feedback
EN | MT  

Educators' Guide for Pedagogy and Assessment

Click the icon below to download the Educators' Guide for Pedagogy and Assessment






Learning Area: Mathematics 

Mathematics > LEVEL 8





Learning Area Outcome: I understand the structure of the number system and the relationship between numbers.

Subject Focus: Number - The number system

1] I am able to use the number line to illustrate simple inequalities. 
2] I can write multiples of numbers using power notation.
3] I can identify all the common factors of up to three numbers.
4] I can identify the highest common factor (HCF) of up to three numbers.
5] I can express any integer as a product of prime factors. I can use prime factorization to work out the square root of large numbers and to work out the LCM and HCF.
6] I can write numbers in standard form and vice-versa.
 WRITING
7] I can find the reciprocal of a number.



Learning Area Outcome: I understand the structure of the number system and the relationship between numbers.

Subject Focus: Number - The number system (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets, computers & calculators) and other learning resources to learn about numbers and their properties.



Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

Subject Focus: Number - Numerical calculations (Whole Numbers, Decimal Numbers & Fraction Numbers - The Four Operations)

1] I can use rounded numbers to make rough approximations.
 COGNITIVE LEARNING
2] I can work out mental calculations involving powers and roots, e.g. √1600, 90², 20³, ³√8000.
 COGNITIVE LEARNING
3] I can round any decimal number to a given number of significant figures.



Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

Subject Focus: Number - Numerical calculations (Percentages)

1] I can work through simple situations involving percentage increase and decrease (e.g. cost and selling price ; discounts ; profit and loss, and percentage error)
2] I can work out reverse percentage calculations.
 COGNITIVE LEARNING 
3] I can work through situations involving successive percentage changes using a multiplying factor.
4] I can work out the simple interest, the principal, the rate, time or the amount.
5] I can use the simple interest formula.
6] I can work out compound interest, appreciation and depreciation.
7] I can use the appreciation and depreciation formulae.
8] I can use the trial and error method to determine the number of years in compound growth and decay situations.
9] I can work out the number of repayments needed to repay a loan.
10] I can work out the total accrued yearly value of an investment.



Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

Subject Focus: Number - Numerical calculations (Money & Consumer Mathematics)

1] I know the difference between selling rate and buying rate in currency exchange rates. I can use buying rate and selling rate to convert currencies.
2] I can work through complex situations involving personal and household finance (e.g. earnings, loans, simple interest, compound interest, income tax and VAT).



Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

Subject Focus: Number - Numerical calculations (Ratio & Proportion)

1] I can use ratio to solve complex problems.
2] I can draw and interpret simple scale drawings involving 2D plans, bearings, angles of elevation and angles of depression.
 WRITTING
3] I can work through situations that involve direct proportion with or without the use of the unitary method.
4] I can use the rules for multiplying and dividing integer powers of numbers (positive, negative and zero indices)
    e.g. 78 x 7 -5 = 73, 65 ÷ 6-2 = 67,  (23)5 = 215, 90 = 1
5] I can apply the four rules on numbers in standard form.



Learning Area Outcome: I can calculate mentally and using pencil and paper and assistive technology. I can calculate to the most appropriate level of accuracy. I can check the reasonableness of the answers obtained in calculations by rounding numbers and making rough approximations.

Subject Focus: Number - Numerical calculations (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets, computers and calculators) and other resources appropriate to this level to calculate and to learn about numerical calculations.



Learning Area Outcome: I can recognise and describe patterns and relationships in various mathematical ways and can use algebraic manipulations.

Subject Focus:  Algebra – Fundamentals of Algebra

1] I can generate the terms of a sequence given the nth term.
2] I can use expressions to describe the nth term of a linear sequence e.g. -3n - 1.
3] I can use algebraic notation to represent two or more unknown values in expressions involving +, −, x, ÷ and squares.
4] I can simplify non-linear algebraic expressions by collecting like terms.
5] I can simplify non-linear algebraic expressions by multiplying a single term over a bracket.
6] I can expand two brackets of the form (ax ± b)(cx ± d) and (ax ± b)2 and can simplify by collecting like terms.
7] I can simplify any algebraic expression by expanding brackets and collecting like terms. 
8] I can add, subtract and simplify algebraic fractions with numerical denominators.
9] I can simplify algebraic fractions with linear algebraic denominators e.g. Simplify 4/(2x + 4)
10] I can evaluate non-linear expressions by substituting directed numbers.
11] I can change the subject of the formula that includes squares and square roots and when the same subject letter occurs more than once.
12] I can write down and solve linear equations involving an unknown and integers or fractions on both sides.
 COGNITIVE LEARNING
13] I can solve simple linear inequalities in one variable and represent the solution on the number line.
14] I can factorise expressions by using the common factor method.
15] I can factorise quadratic expressions involving trinomials and  difference of two squares .
16] I can solve algebraically two simultaneous linear equations.
17] I can solve quadratic equations by factorisation.
18] I can solve quadratic equations by using the formula.
19] I can solve equations involving algebraic fractions with linear denominators.
20] I can find approximate solutions to equations for which there is not a simple method of solution using the trial and improvement method.
     e.g. Solve for x:  x3 - 2x = 100
MANAGING LEARNING
21] I can construct tables of values for quadratic functions.
22] I can plot the graph of a quadratic function from a table of values.
23] I can find the gradient of a line from the coordinates of two points on the line.
24] I can write the equation of a straight line given a set of co-ordinates or the line graph.
 MANAGING LEARNING
25] I can compare and contrast information from two or more straight line graphs concerning real life situations.
26] I can solve graphically two simultaneous linear equations.
27] I can solve graphically two simultaneous equations: one linear and one quadratic.
28] I can draw quadratic graphs and identify maxima/minima.
 MANAGING LEARNING
29] I can use quadratic graphs to find the value of a coordinate given the other.
30] I can use quadratic graphs to solve quadratic equations.
31] I can draw and interpret linear and non-linear graphs arising from real life situations.
32] I can use the function notation. e.g. f(x) = 5x - 3.
33] I can use the rules for multiplying and dividing integer powers (positive, negative and zero indices).
    e.g. a8 × a-5 = a3 ; y5÷ y-2 = y; (c3)5 = c15



