| 1 |
Study Plan |
Study plan – Class VIII |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
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. |
| 3 |
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. |
| 4 |
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. |
| 5 |
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. |
| 6 |
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. |
| 7 |
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. |
| 8 |
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. |
| 9 |
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. |
| 10 |
Fractional indices/exponents |
Fractional indices |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. |
| 11 |
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. |
| 12 |
Percentages |
Introduction to percentages, including relating common fractions to percentages |
| Objective: On completion of the lesson the student will be able to recognise that the symbol % means ‘per cent’ and relate common fractions to a percentage. |
| 13 |
Percentages |
Changing fractions and decimals to percentages using tenths and hundredths |
| Objective: On completion of the lesson the student will be able to change simple fractions to percentages and decimals to percentages by using place value conversion. |
| 14 |
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. |
| 15 |
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. |
| 16 |
Percentages |
Calculating Percentages and Fractions of Quantities |
| Objective: To find percentages and fractions of quantities and solve problems with percentages |
| 17 |
Sequences and Series-Compound interest |
Compound interest |
| Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. |
| 18 |
Algebraic expressions |
Algebraic expressions. |
| Objective: On completion of the lesson the student will understand some of the short cuts used in writing algebraic expressions, and the student will be able to write algebraic expressions down in a way that is easier to understand. |
| 19 |
Algebraic expressions |
Substitution into algebraic expressions. |
| Objective: On completion of the lesson the student will be able to replace pronumerals with numbers, and then perform the correct operations. |
| 20 |
Algebraic expressions |
Directed numbers: addition and subtraction. |
| Objective: On completion of the lesson the student will be able to add and subtract positive and negative numbers in any combination, and understand adding and subtracting positive and negative pronumerals. |
| 21 |
Algebraic expressions |
Directed numbers: multiplication and division. |
| Objective: On completion of the lesson the student will understand which combinations of signs produce a positive answer and which ones produce a negative answer. |
| 22 |
Algebraic expressions |
Simplifying algebraic expressions: adding like terms. |
| Objective: On completion of the lesson the student will be able to simplify and evaluate numerical expressions containing patterns, and be able to simplify algebraic expressions that contain like terms. |
| 23 |
Algebraic expressions |
Simplifying algebraic Expressions: subtracting like terms. |
| Objective: On completion of the lesson the student will be able to recognise the difference between like and unlike terms, and be able to simplify an expression using subtraction. |
| 24 |
Algebraic expressions |
Simplifying Algebraic expressions: combining addition and subtraction. |
| Objective: On completion of the lesson the student will understand how to approach algebraic expressions questions and avoid the most common mistakes. |
| 25 |
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. |
| 26 |
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. |
| 27 |
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. |
| 28 |
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. |
| 29 |
Algebraic expressions |
Expanding and simplifying algebraic expressions |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. |
| 30 |
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. |
| 31 |
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. |
| 32 |
Algebraic equations |
Solving two step equations |
| Objective: On completion of the lesson the student will be able to solve two step equations. |
| 33 |
Algebraic equations |
Solving equations containing binomial expressions |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. |
| 34 |
Algebraic equations |
Equations involving grouping symbols. |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols |
| 35 |
Algebra-polynomials |
Introduction to polynomials |
| Objective: On completion of the lesson the student will understand all the terminology associated with polynomials and be able to judge if any algebraic expression is a polynomial or not. |
| 36 |
Algebra-polynomials |
The sum, difference and product of two polynomials. |
| Objective: On completion of the lesson the student will be able to add subtract and multiply polynomials and find the degrees of the answers. |
| 37 |
Algebra-polynomials |
Polynomials and long division. |
| Objective: On completion of the lesson the student will understand the long division process with polynomials. |
| 38 |
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. |
| 39 |
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. |
| 40 |
Sequences and Series-Compound interest |
Compound interest |
| Objective: On completion of the G.P. lesson the student will understand the compound interest formula and how to use it and adjust the values of r and n, if required, for different compounding periods. |
| 41 |
Sequences and Series-Superannuation |
Superannuation. |
| Objective: On completion of the lesson the student will understand the method of finding the accumulated amount of a superannuation investment using the sum formula for a G.P. |
| 42 |
Sequences and Series-Time payments |
Time payments. |
| Objective: On completion of the lesson the student will have examined examples carefully and be capable of setting out the long method of calculating a regular payment for a reducible interest loan. |
| 43 |
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. |
| 44 |
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. |
| 45 |
Algebraic expressions-larger expansions |
Algebraic Expressions – Larger expansions. |
| Objective: On completion of the lesson the student will be capable of expanding larger algebraic expressions. |
| 46 |
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. |
| 47 |
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. |
| 48 |
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. |
| 49 |
Geometry-angles |
Measuring angles |
| Objective: On completion of the lesson the student will be able to measure any angle between 0 and 360 degrees using a protractor, and identify what type of angle it is. |
| 50 |
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. |
| 51 |
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. |
| 52 |
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. |
| 53 |
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. |
| 54 |
Geometry-angles |
Parallel Lines. |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. |
| 55 |
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. |
| 56 |
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. |
| 57 |
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. |
| 58 |
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. |
| 59 |
Geometry-quadrilaterals |
Classifying Quadrilaterals |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. |
| 60 |
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. |
| 61 |
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. |
| 62 |
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. |
| 63 |
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. |
| 64 |
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. |
| 65 |
Geometry-constructions |
Geometric constructions |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
| 66 |
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. |
| 67 |
Geometry-circles |
The semicircle: to select the equation given the semi circle and vice versa |
| Objective: On completion of the lesson the student will be able to sketch a semicircle given its equation and derive the equation of a given semicircle. |
| 68 |
Area |
Comparing and ordering areas. |
| Objective: On completion of the lesson the student will be able to estimate and compare the area of shapes using a standard unit and order shapes according to their area. |
| 69 |
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. |
| 70 |
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. |
| 71 |
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. |
| 72 |
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. |
| 73 |
Area |
Problems with area. |
| Objective: On completion of the lesson the student will be able to solve problems with area. |
| 74 |
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. |
| 75 |
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. |
| 76 |
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. |
| 77 |
Surface area |
Surface area of pyramids |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. |
| 78 |
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. |
| 79 |
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. |
| 80 |
Volume |
Volume of pyramids and cones. |
| Objective: On completion of the lesson the student will be able to: use formulae to find the volume of right pyramids and cones, and calculate the volume of a variety of pyramids and cones. |
| 81 |
Volume |
Composite solids. |
| Objective: On completion of the lesson the student will be able to: dissect composite solids into simpler shapes so that the volume can be calculated, calculate the volume of a variety of composite solids, and use formulae appropriately. |
| 82 |
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. |
| 83 |
Statistics |
Frequency histograms and polygons |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. |
| 84 |
Exam |
Exam – Class VIII |
| Objective: Exam |
