3 use ruler and compasses only to construct the bisector of an angle. 7.2 use ruler and protractor only to construct the bisector of an angle. 7.1 use ruler only to make a reasonable sketch of the bisector of an angle. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

18 Objective 5 The teacher will teach the students to construct squares and rectangles using ruler and compasses only. 8.1 use ruler and compasses only to construct squares and rectangles and will be able to give adequate verbal justifications why the procedures work. 7.3 use ruler and compasses only to construct squares and rectangles. 7.2 use ruler and protractor only to construct squares and rectangles. 7.1 use ruler only to make reasonable accurate sketches of squares and rectangles. FORM 2 - Mathematics Algebra / Number Unit code and title MTH 8.9 Directed Numbers and Sequences (Levels ) Objective 1 The teacher will teach the students to add/subtract/multiply/ divide directed numbers. 8.1 add/subtract/multiply/divide more than two directed numbers. 7.3 multiply or divide two directed numbers. 7.2 add/subtract any two integers without the help of the calculator. 7.1 add +ve/-ve integers and subtract +ve integers without the help of the calculator/number line; subtract a negative number with the help of the calculator. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

19 Objective 2 The teacher will teach the students to solve problems using directed numbers. 8.1 solve complex problems involving addition/subtraction/multiplication/division of +ve/-ve numbers without the help of the number line or calculator. 7.3 solve simple problems involving addition /subtraction/multiplication/division of +ve/-ve numbers without the help of the number line or calculator. 7.2 solve simple problems involving addition /subtraction of +ve/-ve integers without the help of the number line or calculator. 7.1 solve simple problems involving addition of two +ve/-ve integers and subtraction of +ve integers without the help of the number line or calculator; subtraction of ve integers using a calculator when necessary. Objective 3 The teacher will teach the students to recognise arithmetic and geometric patterns; generate terms of a sequence using term to term and position to term rules. 8.1 generate terms of a complex sequence using position to term rules. 7.3 generate terms of a simple sequence using position to term rules. 7.2 continue complex arithmetic /geometric patterns using term to term rule. 7.1 continue simple arithmetic /geometric patterns using term to term rule. Objective 4 The teacher will teach the students to write the n th term expression of linear sequences of the form kn + m where k and m are integers. 8.1 write the n th term expression of linear sequences of the form kn + m where k and m are integers. 7.3 write down the rule in words of a sequence of the form kn + m where k and m are integers. 7.2 tell that the rule is a combination of addition/subtraction and multiplication. 7.1 describe the rule in words of a sequence of the form n ± k and kn where k is a positive integer Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

20 FORM 2 - Mathematics Algebra Unit code and title MTH 8.10 Expressions and Formulae (Levels ) Objective 1 The teacher will teach the students to simplify algebraic expressions by multiplying a single term over a bracket and/or collecting like terms. 8.1 simplify quadratic algebraic expressions by multiplying a single term over a bracket and/or collecting like terms. 7.3 simplify linear algebraic expressions by multiplying a single term over a bracket and/or collecting like terms. 7.2 multiply an integer over a bracket. 7.1 simplify linear expressions made up of up to two variables by collecting like terms. Objective 2 The teacher will teach the students to factorise expressions by identifying a numerical common factor. 8.1 factorise fully linear expressions by identifying a numerical common factor. 7.3 identify a numerical common factor in linear expressions. 7.2 find the common factor of two or more integers. 7.1 find the factors of an integer. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

21 Objective 3 The teacher will teach the students to evaluate simple formulae by substituting letters with positive and negative inputs. 8.1 evaluate quadratic formulae by substituting letters with positive and negative inputs. 7.3 evaluate linear formulae involving brackets by substituting letters with positive and negative integral or decimal inputs. 7.2 evaluate simple linear formulae by substituting letters with positive and negative inputs. 7.1 evaluate linear formulae involving brackets by substituting letters with positive integral inputs. Objective 4 The teacher will teach the students to derive and use formulae to solve problems. 8.1 derive and use formulae to solve problems involving positive/negative integers. 7.3 derive and use formulae to solve problems involving positive integers only. 7.2 choose the correct variable expression involving two operations to represent a word problem. 7.1 write variable expressions to represent diagrams. FORM 2 - Mathematics Data Handling Unit code and title MTH 8.11 Statistics and Probability (Levels ) Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

