| 1 |
Study Plan |
Study plan – Middle School – Year II |
| Objective: On completion of the course formative assessment a tailored study plan is created identifying the lessons requiring revision. |
| 2 |
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. |
| 3 |
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. |
| 4 |
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. |
| 5 |
Decimals |
Rounding decimals |
| Objective: On completion of the lesson the student will be able to round a number with one or two decimal places to the nearest whole number. |
| 6 |
Decimals |
Decimals to three decimal places |
| Objective: On completion of the lesson the student will be able to express thousandths as a decimal and interpret decimal notation for thousandths. |
| 7 |
Sequences and Series-Sum-infinity |
Limiting sum or sum to infinity. |
| Objective: On completion of the lesson the student will have learnt the formula for the limiting sum of a G.P., the conditions for it to exist and how to apply it to particular problems. |
| 8 |
Sequences and Series-Recurring decimal infinity |
Recurring decimals and the infinite G.P. |
| Objective: On completion of the G.P. lesson the student will have understood how to convert any recurring decimal to a rational number. |
| 9 |
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. |
| 10 |
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. |
| 11 |
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. |
| 12 |
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. |
| 13 |
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. |
| 14 |
Geometry-constructions |
Geometric constructions |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
| 15 |
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. |
| 16 |
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. |
| 17 |
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. |
| 18 |
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. |
| 19 |
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. |
| 20 |
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. |
| 21 |
Fractional indices/exponents |
Fractional indices |
| Objective: On completion of the lesson the student will know how to evaluate or simplify expressions containing fractional indices. |
| 22 |
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. |
| 23 |
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. |
| 24 |
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. |
| 25 |
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. |
| 26 |
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. |
| 27 |
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. |
| 28 |
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. |
| 29 |
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. |
| 30 |
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. |
| 31 |
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. |
| 32 |
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. |
| 33 |
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. |
| 34 |
Algebraic expressions |
Expanding and simplifying algebraic expressions |
| Objective: On completion of the lesson the student will be familiar with expanding and simplifying algebraic expressions. |
| 35 |
Algebra-factorising |
Simplifying easy algebraic fractions. |
| Objective: On completion of the lesson the student will understand how to simplify algebraic fractions by factorising. |
| 36 |
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. |
| 37 |
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. |
| 38 |
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. |
| 39 |
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. |
| 40 |
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. |
| 41 |
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. |
| 42 |
Algebraic equations |
Solving two step equations |
| Objective: On completion of the lesson the student will be able to solve two step equations. |
| 43 |
Algebraic equations |
Solving equations containing binomial expressions |
| Objective: On completion of the lesson the student will be able to move terms in binomial equations. |
| 44 |
Algebraic equations |
Equations involving grouping symbols. |
| Objective: On completion of the lesson the student will be able to solve equations using grouping symbols |
| 45 |
Algebraic equations |
Equations involving fractions. |
| Objective: On completion of the lesson the student will know how to solve equations using fractions. |
| 46 |
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. |
| 47 |
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. |
| 48 |
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. |
| 49 |
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. |
| 50 |
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. |
| 51 |
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. |
| 52 |
Simultaneous equns |
Elimination method |
| Objective: On completion of the lesson the student will be able to solve 2 equations with 2 unknown variables by the elimination method. |
| 53 |
Simultaneous equns |
Elimination method part 2 |
| Objective: On completion of the lesson the student will be able to solve all types of simultaneous equations with 2 unknown variables by the elimination method. |
| 54 |
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. |
| 55 |
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. |
| 56 |
Geometry – triangles |
Triangle inequality theorem |
| Objective: On completion of the lesson the student will understand and use the triangle inequality theorem. |
| 57 |
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. |
| 58 |
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. |
| 59 |
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. |
| 60 |
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. |
| 61 |
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. |
| 62 |
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. |
| 63 |
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. |
| 64 |
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. |
| 65 |
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. |
| 66 |
Statistic-probability |
Probability of Simple Events |
| Objective: On completion of the lesson the student will be able to understand the probability of simple events. |
| 67 |
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. |
| 68 |
Logic |
Inductive and deductive reasoning |
| Objective: On completion of this lesson the student will understand and use the terms hypothesis, conclusion, inductive and deductive. |
| 69 |
Logic |
Definition and use of counter examples |
| Objective: On completion of this lesson the student will be able to create counter examples to statements. |
| 70 |
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. |
| 71 |
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. |
| 72 |
Geometry-constructions |
Geometric constructions |
| Objective: On completion of the lesson the student will able complete constructions with a ruler and a pair of compasses. |
| 73 |
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. |
| 74 |
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. |
| 75 |
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. |
| 76 |
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. |
| 77 |
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. |
| 78 |
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. |
| 79 |
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. |
| 80 |
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. |
| 81 |
Geometry-quadrilaterals |
Classifying Quadrilaterals |
| Objective: On completion of this lesson the student will understand the properties that classify quadrilaterals. |
| 82 |
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. |
| 83 |
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. |
| 84 |
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. |
| 85 |
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. |
| 86 |
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. |
| 87 |
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. |
| 88 |
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. |
| 89 |
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. |
| 90 |
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. |
| 91 |
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. |
| 92 |
Pythagoras |
Pythagorean triples |
| Objective: On completion of the lesson the student will be able to use the 3-4-5 Pythagorean triple. |
| 93 |
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. |
| 94 |
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. |
| 95 |
Pythagoras |
Proofs of Pythagoras theorem |
| Objective: On completion of this lesson the student will have geometric proofs for Pythagoras’ Theorem |
| 96 |
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. |
| 97 |
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. |
| 98 |
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. |
| 99 |
Exam |
Exam – Middle School – Year II |
| Objective: Exam |
