| 1 |
Study Plan |
Study plan – Middle School – Year I |
| 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 |
Multiplication |
Multiples and factors of whole numbers |
| Objective: On completion of the lesson the student will be able to specify multiples and factors of whole numbers, and calculate the product of squared numbers. |
| 4 |
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. |
| 5 |
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. |
| 6 |
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. |
| 7 |
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. |
| 8 |
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. |
| 9 |
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. |
| 10 |
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. |
| 11 |
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. |
| 12 |
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. |
| 13 |
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. |
| 14 |
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. |
| 15 |
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. |
| 16 |
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. |
| 17 |
Algebraic expressions |
Expanding and simplifying algebraic expressions |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. |
| 18 |
Fractions |
Finding equivalent fractions |
| Objective: On completion of the lesson the student will be able to name and find fractions that represent equal amounts between halves, quarters and eighths – using diagrams and number lines. |
| 19 |
Fractions |
Multiplying and dividing to obtain equivalent fractions |
| Objective: On completion of the lesson the student will be able to: obtain equivalent fractions using a number line or diagram, develop mental strategies to obtain equivalent fractions, and reduce a fraction to its lowest equivalent form. |
| 20 |
Fractions |
Reducing fractions to lowest equivalent form |
| Objective: On completion of the lesson the student will be able to reduce a fraction to its lowest equivalent form by dividing the numerator and denominator by a common factor. |
| 21 |
Fractions |
Comparing and ordering fractions greater than (>) 1 |
| Objective: On completion of the lesson the student will be able to use diagrams, number lines and equivalent fractions to compare and order fractions greater than (>) one. |
| 22 |
Fractions |
Subtracting fractions from whole numbers |
| Objective: On completion of the lesson the student will be able to: use a diagram to subtract fractions from a whole number, develop mental strategies for subtracting fractions from whole numbers, and recognise and use the written form for subtracting fractions from |
| 23 |
Fractions |
Adding and subtracting fractions with the same denominator |
| Objective: On completion of the lesson the student will be able to add and subtract fractions with the same denominator. |
| 24 |
Fractions |
Adding and subtracting fractions with different denominators |
| Objective: On completion of the lesson the student will be able to add and subtract fractions where one denominator is a multiple of the other. |
| 25 |
Fractions |
Multiplying fractions by whole numbers |
| Objective: On completion of the lesson the student will be able to multiply simple fractions by whole numbers. |
| 26 |
Fractions |
Fractions of whole numbers |
| Objective: On completion of the lesson the student will be able to calculate unit fractions of a collection. |
| 27 |
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. |
| 28 |
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. |
| 29 |
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). |
| 30 |
Fractions |
Dividing fractions |
| Objective: On completion of the lesson the student will be able to divide fractions. |
| 31 |
Fractions |
Dividing mixed numbers (mixed numerals) |
| Objective: On completion of the lesson the student will be able to divide mixed numbers (mixed numerals). |
| 32 |
Rules properties |
Using Order of Operation procedures (BIDMAS) with Fractions |
| Objective: On completion of the lesson the student will know how to apply the order of operations rules to simplify expressions with integers and fractions. |
| 33 |
Algebra-factorising |
Simplifying easy algebraic fractions. |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. |
| 34 |
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. |
| 35 |
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. |
| 36 |
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. |
| 37 |
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. |
| 38 |
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. |
| 39 |
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. |
| 40 |
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. |
| 41 |
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. |
| 42 |
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. |
| 43 |
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. |
| 44 |
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. |
| 45 |
Fractional indices/exponents |
Fractional indices |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. |
| 46 |
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. |
| 47 |
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. |
| 48 |
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. |
| 49 |
Algebraic equations |
Solving two step equations |
| Objective: On completion of the lesson the student will be able to solve two step equations. |
| 50 |
Algebraic equations |
Solving equations containing binomial expressions |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. |
| 51 |
Algebraic equations |
Equations involving grouping symbols. |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols |
| 52 |
Algebraic equations |
Equations involving fractions. |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. |
| 53 |
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. |
| 54 |
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. |
| 55 |
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. |
| 56 |
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. |
| 57 |
Functions |
Notation and evaluations |
| Objective: On completion of the lesson the student will be understand different notations for functions. |
| 58 |
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. |
| 59 |
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. |
| 60 |
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. |
| 61 |
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. |
| 62 |
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. |
| 63 |
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. |
| 64 |
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. |
| 65 |
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. |
| 66 |
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. |
| 67 |
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. |
| 68 |
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. |
| 69 |
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 |
| 70 |
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. |
| 71 |
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. |
| 72 |
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. |
| 73 |
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. |
| 74 |
Functions |
Evaluating and graphing piecewise functions |
| Objective: On completion of the lesson the student will be able to evaluate and graph piecewise functions. |
| 75 |
Functions |
Functions combinations |
| Objective: On completion of the lesson the student will be able to perform operations with functions while working with their domains. |
| 76 |
Functions |
Composition of functions |
| Objective: On completion of the lesson the student will understand composition of functions or a function of a function. |
| 77 |
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. |
| 78 |
Statistics |
Frequency histograms and polygons |
| Objective: On completion of the lesson the student will be able to construct and interpret frequency histograms and polygons. |
| 79 |
Statistics |
Relative frequency |
| Objective: On completion of the lesson the student will be able to collect, display and make judgements about data. |
| 80 |
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. |
| 81 |
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. |
| 82 |
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. |
| 83 |
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 |
| 84 |
Statistic-probability |
Cumulative frequency |
| Objective: On completion of the lesson the student will be able to construct cumulative frequency columns, histograms and polygons. |
| 85 |
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. |
| 86 |
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. |
| 87 |
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. |
| 88 |
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. |
| 89 |
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. |
| 90 |
Geometry-angles |
Parallel Lines. |
| Objective: On completion of the lesson the student will able to identify corresponding, co-interior and alternate angles. |
| 91 |
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. |
| 92 |
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. |
| 93 |
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. |
| 94 |
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. |
| 95 |
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. |
| 96 |
Geometry-constructions |
Geometric constructions |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
| 97 |
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. |
| 98 |
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. |
| 99 |
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. |
| 100 |
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.’ |
| 101 |
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. |
| 102 |
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. |
| 103 |
3-D shapes |
Recognise and name prisms according to spatial properties |
| Objective: On completion of the lesson the student will be able to recognise and name various prisms according to their spatial properties. |
| 104 |
3-D shapes |
Recognise and name pyramids according to spatial properties |
| Objective: On completion of the lesson the student will be able to recognise, describe and name pyramids according to their spatial properties. |
| 105 |
3-D shapes |
Recognise nets for prisms, pyramids, cubes and cones |
| Objective: On completion of the lesson the student will be able to predict and recognise nets for prisms, pyramids, cubes and cones. |
| 106 |
3-D shapes |
Viewing 3-D shapes. |
| Objective: On completion of the lesson the student will be able to use conventional representations of three-dimensional shapes to show depth etc when drawing or viewing shapes from various angles. |
| 107 |
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. |
| 108 |
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. |
| 109 |
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. |
| 110 |
Surface area |
Surface area of pyramids |
| Objective: On completion of the lesson the student will be able to find the surface areas of pyramids. |
| 111 |
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 |
| 112 |
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. |
| 113 |
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. |
| 114 |
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. |
| 115 |
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. |
| 116 |
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. |
| 117 |
Exam |
Exam – Middle School – Year I |
| Objective: Exam |