22 Objective 1 The teacher will teach the students to draw and interpret bar charts and pie charts. 8.1 interpret bar charts and pie charts for grouped data. 7.3 compile tally charts and use them to draw bar charts/pie charts for grouped data. 7.2 draw pie charts from tally charts / bar charts, by finding the necessary angle. They will be able to interpret pie charts. 7.1 interpret simple pie charts, limited to sectors of 180, 90, 60 and 30. Objective 2 Objective 3 The teacher will teach the students to compile and interpret frequency tables for grouped / ungrouped discrete and continuous data. 8.1 interpret frequency tables by answering complex questions about the grouped continuous data. 7.3 interpret frequency tables of grouped continuous data by answering simple questions about the grouped data. 7.2 sort and classify numerical data in groups, using the inequality sign grouping notations and to compile frequency tables for grouped data, applying the most appropriate grouping. 7.1 sort and classify numerical discrete data in groups. They will be able to compile and interpret frequency tables of grouped discrete data. The teacher will teach the students to understand, compute and interpret the mean, mode, median and range of a set of ungrouped data. 8.1 find missing entries of data, given their mean, mode, median and range. 7.3 identify the outliers of a set of data and understand that such outliers effect the mean and range of the data. 7.2 compare two sets of data according to their mean, median, mode and range. 7.1 find the mean, median, mode and range from lists, bar charts or frequency table of discrete ungrouped data and decide which one represents the best data. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

23 Objective 4 The teacher will teach the students to use a spreadsheet to construct bar charts and pie charts and compute the mean and range of a set of ungrouped data. 8.1 understand the meaning of the functions MAX and MIN and be able to use them to find the range of a list of data inputted in a spreadsheet. 7.3 use the AVERAGE function to be able to find the mean of a list of data inputted in a spreadsheet. 7.2 convert a given/compiled spreadsheet table into a Column/Bar chart or Pie chart, including the category names. 7.1 input the data in a spreadsheet and use it to construct simple bar charts. Objective 5 The teacher will teach the students to understand and work out the probability of an event. 8.1 use probabilities to estimate the number of times an event will occur. 7.3 understand that the probabilities of all possible outcomes add up to understand that the probabilities of an event happening and not happening add up to calculate probabilities of an event having more than one possible outcome. Objective 6 The teacher will teach the students to compile a possibility space and use it to find the probability of two events. 8.1 find the probability of two events occurring at the same time by multiplying their probabilities. 7.3 use a possibility space diagram to calculate harder probabilities, such as the probability of two normal dice showing numbers which differ by 3 but add up to use a possibility space diagram to calculate simple probabilities such as getting a total of 7 when rolling two normal dice. 7.1 calculate the number of all possible outcomes given the two events. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

24 FORM 2 - Mathematics Number Unit code and title MTH 8.12 Ratio & Proportion (Levels ) Objective 1 The teacher will teach the students to solve problems involving direct proportion using the unitary method. 8.1 solve complex problems involving direct proportion with and without the use of the unitary method (e.g.: including exchange rates, recipes etc.). 7.3 solve complex problems involving direct proportion using the unitary method (e.g.: finding rates). 7.2 solve simple problems involving direct proportion using the unitary method (that is, finding a unit measure including the price, distance, time, weight and capacity). 7.1 solve simple problems involving finding the unit price. Objective 2 The teacher will teach the students to use the ratio notation to compare two or more quantities and write ratios in their simplest form. 8.1 apply the ratio notation to compare two or more quantities within real-life situations. 7.3 use the ratio notation to compare and simplify two or more quantities involving different units. 7.2 compare and simplify the ratio of two quantities involving different units. 7.1 compare and simplify the ratio of two quantities involving common units. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

25 Objective 3 The teacher will teach the students to divide a quantity in a given ratio. 8.1 divide a quantity in a given ratio of three or more unequal parts. 7.3 divide a quantity in a given ratio of up to three parts. 7.2 divide a quantity into two unequal parts. 7.1 divide a quantity into unequal parts indicated by the given ratio. FORM 2 Mathematics Shape, Space and Measures Unit code and title MTH 8.13 Transformations (Levels ) Objective 1 The teacher will teach the students to identify shapes having reflection and/or rotational symmetry in 2D; determine the order of rotational symmetry in 2D; determine the symmetrical properties of a polygon. 8.1 determine the symmetrical properties of any 2D shape. 7.3 determine the symmetrical properties of triangles and special quadrilaterals. 7.2 determine the symmetrical properties of regular polygons. 7.1 identify shapes having reflection and/or rotational symmetry, determine the order of rotational symmetry and be able to complete part shapes using two lines of symmetry. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

