mathematics - curriculum teaching objectives and learning outcomes (form 2) directorate for quality...

Directorate for Quality and Standards in Education Curriculum Management and eLearning Department – English -2012 2

MATHEMATICS Teaching Objectives and Learning Outcomes (Form 2)

Directorate for Quality and Standards in Education Curriculum Management and eLearning Department Malta 2012


FORM 2 - Mathematics

Strand Number

Unit code and title MTH 8.1 Factors, Multiples and Using a Calculator (Levels 7.1 – 8.1)

Objective 1 The teacher will teach the students to recognise and find common factors and multiples, up to three numbers.

Learning Outcomes Students will be able to

Level 8 8.1 recognise and find common factors and common multiples of three numbers.

Level 7 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 12. 7.1 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.


Level 8 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

Level 7 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.


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.


Level 8 8.1 solve simple problems involving the use of HCF.

Level 7 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.


Level 8 Students will be able to use the four rules for calculations including the correct use of operations and brackets.

Level 7

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.


Level 8 8.1 use the required key calculator functions in complex calculations involving fractions, brackets squares, cubes, square roots and cube roots.

Level 7 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.


Strand Shape, Space and Measures

Unit code and title MTH 8.2 Angles (Levels 7.1 – 8.1)

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°.


Level 8 Students will be able to estimate, measure and draw angles up to 360°.

Level 7 7.3 Students will be able to estimate, measure and draw angles up to 180° 7.2 Students will be able to estimate and measure angles up to 180°. 7.1 Students will be able 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.


Level 8 8.1 Students will be able to find missing angles in geometric diagrams by forming and solving algebraic equations.

Level 7

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.


Objective 3 The teacher will teach the students to find unknown angles in triangles and quadrilaterals.


Level 8 8.1 find the interior angles in regular polygons.

Level 7 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.


Level 8 8.1 write a general proof that the exterior angle of a triangle is equal to the sum of the two interior opposite angles.

Level 7

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°.


Strand Number

Unit code and title MTH 8.3 Fractions (Levels 7.1 – 8.1)


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.


Level 8 8.1 write a fraction that is equivalent to another fraction and change improper fractions to mixed numbers and vice-versa.

Level 7 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 The teacher will teach the students to add and/or subtract two fractions, including mixed numbers.


Level 8 8.1 add and subtract mixed numbers in parts: first the wholes, then the fractions.

Level 7 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.

Objective 3 The teacher will teach the students to arrange fractions in ascending/descending order; understand that the reciprocal of a number is its multiplicative inverse.


Level 8 8.1 manipulate reciprocals as multiplicative inverses of fractions and whole numbers.

Level 7 7.3 understand that multiplication and division are functions opposite to each other and that x

1

and x are multiplicative inverses 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).


Objective 4 The teacher will teach the students to multiply and divide one fraction by another fraction (excluding mixed numbers).


Level 8 8.1 multiply and divide one fraction by another fraction without using the calculator; numerators and denominators may or may

not be simplified.

Level 7

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.


Level 8 8.1 solve problems in addition and subtraction involving mixed numbers, and multiplication and division involving fractions but

not mixed numbers.

Level 7 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.


Strand Number

Unit code and title MTH 8.4 Decimals (Levels 7.1 – 8.1)


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.


Level 8 8.1 illustrate simple cases of inequalities on a number line.

Level 7 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.


Level 8 8.1 read multiple dials to get one reading.

Level 7 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.


Level 8 8.1 find a number between any two given decimal numbers.

Level 7 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.


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.


Level 8 8.1 Students will be able to recognise the difference between decimal places and significant figures.

Level 7 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.


Level 8 8.1 recognise that particular fractions have specific recurring decimal patterns.

Level 7

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.


Strand Number

Unit code and title MTH 8.5 Percentages


Objective 1 The teacher will teach the students to change percentages to fractions and decimals and vice-versa.


Level 8 8.1 change mixed numbers to percentages and decimals and vice versa.

Level 7 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.


Level 8 8.1 solve complex problems involving a quantity as a percentage of another.

Level 7 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.


Level 8 8.1 solve problems which involve finding the percentage of a quantity, where the percentage is a mixed number.

Level 7 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.


Objective 4 The teacher will teach the students to work out the percentage increase and decrease.


Level 8 8.1 solve problems which involve percentage increase/decrease where the percentage is a mixed number.

Level 7 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.



Unit code and title MTH 8.6 Area and Volume (Levels 7.1 – 8.1)

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.


Level 8 8.1 derive the formula A = ½bh for the area of a triangle.

Level 7 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.


Objective 2 The teacher will teach the students to calculate the area of compound shapes.


Level 8 8.1 find the area of compound shapes formed of squares/rectangles and triangles which need not be right-angled, using formulae.

Level 7 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.


Level 8 8.1 derive the formulae for the surface area of a cube, A = 6l2 and a cuboid, A = 2(lb+lw+bw)

Level 7 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 Students will be able to 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.


Level 8 8.1 find the volume of compound shapes involving more than 2 components (cubes/cuboids).

Level 7 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.


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.


Level 8 8.1 derive the formula: V= area of cross-section length.

Level 7 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.



Unit code and title MTH 8.7 Triangles and Quadrilaterals (Levels 7.1 – 8.1)

Objective 1 The teacher will teach the students to classify triangles and quadrilaterals by identifying their geometric properties through line and/or rotational symmetry.


Level 8 8.1 classify triangles and quadrilaterals by identifying their geometric properties through line and rotational symmetry.

Level 7

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.


Objective 2 The teacher will teach the students to identify tessellating shapes and cover a given area with tessellating shapes.


Level 8 8.1 create tessellating shapes and use it to cover a given area, such as tiling a room.

Level 7 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.


Level 8 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.

Level 7

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.


Level 8 8.1 draw scale drawings from given data and use scale drawings to find actual distances and areas.

Level 7 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.


Objective 5 The teacher will teach the students to draw scale drawings to solve problems involving angles of elevation and depression.


Level 8 8.1 draw scale drawings to solve complex problems involving angles of elevation and depression.

Level 7 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.



Unit code and title MTH 8.8 Constructions (Levels 7.1 – 8.1)

Objective 1 The teacher will teach the students to use ruler and compasses only to construct a perpendicular at a point on a line.


Level 8 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

Level 7 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.


Objective 2 The teacher will teach the students to use ruler and compasses only to construct a perpendicular from a point to a line.


Level 8 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.

Level 7 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.


Level 8 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.

Level 7 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.


Level 8 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.

Level 7 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.


Objective 5 The teacher will teach the students to construct squares and rectangles using ruler and compasses only.


Level 8 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.

Level 7 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.


Strand Algebra / Number

Unit code and title MTH 8.9 Directed Numbers and Sequences (Levels 7.1 – 8.1)

Objective 1 The teacher will teach the students to add/subtract/multiply/ divide directed numbers.


Level 8 8.1 add/subtract/multiply/divide more than two directed numbers.

Level 7

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.


Objective 2 The teacher will teach the students to solve problems using directed numbers.


Level 8 8.1 solve complex problems involving addition/subtraction/multiplication/division of +ve/-ve numbers without the help of the

number line or calculator.

Level 7

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.


Level 8 8.1 generate terms of a complex sequence using position to term rules.

Level 7 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 nth term expression of linear sequences of the form kn + m where k and m are integers.


Level 8 8.1 write the nth term expression of linear sequences of the form kn + m where k and m are integers.

Level 7

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



Strand Algebra

Unit code and title MTH 8.10 Expressions and Formulae (Levels 7.1 – 8.1)

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.


Level 8 8.1 simplify quadratic algebraic expressions by multiplying a single term over a bracket and/or collecting like terms.

Level 7

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.


Level 8 8.1 factorise fully linear expressions by identifying a numerical common factor.

Level 7 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.


Objective 3 The teacher will teach the students to evaluate simple formulae by substituting letters with positive and negative inputs.


Level 8 8.1 evaluate quadratic formulae by substituting letters with positive and negative inputs.

Level 7 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.


Level 8 8.1 derive and use formulae to solve problems involving positive/negative integers.

Level 7

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.


Strand Data Handling

Unit code and title MTH 8.11 Statistics and Probability (Levels 7.1 – 8.1)


Objective 1 The teacher will teach the students to draw and interpret bar charts and pie charts.


Level 8 8.1 interpret bar charts and pie charts for grouped data.

Level 7 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 The teacher will teach the students to compile and interpret frequency tables for grouped / ungrouped discrete and continuous data.


Level 8 8.1 interpret frequency tables by answering complex questions about the grouped continuous data.

Level 7

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.

Objective 3 The teacher will teach the students to understand, compute and interpret the mean, mode, median and range of a set of ungrouped data.


