### Middle School Year II Mathematics

# TOPIC TITLE
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.
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.
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.
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.
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.
Objective: On completion of the lesson the student will be able to use coordinate geometry to apply the midsegment properties of a triangle.
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.
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