26 Objective 2 The teacher will teach the students to reflect a shape in the x axis, y axis, x = c, y = c and y = x; describe a reflection. Objective 3 Objective label correctly the vertices of the object and image in a reflection. 7.3 reflect a shape in y = x and describe the reflection in words. 7.2 reflect a shape in x = c or y = c and describe the reflection in words. 7.1 reflect a shape in the x axis and/or y axis, describe the reflection in words and understand that in a reflection the object and image are congruent and inverted. The teacher will teach the students to translate a shape horizontally and/or vertically given a column vector; describe a translation by a column vector. 8.1 apply multiple translations to a shape. 7.3 translate shapes given a column vector and describe translations by a column vector. 7.2 translate a shape given a column vector. 7.1 translate a shape horizontally and/or vertically through descriptions: right, left, up and down and understand that in a translation the object and image are congruent. The teacher will teach the students to rotate a shape about the origin or one of the vertices, using angles of 90 and 180 ; describe a rotation. 8.1 rotate a shape when the centre of rotation is outside the shape and describe the transformation in words. 7.3 rotate a shape about one of the vertices using angles of 90 and 180 and describe the transformation in words. 7.2 rotate a shape about one of the vertices through an angle of rotate squares, rectangles and right-angled triangles about one of the vertices using angles of 90 and 180 and understand that in a rotation the object and image are congruent. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

27 Objective 5 The teacher will teach the students to enlarge a shape by a positive integral scale factor using a centre of enlargement; describe an enlargement. 8.1 understand that in an enlargement the object and image are similar. 7.3 find the centre of enlargement and the scale factor (limited to positive integers) and describe an enlargement in words. 7.2 enlarge a shape by a positive integral scale factor, using the origin as the centre of enlargement. 7.1 enlarge squares, rectangles and right-angled triangles by a positive integral scale factor. FORM 2 - Mathematics Algebra Unit code and title MTH 8.14 Solving Equations (Levels ) Objective 1 The teacher will teach the students to solve linear equations in one unknown. 8.1 solve linear equations with one unknown on both sides. 7.3 solve linear equations with one unknown on both sides involving up to two operations. 7.2 solve linear equations with one unknown on one side involving up to two operations. 7.1 solve linear equations involving one operation. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

28 Objective 2 The teacher will teach the students to solve linear equations involving brackets. 8.1 solve linear equations involving brackets. 7.3 solve linear equations involving one pair of brackets on one side only. 7.2 collect like terms in an expression and will be able to multiply a single term over a bracket. 7.1 collect terms in an expression involving like terms. Objective 3 The teacher will teach the students to use equations to solve problems. 8.1 form and solve linear equations with one unknown on both sides. 7.3 form and solve linear equations with one unknown on both sides involving up to two operations. 7.2 form and solve linear equations with one unknown on one side involving up to two operations. 7.1 form and solve linear equations involving one operation. FORM 2 - Mathematics Algebra Unit code and title MTH 7.15 Coordinates and Straight Line Graphs (Levels ) Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

29 Objective 1 The teacher will teach the students to understand that the equation of a straight-line describes the relationship between the x and y coordinates, given the line-graph or the coordinates. 8.1 find the equation of a straight line graph given the co-ordinates of any two points on the line. 7.3 find the equation of a straight line graph given the co-ordinates of many points on the line. 7.2 find the equation of the form y = mx + c given a simple line-graph. 7.1 find the equation of a straight line graph of the form y = mx given a simple line-graph. Objective 2 The teacher will teach the students to use the equation of a straight-line to generate a sequence of ordered pairs and plot them to produce its graph. 8.1 draw the graph of a linear equation given in the form y = mx+ c 7.3 draw the graph of a linear equation given in the form y = mx 7.2 draw the graph of a linear equation given in the form y = x + c 7.1 understand that a linear equation can be represented as a straight line on a coordinate grid. Objective 3 The teacher will teach the students to understand what is meant by the gradient of a line and find the gradient from the graph. (Restrict to positive gradients) 8.1 find the gradient of a line from any two points on the line and sketch a line given the gradient. 7.3 identify whether a line has a gradient equal to 1, less than 1 or equal to calculate the gradient of a line using the triangle method. 7.1 understand the meaning of the gradient of a line. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

30 Objective 4 The teacher will teach the students to interpret information presented in a variety of linear graphs; use and draw conversion graphs. 8.1 interpret the relationship between two journeys represented on one travel graph. 7.3 interpret the gradient of real-life linear graphs. 7.2 read distance travelled and time taken from a travel graph. 7.1 draw and interpret a conversion graph. FORM 2 - Mathematics Number Unit code and title MTH 8.1 Factors, Multiples and Using a Calculator (Levels ) Objective 1 The teacher will teach the students to recognise and find common factors and multiples of two numbers. 7.3 find common factors and common multiples of two numbers. 7.2 find all the factors of given numbers up to 100 and list all the multiples of the numbers from 1 to find all the factors of given numbers up to 50 and list all the multiples of the numbers from 1 to find all the factors of numbers up to 25 and list all the multiples of 2, 3, 5 and 10 Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