Level 8 8.1 find missing entries of data, given their mean, mode, median and range.

Level 7

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.


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.


Level 8 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.

Level 7 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.


Level 8 8.1 use probabilities to estimate the number of times an event will occur.

Level 7 7.3 understand that the probabilities of all possible outcomes add up to 1. 7.2 understand that the probabilities of an event happening and not happening add up to 1. 7.1 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.


Level 8 8.1 find the probability of two events occurring at the same time by multiplying their probabilities.

Level 7

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 7.

7.2 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.



Strand Number

Unit code and title MTH 8.12 Ratio & Proportion (Levels 7.1 – 8.1)

Objective 1 The teacher will teach the students to solve problems involving direct proportion using the unitary method.


Level 8 8.1 solve complex problems involving direct proportion with and without the use of the unitary method (e.g.: including exchange rates, recipes etc.).

Level 7

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.


Level 8 8.1 apply the ratio notation to compare two or more quantities within real-life situations.

Level 7 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.


Objective 3 The teacher will teach the students to divide a quantity in a given ratio.


Level 8 8.1 divide a quantity in a given ratio of three or more unequal parts.

Level 7

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


Unit code and title MTH 8.13 Transformations (Levels 7.1 – 8.1)

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.


Level 8 8.1 determine the symmetrical properties of any 2D shape.

Level 7

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.


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.


Level 8 8.1 label correctly the vertices of the object and image in a reflection.

Level 7

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.

Objective 3 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.


Level 8 8.1 apply multiple translations to a shape.

Level 7

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.

Objective 4 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.


Level 8 8.1 rotate a shape when the centre of rotation is outside the shape and describe the transformation in words.

Level 7

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 90°. 7.1 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.


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.


Level 8 8.1 understand that in an enlargement the object and image are similar.

Level 7 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.


Strand Algebra

Unit code and title MTH 8.14 Solving Equations (Levels 7.1 – 8.1)

Objective 1 The teacher will teach the students to solve linear equations in one unknown.


Level 8 8.1 solve linear equations with one unknown on both sides.

Level 7 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.


Objective 2 The teacher will teach the students to solve linear equations involving brackets.


Level 8 8.1 solve linear equations involving brackets.

Level 7 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.


Level 8 8.1 form and solve linear equations with one unknown on both sides.

Level 7

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.


Strand Algebra

Unit code and title MTH 7.15 Coordinates and Straight Line Graphs (Levels 7.1 – 8.1)


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.


Level 8 8.1 find the equation of a straight line graph given the co-ordinates of any two points on the line.

Level 7 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.


Level 8 8.1 draw the graph of a linear equation given in the form y = mx+ c

Level 7 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)


Level 8 8.1 find the gradient of a line from any two points on the line and sketch a line given the gradient.

Level 7 7.3 identify whether a line has a gradient equal to 1, less than 1 or equal to 1. 7.2 calculate the gradient of a line using the triangle method. 7.1 understand the meaning of ‘the gradient of a line’.


Objective 4 The teacher will teach the students to interpret information presented in a variety of linear graphs; use and draw conversion graphs.


Level 8 8.1 interpret the relationship between two journeys represented on one travel graph.

Level 7 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.


Strand Number


Objective 1 The teacher will teach the students to recognise and find common factors and multiples of two numbers.


Level 7 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 12. 7.1 find all the factors of given numbers up to 50 and list all the multiples of the numbers from 1 to 10.

Level 6 6.3 Students will be able to find all the factors of numbers up to 25 and list all the multiples of 2, 3, 5 and 10


Objective 2 The teacher will teach the students to recognise prime numbers and write numbers as a product of their prime factors.


Level 7 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 50.

Level 6 6.3 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.


Level 7 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.

Level 6 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.


Level 7

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

Level 6 6.3 use the correct order of the four basic rules for calculations involving two operations one of which includes the use of brackets.


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.


Level 7

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.

Level 6 6.3 make efficient use of the basic calculator functions in simple calculations




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°.


Level 7 7.3 estimate, measure and draw angles up to 180° 7.2 estimate and measure angles up to 180°. 7.1 estimate angles up to 180°.

Level 6 6.3 distinguish between acute, right, obtuse and reflex angles.


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.


Level 7

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.

Level 6 6.3 identify parallel lines in diagrams.

Objective 3 The teacher will teach the students to find unknown angles in triangles and quadrilaterals.


Level 7 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.

Level 6 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.


Level 7 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°.

Level 6 6.3 know that angles in a triangle add up to 180°, and angles on a straight line add up to 180°.



Strand Number


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.


Level 7 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 .

Level 6 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.


Level 7 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.

Level 6 6.3 add and subtract two fractions through fraction circles and picture cards.


Objective 3 The teacher will teach the students to arrange fractions in ascending/descending order.


Level 7 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).

Level 6 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.


Level 7 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.

Level 6 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.


Level 7 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.

Level 6 6.3 solve problems in finding fractions of quantities (integers).



Strand Number


Objective 1 The teacher will teach the students to recognise and use the symbols <, >, ≤ and ≥ to compare two quantities.


Level 7 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.

Level 6 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.


Level 7 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.

Level 6 6.3 read decimal numbers up to one decimal place from number lines and scales measuring length, weight, capacity, speed and

fuel gauge.




Level 7 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.

Level 6 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.


Level 7 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.

Level 6 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.


Level 7 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.

Level 6 6.3 change decimals with up to 2 decimal places to fractions in their lowest terms.



Strand Number

Unit code and title MTH 8.5 Percentages (Levels 6.3 – 7.3)



Level 7 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.

Level 6 6.3 change fractions with a factor of 100 as denominator, to decimals and vice versa.



Level 7 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.

Level 6 6.3 express quantities out of multiples of 100 as a percentage.




Level 7 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.

Level 6 6.3 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.


Level 7 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.

Level 6 6.3 work out the percentage increase / decrease of a quantity where the percentage and/or the quantity is a multiple of 10.





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.


Level 7 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.

Level 6 6.3 find the area of a rectangle/square by adding unit squares.

Objective 2 The teacher will teach the students to calculate the area of compound shapes.


Level 7 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.

Level 6 6.3 find the area of compound shapes which can be split in squares / rectangles, by counting squares on a grid.

Objective 3 The teacher will teach the students to work out the surface area of a cube and cuboid.


Level 7 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.

Level 6 6.3 find the surface area of cubes and cuboids by adding the areas of each face.




Level 7 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.

Level 6 6.3 calculate the volume of simple compound shapes given the description of its 2 components.

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.


Level 7 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.

Level 6 6.3 identify prisms, their cross-section and length.







Level 7

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.

Level 6 6.3 name triangles and quadrilaterals given their properties.



Level 7 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.

Level 6 6.3 identify shapes that do not need to be rotated to tessellate and be able to continue a pattern with such shapes.


Objective 3 The teacher will teach the students to make accurate drawings of triangles.


Level 7

7.3 Students will be able to 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 Students will be able to 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 Students will be able to make an accurate drawing of triangles given two sides and the included angle using ruler and protractor.

Level 6 6.3 Students will be able to make an accurate drawing of triangles given the length of the three sides using ruler and compasses.



Level 7 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.

Level 6 6.3 read a simple scale drawing (in the ratio 1:2, 1: 5 and 1:10).





Objective 1 The teacher will teach the students to use ruler and compasses only to draw angles of 60˚.


Level 7 7.3 use ruler and compasses only to construct an angle of 60˚. 7.2 use ruler and protractor to construct an angle of 60˚. 7.1 use ruler and appropriate set square only to construct an angle of 60˚.

Level 6 6.3 use ruler only to make a reasonable accurate sketch of an angle of 60˚.

Objective 2 The teacher will teach the students to use ruler and compasses only to draw angles of 90˚.


Level 7 7.3 use ruler and compasses only to construct an angle of 90˚. 7.2 use ruler and protractor to construct an angle of 90˚. 7.1 use ruler and appropriate set square only to construct an angle of 90˚.

Level 6 6.3 use ruler only to make a reasonable accurate sketch of an angle of 90˚.

Objective 3 The teacher will teach the students to use ruler and compasses only to construct the perpendicular bisector of a line segment.


Level 7 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 sketch of the perpendicular bisector of a line segment.

Level 6 6.3 recognise that a line is the perpendicular bisector of a line segment by measuring the angles the line makes with the line

segment using a protractor.


Objective 4 Use ruler and compasses only to construct the bisector of an angle.


Level 7 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 sketch of the bisector of an angle

Level 6 6.3 recognise that a line is the bisector of an angle by measuring the angles the line makes with the arms of the angle using a

protractor

Objective 5 Construct squares and rectangles using ruler, protractor and compasses only.


