| 1 |
Study Plan |
Study plan – Year 9 |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
Number theory – sets |
Number sets and their members |
| Objective: On completion of the lesson the student will understand the notation used with sets and the subsets of the real number system. |
| 3 |
Number theory – operations |
Properties of real numbers using addition and multiplication |
| Objective: On completion of the lesson the student will know and use the closure, identity, commutative, associative, identity and distributive properties for addition and multiplication. |
| 4 |
Number theory – equations |
Transformations that produce equivalent equations |
| Objective: On completion of the lesson the student will know and use the correct terms to describe the processes in solving equations. |
| 5 |
Scientific notation |
Scientific notation with larger numbers |
| Objective: On completion of the lesson the student will be able to change numbers greater than 1 to scientific notation. |
| 6 |
Scientific notation |
Scientific notation with small numbers |
| Objective: On completion of the lesson the student will be able to change numbers between zero and 1 to scientific notation. |
| 7 |
Scientific notation |
Changing scientific notation to numerals |
| Objective: On completion of the lesson the student will be able to change numbers written in scientific notation to basic numerals and be capable of solving problems on the calculator in scientific notation. |
| 8 |
Significant figures |
Significant figures |
| Objective: On completion of the lesson the student will be able to observe how many significant figures are in a number and how to express a number to a certain level of significant figures. |
| 9 |
Percentages |
Changing percentages to fractions and decimals |
| Objective: On completion of the lesson the student will be able to change percentages to fractions and know how to change percentages to decimals. |
| 10 |
Percentages |
One quantity as a percentage of another |
| Objective: On completion of the lesson the student will be able to find a percentage of an amount and how to express one quantity as a percentage of another. |
| 11 |
Geometry-angles |
Complementary and supplementary angles |
| Objective: On completion of the lesson the student will able to identify Complementary and Supplementary Angles and use this knowledge to solve simple geometric angle problems. |
| 12 |
Geometry-angles |
Vertically opposite angles |
| Objective: On completion of the lesson the student will able to identify Vertically Opposite Angles and use this knowledge to solve simple geometric angle problems. |
| 13 |
Geometry-angles |
Angles at a Point. |
| Objective: On completion of the lesson the student will able to identify Angles at a Point and use this knowledge and other angles concepts to solve simple geometric angle problems. |
| 14 |
Geometry-angles |
Parallel Lines. |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. |
| 15 |
Geometry-problems |
Additional questions involving parallel lines |
| Objective: On completion of the lesson the student will able to complete two step parallel line questions, and identify other ways to solve them. |
| 16 |
Geometry-triangles |
Angle sum of a triangle |
| Objective: On completion of the lesson the student will able to identify and use the angle sum of a triangle theorem to solve geometric problems. |
| 17 |
Geometry-triangles |
Exterior angle theorem |
| Objective: On completion of the lesson the student will able to identify and use the exterior angle of a triangle theorem to solve geometric questions. |
| 18 |
Special triangles |
Special triangles |
| Objective: On completion of the lesson the student will able to identify an equilateral and an isosceles triangle and solve geometry questions involving these triangles. |
| 19 |
Geometry-quadrilaterals |
Quadrilaterals |
| Objective: On completion of the lesson the student will able to find missing angles by using the fact that a quadrilateral’s angle sum is 360 degrees. |
| 20 |
Geometry-constructions |
Geometric constructions |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
| 21 |
Geometry |
To identify collinear points, coplanar lines and points in 2 and 3 dimensions |
| Objective: On completion of the lesson the student will use correct terms to describe points, lines, intervals and rays. |
| 22 |
Geometry – angles |
To determine angle labelling rules, naming angles according to size, angle bisector properties and related algebra |
| Objective: On completion of the lesson the student will label angles, use a protractor and perform calculations using algebra involving angles. |
| 23 |
Geometry-constructions |
Angle bisector construction and its properties (Stage 2) |
| Objective: On completion of the lesson the student will be able to bisect an angle using a pair of compasses and a straight edge. |
| 24 |
Geometry-constructions |
Circumcentre and incentre (Stage 2) |
| Objective: On completion of the lesson the student will be able geometrically construct the circumcentre and incentre for a triangle and to use Pythagoras’ Theorem to calculate values. |
| 25 |
Geometry-constructions |
Orthocentre and centroids (Stage 2) |
| Objective: On completion of the lesson the student will be able geometrically construct the orthocentre and centroid for a triangle and to use algebra to calculate values. |
| 26 |
Geometry-quadrilaterals |
Midsegments of Triangles |
| Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle. |
| 27 |
Geometry-quadrilaterals |
Classifying Quadrilaterals |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. |
| 28 |
Geometry-quadrilaterals |
Using the Properties of a Parallelogram |
| Objective: On completion of this lesson the student will be able to use and prove the properties of a parallelogram. |
| 29 |
Geometry-quadrilaterals |
Proving a Shape is a Parallelogram |