31 Objective 2 The teacher will teach the students to recognise prime numbers and write numbers as a product of their prime factors. 7.3 understand the definition of a prime number and be able to identify and distinguish between factors and prime factors. 7.2 use prime numbers to write numbers as a product of prime factors. 7.1 to identify all the prime numbers up to identify the prime numbers up to 35. Objective 3 The teacher will teach the students to find the least common multiple and highest common factor of two numbers and solve simple problems using LCM and HCF. 7.3 solve simple problems involving the use of LCM. 7.2 find the HCF and LCM of two numbers. 7.1 find the LCM of two numbers. 6.3 find common factors and common multiples of two numbers. Objective 4 The teacher will teach the students to use the four rules for calculations with integers including the correct use of operations and the use of brackets. 7.3 use the four rules for calculations with integers including the correct use of operations and brackets. 7.2 use the correct order of the four basic rules with integers including the use of brackets for calculations involving up to three operations. 7.1 use the correct order of the four basic rules with integers for calculations involving two operations 6.3 use the correct order of the four basic rules for calculations involving two operations one of which includes the use of brackets. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

32 Objective 5 The teacher will teach the students to make efficient use of the basic functions on a calculator; including the fraction, bracket, square, cube, square root and cube root keys. 7.3 make efficient use of the basic calculator functions in simple calculations involving fractions, brackets, squares, cubes and square roots. 7.2 make efficient use of the basic calculator functions in simple calculations involving fractions, brackets, squares and cubes. 7.1 make efficient use of the basic calculator functions in simple calculations involving squares and cubes. 6.3 make efficient use of the basic calculator functions in simple calculations FORM 2 - Mathematics Shape, Space and Measures Unit code and title MTH 8.2 Angles (Levels ) Objective 1 The teacher will teach the students to estimate the size of an angle and use a protractor to measure and draw angles up to estimate, measure and draw angles up to estimate and measure angles up to estimate angles up to distinguish between acute, right, obtuse and reflex angles. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

33 Objective 2 The teacher will teach the students to solve problems involving angles at a point, angles on a straight line and vertically opposite angles; solve problems involving parallel lines. 7.3 solve simple problems involving angles at a point, angles on straight line, vertically opposite angles, and angles formed between parallel lines. 7.2 identify vertically opposite angles and angles formed between parallel lines in diagrams. 7.1 calculate missing angles using the facts that angles at a point add up to 360 and angles on a straight line are supplementary. 6.3 identify parallel lines in diagrams. Objective 3 The teacher will teach the students to find unknown angles in triangles and quadrilaterals. 7.3 work out missing angles in complex diagrams involving triangles and quadrilaterals. 7.2 understand that the angle sum of a quadrilateral is 360 and find missing angles. 7.1 find unknown angles in any type of triangle. 6.3 find unknown angles in scalene triangles. Objective 4 The teacher will teach the students to understand a proof that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 7.3 understand a proof that the exterior angle of a triangle is equal to the sum of the two interior opposite angles. 7.2 find the value of an exterior angle of a triangle given the two interior opposite angles 7.1 know that an exterior and an interior angle of a triangle add up to know that angles in a triangle add up to 180, and angles on a straight line add up to 180. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

34 FORM 2 - Mathematics Number Unit code and title MTH 8.3 Fractions (Levels ) Objective 1 The teacher will teach the students to write a fraction that is equivalent to another fraction and reduce a fraction to its simplest form by cancelling common factors. 7.3 express whole numbers and fractions into different equivalent fractions. 7.2 reduce a fraction to its simplest form by cancelling common factors. 7.1 use equivalent fractions in comparing/ordering. 6.3 write equivalent fractions by multiplying or dividing numerator and denominator by a scale factor. Objective 2 The teacher will teach the students to add and/or subtract two fractions. 7.3 add and subtract improper fractions, using both equivalent fractions and L.C.M. 7.2 add and subtract two fractions with different denominators using equivalent fractions. 7.1 add and subtract two fractions with same denominators. 6.3 add and subtract two fractions through fraction circles and picture cards. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