Level 7 7.3 use ruler and compasses only to construct squares and rectangles of given dimensions. 7.2 use ruler and protractor only to construct squares and rectangles of given dimensions. 7.1 use ruler and appropriate set square only to construct squares and rectangles of given dimensions.

Level 6 6.3 use ruler only to make reasonable accurate sketches of squares and rectangles of given dimensions.





Objective 1 The teacher will teach the students to recognise and understand negative numbers through practical examples and represent directed numbers on the number line.


Level 7

7.3 place integers in order of size without the use of a number line 7.2 compare the value of two or more positive/negative integers. 7.1 distinguish between positive and negative numbers. They can also represent both positive and negative integers on the number line.

Level 6 6.3 compare the value of two positive integers.

Objective 2 The teacher will teach the students to add/subtract/multiply/ divide directed numbers.


Level 7

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.

Level 6 6.3 add/subtract two positive integers which give a positive/negative result, using the number line.



Level 7

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.

Level 6 6.3 solve simple problems involving addition of two +ve/-ve integers and subtraction of +ve integers.


Objective 4 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.


Level 7 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.

Level 6 6.3 fill in a missing term in arithmetic patterns.

Objective 5 The teacher will teach the students to write the nth term expression of linear sequences of the form kn + m where k and m are integers.


Level 7

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

Level 6 6.3 tell that the rule involves only multiplication.


Strand Algebra



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.


Level 7

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.

Level 6 6.3 simplify linear expressions made up of one variable by collecting like terms.

Objective 2 The teacher will teach the students to evaluate simple linear formulae by substituting letters with positive and negative inputs.


Level 7 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.

Level 6 6.3 evaluate simple linear formulae involving more than two variables by substituting letters with positive integral inputs.

Objective 3 The teacher will teach the students to derive and use formulae to solve problems.


Level 7

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.

Level 6 6.3 choose the correct variable expression involving one operation to represent a word problem.





Objective 1 The teacher will teach the students to draw and interpret bar charts and pie charts.


Level 7 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°.

Level 6 6.3 interpret simple pie charts, limited to sectors of 180°, 90° and 45°.

Objective 2 The teacher will teach the students to compile and interpret frequency tables for grouped / ungrouped discrete and continuous data.


Level 7

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.

Level 6 6.3 Students will be able to compile a frequency table for a set of ungrouped discrete numerical data.


Objective 3 The teacher will teach the students to understand, compute and interpret the mean, mode, median and range of a set of ungrouped data.


Level 7

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.

Level 6 6.3 find the mean, median, mode and range from a longer list of entries, with an even number of entries.



Level 7 7.3 understand that the probabilities of all possible outcomes add up to 1. 7.2 understand that the probabilities of an event happening and not happening add up to 1. 7.1 calculate probabilities of an event having more than one possible outcome.

Level 6 6.3 understand the notion of equally likely events and find simple probabilities, of events having just one possible outcome, such as getting a 5 when rolling a die.

Objective 5 The teacher will teach the students to compile a possibility space and use it to find the probability of two events.


Level 7

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 7.

7.2 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.

Level 6 6.3 calculate the number of all possible outcomes given the two events.



Strand Number




Level 7

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.

Level 6 6.3 solve simple problems when given the unit measure.



Level 7 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.

Level 6 6.3 understand the concept of ratio through pictorial representations.




Level 7

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.

Level 6 6.3 understand order of ratio. Eg: the ratio 2:3 is not the same as the ratio 3:2.




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.


Level 7

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.

Level 6 6.3 Students will be able to identify shapes having reflection and/or rotational symmetry.


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.


Level 7

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.

Level 6 6.3 reflect a shape in the x axis and/or y axis and describe the reflection in words.

Objective 3 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.


Level 7

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.

Level 6 6.3 translate shapes right, left, up and down.

Objective 4 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.


Level 7

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 90°. 7.1 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.

Level 6 6.3 rotate squares and rectangles about one of the vertices through an angle of 90° and 180°.


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.


Level 7 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.

Level 6 6.3 recognise an enlargement.


Strand Algebra


Objective 1 The teacher will teach the students to solve linear equations in one unknown up to two operations.


Level 7 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.

Level 6 6.3 solve equations by drawing scales, given unknown on one side and involving up to two operations.


Objective 2 The teacher will teach the students to solve linear equations involving one pair of brackets on one side only.


Level 7 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.

Level 6 6.3 carry out operations in the correct order (BIDMAS).

Objective 3 The teacher will teach the students to use equations to solve problems.


Level 7

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.

Level 6 6.3 form and solve equations by drawing pictorial representations, given unknown on one side and involving up to two operations.


Strand Algebra



Objective 1 The teacher will teach the students to read and plot co-ordinates using ordered pairs in all four quadrants.


Level 7 7.3 draw both axes; use ordered pairs to identify and plot points in all four quadrants including decimal values. 7.2 use ordered pairs to identify and plot points in all four quadrants including decimal values. 7.1 plot points in all four quadrants excluding decimal values.

Level 6 6.3 identify points in all four quadrants.

Objective 2 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.


Level 7 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.

Level 6 6.3 understand that a linear relationship between the x and y coordinates can be represented as a graph on a coordinate grid.

Objective 3 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.


Level 7 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.

Level 6 6.3 use the equation of a straight-line to generate a sequence of ordered pairs.


Objective 4 The teacher will teach the students to interpret information presented in a variety of linear graphs; use and draw conversion graphs.


Level 7 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.

Level 6 6.3 convert values, including decimal values beyond the ranges in the conversion graph.


Strand Number


Objective 1 The teacher will teach the students to order a set of numbers and round numbers to the nearest unit, 10, 100 and 1000.


Level 7 7.1 order a set of numbers between 0 and 9999 and round numbers to the nearest unit, 10, 100 and 1000.

Level 6 6.3 order a set of numbers between 0 and 999, and round numbers to the nearest unit, 10 and 100. 6.2 order a set of 3-digit numbers and round numbers to the nearest unit and 10. 6.1 order a set of 2-digit numbers on a number line, and round numbers to the nearest 10.

Level 5 5.3 order a set of numbers between 0 and 100, putting them in ascending and/or descending order.


Objective 2 The teacher will teach the students to recognise factors, multiples, prime, square and cube numbers.


Level 7 7.1 list all the multiples of numbers up to 10, factors of given numbers up to 50, identify prime numbers up to 50 and square/cube numbers up to 100.

Level 6

6.3 list all the multiples of 2, 5 and 10, the factors of given numbers up to 30, identify the prime numbers up to 35 and square numbers up to 50.

6.2 find some factors of given numbers up to 30 and identify the prime and square numbers up to 30. 6.1 list the multiples of 2, 5 and 10 and identify the first five prime and square numbers.

Level 5 5.3 list the factors of numbers up to 12 and the multiples of 2, 5 and 10.

Objective 3 The teacher will teach the students to use brackets correctly to help with multiplication and use tests of divisibility restricted to multiples of 2, 3, 5 and 10.


Level 7 7.1 use brackets correctly to help with multiplication of two 2-digit numbers and use tests of divisibility restricted to multiples of 2, 3, 5 and 10.

Level 6

6.3 use brackets correctly to help with multiplying a 2-digit number with a single digit and use tests of divisibility restricted to 2, 5 and 10.

6.2 list common multiples of say 2 and 5, 5 and 10, and 2 and 10. 6.1 list the multiples of 2, 5 and 10.

Level 5 5.3 list the multiples of 2 and 10.





Objective 1 The teacher will teach the students to understand that a revolution is divided into 360 parts called degrees; estimate the size of an angle, and distinguish between acute, right, obtuse and reflex angle


Level 7 7.1 estimate angles up to 180°.

Level 6 6.3 distinguish between acute, right, obtuse and reflex angles.

6.2 know that a revolution is made up of 360. 6.1 understand that a whole turn is equivalent to 4 right angles and half a turn is equivalent to 2 right angles

Level 5 5.3 recognise right angles in 2D shapes and understand that a right angle is a quarter turn.

Objective 2 The teacher will teach the students to use a protractor to measure and draw angles up to 180.


Level 7 7.1 use a protractor to measure and draw angles up to 180°.

Level 6

6.3 use a protractor to measure angles up to 180°.

6.2 use a protractor to measure and draw angles in multiples of 5 up to 180.

6.1 use a protractor to measure and draw angles in multiples of 10 up to 180.

Level 5 5.3 measure and draw angles of 90 and 180.


Objective 3 The teacher will teach the students to solve problems involving angles at a point and angles on a straight line.


Level 7 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.

Level 6 6.3 work missing angles in diagrams involving angles at a point. 6.2 identify angles at a point in given diagrams. 6.1 work out missing angles in diagrams involving angles on a straight line.

