Number Systems; N: the set of natural numbers, N = {1,2,3,4...}; Z: the set of integers, including 0; Q: the set of rational numbers; R: the set of real numbers; R/Q: the set of irrational numbers • The binary operations of addition, subtraction multiplication and division and the relationships between these operations, beginning with whole numbers and integers. They explore some of the laws that govern these operations and use mathematical models to reinforce the algorithms they commonly use. Later, they revisit these operations in the context of rational numbers and irrational numbers (R/Q) and refine, revise and consolidate their ideas. Students learn strategies for computation that can be applied to any numbers; implicit in such computational methods are generalisations about numerical relationships with the operations being used. • Students articulate the generalisation that underlies their strategy, firstly in the vernacular and then in symbolic language. • Problems set in context, using diagrams to solve the problems so they can appreciate how the mathematical concepts are related to real life. Algorithms used to solve problems involving fractional amounts.
Multiply Fractions with Models
Divide Unit Fractions by Whole Numbers Up to 20 I
Prime and Composite Numbers
Integer Addition and Subtraction Rules
Add and Subtract Integers
Complete Addition and Subtraction Sentences with Integers
Add and Subtract Integers
Complete Addition and Subtraction Sentences with Integers
Integer Multiplication and Division Rules
Multiply and Divide Integers
Complete the Mixed Equation Sentence
Order of Operations
Evaluate Expressions Involving Integers
Simplify Expressions Involving Integers
Add and Subtract Decimal Numbers
Mixed Equations with Decimals
Add and Subtract Decimals Up to 10
Add and Subtract Decimal Up to 100
Add and Subtract Decimals
Multiply Decimals with Numbers Up to 100
Multiply Decimals
Multiply Decimals and Whole Numbers
Divide Decimals
Divide Decimals by Whole Numbers
Estimate Products of Decimal Numbers
Estimate Sums and Differences of Decimals Up to 100
Estimate Sums, Differences and Products of Decimals
Mixed Decimal Equations
Multi Step Inequalities with Decimals
Maps with Decimal Distances
Evaluate Expressions with Decimals
Add and Subtract Fractions
Add and Subtract Mixed Numbers
Add and Subtract Mixed Numbers
Add, Subtract Inequalities with Fractions and Mixed Numbers
Estimate Sums and Differences of Mixed Numbers
Multiply Fractions by Whole Numbers
Multiply Fractions
Divide and Multiply Mixed Numbers
Multiply Mixed Numbers
Multiply Fractions by Whole Numbers
Divide Fractions Up to 1/5, 1/7, 1/9
Divide Fractions and Mixed Numbers Up to 1/16, 1/32
Divide Fractions and Mixed Numbers Up to 1/32
Divide Fractions and Mixed Numbers
Divide Fractions and Mixed Numbers Up to 1/16
Estimate Products of Fractions and Mixed Numbers
Mixed Fraction Equations Up to 10
Mixed Equations with Fractions, Mixed Numbers
Add and Subtract Rational Numbers
Multiply and Divide Rational Numbers
Describe Pictures as Ratios
Equivalent Ratios
Equivalent Ratios
Unit Rates
Compare Ratios
Scale Drawings and Scale Factors
Ratios and Proportions
Ratios and Proportions
Solving Proportions
Constant of Variation
Solving Proportions
Find the Constant of Variation
Estimate Using Proportions
Rate of Change
Constant Rate of Change
Find the Constant of Variation Graphs
Convert Between Percents, Fractions and Decimals
Estimate Percents of Numbers
Percents of Numbers and Money Amounts
Percents of Numbers
Percent Equations
Percents with Multi-Step Problems
Percent Equations
Estimate Mixed Equations
Multi-Step
Guess and Check
Properties of Addition and Multiplication
Distributive Property
Simplify Variable Expressions
Solve Equations Using Properties
Identify Factors
Divisibility Rules with Numbers Up to 10,000
Divisibility Rules with Dividend Up to 10,000,000
Divisibility Rules
Reciprocals
Multiplicative Inverses
Evaluate Variable Expressions with Decimals and Fractions
Compare Percents to Fractions and Decimals
Percents of Numbers and Money Amounts
Percent Change
Evaluate Multi-Variable Expressions
Evaluate Exponents
Exponents: Solve for the Variable
Solve Two-Step Linear Equations
Solve One-Step Linear Equations
Solve Multi Step Equations
Indices • Binary operations of addition, subtraction, multiplication and division in the context of numbers in index form.
Place Values and Number Sense: Scientific Notation
Convert Scientific Notation
Inequalities with Scientific Notation
Compare Numbers Written in Scientific Notation
Understanding Exponents
Exponents with Negative Bases
Exponents with Decimal and Fractional Bases
Square Roots of Perfect Squares
Estimate Positive and Negative Square Roots
Understanding Negative Exponents
Evaluate Negative Exponents
Multiplication with Exponents
Division with Exponents
Multiplication and Division with Exponents
Power Rule
Simplify Expressions Involving Exponents
Positive and Negative Square Roots
Relationship Between Squares and Square Roots
Cube Roots of Perfect Cubes
Estimate Cube Roots
Evaluate Variable Expressions with Squares and Square Roots
Powers of Monomials
Convert Between Standard and Scientific Notation
Multiply Numbers Written in Scientific Notation
Divide Numbers Written in Scientific Notation
Applied arithmetic • Solving problems involving, e.g., mobile phone tariffs, currency transactions, shopping, VAT and meter readings. • Making value for money calculations and judgments. • Using ratio and proportionality.