35 Objective 3 The teacher will teach the students to arrange fractions in ascending/descending order. 7.3 arrange a set of fractions in ascending/descending order. 7.2 arrange fractions (denominators having common multiples) in ascending/descending order using LCM. 7.1 arrange a set of fractions (with denominators 2, 5 or 10) on a number line from 0 to 1 (divided in tenths). 6.3 understand that numerators can be used to put fractions in ascending/descending order when there is a common denominator. Objective 4 The teacher will teach the students to work out the fraction of a quantity. 7.3 multiply one fraction by another fraction without using the calculator. 7.2 multiply one fraction by another using the calculator. 7.1 work out the fraction of a quantity (whole number), without the use of a calculator. 6.3 find half, a quarter, a tenth and a fifth of an integer. Objective 5 The teacher will teach the students to solve problems involving fractions. 7.3 solve problems in finding fractions of any quantity. 7.2 solve simple problems in addition and subtraction of fractions with different denominators. 7.1 solve simple problems in addition and subtraction of fractions with common denominators. 6.3 solve problems in finding fractions of quantities (integers). Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

36 FORM 2 - Mathematics Number Unit code and title MTH 8.4 Decimals (Levels ) Objective 1 The teacher will teach the students to recognise and use the symbols <, >, and to compare two quantities. 7.3 recognise and use the symbols and for integers, decimals and fractions. 7.2 recognise and use the symbols < and > for integers and decimals. 7.1 compare integers and decimals and determine which is larger or smaller. 6.3 compare two pictorial quantities and determine which is larger or smaller. Objective 2 The teacher will teach the students to read decimal numbers from number lines and scales; read and use scales in practical situations. 7.3 read from scales such as speedometer, ampere meter, altimeter and air speed indicator. 7.2 read decimal numbers up to three places of decimals from number lines and scales. 7.1 read decimal numbers up to two places of decimals from scales measuring length, weight, capacity, speed and fuel gauge. 6.3 read decimal numbers up to one decimal place from number lines and scales measuring length, weight, capacity, speed and fuel gauge. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

37 Objective 3 The teacher will teach the students to arrange decimal numbers in order of size. 7.3 arrange any set of decimal numbers in ascending and descending order. 7.2 arrange numbers in ascending and descending order up to 3 decimal places. 7.1 arrange numbers in ascending and descending order up to 2 decimal places. 6.3 arrange numbers in ascending and descending order up to 1 decimal place. Objective 4 The teacher will teach the students to round numbers to a given number of decimal places and carry out rough estimates to check accuracy. 7.3 carry rough estimates to check accuracy. 7.2 round numbers to a given number of decimal places. 7.1 round numbers to one decimal place. 6.3 round numbers to the nearest whole. Objective 5 The teacher will teach the students to change fractions into decimals and vice versa; recognise recurring and non-recurring decimals. 7.3 change fractions to decimals. 7.2 change decimals, with a finite number of decimal places to fractions in their lowest terms. 7.1 change decimals with up to 3 decimal places to fractions in their lowest terms. 6.3 change decimals with up to 2 decimal places to fractions in their lowest terms. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

38 FORM 2 - Mathematics Number Unit code and title MTH 8.5 Percentages (Levels ) Objective 1 The teacher will teach the students to change percentages to fractions and decimals and vice-versa. 7.3 change fractions and decimals to percentages without the use of calculator. 7.2 change percentages to fractions and decimals without the use of calculator. 7.1 change percentages to fractions and decimals and vice versa using calculator when necessary. 6.3 change fractions with a factor of 100 as denominator, to decimals and vice versa. Objective 2 The teacher will teach the students to express one quantity as a percentage of another. 7.3 solve simple problems involving a quantity as a percentage of another. 7.2 express one quantity as a percentage of another by calculation and/or spreadsheet software. 7.1 express one quantity as a percentage of another. 6.3 express quantities out of multiples of 100 as a percentage. Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

39 Objective 3 The teacher will teach the students to work out the percentage of a quantity. 7.3 solve problems which involve finding the percentage of a quantity, using integral values. 7.2 work out more complex examples which involve finding the percentage of a quantity. 7.1 work out the percentage of a quantity where the percentage and/or the quantity is a multiple of work out the percentage of a quantity where the percentage and/or the quantity is a multiple of 10. Objective 4 The teacher will teach the students to work out the percentage increase and decrease. 7.3 solve problems which involve percentage increase/decrease using integral values. 7.2 work out the new amount after a percentage increase/decrease. 7.1 work out the percentage increase/decrease of a quantity. 6.3 work out the percentage increase / decrease of a quantity where the percentage and/or the quantity is a multiple of 10. FORM 2 - Mathematics Shape, Space and Measures Unit code and title MTH 8.6 Area and Volume (Levels ) Directorate for Quality and Standards in Education Curriculum Management and elearning Department English

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