Level 5 5.3 identify angles on a straight line in given diagrams.

Objective 4 The teacher will teach the students to find unknown angles in triangles.


Level 7 7.1 find unknown angles in any type of triangle.

Level 6

6.3 find unknown angles in scalene triangles.

6.2 understand that the angles in a triangle add up to 180. 6.1 identify different types of triangles (scalene, isosceles, right-angled and equilateral triangles).

Level 5 5.3 distinguish triangles from other shapes.


Strand Number



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.


Level 7 7.1 use equivalent fractions in comparing/ordering fractions.

Level 6 6.3 write equivalent fractions by multiplying or dividing numerator and denominator by a scale factor. 6.2 write equivalent fractions by multiplying numerator and denominator by a scale factor. 6.1 write equivalent fractions involving halves, fourths, fifths and tenths.

Level 5 5.3 write equivalent fractions using pictures, fraction cards and blocks.

Objective 2 The teacher will teach the students to add and subtract two fractions that have a common denominator.


Level 7 7.1 add and subtract two fractions with same denominators.

Level 6 6.3 add and subtract two fractions through fraction circles and picture cards. 6.2 add two fractions through fraction circles and picture cards. 6.1 add and subtract halves, fourths, fifths and tenths, each time with the same denominator.

Level 5 5.3 add and subtract halves, fourths, fifths and tenths through fraction circles and picture cards.

Objective 3 The teacher will teach the students to work out the fraction of a quantity (integer).


Level 7 7.1 work out the fraction of a quantity (whole number), without the use of a calculator.

Level 6 6.3 find half, a quarter, a tenth and a fifth of an integer. 6.2 find half, a quarter and a tenth of an integer. 6.1 work out half and a quarter of an integer.

Level 5 5.3 manipulate picture cards and blocks to work out the fraction of a quantity.


Objective 4 The teacher will teach the students to solve simple problems involving fractions.


Level 7 7.1 solve simple problems in addition and subtraction of fractions with common denominators.

Level 6 6.3 solve problems in finding fractions of quantities (integers). 6.2 solve simple problems in addition and subtraction of fractions. 6.1 solve simple problems involving addition of two fractions.

Level 5 5.3 identify two simple fractions with a total of 1.


Strand Number


Objective 1 The teacher will teach the students to read decimal numbers from scales; read and use scales in practical situations up to two decimal places.


Level 7 7.1 decimal numbers up to two places of decimals from number lines and scales measuring length, weight, capacity, speed and fuel gauge.

Level 6

6.3 read decimal numbers up to one decimal place from number lines and scales measuring length, weight, capacity, speed and fuel gauge. 6.2 read decimal numbers up to one decimal place from a number line. 6.1 read scales involving half unit and quarter unit intervals.

Level 5 5.3 read scales involving half unit intervals.




Level 7 7.1 arrange numbers in ascending and descending order up to 2 decimal places.

Level 6 6.3 arrange numbers in ascending and descending order up to 1 decimal place. 6.2 arrange decimal numbers represented as wholes, halves and quarters, in ascending and descending order. 6.1 arrange decimal numbers represented as wholes and halves, in ascending and descending order.

Level 5 5.3 arrange integers, in ascending and descending order.

Objective 3 The teacher will teach the students to add and subtract decimal numbers.


Level 7 7.1 add and subtract decimal numbers with 2 decimal places.

Level 6 6.3 subtract decimals with 1 decimal place, involving change over place value (borrowing). 6.2 add decimal numbers with 1 decimal place, involving carrying over. 6.1 subtract decimals with 1 decimal place, not involving change over place value (borrowing).

Level 5 5.3 add decimal numbers with 1 decimal place, not involving carrying over.

Objective 4 The teacher will teach the students to round numbers to one decimal place.


Level 7 7.1 round numbers to one decimal place.

Level 6 6.3 round numbers to the nearest hundred. 6.2 round numbers to the nearest ten. 6.1 round numbers to the nearest whole.

Level 5 5.3 understand that the decimal system uses a base of ten.


Objective 5 The teacher will teach the students to multiply and divide decimal numbers by an integer.


Level 7 7.1 multiply and divide any decimal number by an integer.

Level 6 6.3 multiply decimal numbers up to 2 decimal places by an integer. 6.2 multiply decimal numbers up to 1 decimal place by an integer. 6.1 multiply and divide decimal numbers by 10, 100 and 1000.

Level 5 5.3 multiply and divide decimal numbers by 10.

Objective 6 The teacher will teach the students to work out simple problems on multiplication and division of decimals.


Level 7 7.1 work out simple worded problems involving both multiplication and division of quantities.

Level 6 6.3 work out simple worded problems involving division of decimals. 6.2 work out simple worded problems involving multiplication of decimals. 6.1 decide which operation to use to solve a simple worded problem.

Level 5 5.3 decide which operation to use given a simple practical situation.


Strand Number

Unit code and title MTH 8.5 Percentages (Levels 5.3 – 7.1)




Level 7 7.1 change percentages to fractions and decimals and vice versa using calculator when necessary.

Level 6 6.3 change fractions with a factor of 100 as denominator, to decimals and vice versa. 6.2 change fractions with a factor of 100 as denominator, to percentages and vice versa. 6.1 change integral percentages to fractions and simplify when necessary.

Level 5 5.3 list all the factors of 100.



Level 7 7.1 express one quantity as a percentage of another.

Level 6 6.3 express quantities out of multiples of 100 as a percentage. 6.2 express quantities out of factors of 100 as percentages. 6.1 express quantities out of 10 as percentages.

Level 5 5.3 express quantities out of 100 as percentages.



Level 7 7.1 work out the percentage of a quantity where the percentage and/or the quantity is a multiple of 5.

Level 6 6.3 work out the percentage of a quantity where the percentage and/or the quantity is a multiple of 10. 6.2 work out the percentage of a quantity where the percentage is a multiple of 10. 6.1 work out the percentage of a quantity which is a multiple of 100. (Level 6.1)

Level 5 5.3 appreciate that 100% represents the total amount.





Objective 1 The teacher will teach the students to find the perimeter of simple shapes by adding side lengths.


Level 7 7.1 find the perimeter of flat shapes by adding the lengths of all sides; practice their addition skills as they learn how to find the perimeter of a figure

Level 6 6.3 find the perimeter of composite shapes drawn on a grid, by counting unit squares on each side of each flat shape. 6.2 find the perimeter of rectangles/squares drawn on a grid, by counting unit squares on each side. 6.1 understand that perimeter is a linear measurement. Restrict to cm and mm.

Level 5 5.3 understand the notion of perimeter as adding all sides.

Objective 2 The teacher will teach the students to use the formula to find the area of a rectangle; find the area of simple shapes made up of rectangles.


Level 7 7.1 find the area of compound shapes made up of unmarked squares and rectangles using the formula.

Level 6 6.3 find the area of compound shapes made up of squares and rectangles indicated on the shape and by using the formula. 6.2 solve a worded problem on finding the area of a rectangle by using the formula. 6.1 find the area of a rectangle by using the formula.

Level 5 5.3 find the area of a rectangle drawn on a grid by counting squares.


Objective 3

The teacher will teach the students to find the volume of cubes and cuboids by counting cubes/using formula.


Level 7 7.1 solve worded problems involving finding the volume of a cuboid as part of the solution. E.g. How many cubes of volume 4 cm3

can be filled with sand from a cuboid which is 2 cm 4 cm 8 cm

Level 6 6.3 solve worded problems involving finding the volume of a cuboid. 6.2 find the volume of a cuboid using the formula. 6.1 understand that volume is measured in unit cubes

Level 5 5.3 understand the concept of volume as the amount of space occupied by the solid shape.



Level 7 7.1 identify the components (cubes and cuboids) making up a compound shape and find its volume.

Level 6 6.3 calculate the volume of simple compound shapes given the description of its components 6.2 find the volume of the compound shapes by adding the volume of the different components. 6.1 identify the 2 components (cubes or cuboids) making up the compound shape.

Level 5 5.3 find the volume of a compound shape by counting cubes.







Level 7 7.1 classify triangles and quadrilaterals according to number of sides, length of sides, right angles and size of angles.

Level 6

6.3 name triangles and quadrilaterals given their properties. 6.2 distinguish between regular and irregular triangles and regular and irregular quadrilaterals using length of sides and size of

angles. 6.1 identify and draw lines of symmetry in triangles and quadrilaterals.

Level 5 5.3 distinguish between equilateral, isosceles and scalene triangles, squares and rectangles from the number of sides and length of

the sides.



Level 7 7.1 identify shapes that need to be rotated to tessellate.