Applied measure • Measure and time. • 2D shapes and 3D solids, including nets of solids (two-dimensional representations of three-dimensional objects). • Using nets to analyse figures and to distinguish between surface area and volume. • Problems involving surface area and volume. • Modelling real-world situations and solve a variety of problems (including multi-step problems) involving surface areas, and volumes of prisms and cylinders. • Students learn about the circle and develop an understanding of the relationship between its circumference, diameter and pi.
Sets • Set language as an international symbolic mathematical tool; the concept of a set as being a well-defined collection of objects or elements. They are introduced to the concept of the universal set, null set, sub-set, cardinal number; the union, intersection, set difference operators, and Venn diagrams. They investigate the properties of arithmetic as related to sets and solve problems involving sets.
Synthesis and problem-solving skills • explore patterns and formulate conjectures • explain findings • justify conclusions • communicate mathematics verbally and in written form • apply their knowledge and skills to solve problems in familiar and unfamiliar contexts • analyse information presented verbally and translate it into mathematical form • devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions
Counting • Listing outcomes of experiments in a systematic way.
Concepts of probability • The probability of an event occurring: student progress from informal to formal descriptions of probability. • Predicting and determining probabilities. • Difference between experimental and theoretical probability.
Probability of Simple Events
Probability of Opposite and Overlapping Events
Identify Independent and Dependent Events
Probability of Independent and Dependent Events
Factorials
Factorial Division
Making Predictions
Prediction Problems
Experimental Probability
Probability Problems
Outcomes of simple random processes • Finding the probability of equally likely outcomes.
Statistical reasoning with an aim to becoming a statistically aware consumer • The use of statistics to gather information from a selection of the population with the intention of making generalisations about the whole population. They consider situations where statistics are misused and learn to evaluate the reliability and quality of data and data sources.
Finding, collecting and organising data • Formulating a statistics question based on data that vary allows for distinction between different types of data.
Representing data graphically and numerically • Methods of representing data. Students develop a sense that data can convey information and that organising data in different ways can help clarify what the data have to tell us. They see a data set as a whole and so are able to use fractions, quartiles and median to describe the data. • Mean of a grouped frequency distribution.
Interpret Charts to Find Mode
Interpret Charts to Find Mean, Median, Mode, and Range
Interpret Charts to Find Median
Interpret Charts to Find Range
Interpret Charts to Find Mean
Interpret Stem and Leaf Plots
Calculate Mode
Calculate Mean, Median, Mode and Range
Calculate Range
Calculate Median
Calculate Mean
Mean: Find the Missing Number
Range: Find the Missing Number
Mean, Median, Mode, and Range: Find the Missing Number
Mode: Find the Missing Number
Median: Find the Missing Number
Changes in Median
Changes in Mean, Median, Mode, and Range
Changes in Mode
Changes in Range
Changes in Mean
Analysing, interpreting and drawing conclusions from data • Drawing conclusions from data; limitations of conclusions.
Synthesis and problem-solving skills • explore patterns and formulate conjectures • explain findings • justify conclusions • communicate mathematics verbally and in written form • apply their knowledge and skills to solve problems in familiar and unfamiliar contexts • analyse information presented verbally and translate it into mathematical form • devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions.
Synthetic Geometry • Axioms • Theorems • Corollaries • Constructions
Congruent Triangles SSS SAS and ASA
Find Missing Angles in Triangles and Quadrilaterals
Interior Angles of Polygons
Identify Angles by Type
Complementary, Supplementary, Vertical and Adjacent Angles
Find Complementary, Vertical, and Adjacent Angles
Transversal of Parallel Lines
Similar and Congruent Figures
Congruent Figures: Side Lengths and Angle Measures
Congruence Statements and Corresponding Parts
Similar Figures Side Lengths and Angle Measures
Similar Figures: Side Lengths and Angle Measures
Similar Figures and Indirect Measurement
Measures of Bisected Lines and Angles
Names and Bases of 3-Dimensional Figures
Nets of 3-Dimensional Figures
Front, Side, and Top View
Transformation Geometry • Translations, central symmetry and axial symmetry.
Symmetry
Identify Reflections, Rotations and Translations
Translations: Graph the Image
Translations Find the Coordinates
Reflections: Graph the Image
Reflections Find the Coordinates
Rotations: Graph the Image
Rotations Find the Coordinates
Dilations Graph the Image
Dilations: Find the Coordinates
Co-ordinate Geometry • Co-ordinating the plane. • Properties of lines and line segments including midpoint, slope, distance and the equation of a line in the form: y - y1 = m(x - x1) y = mx + c; ax + by + c = 0 where a, b, c, are integers and m is the slope of the line • Intersection of lines. • Parallel and perpendicular lines and the relationships between the slopes.