| Objective: On completion of this lesson the student will be able to use properties to prove a given quadrilateral is a parallelogram. |
| 30 |
Geometry-quadrilaterals |
Properties of the Rectangle, Square and Rhombus |
| Objective: On completion of this lesson students will be able to use the properties of the rectangle, square and rhombus for formal proofs and to find values. |
| 31 |
Geometry-quadrilaterals |
Properties of the Trapezium and Kite |
| Objective: On completion of this lesson students will be able to use the properties of the trapezium and kite for formal proofs and to find values. |
| 32 |
Geometry-quadrilaterals |
The quadrilateral family and coordinate methods in geometry |
| Objective: On completion of this lesson the student will know the relationships between quadrilaterals and use coordinate methods to prove some of the properties. |
| 33 |
Geometry-locus |
Constructions and loci – single condition |
| Objective: On completion of the lesson the student will understand the term locus and describe several using a single condition. |
| 34 |
Geometry-locus |
Constructions and loci – multiple conditions |
| Objective: On completion of the lesson the student will describe a locus that satisfies multiple conditions on a number plane. |
| 35 |
Geometry problems |
More difficult exercises involving parallel lines |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles in questions that are more difficult than previously completed. Students will also learn to use other geometric properties as well as set out log |
| 36 |
Geometry-reasoning |
Further difficult exercises involving formal reasoning |
| Objective: On completion of the lesson the student will be able to identify which geometric properties are needed to complete a question and be able to use formal reasoning to write out this information. |
| 37 |
Geometry-polygons |
Angles of regular polygons |
| Objective: On completion of the lesson the student will be able to identify and use the angle sum of a polygon formula, and understand that the external angles of a polygon add up to 360 degrees. |
| 38 |
Geometry-congruence |
Congruent triangles, Test 1 and 2 |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are congruent. |
| 39 |
Geometry-congruence |
Congruent triangles, Test 3 and 4 |
| Objective: On completion of the lesson the student will be able to identify other tests to use to show two triangles are congruent. |
| 40 |
Geometry-congruence |
Proofs and congruent triangles. |
| Objective: On completion of the lesson the student will be able to set out a formal proof to show that two triangles are congruent. |
| 41 |
Similar triangles |
Similar triangles |
| Objective: On completion of the lesson the student will be able to identify which test to use to show two triangles are similar. |
| 42 |
Similar triangles |
Using similar triangles to calculate lengths |
| Objective: On completion of the lesson the student will be able to calculate lengths using similar triangles. |
| 43 |
Overlapping triangles |
Examples involving overlapping triangles |
| Objective: On completion of the lesson the student will be able to calculate unknown sides in overlapping or adjacent similar triangles. |
| 44 |
Geometry – triangles |
Triangle inequality theorem |
| Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. |
| 45 |
Weight/mass |
The tonne – converting units and problems |
| Objective: On completion of the lesson the student should be able to: choose the correct unit to measure the mass of small, medium or large objects, and convert measurements from one unit to another. |
| 46 |
Time, distance, speed |
Average speed |
| Objective: On completion of the lesson the student will be able to understand what is meant by the speed of an object, read the instantaneous speed of a vehicle on a speedometer and find the average speed of an object. |
| 47 |
Pythagoras |
Pythagorean triples |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. |
| 48 |
Pythagoras |
Find the hypotenuse Part 2 |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse using decimals and surds. |
| 49 |
Statistic-probability |
Probability of Simple Events |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. |
| 50 |
Statistic-probability |
Rolling a pair of dice |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results when 2 dice are thrown simultaneously. |
| 51 |
Statistic-probability |
Experimental probability |
| Objective: On completion of this lesson the student will be able to find the probabilities in an experimental trial. |
| 52 |
Statistic-probability |
Tree diagrams – not depending on previous outcomes |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of a multi stage probability problem and then finding probabilities of certain events not depending on previous outcomes. |
| 53 |
Statistic-probability |
Tree diagrams – depending on previous outcomes |
| Objective: On completion of the lesson the student will be confident in drawing tree diagrams to list outcomes of other multi stage probability problems and then finding probabilities of certain events depending on previous outcomes. |
| 54 |
Statistic-probability |
The complementary result .. |
| Objective: On completion of the lesson the student will be capable of ascertaining the probability of certain results where the complementary event is involved. |
| 55 |
Statistic-probability |
P[A or B] When A and B are both mutually and NOT mutually exclusive |
| Objective: On completion of this lesson the student will be able to distinguish between mutually exclusive and non mutually exclusive events and be able to find the probabilities of both. |
| 56 |
Algebraic expressions |
Simplifying algebraic expressions: multiplication |
| Objective: On completion of the lesson the student will be able to simplify expressions involving multiplication of pronumerals and write them in the simplest form. |
| 57 |
Algebraic expressions |
Simplifying algebraic expressions: division |