Level 6 6.3 identify shapes that do not need to be rotated to tessellate and be able to continue a pattern with such shapes. 6.2 identify shapes that do not need to be rotated to tessellate. 6.1 understand the meaning of regular and non-regular tessellations.

Level 5 5.3 understand the meaning of the term tessellation.




Level 7 7.1 draw and interpret scale drawings using a ratio of 1cm to represent 1m and/or 1 km.

Level 6 6.3 read a simple scale drawing (in the ratio 1:2, 1: 5 and 1:10). 6.2 understand the general notion of ratios in the form: 1 cm to represent 1 m or 1 km. 6.1 understand that scale drawings are accurate drawing representing larger areas.

Level 5 5.3 draw simple shapes with a given set of measurements (in cm).

Objective 4 The teacher will teach the students to use squared paper to draw nets of solid shapes and use isometric paper to draw solids.


Level 7 7.1 Students will be able to draw solid shapes using isometric paper and their nets on squared paper.

Level 6 6.3 draw prisms using isometric paper and their nets on squared paper. 6.2 draw the cube and cuboid using isometric paper and their respective nets on squared paper. 6.1 draw the nets of a cube and a cuboid on squared paper.

Level 5 5.3 draw the net of a cube on squared paper.





Objective 1 The teacher will teach the students to construct triangles given the length of the sides using ruler and protractor only.


Level 7 7.1 construct a triangle given the length of the sides using ruler and protractor only with continual teacher guidance.

Level 6

6.3 produce a reasonably accurate sketch of a triangle given the length of the sides using ruler only. 6.2 produce a reasonably accurate sketch of a triangle given the length of the sides using ruler only with teacher guidance. 6.1 produce a reasonably accurate sketch of a triangle given the length of the sides using ruler only with continual teacher

guidance.

Level 5 5.3 produce a rough sketch of a triangle given the length of the sides using a freehand approach.

Objective 2 The teacher will teach the students to construct triangles given the length of one side and two angles using ruler and protractor only.


Level 7 7.1 construct a triangle given the length of one side and two angles using ruler and protractor only with continual teacher

guidance.

Level 6

6.3 produce a reasonably accurate sketch of a triangle given the length of one side and two angles using ruler only. 6.2 produce a reasonably accurate sketch of a triangle given the length of one side and two angles using ruler only with teacher

guidance. 6.1 produce a reasonably accurate sketch of a triangle given the length of one side and two angles using ruler only with continual

teacher guidance.

Level 5 5.3 produce a rough sketch of a triangle given the length of one side and two angles using a freehand approach.


Objective 3 The teacher will teach the students to construct triangles given the length of two sides and the included angle using ruler and protractor only.


Level 7 7.1 construct a triangle given the length of two sides and the included angle using ruler and protractor only with continual teacher

guidance.

Level 6

6.3 produce a reasonably accurate sketch of a triangle given the length of two sides and the included angle using ruler only. 6.2 produce a reasonably accurate sketch of a triangle given the length of two sides and the included angle using ruler only with teacher guidance. 6.1 produce a reasonably accurate sketch of a triangle given the length of two sides and the included angle using ruler only with continual teacher guidance.

Level 5 5.3 produce a rough sketch of a triangle given the length of two sides and the included angle using a freehand approach.

Objective 4 The teacher will teach the students to use ruler and protractor only to draw angles of 60˚.


Level 7 7.1 use ruler and protractor to construct an angle of 60˚ with continual teacher guidance.

Level 6 6.3 use ruler only to make a reasonable accurate sketch of an angle of 60˚. 6.2 use ruler only to make a reasonable accurate sketch of an angle of 60˚ with teacher guidance. 6.1 use ruler only to make a reasonable accurate sketch of an angle of 60˚ with continual teacher guidance.

Level 5 5.3 produce a rough sketch of an angle of 60˚using a freehand approach.


Objective 5 The teacher will teach the students to use ruler and protractor only to draw angles of 90˚.


Level 7 7.1 use ruler and protractor to construct an angle of 90˚ with continual teacher guidance.

Level 6 6.3 use ruler only to make a reasonable accurate sketch of an angle of 90˚. 6.2 use ruler only to make a reasonable accurate sketch of an angle of 90˚ with continual teacher guidance. 6.1 use ruler only to make a reasonable accurate sketch of an angle of 90˚ with continual teacher guidance.

Level 5 5.3 produce a rough sketch of an angle of 90˚using a freehand approach.

Objective 6 The teacher will teach the students to construct squares and rectangles using ruler and protractor only.


Level 7 7.1 use ruler and protractor only to construct squares and rectangles of given dimensions with continual teacher guidance.

Level 6

6.3 use ruler only to make reasonable accurate sketches of squares and rectangles of given dimensions. 6.2 use ruler only to make reasonable accurate sketches of squares and rectangles of given dimensions with teacher guidance. 6.1 use ruler only to make reasonable accurate sketches of squares and rectangles of given dimensions with continual teacher

guidance.

Level 5 5.3 produce rough sketches of squares and rectangles of given dimensions using a freehand approach.





Objective 1 The teacher will teach the students to recognise and understand negative numbers through practical examples and represent directed numbers on the number line.


Level 7 7.1 distinguish between positive and negative numbers. They can also represent both positive and negative integers on the

number line.

Level 6

6.3 compare the value of two positive integers. 6.2 put positive integers in order of size on a number line. 6.1 understand that on a number line, the positive numbers are found on the right hand side of zero while the negative

numbers are found on the left hand side.

Level 5 5.3 understand that positive numbers carry a “+” sign while negative numbers carry a “-” sign and apply this to real life

situations.

Objective 2 The teacher will teach the students to add and subtract directed numbers; use a calculator to subtract a negative number.


Level 7 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.

Level 6 6.3 subtract two positive integers which give a positive/negative result, using the number line. 6.2 add a positive integer to a negative integer which gives a positive/negative result, without the help of the number line. 6.1 add a positive integer to a negative integer which gives a positive/negative result, using the number line.

Level 5 5.3 add two or more positive integers.




Level 7 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.

Level 6 6.3 solve simple problems involving addition of +ve/-ve integers and subtraction of +ve integers. 6.2 solve problems involving addition of more than two +ve/-ve integers. 6.1 solve simple problems involving addition of two +ve/-ve integers.

Level 5 5.3 express actions as +ve/-ve numbers, i.e. go up 3 levels and down 2 expressed as +3 and -2.

Objective 4 The teacher will teach the students to recognise arithmetic and geometric patterns; complete a given sequence using term to term rule.


Level 7 7.1 continue simple arithmetic/ geometric patterns using term to term rule.

Level 6 6.3 fill in a missing term in arithmetic patterns. 6.2 6.2 recognise arithmetic patterns. 6.1 6.1 continue pictorial patterns.

Level 5 5.3 recognise pictorial patterns.


Objective 5 The teacher will teach the students to describe the rule in words of a sequence of the form n ± k and kn where k is a positive integer.


Level 7 7.1 describe the rule in words of a sequence of the form n ± k and kn where k is a positive integer.

Level 6 6.3 tell that the rule involves only multiplication. 6.2 write the rule in words in number sequences of the form n ± k where k is a positive integer. 6.1 write the rule in words in number sequences of the form n + k where k is a positive integer.

Level 5 5.3 tell the pattern is increasing /decreasing in number sequences of the form n + k where k is an integer.


Strand Algebra


Objective 1 The teacher will teach the students to use letter symbols to represent unknown numbers.


Level 7 7.1 use letters to represent two or three unknown values in linear expressions involving up to two operations of addition,

subtraction, multiplication or division.

Level 6

6.3 use letters to represent two or three unknown values in simple linear expressions. 6.2 use a letter to represent an unknown value in simple linear expressions. 6.1 use a letter symbol to represent an unknown number.

Level 5 5.3 represent an unknown value by means of an empty space or picture in simple expressions.


Objective 2 The teacher will teach the students to evaluate simple formulae by substituting letters with positive integral inputs.


Level 7 7.1 evaluate linear formulae involving brackets by substituting letters with positive integral inputs.

Level 6 6.3 evaluate simple linear formulae involving more than two variables by substituting letters with positive integral inputs. 6.2 evaluate simple linear formulae involving two variables by substituting letters with positive integral inputs. 6.1 evaluate simple linear formulae involving one variable by substituting letters with positive integral inputs.

Level 5 5.3 evaluate simple linear formulae involving one variable by substituting letters with small positive integral inputs and involving

one operation.

Objective 3 The teacher will teach the students to work simple formulae backwards.


Level 7 7.1 work simple formulae backwards.

