EN | MT   ## Educators' Guide for Pedagogy and Assessment

Click the icon below to download the Educators' Guide for Pedagogy and Assessment # Mathematics > LEVEL 8

## 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.

## 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.

## 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.

## 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.

## 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).

## 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.

## 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.

## 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.
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

## 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.

## 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.

## 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.

## 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.

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

1] I can distinguish between lines and line segments.

## 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.

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

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

## 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.

## 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.

## 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.

## 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.

## 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

## 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.

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

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

## 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

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

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

## 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

## 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

## 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.

## 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.

## 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.

## 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.

## 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.