| Objective: On completion of the lesson the student will be able to use all the operations needed for simplifying algebraic expressions. |
| 58 |
Algebraic expressions |
Expanding algebraic expressions: multiplication |
| Objective: On completion of the lesson the student will be able mentally to multiply and remove parentheses from simple algebraic expressions in one step. |
| 59 |
Algebraic expressions |
Expanding algebraic expressions: negative multiplier |
| Objective: On completion of the lesson the student will be able to expand expressions using a negative multiplier. |
| 60 |
Algebraic expressions |
Expanding and simplifying algebraic expressions |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. |
| 61 |
Algebraic equations |
Solving equations containing addition and subtraction |
| Objective: On completion of the lesson the student will understand how solve simple equations involving addition and subtraction by moving everything but the pronumeral onto one side of the equation, leaving the pronumeral by itself on the other side. |
| 62 |
Algebraic equations |
Solving equations containing multiplication and division |
| Objective: On completion of the lesson the student will be able to solve simple equations involving all operations. |
| 63 |
Algebraic equations |
Solving two step equations |
| Objective: On completion of the lesson the student will be able to solve two step equations. |
| 64 |
Algebraic expressions-products |
Products in simplification of algebraic expressions |
| Objective: On completion of the lesson the student will understand simplification of algebraic expressions in step-by-step processing. |
| 65 |
Algebraic expressions-larger expansions |
Algebraic Expressions – Larger expansions. |
| Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. |
| 66 |
Algebra-highest common factor |
Highest common factor. |
| Objective: On completion of the lesson the student will be capable of turning a simple algebraic expression into the product of a factor in parentheses and identifying the highest common factors of the whole expression. |
| 67 |
Factors by grouping |
Factors by grouping. |
| Objective: On completion of the lesson the student will be able to complete the process given just two factors for the whole expression. |
| 68 |
Coordinate Geometry-the plane |
Distance formula. |
| Objective: On completion of the lesson the student will be able to calculate the distance between any two points on the number plane and interpret the results. |
| 69 |
Coordinate Geometry-midpoint, slope |
Mid-point formula |
| Objective: On completion of the lesson the student will be able to understand the mid point formula and use it practically. |
| 70 |
Coordinate Geometry-gradient |
Gradient |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given its inclination, or angle to the positive direction of the x-axis; or its rise and run. |
| 71 |
Coordinate Geometry-gradient |
Gradient formula. |
| Objective: On completion of the lesson the student will be able to calculate the gradient of a line given any two points on the line and also be capable of checking whether 3 or more points lie on the same line and what an unknown point will make to parallel lines. |
| 72 |
Coordinate Geometry-straight line |
The straight line. |
| Objective: On completion of the lesson the student will be able to draw a line which is parallel to either axis and comment on its gradient, where that gradient exists. |
| 73 |
Coordinate Geometry-slope, etc. |
Lines through the origin. |
| Objective: On completion of the lesson the student will be able to draw a line which passes through the origin of the form y=mx and comment on its gradient compared to the gradients of other lines through the origin and use the information to solve problems. |
| 74 |
Coordinate Geometry-equation of line |
General form of a line and the x and y Intercepts. |
| Objective: On completion of the lesson the student will be able to change the equation of a straight line from the form, written as y=mx+c, into the general form and vice versa. |
| 75 |
Coordinate Geometry-intercept |
Slope intercept form of a line. |
| Objective: On completion of the lesson the student will be able to find the slope and intercept given the equation and given the slope and intercept, derive the equation. |
| 76 |
Coordinate Geometry-point slope |
Point slope form of a line |
| Objective: On completion of the lesson the student will understand how to derive the equation of a straight line given the gradient and a point on the line. |
| 77 |
Co-ordinate Geometry-Two point formula |
Two point formula: equation of a line which joins a pair of points. |
| Objective: On completion of the lesson the student will be able to calculate the equation of a line given any two named points on the line. |
| 78 |
Co-ordinate Geometry-Intercept form |
Intercept form of a straight line: find the equation when given x and y |
| Objective: On completion of the lesson the student will have an effective and efficient method for calculating the equation of a straight line. |
| 79 |
Co-ordinate Geometry-Parallel lines equations |
Parallel lines: identify equation of a line parallel to another |
| Objective: On completion of the lesson the student will be able to decide if two or more lines are parallel or not and to solve problems involving parallel lines. |
| 80 |
Co-ordinate Geometry-Perpendicular lines |
Perpendicular lines. |
| Objective: On completion of the lesson the student will be able to derive the equation of a line, given that it is perpendicular to another stated line. |
| 81 |
Co-ordinate Geometry-Inequalities |
Inequalities on the number plane. |
| Objective: On completion of the lesson the student will be able to derive the expression for an inequality given its graph. The student will also be able to solve some problems using inequalities. |
| 82 |
Decimals |
Multiplication of decimals by decimals to two decimal places |