Level 6 6.3 find the input when given the output in one/two operation number machines. 6.2 solve one/two operation number puzzles through inverse operations. 6.1 give the inverse of simple mathematical operations.

Level 5 5.3 evaluate linear formulae with one operation by trial and error given a set of options.





Objective 1 The teacher will teach the students to draw and interpret bar charts, pie charts and pictograms.


Level 7 7.1 interpret simple pie charts, limited to sectors of 180°, 90°, 60° and 30°.

Level 6 6.3 draw pie charts (limited to fractions of 4

1

2

1 , and 8

1

, using a given table to guide them find the necessary angles. 6.2 draw and interpret simple bar charts for ungrouped data. 6.1 draw and interpret pictograms where each picture represents a group of units.

Level 5 5.3 draw and interpret pictograms where each picture represents only one unit.

Objective 2 The teacher will teach the students to compile and interpret frequency tables for ungrouped discrete data.


Level 7 7.1 sort and classify numerical discrete data in groups. They will be able to compile and interpret frequency tables of grouped discrete data.

Level 6 6.3 compile a frequency table for a set of ungrouped discreet numerical data. 6.2 answer simple questions about simple data displayed in frequency table, with/without the tally column. 6.1 compile a frequency table, with a tally column, from a set of given pictures/words.

Level 5 5.3 sort and classify given pictures in a table with specified categories.


Objective 3 The teacher will teach the students to understand, compute and interpret the mean, mode, median and range of a set of

ungrouped data.


Level 7 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.

Level 6 6.3 find the mean, median, mode and range from a longer lists of entries, including lists with an even number of entries. 6.2 find the mean, median, mode and range from a short list of entries, limited to lists with odd number of entries only. 6.1 understand the meaning of range as the spread of data.

Level 5 5.3 know the meaning of average and understand the difference between mean, median and mode.



Level 7 7.1 calculate probabilities of an event having more than one possible outcome.

Level 6

6.3 understand what it means for events to be equally likely to happen and find simple probabilities, such as getting a 5 when rolling a die.

6.2 understand that probabilities for unlikely and likely events fall in the ranges 0 to 21

and 21

to 1 respectively. They will be able to mark such probabilities on a numerical scale.

6.1 relate the basic language use for probabilities to their numerical value, i.e impossible = 0, evens = 21

and certain = 1.

Level 5 5.3 describe events as being impossible, unlikely, evens, likely and certain, and mark the probabilities on a scale marked with a range from impossible to certain.


Objective 5 The teacher will teach the students to compile a possibility space.


Level 7 7.1 use a possibility space diagram to calculate simple probabilities such as getting a total of 7 when rolling two normal dice.

Level 6 6.3 compile the possibility space diagram by inserting all the possible outcomes in cells of the grid. 6.2 construct the grid for a possibility space diagram according to the two simple events. 6.1 list all the possible outcome of 2 simple events happening together, such as two coins.

Level 5 5.3 understand that when having two events happening together, the number of all possible outcomes is given by all the possible

combinations of both events.


Strand Number




Level 7 7.1 solve simple problems involving finding the unit price.

Level 6 6.3 solve simple problems involving direct proportion when they are given the unit measure. 6.2 understand that solving problems involving direct proportion requires using multiplication or division. 6.1 understand that by direct proportion the value of a larger quantity is represented by a greater amount.

Level 5 5.3 understand that the price indicated on an item at a store is its unit price.




Level 7 7.1 compare and simplify the ratio of two quantities involving common units.

Level 6 6.3 compare two quantities identifying a simple scale factor. 6.2 recognise the use of simple ratios in real life situations. Eg: doubling or halving a recipe. 6.1 understand the concept of ratio through pictorial representations which compare one part with another part or several parts.

Level 5 5.3 know that a fraction compares a part with the whole.



Level 7 7.1 divide a quantity into unequal parts indicated by the given ratio.

Level 6 6.3 understand order of ratio. Eg: the ratio 2:3 is not the same as the ratio 3:2. 6.2 understand that equal division is not always appropriate. 6.1 use the ratio 1:1 to divide a given quantity into two equal parts.

Level 5 5.3 understand that the ratio indicates the number of parts in a whole. Eg: a ratio of 1:5 means “1 for every 5” (a total of 6)





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.


Level 7 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.

Level 6 6.3 identify shapes having reflection and/or rotational symmetry. 6.2 complete part shapes using two lines of symmetry. 6.1 complete part shapes using one line of symmetry.

Level 5 5.3 identify shapes having reflection symmetry.

Objective 2 The teacher will teach the students to reflect a shape in the x axis and y axis; describe a reflection.


Level 7 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 inverted and have the same shape and size.

Level 6 6.3 reflect a shape in the x axis and/or y axis and describe the reflection in words. 6.2 reflect a shape in the x axis or y axis. 6.1 reflect a shape in one line of symmetry.

Level 5 5.3 recognise a reflection.


Objective 3 The teacher will teach the students to translate a shape horizontally and/or vertically through descriptions: right, left, up and down.


Level 7 7.1 translate a shape horizontally and/or vertically and understand that in a translation the object and image have the same shape

and size.

Level 6 6.3 translate shapes right, left, up and down. 6.2 translate simple shapes to the right/left only or up/down only. 6.1 recognise a translation.

Level 5 5.3 understand the meaning of the vocabulary: right, left, up and down.

Objective 4 The teacher will teach the students to rotate a shape about one of the vertices using angles of 90° and 180°.


Level 7 7.1 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 have the same shape and size.

Level 6 6.3 rotate squares and rectangles about one of the vertices through an angle of 90° and 180°. 6.2 recognise a rotation. 6.1 understand the meaning of clockwise and anticlockwise.

Level 5 5.3 recognise the size of a 90° angle and multiple angles of 90°.


Strand Algebra



Objective 1 The teacher will teach the students to work out the output/input of a number machine.


Level 7 7.1 work out the output/input of number machines involving up to two operations.

Level 6 6.3 work out the output/input of number machines involving one operation. 6.2 work out the output of number machines involving one operation. 6.1 work out the output of number machines involving one operation from addition or subtraction.

Level 5 5.3 understand the terms input, output and reverse operation.

Objective 2 The teacher will teach the students to solve linear equations involving one operation; balance and solve equations pictorially.


Level 7 7.1 solve linear equations involving one operation.

Level 6 6.3 solve equations by drawing scales, given unknown on one side and involving up to two operations. 6.2 solve equations by drawing scales, given unknown on one side and involving one operation. 6.1 solve equations by drawing scales, given unknown on one side and involving one operation (addition or subtraction).

Level 5 5.3 understand that the left side and the right side of a balanced scale represent equal amounts.



Strand Algebra


Objective 1 The teacher will teach the students to read and plot co-ordinates using ordered pairs in all four quadrants; draw lines and shapes given the coordinates of their endpoints/vertices.


Level 7 7.1 plot points in all four quadrants.

Level 6 6.3 identify points in all four quadrants. 6.2 plot points in the first quadrant including points on the lines x = 0 and y = 0. 6.1 identify points in the first quadrant excluding those on the lines x = 0 and y = 0.

Level 5 5.3 identify objects in the first quadrant excluding those on the lines x = 0 and y = 0.

Objective 2 The teacher will teach the students to generate and plot ordered pairs that satisfy a simple linear rule; generate a sequence of ordered pairs and plot them to produce straight line graphs.


Level 7 7.1 understand that a linear equation can be represented as a straight line on a coordinate grid

Level 6 6.3 use the equation of a straight-line to generate a sequence of ordered pairs. 6.2 draw a straight line given a number of ordered pairs. 6.1 generate a sequence of ordered pairs given a simple linear rule.

Level 5 5.3 complete a simple linear sequence of ordered pairs.


Objective 3 The teacher will teach the students to plot and interpret information presented in a variety of linear graphs.


Level 7 7.1 draw and interpret a conversion graph.

Level 6 6.3 convert values, including decimal values beyond the ranges in the conversion graph. 6.2 convert values, including decimal values but restricted to the ranges in the conversion graph. 6.1 convert values, excluding decimal values and restricted to the ranges in the conversion graph.

Level 5 5.3 read the distance travelled and time taken from a ‘one -line’ travel graph.


Strand Number

Unit code and title MTH 8.1 Factors, Multiples and Using a Calculator (Levels 1 - 4)

Objective 1 The teacher will teach the students to order a set of numbers within a specific range and round it to the nearest 10 and 100.


Level 4 order a set of numbers, count, compare and decide on the closest multiple of ten.

Level 3 order a set of numbers up to 10, choose a number and point to the closest end.

Level 2 match the numbers correctly and at the same time notice the differences between the ends.

Level 1 get involved in ordering of objects through stacking.


Objective 2 The teacher will teach the students to develop the idea of factors through the use of sets of objects.