Learning Area Outcome: I can recognise and describe patterns and relationships in various mathematical ways and can use algebraic manipulations.

Subject Focus:  Algebra – Fundamentals of Algebra (Assistive Technology & Other Resources)

1] I can use assistive technology, (e.g. tablets and computers) and other resources, (e.g. algebra blocks) appropriate to this level to learn about the fundamentals of algebra.



Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

Subject Focus: Shape, space and measures – Measures (Angles)

1] I can show and label the sixteen main compass points.
2] I can interpret and use three-figure bearings.
3] I can define the trigonometric ratios (sine, cosine and tangent) as the ratios of sides in a right-angled triangle.
4] I can use trigonometric ratios to find unknown lengths and angles in right-angled triangles.
5] I can use trigonometric ratios in situations that involve angles of elevation and/or depression and bearings.
6] I am able to find missing angles in diagrams by forming and solving algebraic equations.



Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

Subject Focus: Shape, space and measures – Measures (Length, Area, Volume, Mass & Capacity)

1] I can calculate the area of a sector of a circle
2] I can calculate the area of compound shapes that include sectors of circles.
3] I can calculate the length of an arc of a circle.
4] I can derive and use the formula for the surface area and volume of a prism or cylinder.
 COGNITIVE
5] I can calculate:(i) the surface area of a square-based right pyramid; (ii) the surface area of a right circular cone; (iii) the surface area of a sphere; (iv) the volume of a square-based right pyramid; (v) the volume of a square-based right frustum of a pyramid; (vi) the volume of a right circular cone (vii) the volume of a frustum of a right circular cone; (viii) the volume of a sphere; (ix) the volume of compound shapes.
6] I can rearrange formulae for surface area/volume of solids to find the radius, height and to find the slant height of a cone.
 



Learning Area Outcome: I understand and can use forms of measurement and can make reasonable estimations.

Subject Focus: Shape, space and measures – Measures (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets computers and calculators) and other resources (e.g. 2D and 3D plastic shapes, measuring instruments) appropriate to this level to learn about measures.



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space  and measures – Euclidean geometry (Lines & Lines Segments)

1] I can distinguish between lines and line segments.



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space and measures – Euclidean geometry (Triangles)

1] I can interpret and use Pythagoras’ Theorem in 2D shapes.
 COGNITIVE LEARNING
2] I can interpret and use the Converse of Pythagoras’ Theorem in 2D shapes. I can deduce that a triangle whose sides are in the ratio of 3:4:5 or in the ratio of 5:12:13 is a right angled triangle.



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space and measures – Euclidean geometry (Quadrilaterals)

1] I can follow a proof that the angle sum of a quadrilateral is 360˚.



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space and measures – Euclidean geometry (Polygons)

1] I can describe the properties of regular polygons related to sides, angles and diagonals, and can describe their symmetrical properties.
 READING AND UNDERSTANDING
2] I can calculate and use the sums of the interior and exterior angles of regular and irregular polygons.



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space and measures – Euclidean geometry (3D Shapes)

1] I can draw the plan, front elevation and side elevation of a given simple 3D shape.
2] I can draw the net of a cube, a cuboid, a triangular prism and a square-based right pyramid.