| Objective: On completion of the lesson the student will be able to multiply decimals to two digits. |
| 83 |
Decimals |
Dividing numbers by a decimal fraction |
| Objective: On completion of the lesson the student will be able to divide numbers by a decimal fraction. |
| 84 |
Circle Geometry |
Theorem – Equal arcs on circles of equal radii subtend equal angles at the centre. Theorem – Equal angles at the centre of a circle on equal arcs. |
| Objective: On completion of the lesson the student will be able to prove that ‘Equal arcs on circles of equal radii, subtend equal angles at the centre’, and that ‘Equal angles at the centre of a circle stand on equal arcs.’ They should then be able to use these pro |
| 85 |
Circle Geometry |
Theorem – The perpendicular from the centre of a circle to a chord bisects the chord. Theorem – The line from the centre of a circle to the mid-point of the chord is perpendicular to the chord. |
| Objective: On completion of the lesson the student will be able to prove that ‘The perpendicular from the centre of a circle to a chord bisects the chord.’ and its converse theorem ‘The line from the centre of a circle to the mid-point of the chord is perpendicular’ |
| 86 |
Circle Geometry |
Theorem – Equal chords in equal circles are equidistant from the centres. Theorem – Chords in a circle which are equidistant from the centre are equal. |
| Objective: On completion of the lesson the student will be able to prove that equal chords in equal circles are equidistant from the centre. |
| 87 |
Circle Geometry |
Theorem – The angle at the centre of a circle is double the angle at the circumference standing on the same arc. |
| Objective: On completion of the lesson the student will be able to prove that the angle at the centre of a circle is double the angle at the circumference standing on the same arc. |
| 88 |
Circle Geometry |
Theorem – Angles in the same segment of a circle are equal. |
| Objective: On completion of the lesson the student will be able to prove that the angles in the same segment are equal. |
| 89 |
Circle Geometry |
Theorem – The angle of a semi-circle is a right angle. |
| Objective: On completion of the lesson the student will be able to prove that ‘The angle of a semi-circle is a right-angle.’ |
| 90 |
Circle Geometry |
Theorem – The opposite angles of a cyclic quadrilateral are supplementary. |
| Objective: On completion of the lesson the student will be able to prove that the opposite angles of a cyclic quadrilateral are supplementary. |
| 91 |
Circle Geometry |
Theorem – The exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite angle. |
| Objective: On completion of the lesson the student will be able to prove that the exterior angle at a vertex of a cyclic quadrilateral equals the interior opposite. |
| 92 |
Circle Geometry |
Theorem – The tangent to a circle is perpendicular to the radius drawn to it at the point of contact. |
| Objective: On completion of the lesson the student will be able to prove that the tangent and the radius of a circle are perpendicular at the point of contact. |
| 93 |
Circle Geometry |
Theorem – Tangents to a circle from an external point are equal. |
| Objective: On completion of the lesson the student will be able to prove that tangents to a circle from an external point are equal. |
| 94 |
Circle Geometry |
Theorem – The angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. |
| Objective: On completion of the lesson the student will be able to prove that the angle between a tangent and a chord through the point of contact is equal to the angle in the alternate segment. |
| 95 |
Time zones |
Time zones |
| Objective: On completion of the lesson the student will be able to: recognise that there are different time zones, compare time zones, understand daylight saving and adjust times accordingly, and determine the local time in different regions. |
| 96 |
Pythagoras |
Calculating a leg of a right-angled triangle |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of one of the shorter sides of a right triangle. |
| 97 |
Pythagoras |
Proofs of Pythagoras theorem |
| Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem |
| 98 |
Trigonometry-ratios |
Trigonometric ratios. |
| Objective: On completion of the lesson the student will be able to identify the hypotenuse, adjacent and opposite sides for a given angle in a right angle triangle. The student will be able to label the side lengths in relation to a given angle e.g. the side c is op |
| 99 |
Trigonometry-ratios |
Using the calculator. |
| Objective: On completion of the lesson the student will be able to use the calculator to find values for the sine, cosine and tangent ratios of acute angles. |
| 100 |
Trigonometry-ratios |
Using the trigonometric ratios to find unknown length. [Case 1 Sine]. |
| Objective: On completion of the lesson the student will be able to use the sine ratio to calculate lengths and distances. |
| 101 |
Trigonometry-ratios |
Using the trigonometric ratios to find unknown length. [Case 2 Cosine]. |
| Objective: On completion of the lesson the student will be able to use the cosine ratio to find the length of the adjacent side of a right angle triangle. |
| 102 |
Trigonometry-ratios |
Using the trigonometric ratios to find unknown length. [Case 3 Tangent Ratio]. |
| Objective: On completion of the lesson the student will be able to use the tangent ratio to calculate the length of the opposite side in a right angle triangle. |
| 103 |
Trigonometry-ratios |
Unknown in the denominator. [Case 4]. |
| Objective: On completion of the lesson the student will understand how to use the trig ratios to calculate lengths and distances when the denominator is unknown. |
| 104 |
Trigonometry-compass |
Bearings – the compass. |
| Objective: On completion of the lesson the student will be able to identify compass bearings, compass bearings with acute angles and 3 figure bearings from true north. |
