| 1 |
Study Plan |
Study plan – Grade 9 |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
Fractions |
Multiplying fractions |
| Objective: On completion of the lesson the student will be able to multiply fractions and reduce the answer to its lowest form. |
| 3 |
Fractions |
Multiplying mixed numbers (mixed numerals) |
| Objective: On completion of the lesson the student will be able to multiply mixed numbers (mixed numerals) and reduce the answer to its lowest form. |
| 4 |
Fractions |
Finding reciprocals of fractions and mixed numbers (mixed numerals) |
| Objective: On completion of the lesson the student will be able to find the reciprocals of fractions and mixed numbers (mixed numerals). |
| 5 |
Fractions |
Dividing fractions |
| Objective: On completion of the lesson the student will be able to divide fractions. |
| 6 |
Fractions |
Dividing mixed numbers (mixed numerals) |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). |
| 7 |
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. |
| 8 |
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. |
| 9 |
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. |
| 10 |
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. |
| 11 |
Area |
Area of a trapezium. |
| Objective: On completion of the lesson the student will be able calculate the area of all types of different shaped trapeziums using a given formula. |
| 12 |
Area |
Area of a rhombus. |
| Objective: On completion of the lesson the student will be able to: identify a rhombus, learn how to find the formula for the area of a rhombus, and use it in solving problems. |
| 13 |
Area |
Area of a circle. |
| Objective: On completion of the lesson the student will be able calculate the area of a circle, and also calculate the radius and diameter of a circle. |
| 14 |
Area |
Area of regular polygons and composite figures. |
| Objective: On completion of the lesson the student will be able calculate the area of a number of different shapes by applying the appropriate formula. |
| 15 |
Volume |
Finding the volume of prisms |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of prisms, calculate the volume of a variety of prisms, and explain the relationship between units of length and units of volume. |
| 16 |
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. |
| 17 |
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. |
| 18 |
Volume |
Volume of a cylinder and sphere. |
| Objective: On completion of the lesson the student will be able to: calculate the volume of cylinders, spheres and hemispheres using the appropriate formulae, and use the relationship between litres and other measures of volume. |
| 19 |
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. |
| 20 |
Area |
Larger areas: square metre, hectare, square kilometre. |
| Objective: On completion of the lesson the student will be able to calculate larger areas using the correct square unit. |
| 21 |
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. |
| 22 |
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. |
| 23 |
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. |
| 24 |
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. |
| 25 |
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. |
| 26 |
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. |
| 27 |
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. |
| 28 |
Algebra-factorising |
Simplifying easy algebraic fractions. |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. |
| 29 |
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. |
| 30 |
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. |
| 31 |
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. |
| 32 |
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. |
| 33 |
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. |
| 34 |
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. |
| 35 |
Geometry-angles |
Adjacent angles |
| Objective: On completion of the lesson the student will be able to understand the parts of an angle, what adjacent angles are and how they are used to solve simple angle problems. |
| 36 |
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. |
| 37 |
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. |
| 38 |
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. |
| 39 |
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. |
| 40 |
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. |
| 41 |
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. |
| 42 |
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. |
| 43 |
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. |
| 44 |
Geometry-constructions |
Geometric constructions |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
| 45 |
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 |
| 46 |
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. |
| 47 |
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. |
| 48 |
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. |
| 49 |
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. |
| 50 |
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. |
| 51 |
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. |
| 52 |
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. |
| 53 |
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. |
| 54 |
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. |
| 55 |
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. |
| 56 |
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. |
| 57 |
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. |
| 58 |
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. |
| 59 |
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. |
| 60 |
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. |
| 61 |
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. |
| 62 |
Geometry-circles |
The equation of a circle: to find radii of circles |
| Objective: On completion of the lesson the student will be able to describe a circle mathematically given its equation or its graph. Additionally, the student will be able to work out the equation of a circle given its centre and radius. |
| 63 |
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. |
| 64 |
Pythagoras |
Find the hypotenuse |
| Objective: On completion of this lesson the student will be able to use Pythagoras’ Theorem to calculate the length of the hypotenuse. |
| 65 |
Pythagoras |
Pythagorean triples |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. |
| 66 |
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. |
| 67 |
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. |
| 68 |
Pythagoras |
Proofs of Pythagoras theorem |
| Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem |
| 69 |
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. |
| 70 |
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. |
| 71 |
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. |
| 72 |
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 |
| 73 |
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. |
| 74 |
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. |
| 75 |
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. |
| 76 |
Algebraic equations |
Solving two step equations |
| Objective: On completion of the lesson the student will be able to solve two step equations. |
| 77 |
Algebraic equations |
Solving equations containing binomial expressions |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. |
| 78 |
Algebraic equations |
Equations involving grouping symbols. |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols |
| 79 |
Algebraic equations |
Equations involving fractions. |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. |
| 80 |
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. |
| 81 |
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. |
| 82 |
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. |
| 83 |
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. |
| 84 |
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. |
| 85 |
Graphing binomials |
Binomial products [non-monic]. |
| Objective: On completion of the lesson, the student will have examined more complex examples with binomial products. |
| 86 |
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. |
| 87 |
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. |
| 88 |
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. |
| 89 |
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. |
| 90 |
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. |
| 91 |
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. |
| 92 |
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. |
| 93 |
Quadratic trinomials |
Quadratic trinomials [monic] – Case 1. |
| Objective: On completion of the lesson the student will understand the factorisation of quadratic trinomial equations with all terms positive. |
| 94 |
Factorising quads |
Factorising quadratic trinomials [monic] – Case 2. |
| Objective: On completion of the lesson the student will accurately identify the process if the middle term of a quadratic trinomial is negative. |
| 95 |
Factorising quads |
Factorising quadratic trinomials [monic] – Case 3. |
| Objective: On completion of the lesson the student will have an increased knowledge on factorising quadratic trinomials and will understand where the 2nd term is positive and the 3rd term is negative. |
| 96 |
Factorising quads |
Factorising quadratic trinomials [monic] – Case 4. |
| Objective: On completion of the lesson the student will understand how to factorise all of the possible types of monic quadratic trinomials and specifcally where the 2nd term and 3rd terms are negative. |
| 97 |
Factorising quads |
Factorisation of non-monic quadratic trinomials |
| Objective: On completion of the lesson the student will be capable of factorising any quadratic trinomial. |
| 98 |
Factorising quads |
Factorisation of non-monic quadratic trinomials – moon method |
| Objective: On completion of the lesson the student know two methods for factorisation of quadratic trinomials including the cross method. |
| 99 |
Algebraic fractions |
Simplifying algebraic fractions. |
| Objective: On completion of the lesson the student should be familiar with all of the factorisation methods presented to this point. |
| 100 |
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. |
| 101 |
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. |
| 102 |
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. |
| 103 |
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. |
| 104 |
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. |
| 105 |
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. |
| 106 |
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. |
| 107 |
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. |
| 108 |
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. |
| 109 |
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. |
| 110 |
Exam |
Exam – Grade 9 |
| Objective: Exam |