Level 4 order a set of numbers and count on and back in one’s, two’s etc. whilst talking about the sequence.

Level 3 be able to count the number of objects in an odd or even set.

Level 2 match diagrams or objects that have the same amount of numbers (odd with odd and even with even).

Level 1 observe, notice and if possible indicate anticipation for clapping or beating.

Objective 3a The teacher will teach the students to create equal sets of objects, express them as repeated addition of and then as a multiplication sum.


Level 4 group equal sets of objects and translate the pictorial representation into repeated addition and then into a multiplication sum.

Level 3 make equal sets of objects up to 5 and check their work by rote counting.

Level 2 match equal sets of objects.

Level 1 Get involved in grabbing and dropping equal amounts of objects into two containers and they follow the movement of the object.


Objective 3b The teacher will teach the students to share a number of items into equal groups and then include the concept of left overs.


Level 4 separate a group of objects into three equal groups and they will be able to use this knowledge in everyday calculations.

Level 3 separate a group of objects into two equal groups.

Level 2 separate a fixed number of objects in equal amounts.

Level 1 experience and may be involved in separating a set of interlocking objects.



Unit code and title MTH 8.2 Angles (Levels 1 – 4)

Objective 1 The teacher will teach the students to start tracking objects within their field of awareness and distinguish between whole and half turn movement and indicate whether an angle is a right angle, less than half a turn or more.


Level 4 mark or tick the right angles, sort the shapes into categories of right angle, and those that are bigger/smaller than a right angle.

Level 3 talk about and write whether the angle given has made a whole or half turn.

Level 2 fill angle points with colour and sort pictures according to angle category.

Level 1 follow an object, visually, moving past their midline.


Objective 2 The teacher will teach the students to become aware of the angle positions in a shape.


Level 4 mark the angles in a shape and write the number of angles as well as talk about the size of these angles.

Level 3 match and talk about their choice of shapes with the same angles. E.g. same inside angle colour. They can also count how many angles each shape has.

Level 2 sort shapes by their size.

Level 1 encounter and experience activities related with the shape and its space.

Objective 3 The teacher will teach the students to move around a square by following given directions.


Level 4 follow the trail according to the instructions given thus showing understanding of directionality.

Level 3 show that they can follow instructions to go to a particular point after they have taken a certain path.

Level 2 skim through the pictures and show the position of a requested object by pointing or otherwise.

Level 1 look at the board, skim through it and focus on the requested object.



Strand Number

Unit code and title MTH 8.3 Fractions (Levels 1 – 4)

Objective 1 The teacher will teach the students to identify the shapes with equal shaded parts.


Level 4 identify and talk about the shaded fraction. They become aware of equivalent fractions.

Level 3 apply the concept of counting to colour the same part of a shape.

Level 2 match shapes by their number of parts.

Level 1 encounter and experience the cutting shapes in different parts.

Objective 2 The teacher will teach the students to use simple addition and subtraction facts to work out the number of parts of two equal partitioned shapes.


Level 4 use simple addition facts to work out the number of shaded parts of two shapes. Conversely, they will use subtraction to find out the unshaded parts.

Level 3 use number value to count the parts and colour accordingly.

Level 2 identify the odd one out by pointing.

Level 1 observe and focus on the activity that it is taking place.



Strand Number

Unit code and title MTH 8.4 Decimals (Levels 1 – 4)

Objective 1 The teacher will teach the students to read numbers on a number line; read and use scales in practical situations


Level 4 use their knowledge of mathematical facts to find and read numbers on a number line.

Level 3 recognise and read numbers on a scale (integers only)and find them on the number line.

Level 2 able to match different scale readings.

Level 1 observe the process of cause and effect when an item is placed on the scale.

Objective 2 The teacher will teach the students to arrange one set of numbers in order of size from ascending/ descending order.


Level 4 choose the correct missing number and put a sequence in order of size in both ascending and descending form.

Level 3 order a set of three numbers in ascending order.

Level 2 match sequences of ordered numbers together.

Level 1 maintain eye contact whilst listening to a voice saying the numbers.


Objective 3 The teacher will teach the students to add and subtract simple numbers.


Level 4 work out simple totals by adding two’s, three’s, five’s and taking away by the same quantities and write simple sum representations e.g.1 4 + 3 or 100 + 3.

Level 3 indicate one more and count total. Also, they will observe taking away one and count the total.

Level 2 match same number of objects.

Level 1 observe the movement of an object and its disappearance.

Objective 4 The teacher will teach the students to group and count in ten’s and apply this to solve simple problems like rounding to 10.


Level 4 create simple problems themselves and round answer to the nearest 10 .

Level 3 count and group ten objects.

Level 2 Count with adult support and group into three’s and five’s.

Level 1 participate in tipping objects into a container.


Strand Number

Unit code and title MTH 8.5 Percentages (Levels 1 – 4)


Objective 1 The teacher will teach the students to develop the basic idea of percentages as the number of parts out of 10 and out of 100.


Level 4 count the number of parts out of a whole number and talk about it.

Level 3 count and choose the number matching the number of shaded parts.

Level 2 sort and match same number of parts together.

Level 1 Get involved in sensory activities by touching a screen to click on the parts and drag them to form a whole picture.

Objective 2 The teacher will teach the students to identify the percentage and represent it as a number of parts out of a whole.


Level 4 understand, interpret mathematical statements and be able to communicate them through drawing.

Level 3 understand verbal mathematical statements by marking, shading, colouring or moving on in a grid.

Level 2 point out the odd one out of a selection of three different items.

Level 1 follow and focus on a line of movement from one direction to the next.



Unit code and title MTH 8.6 Area and Volume (Levels 1 – 4)


Objective 1 The teacher will teach the students to students will recognise about the space enclosed by the boundary and use simple addition facts to find the total space enclosed.


Level 4 use simple addition facts to work out the perimeter of the shape.

Level 3 use rote counting up to ten to find the total perimeter and possibly compare the perimeter of two shapes by indicating the larger/smaller one.

Level 2 develop awareness of distance and direction when placing objects in the surrounding path.

Level 1 grab an object and with support put it in a peg hole.

Objective 2 The teacher will teach the students to students will be familiar with standard measurement tools.


Level 4 investigate and discuss the disadvantages of non-standard and the advantages of standard measurement tools.

Level 3 compare sizes and recognise differences in size.

Level 2 develop knowledge of size and begin to group a set of objects by size.

Level 1 participate and focus their attention on their hand movement along a line.


Objective 3 The teacher will teach the students to students will use simple addition or multiplication or doubling facts to work out the area.


Level 4 use and apply their knowledge of counting in 2’s, 3’s, 5’s and 10’s to calculate the area of a shape.

Level 3 become aware of the space taken by different flat objects placed on a square grid.

Level 2 match shapes with the same area.

Level 1 pour in and remove contents from a container whilst feeling the different texture of the shape.

Objective 4 The teacher will teach the students to students explore and compare the use of the space in a 3D shape.


Level 4 calculate the space to be filled in a 3D shape by counting.

Level 3 start to compare sizes and quantities in relation to shapes.

Level 2 start developing knowledge of shape and its size in terms of the amount needed to fill a space.

Level 1 react to the auditory responses made by adults.



Unit code and title MTH 8.7 Triangles and Quadrilaterals (Levels 1 – 4)


Objective 1 The teacher will teach the students to differentiate between different types of the same shape and between the properties of a rectangle and a square.


Level 4 talk about the different shapes using terms like bigger, longer sides and wider, opposite sides and other properties.

Level 3 identify the right shape size to match the ones on the template.

Level 2 sort and match the shapes according to the size.

Level 1 be involved in a sensorial experience of shapes.

Objective 2 The teacher will teach the students to complete a tessellation based on two coloured shapes.


Level 4 create a tessellating pattern by following the given instructions.

Level 3 recognise an equal tessellating shape from a selection and possibly explain their choice in a very simple way.

Level 2 create a simple tessellation through a process of copying by imitation.

Level 1 be exposed to a sequence of moves by pressing switches.


Objective 3 The teacher will teach the students to measure and compare the lengths of objects and the distance between two objects.


Level 4 use objects to find the length and width and talk about the size differences.

Level 3 recognise and choose the smaller/shorter and then the largest/tallest from a set.

Level 2 make sets of objects by size.

Level 1 become aware that things can have different sizes.



Unit code and title MTH 8.8 Constructions (Levels 1 – 4)

Objective 1 The teacher will teach the students to measure and compare the lengths of objects and the distance between two objects.


Level 4 use objects to find the length and width and talk about the size differences.

Level 3 recognise and choose the smaller/shorter and then the largest/tallest from a set.