| 105 |
Trigonometry-elevation |
Angles of elevation and depression. |
| Objective: On completion of the lesson the student will be able to identify angles of depression and angles of elevation, and the relationship between them. |
| 106 |
Trigonometry-practical |
Trigonometric ratios in practical situations. |
| Objective: On completion of the lesson the student will be able to use trigonometric ratios to solve problems involving compass bearings and angles of depression and elevation. |
| 107 |
Sequences and Series |
General sequences. |
| Objective: On completion of the lesson the student will be able to work out a formula from a given number pattern and then be able to find particular terms of that sequence using the formula. |
| 108 |
Sequences and Series |
Finding Tn given Sn. |
| Objective: On completion of the lesson the student will understand the concept that the sum of n terms of a series minus the sum of n minus one terms will yield the nth term. |
| 109 |
Arithmetic Progression |
The arithmetic progression |
| Objective: On completion of the lesson the student will be able to test if a given sequence is an Arithmetic Progression or not and be capable of finding a formula for the nth term, find any term in the A.P. and to solve problems involving these concepts. |
| 110 |
Arithmetic Progression |
Finding the position of a term in an A.P. |
| Objective: On completion of the lesson the student will be able to solve many problems involving finding terms of an Arithmetic Progression. |
| 111 |
Arithmetic Progression |
Given two terms of A.P., find the sequence. |
| Objective: On completion of the lesson the student will be able to find any term of an Arithmetic Progression when given two terms |
| 112 |
Arithmetic Progression |
Arithmetic means |
| Objective: On completion of the lesson the student will be able to make an arithmetic progression between two given terms. This could involve finding one, two, or even larger number of arithmetic means. |
| 113 |
Arithmetic Progression |
The sum to n terms of an A.P. |
| Objective: On completion of the lesson the student will understand the formulas for the sum of an Arithmetic Progression and how to use them in solving problems. |
| 114 |
Geometric Progression |
The geometric progression. |
| Objective: On completion of the lesson the student will be able to test if a given sequence is a Geometric Progression or not and be capable of finding a formula for the nth term, find any term in the G.P. and to solve problems involving these concepts. |
| 115 |
Geometric Progression |
Finding the position of a term in a G.P. |
| Objective: On completion of the lesson the student will understand how to find terms in a geometric progression and how to apply it different types of problems. |
| 116 |
Geometric Progression |
Given two terms of G.P., find the sequence. |
| Objective: On completion of this lesson the student will be able to solve all problems involving finding the common ratio of a Geometric Progression. |
| 117 |
Algebraic equations |
Solving equations containing binomial expressions |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. |
| 118 |
Algebraic equations |
Equations involving grouping symbols. |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols |
| 119 |
Algebraic equations |
Equations involving fractions. |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. |
| 120 |
Algebra- formulae |
Equations resulting from substitution into formulae. |
| Objective: On completion of the lesson the student will be able to substitute into formulae and then solve the resulting equations. |
| 121 |
Algebra- formulae |
Changing the subject of the formula. |
| Objective: On completion of the lesson the student will be able to move pronumerals around an equation using all the rules and operations covered previously. |
| 122 |
Algebra-inequalities |
Solving Inequalities. |
| Objective: On completion of the lesson the student will understand the ‘greater than’ and ‘less than’ signs, and be able to perform simple inequalities. |
| 123 |
Algebra-factorising |
Simplifying easy algebraic fractions. |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. |
| 124 |
Algebraic fractions |
Simplifying algebraic fractions using the index laws. |
| Objective: On completion of the lesson the student will be able to simplify most algebraic fractions using different methodologies. |
| 125 |
Algebra-negative indices |
Algebraic fractions resulting in negative indices. |
| Objective: On completion of the lesson the student will be able to understand how to simplify an algebraic fractional expression with a negative index, and also how to write such an expression without a negative index. |
| 126 |
Factorisation |
Factorisation of algebraic fractions including binomials. |
| Objective: On completion of the lesson the student should be able to simplify more complex algebraic fractions using a variety of methods. |
| 127 |
Algebraic fractions-binomial |
Cancelling binomial factors in algebraic fractions. |
| Objective: On completion of the lesson the student should be able to factorise binomials to simplify fractions. |
| 128 |
Absolute value or modulus |
Simplifying absolute values |
| Objective: On completion of the lesson the student will be able to simplify expressions involving absolute values or the modulus of real numbers. |
| 129 |
Absolute value or modulus |
Solving for the variable |
| Objective: On completion of the lesson the student will be able to solve equations involving a single absolute value. |
| 130 |
Absolute value or modulus |
Solving and graphing inequalities |
| Objective: On completion of the lesson the student will be able to solve inequalities involving one absolute value. |
| 131 |
Geometry-parabola |
The parabola: to describe properties of a parabola from its equation |