Coordinate Graphs Review
Relative Coordinates
Distance Between Two Points
Find the Distance Between Two Points
Graph a Line from an Equation
Graph a Line from a Function Table
Complete a Function Table
Write a Rule for a Function Table
Find Slope from Two Points
Algebra: Linear Function with Intercepts
Find the Slope of a Graph
Graph Linear Functions
Graph a Line Using Slope
Parallel, Perpendicular, Intersecting
Trigonometry • Right-angled triangles: theorem of Pythagoras. • Trigonometric ratios • Trigonometric ratios in surd form for angles of 30°, 45° and 60° Right-angled triangles • Decimal and DMS values of angles.
Synthesis and problem-solving skills • explore patterns and formulate conjectures • explain findings • justify conclusions • communicate mathematics verbally and in written form • apply their knowledge and skills to solve problems in familiar and unfamiliar contexts • analyse information presented verbally and translate it into mathematical form • devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions.
Regular and Irregular Polygons
Construct Obtuse, Acute, Right Angle Using a Protractor
Construct Angles with Mixed Equations Using a Protractor
Name, Measure and Classify Angles
Construct Angles with a Protractor
Types of Triangles
Classify Quadrilateral Shapes
Parts of a Circle
Identify Proportional Relationships
Area and Perimeter
Circles
Perimeter with Unit Squares
Area of Rectangles and Parallelograms
Circles: Calculate Area, Radius, Circumference
Volume of Cubes and Rectangular Prisms
Surface Area
Perimeter Area and Volume Changes in Scale
Similar Solids
Area with Unit Squares
Quarter Circles
Volume of Pyramids and Cones
Generating arithmetic expressions from repeating patterns • Patterns and the rules that govern them, and so construct an understanding of a relationship as that which involves a set of inputs, a set of outputs and a correspondence from each input to each output.
Representing situations with tables, diagrams and graphs • Relations derived from some kind of context -- familiar, everyday situations, imaginary contexts or arrangements of tiles or blocks. They look at various patterns and make predictions about what comes next.
Constant of Variation with Tables
Find the Proportional Relationship
Find the Constant of Variation with Tables
Find the Proportional Relationship
Graph a Proportional Relationship
Interpret Double Bar Graphs
Interpret Double Line Graphs
Interpret Bar Graphs
Interpret Line Graphs
Find Points on a Function Graph
Linear Function with Intercepts
Algebra: Linear Function
Finding Formulae • Ways to express a general relationship arising from a pattern or context.
Examining algebraic relationships • Features of a relationship and how these features appear in the different representations. • Constant rate of change: linear relationships. • Non-constant rate of change: quadratic relationships • Proportional relationships
Relations without Formulae • Using graphs to represent phenomena quantitatively.
Identify Linear and Nonlinear Functions
Interpret Line Plots with Up to 5 Data Points
Interpret Line Plots
Interpret Line Plots with Numbers Up to 40
Create Line Plots
Create Line Plots II
Create Bar Graphs Using Tables
Create Bar Graphs
Interpret Histograms
Create Histograms
Create Frequency Charts
Convert Graphs to Input/Output Tables
Create Line Graphs
Interpret Box-And-Whisker Plots
Scatter Plots
Expressions • Using letters to represent quantities that are variable. • Arithmetic operations on expressions; applications to real life contexts. • Transformational activities: collecting like terms, simplifying expressions, substituting, expanding and factoring.
Write Variable Expressions
Write Variable Equations to Represent
Write Variable Expressions
Linear Function
Evaluate Variable Expressions with Whole Numbers
Identify Terms, Coefficients, and Monomials
Add and Subtract Like Terms
Solve Two-Step Linear Equations
Solve One-Step Linear Equations
Simplify Variable Expressions Using Properties
Simplify Variable Expressions Using Properties
Model and Solve Equations Using Algebra Tiles
Divide Monomials
Multiply and Divide Monomials
Powers of Monomials
Equations and Inequalities • Using a variety of problem solving strategies to solve equations and inequalities. They identify the necessary information, represent problems mathematically, making correct use of symbols, words, diagrams, table and graphs.
Synthesis and problem-solving skills • explore patterns and formulate conjectures • explain findings • justify conclusions • communicate mathematics verbally and in written form • apply their knowledge and skills to solve problems in familiar and unfamiliar contexts • analyse information presented verbally and translate it into mathematical form • devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions
Graphing functions • Interpreting and representing linear, quadratic and exponential functions in graphical form.
Synthesis and problem-solving skills • explore patterns and formulate conjectures • explain findings • justify conclusions • communicate mathematics verbally and in written form • apply their knowledge and skills to solve problems in familiar and unfamiliar contexts • analyse information presented verbally and translate it into mathematical form • devise, select and use appropriate mathematical models, formulae or techniques to process information and to draw relevant conclusions