Level 2 make sets of objects by size.

Level 1 become aware that things can have different sizes.


Objective 2 The teacher will teach the students to make and describe patterns using construction kits.


Level 4 decide on the missing shape and put the correct shape into the pattern.

Level 3 use the right construction tools (eg: magnifier) to see an enlarged version of a model.

Level 2 match up to 6 familiar objects.

Level 1 become aware and engage in the exploration of objects of different sizes.



Unit code and title MTH 8.9 Directed Numbers and Sequences (Levels 1 – 4)

Objective 1 The teacher will teach the students to understand the basic idea of negative numbers through practical games.


Level 4 discuss and compare different numbers. They are shown that the colder the weather the less the temperature is.

Level 3 differentiate between the two number representations by colouring a negative number in red and a positive number in blue (a model example is shown).

Level 2 match the negative numbers with the negative numbers and the positive with the positive.

Level 1 follow a slow moving object on the screen and turn head to look for a disappeared object.


Objective 2 The teacher will teach the students to follow instructions to work out sums with simple operations.


Level 4 begin to use the vocabulary involved in addition and subtraction of number patterns.

Level 3 start applying adding and subtracting in practical situations.

Level 2 show an interest in number activities and join in rote counting and familiar number activities up to 3.

Level 1 watch their hands when it moves and maybe laugh at the one two three movements.

Objective 3 The teacher will teach the students to continue a simple sequence.


Level 4 recognise and extend on a given pattern whilst explaining their choice.

Level 3 recognise and continue a given pattern using two variations.

Level 2 match sets of patterns together.

Level 1 anticipate and be involved in musical rhythm experiences.


Objective 4 The teacher will teach the students to identify and write the action that is leading to the end result.


Level 4 use addition and subtraction facts to find the hidden rule.

Level 3 understand the differences in quantities by using more or less.

Level 2 recognise the differences in quantities by using more or less.

Level 1 participate in activities involving objects in the line of vision and out of their sight.


Strand Algebra

Unit code and title MTH 8.10 Expressions and Formulae (Levels 1 – 4)

Objective 1 The teacher will teach the students to use letters instead of a symbol to represent a missing number.


Level 4 apply their simple arithmetic knowledge to solve the equation(eg: 4 + □ = 7) and find the missing quantity.

Level 3 participate in activities involving the exchange of something for another. They would show they have understood by giving the correct value card.

Level 2 match same value groups.

Level 1 show an interest in the activity by sustaining attention and possibly by initial interaction with adults.


Objective 2 The teacher will teach the students to use addition and subtraction to solve equations first pictorially and then in a more formal

way.


Level 4 find the missing quantity by using addition and subtraction skills.

Level 3 match a group of pictures to its number value.

Level 2 match pictures.

Level 1 be involved in activities involving changing in quantities (eg: adding or removing items).



Unit code and title MTH 8.11 Statistics and Probability (Levels 1 – 4)

Objective 1 The teacher will teach the students to put data in a table, read data from a table and draw bar charts on a grid and picture charts.


Level 4 put the sorted data into a table and answer questions related to what is in the table. Then they apply it to build a bar chart or a picture chart.

Level 3 classify objects into particular categories and start finding information from the table by counting. Eventually, they will represent this onto a grid.

Level 2 sort objects and materials according to given criteria. They can use colours to fill a grid.

Level 1 show interest in activities presented by moving their hands.


Objective 2 The teacher will teach the students to recognise the most frequent number, the range and the median in a set of ungrouped data.


Level 4 identify and talk about the data at hand e.g. most number shown, the difference between the largest and the smallest number, and the median.

Level 3 identify the largest group.

Level 2 give consistently the same requested object to an adult.

Level 1 respond to sounds and try to activate the object.

Objective 3 The teacher will teach the students to find the chances of occurrence and non-occurrence and fill-in the results in a grid.


Level 4 answer questions about the probable outcome of an event. E.g. it is impossible to find an elephant at home as it is neither a domestic animal nor an animal found in our country.

Level 3 start to respond appropriately to simple questions.

Level 2 be aware of a certainty (eg: if a ball is released, it falls)

Level 1 develop the concept of object permanence.


Strand Number

Unit code and title MTH 8.12 Ratio & Proportion (Levels 1 – 4)


Objective 1 The teacher will teach the students to develop the basic idea of ratios.


Level 4 ask, write the information and compare the choices.

Level 3 choose the named object, group it by category, count and match the set to its value.

Level 2 match same objects by categories.

Level 1 observe the differences in size of the same object.

Objective 2 The teacher will teach the students to read, understand and talk about the basic idea of ratio.


Level 4 read, draw, talk about and interpret visual representations to come up with the correct mathematical ratio.

Level 3 use their basic knowledge of number value to represent the ratios pictorially.

Level 2 sort a pre-selected set of data.

Level 1 be involved and participate in sensory experiences of different sizes of objects.


Objective 3 The teacher will teach the students to share two quantities in a given amount.


Level 4 translate (change) simple communication into mathematical representations.

Level 3 talk about the visual ratio representations.

Level 2 participate in the ideas of sharing through their matching skills.

Level 1 focus for a longer period of time to observe the activities.



Unit code and title MTH 8.13 Transformations (Levels 1 – 4)

Objective 1 The teacher will teach the students to recognise and count the rotational symmetry of a shape.


Level 4 rotate a shape and state the number of times they rotated it.

Level 3 count the number of times the shape looks like the original shape.

Level 2 match the shapes and count by rote with adult support.

Level 1 focus on an object being rotated with sustained attention.


Objective 2 The teacher will teach the students to identify the reflection of a shape; draw the reflection of a shape by imitation.


Level 4 recognize the reflection of a shape and draw the reflection of an object.

Level 3 choose the shape that is the odd one out.

Level 2 match the shape and its reflection with an equal shape and its reflection.

Level 1 focus their attention on named objects being seen in a mirror.

Objective 3 The teacher will teach the students to recognise and draw the new position of a shape after they have moved it sideways, upward and downward.


Level 4 describe the movement of a shape, describe the movement and have to draw/mark the final position.

Level 3 recognise and reinforce up and down movement in translations.

Level 2 recognise the upward movement in translations.

Level 1 participate in click and drag or drag and drop activities on the computer.


Objective 4 The teacher will teach the students to rotate a shape by a quarter and half a turn.


Level 4 Stuents will be able to apply the rotational instruction in practice as well as describe the rotation that a shape has gone through.

Level 3 continue a pattern of quarter and half turns without any example prompt.

Level 2 choose the odd one out from a category of shapes.

Level 1 focus their attention on click and drop techniques to continue a pattern of half turns.


Strand Algebra

Unit code and title MTH 8.14 Solving Equations (Levels 1 – 4)

Objective 1 The teacher will teach the students to work out the end result and the pattern rule that is leading to that result.


Level 4 work out the output of number machine involving the four rules up to one operation.

Level 3 work out the output of number machine involving one operation from addition or subtraction.

Level 2 match the same equations together.

Level 1 produce something following an action e.g. smile.


Objective 2 The teacher will teach the students to work out the value of the missing letter in simple equations both in writing and pictorially.


Level 4 solve linear equations involving one operation (eg: 12 + □ = 20).

Level 3 solve equations with given scales, to find the unknown quantity on one side.

Level 2 matching quantities on scales.

Level 1 observe their hand whilst grabbing and removing or putting objects on a scale.


Strand Algebra

Unit code and title MTH 7.15 Coordinates and Straight Line Graphs (Levels 1 – 4)

Objective 1 The teacher will teach the students to find and place objects according to their coordinates and join the points to form a shape.


Level 4 locate and read the position, of an object and name it. Or else they are given the position and have to place an object on the grid.

Level 3 follow a given path, count how many steps they have moved and locate the position of the named object and read the box number.

Level 2 find the position of a requested object by pointing and then, through matching, find same shapes or objects on a given grid.

Level 1 focus on a particular picture for a short period of time and confirm this by selecting it through sensory experiences.


Objective 2 The teacher will teach the students to use their mathematical knowledge of doubling or halving or counting to generate points and plot them.


Level 4 use and apply previous mathematical knowledge like doubling, halving and counting on in the same rule to form points.

Level 3 press the arrow buttons on the beebot or any similar tool so it moves accordingly.

Level 2 paint on the indicated point and then follow a path of points to form a line.

Level 1 follow their hand movement to perform an action.

Objective 3 The teacher will teach the students to get information from a given grid.


Level 4 read and share information from a grid

Level 3 find the requested object from a group of objects.

Level 2 find the requested information through matching.

Level 1 scan a number of objects and focus momentarily on the requested object.

mathematics - curriculum teaching objectives and learning outcomes (form 2) directorate for quality...

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