| Objective: On completion of the lesson the student will be able to predict the general shape and important features of a parabola and then graph the parabola to check the predictions. |
| 132 |
Functions and graphs |
Quadratic polynomials of the form y = ax. + bx + c. |
| Objective: On completion of the lesson the student will be able to predict the general shape of a parabola and verify the predictions by sketching the parabola. The student will also be introduced to the discriminant and the axis. |
| 133 |
Functions and graphs |
Graphing perfect squares: y=(a-x) squared |
| Objective: On completion of the lesson the student will be able to analyse a curve and then check their work by graphing the curve. |
| 134 |
Graphing roots |
Graphing irrational roots |
| Objective: On completion of the lesson the student will be able to solve any polynomial which has real roots, whether they are rational or irrational. |
| 135 |
Rules for indices/exponents |
Adding indices when multiplying terms with the same base |
| Objective: On completion of the lesson the student will know how to use the index law of addition of powers when multiplying terms with the same base. |
| 136 |
Rules for indices/exponents |
Subtracting indices when dividing terms with the same base |
| Objective: On completion of the lesson the student will know how to use the index law of subtraction of powers when dividing terms with the same base. |
| 137 |
Rules for indices/exponents |
Multiplying indices when raising a power to a power |
| Objective: On completion of the lesson the student will use the law of multiplication of indices when raising a power to a power. |
| 138 |
Rules for indices/exponents |
Multiplying indices when raising to more than one term |
| Objective: On completion of the lesson the student will be able to use the law of multiplication of indices when raising more than one term to the same power. |
| 139 |
Rules for indices/exponents |
Terms raised to the power of zero |
| Objective: On completion of the lesson the student will learn how to evaluate or simplify terms that are raised to the power of zero. |
| 140 |
Rules for indices/exponents |
Negative Indices |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing negative indices. |
| 141 |
Fractional indices/exponents |
Fractional indices |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. |
| 142 |
Fractional indices/exponents |
Complex fractions as indices |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing complex fractional indices. |
| 143 |
Surds |
Introducing surds |
| Objective: On completion of the lesson the student will be able to identify and know the properties of surds as irrational numbers and be able to distinguish them from rational numbers. |
| 144 |
Surds |
Some rules for the operations with surds |
| Objective: On completion of the lesson the student will know how to use the rules for division and multiplication of surds. |
| 145 |
Surds |
Simplifying surds |
| Objective: On completion of the lesson the student will know how to use the rules for simplifying surds using division and multiplication. |
| 146 |
Surds |
Creating entire surds |
| Objective: On completion of the lesson the student will be able to write numbers as entire surds and compare numbers by writing as entire surds |
| 147 |
Surds |
Adding and subtracting like surds |
| Objective: On completion of the lesson the student will be able to add and subtract surds and simplify expressions by collecting like surds. |
| 148 |
Surds |
Expanding surds |
| Objective: On completion of the lesson the student will be able to expand and then simplify binomial expressions involving surds. |
| 149 |
Surds |
Binomial expansions |
| Objective: On completion of the lesson the student will be able to expand and simplify the squares of binomial sums and differences involving surds. |
| 150 |
Surds |
Conjugate binomials with surds |
| Objective: On completion of the lesson the student will be able to expand and simplify conjugate binomial expressions involving surds. |
| 151 |
Surds |
Rationalising the denominator |
| Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves surds. |
| 152 |
Surds |
Rationalising binomial denominators |
| Objective: On completion of the lesson the student will be able to rationalise denominators of fractions where the denominator involves binomial expressions. |
| 153 |
Graphing binomials |
Binomial products. |
| Objective: On completion of the lesson the student will understand the term binomial product and be capable of expanding and simplifying an expression. |
| 154 |
Graphing binomials |
Binomial products with negative multiplier |
| Objective: On completion of the lesson the student will understand specific terms and be prepared to expand and simplify different monic binomial products. |
| 155 |
Graphing binomials |
Binomial products [non-monic]. |
| Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. |
| 156 |
Squaring binomial |
Squaring a binomial. [monic] |
| Objective: On completion of the lesson the student should understand the simple one-step process of squaring a monic binomial. |
| 157 |
Squaring binomial |
Squaring a binomial [non-monic]. |
| Objective: On completion of the lesson the student will apply the same rule that is used with monic binomials. |
| 158 |
Factorising |
Expansions leading to the difference of two squares |
| Objective: On completion of the lesson the student will understand expansions leading to differences of 2 squares. |
| 159 |
Difference of 2 squares |
Difference of two squares |
| Objective: On completion of the lesson the student understand the difference of two squares and be capable of recognising the factors. |
| 160 |
Common fact and diff |
Common factor and the difference of two squares |
| Objective: On completion of the lesson the student will be aware of common factors and recognise the difference of two squares. |
| 161 |
Trigonometry-ratios |
Using the calculator to find an angle given a trigonometric ratio. |