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space and measures – Euclidean geometry (Circles)

1] I can identify a chord, a tangent, an arc, a sector and a segment of a circle.
2] I can interpret and apply the circle theorems. I can also follow a proof for each circle theorem.
The circle theorems are:
    (i)The angle in a semicircle is a right angle.
    (ii) The angle which an arc of a circle subtends at the centre is twice that which it subtends at any other point on the remaining part of the circumference.
    (iii) Angles in the same segment of a circle are equal.
    (iv) The opposite angles of a cyclic quadrilateral are supplementary. (Angles in opposite segments are supplementary).
    (v) The exterior angle of a cyclic quadrilateral is equal to the interior opposite angle. 
    (vi)The angle between the radius and the tangent at the point of contact is a right angle.
    (vii) Equal chords are equidistant from the centre.
    (viii) Chords which are equidistant from the centre of a circle are equal.
    (ix) The perpendicular bisector of a chord passes through the centre.
    (x) A straight line drawn from the centre of a circle to bisect a chord is at right angles to the chord.
    (xi) If two tangents are drawn to a circle from a point outside the circle, then (a) the tangents are equal in length; (b) the angle between the tangents is bisected by the line joining the point of intersection of the tangents to the centre; and (c) this line also bisects the angle between the radii drawn to the points of contact.
    (xii)  If a straight line touches a circle, and from the point of contact a chord is drawn, the angle which the chord makes with the tangent is equal to the angle in the alternate segment.



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space and measures – Euclidean geometry (Constructions)

1] I can construct the perpendicular bisector of a line segment, the perpendicular from a point to a line and the angle bisector of a pair of intersecting lines using a straight edge and compasses only and by using a dynamic geometry software package.
2] I can construct triangles given various conditions using a ruler and compasses and dynamic geometry software.
3] I can construct regular polygons using ruler, protractor and compasses and a suitable programming environment such as Logo.



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space and measures – Euclidean geometry (Congruency & Similarity)

1] I can explain the concept of congruency. I can identify congruent shapes.
2] I can prove two triangles are congruent using SSS, SAS, ASA and RHS. I can use the fact that two triangles are congruent in order to find the lengths of missing sides and angles.
 COGNITIVE LEARNING



Learning Area Outcome: I can recognise and describe the properties of shapes. I can use these properties to construct shapes using appropriate mathematical instruments and to prove given geometric statements.

Subject Focus: Shape, space and measures – Euclidean geometry (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets and computers) and other resources (e.g. 2D and 3D plastic shapes) appropriate to this level to learn about properties of shapes.



Learning Area Outcome: I can describe position and movement of shapes in a plane.

Subject Focus: Shape, space and measures – Transformation geometry (Reflections)

1] I can deduce that reflections preserve length and angle.
 COGNITIVE LEARNING



Learning Area Outcome: I can describe position and movement of shapes in a plane.

Subject Focus: Shape, space and measures – Transformation geometry (Rotations)

1] I can find the centre of rotation by inspection and/or by construction.
 COGNITIVE
2] I can deduce that rotations preserve length and angle.
 COGNITIVE LEARNING



Learning Area Outcome: I can describe position and movement of shapes in a plane.

Subject Focus: Shape, space and measures – Transformation geometry (Translations)

1] I can deduce that translations preserve length and angle.



Learning Area Outcome: I can describe position and movement of shapes in a plane.

Subject Focus: Shape, space and measures – Transformation geometry (Enlargements)

1] I can enlarge a shape given the centre of enlargement using positive and negative scale factors (integral and fractional).
2] I can deduce that enlargements preserve angle but not length.
 COGNITIVE LEARNING



Learning Area Outcome: I can describe position and movement of shapes in a plane.

Subject Focus: Shape, space and measures – Transformation geometry (Combining Transformations)

1] I can create tessellating shapes and draw a tessellation.
2] I can transform 2D shapes by a combination of transformations.
 COGNITIVE LEARNING



Learning Area Outcome: I can describe position and movement of shapes in a plane.

Subject Focus: Shape, space and measures – Transformation geometry (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets and computers) and other resources (e.g. 2D and 3D plastic shapes) appropriate to this level to learn about transformation geometry.



Learning Area Outcome: I can collect, analyse, interpret and communicate statistical information.

Subject Focus:  Data handling and chance – Statistics

1] I can explain the difference between discrete and continuous data.
2] I can construct a frequency table using grouped or ungrouped continuous data.
 PRACTICAL
3] I can interpret a histogram with equal class intervals.
4] I can construct a histogram with equal class intervals.
5] I can find the mean of a set of grouped or ungrouped data from a frequency table.
6] I can find the median of a set of ungrouped data from a frequency table.
7] I can find the mode of a set of ungrouped data from a frequency table.
8] I can find the range of a set of ungrouped data from a frequency table.



Learning Area Outcome: I can collect, analyse, interpret and communicate statistical information.

Subject Focus:  Data handling and chance – Statistics (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets and computers) and other learning resources to learn about statistics.



Learning Area Outcome: I understand ideas of chance and uncertainty.

Subject Focus: Data handling & chance – Probability

1] I can work out the probability of an event from a frequency table.
2] I can work out the probability of mutually exclusive events.
3] I know the difference between dependent and independent events.
4] I can work out the probability of independent and dependent events.
5] I can construct and use a probability tree (tree diagram) to work out the probability of independent and dependent events.



Learning Area Outcome: I understand ideas of chance and uncertainty.

Subject Focus: Data handling & chance – Probability (Assistive Technology & Other Resources)

1] I can use assistive technology (e.g. tablets, computers and calculators) and other learning resources to learn about probability.




Submit your feedback here