| Objective: On completion of the lesson the student will be capable of using a calculator to find the value of an unknown angle when given a trigonometric ratio. |
| 162 |
Trigonometry- ratios |
Using the trigonometric ratios to find an angle in a right-angled triangle. |
| Objective: On completion of the lesson the student will be able to find the value of an unknown angle in a right angle triangle given the lengths of 2 of the sides. |
| 163 |
Trigonometry-exact ratios |
Trigonometric ratios of 30., 45. and 60. – exact ratios. |
| Objective: On completion of the lesson the student will be able to find the exact sine, cosine and tangent ratios for the angles 30., 45.and 60. |
| 164 |
Simultaneous equns |
Simultaneous equations |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the substitution method. |
| 165 |
Simultaneous equns |
Applications of simultaneous equations |
| Objective: On completion of this lesson the student will be able to derive simultaneous equations from a given problem and then solve those simultaneous equations. |
| 166 |
Decimals |
Dividing decimal fractions by whole numbers |
| Objective: On completion of the lesson the student will be able to divide decimal fractions by whole numbers. |
| 167 |
Multiplication |
Multiplication by 2 and 3 digits |
| Objective: On completion of the lesson the student will be able to solve and record 2 and 3 digit multiplication problems in extended and short form. |
| 168 |
Division/repeat subtraction |
Using divide, multiply and subtraction in the bring down method |
| Objective: On completion of the lesson the student will be able to use Long Division using the Divide, Multiply, Subtract and Bring Down method. |
| 169 |
Matrices |
Basic concepts – Matrices |
| Objective: On completion of the lesson the student will have had an introduction to matrices |
| 170 |
Matrices |
Addition and subtraction of matrices |
| Objective: On completion of this lesson the student will be able to recognise when addition and subtraction of matrices is possible, and perform these operations. |
| 171 |
Matrices |
Scalar matrix multiplication |
| Objective: On completion of this lesson the student will be able to perform scalar multiplication of a matrix. |
| 172 |
Matrices |
Multiplication of one matrix by another matrix |
| Objective: On completion of the lesson the student will be able to state whether matrix by matrix multiplication is possible, predict the order of the answer matrix, and then perform matrix by matrix multiplication. |
| 173 |
Matrices |
Translation in the number plane |
| Objective: On completion of the lesson the student will be able to place ordered pairs into a matrix, then perform translation by addition using a transformation matrix, then extract ordered pairs from an answer matrix. |
| 174 |
Matrices |
Translation by matrix multiplication |
| Objective: On completion of the lesson the student will be able to convert ordered pairs to elements of a matrix, multiply matrices together, where possible, and interpret the answer matrix on a number plane. |
| 175 |
Transformations |
Special transformations – reflections, rotations and enlargements. |
| Objective: On completion of the lesson the student will be able to perform transformations: to rotate, reflect and change the size of various shapes and or points where applicable. |
| 176 |
Vectors |
Vectors |
| Objective: On completion of the lesson the student will be able to represent a vector in matrix and diagrammatic form, as well as add two vectors using matrices and/or a diagram. |
| 177 |
Surface area |
Surface area of a cube/rectangular prism. |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of different shapes by applying the appropriate formula. |
| 178 |
Surface area |
Surface area of a triangular/trapezoidal prism. |
| Objective: On completion of the lesson the student will be able calculate the surface area of a number of triangular and trapezoidal shapes by applying the appropriate formula. |
| 179 |
Surface area |
Surface area of a cylinder and sphere. |
| Objective: On completion of the lesson the student will be able calculate the surface area of different cylindrical and spherical shapes by applying the appropriate formula. |
| 180 |
Surface area |
Surface area of pyramids |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. |
| 181 |
Surface area |
Surface area of cones |
| Objective: On completion of the lesson the student will be able to find the surface areas of cones by finding the area or the base ‘p r . ‘and the area of the curved surface ‘ p r l’. The student will also be able to find the slant height ‘l’ given the perpendicul |
| 182 |
Surface area |
Surface area of composite solids |
| Objective: On completion of the lesson the student will be able to find the surface areas of Composite solids. |
| 183 |
Statistics |
Frequency distribution table |
| Objective: On completion of the lesson the student will be able to construct a frequency distribution table for raw data and interpret the table. |
| 184 |
Statistics |
Frequency histograms and polygons |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. |
| 185 |
Statistics |
Relative frequency |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. |
| 186 |
Statistics |
The range. |
| Objective: On completion of the lesson the student will be able to determine the range of data in either raw form or in a frequency distribution table. |
| 187 |
Statistic-probability |
The mode |
| Objective: On completion of the lesson the student will understand how to find the mode from raw data, a frequency distribution table and polygon. |
| 188 |
Statistic-probability |
The mean |
| Objective: On completion of the lesson the student will be able to calculate means from raw data and from a frequency table using an fx column. |
| 189 |
Statistic-probability |
The median |
| Objective: On completion of the lesson the student will be able to determine the median of a set of raw scores |
| 190 |
Statistic-probability |
Cumulative frequency |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. |
| 191 |
Statistic-probability |
Calculating the median from a frequency distribution |
| Objective: On completion of the lesson the student will be able to determine the median from a cumulative frequency polygon. |
| 192 |
Statistics – grouped data |
Calculating mean, mode and median from grouped data |
| Objective: On completion of the lesson the student will be capable of identifying class centres, get frequency counts and determine the mean and mode values. |
| 193 |
Statistics – Range and dispersion |
Range as a measure of dispersion |
| Objective: On completion of the lesson the student will be able to determine the range and using it in decision making. |
| 194 |
Statistics – Spread |
Measures of spread |
| Objective: On completion of the lesson the student will be able to find the standard deviation, using a data set or a frequency distribution table and calculator. |
| 195 |
Statistics – Standard deviation |
Standard deviation applications |
| Objective: On completion of the lesson the student will be able to use standard deviation as a measure of deviation from a mean. |
| 196 |
Statistics – Standard deviation |
Normal distribution |
| Objective: On completion of the lesson the student will be able to use the standard deviation of a normal distribution to find the percentage of scores within ranges. |
| 197 |
Statistics – Interquartile range |
Measures of spread: the interquartile range |
| Objective: On completion of the lesson the student will be able to find the upper and lower quartiles and the interquartile range |
| 198 |
Statistics |
Stem and Leaf Plots along with Box and Whisker Plots |
| Objective: On completion of the lesson the student will be familiar with vocabulary for statistics including quartiles, mode, median, range and the representation of this information on a Box and Whisker Plot. |
| 199 |
Statistics |
Scatter Diagrams |
| Objective: On completion of the lesson the student will be able to construct scatter plots and draw conclusions from these. |
| 200 |
Functions |
Definition, domain and range |
| Objective: On completion of this lesson the student will be able to select functions from relations by referring to the domain and range. |
| 201 |
Functions |
Notation and evaluations |
| Objective: On completion of the lesson the student will be understand different notations for functions. |
| 202 |
Functions |
More on domain and range |
| Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation. |
| 203 |
Functions |
Domain and range from graphical representations |
| Objective: On completion of the lesson the student will be able to describe the domain and range using appropriate set notation from graphical representations. |
| 204 |
Functions |
Evaluating and graphing piecewise functions |
| Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. |
| 205 |
Functions |
Functions combinations |
| Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. |
| 206 |
Functions |
Composition of functions |
| Objective: On completion of the lesson the student will understand composition of functions or a function of a function. |
| 207 |
Logic |
Inductive and deductive reasoning |
| Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. |
| 208 |
Logic |
Definition and use of counter examples |
| Objective: On completion of this lesson the student will be able to create counter examples to statements. |
| 209 |
Logic |
Indirect proofs |
| Objective: On completion of the lesson the student will be able to use indirect proofs by assuming the opposite of the statement being proved. |
| 210 |
Logic |
Conditional statements (converse, inverse and contrapositive) (Stage 2) |
| Objective: On completion of the lesson the student will be able to form related conditional statements. |
| 211 |
Graphing-polynomials |
Graphing complex polynomials: quadratics with no real roots |
| Objective: On completion of the lesson the student will be able to determine whether a quadratic has real or complex roots and then graph it. |
| 212 |
Graphing-polynomials |
General equation of a circle: determine and graph the equation |
| Objective: On completion of the lesson the student will be able to solve these types of problems. Working with circles will also help the student in the topic of circle geometry, which tests the student’s skills in logic and reasoning. |
| 213 |
Graphing-cubic curves |
Graphing cubic curves |
| Objective: On completion of this lesson the student will be able to graph a cubic given its equation or derive the equation of a cubic given its graph or other relevant information. |
| 214 |
Absolute value equations |
Absolute value equations |
| Objective: On completion of this lesson the student will be able to relate to graphs involving the absolute value function. The student will be capable of graphing the function given its equation and be able to solve for the intersection of an absolute value functio |
| 215 |
Rect.hyperbola |
The rectangular hyperbola. |
| Objective: On completion of the lesson the student will be able to analyse and graph a rectangular hyperbola and describe its important features. |
| 216 |
Exponential function |
The exponential function. |
| Objective: On completion of the lesson the student will be able to graph any equation in the form y equals a to the power x, where a is any positive real number apart from 1. |
| 217 |
Log functions |
Logarithmic functions. |
| Objective: On completion of this lesson the student will be able to define basic logarithmic functions and describe the relationship between logarithms and exponents including graph logarithmic functions. The student will understand the relationship between logarit |
| 218 |
Exam |
Exam – Year 9 – Level 6 leading beyond in Year 10 |
| Objective: Exam |
