WM: Working mathematically

WM.DF: Develop fluency

WM.DF.1: consolidate their numerical and mathematical capability from key stage 2 and extend their understanding of the number system and place value to include decimals, fractions, powers and roots

Treasure Hunter (Decimals on the Number Line)

WM.DF.2: select and use appropriate calculation strategies to solve increasingly complex problems

Estimating Population Size

WM.DF.3: use algebra to generalise the structure of arithmetic, including to formulate mathematical relationships

Adding Real Numbers

WM.DF.5: move freely between different numerical, algebraic, graphical and diagrammatic representations [for example, equivalent fractions, fractions and decimals, and equations and graphs]

Percents, Fractions, and Decimals

WM.DF.6: develop algebraic and graphical fluency, including understanding linear and simple quadratic functions

Distance-Time Graphs
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B

WM.DF.7: use language and properties precisely to analyse numbers, algebraic expressions, 2-D and 3-D shapes, probability and statistics.

Classifying Triangles
Parallelogram Conditions
Prisms and Cylinders - Activity A
Special Parallelograms
Spin the Big Wheel! (Probability)

WM.RM: Reason mathematically

WM.RM.1: extend their understanding of the number system; make connections between number relationships, and their algebraic and graphical representations

Elevator Operator (Line Graphs)

WM.RM.2: extend and formalise their knowledge of ratio and proportion in working with measures and geometry, and in formulating proportional relations algebraically

Beam to Moon (Ratios and Proportions)
Estimating Population Size
Geometric Probability - Activity A
Part-to-part and Part-to-whole Ratios
Perimeters and Areas of Similar Figures
Polling: Neighborhood
Proportions and Common Multipliers
Similar Figures - Activity A

WM.RM.3: identify variables and express relations between variables algebraically and graphically

Elevator Operator (Line Graphs)

WM.RM.4: make and test conjectures about patterns and relationships; look for proofs or counter-examples

Introduction to Functions

WM.RM.6: interpret when the structure of a numerical problem requires additive, multiplicative or proportional reasoning

Adding Real Numbers
Estimating Population Size

WM.RM.7: explore what can and cannot be inferred in statistical and probabilistic settings, and begin to express their arguments formally.

Reaction Time 2 (Graphs and Statistics)
Spin the Big Wheel! (Probability)

WM.SP: Solve problems

WM.SP.3: begin to model situations mathematically and express the results using a range of formal mathematical representations

Estimating Population Size

N: Number

N.1: understand and use place value for decimals, measures and integers of any size

Treasure Hunter (Decimals on the Number Line)

N.2: order positive and negative integers, decimals and fractions; use the number line as a model for ordering of the real numbers; use the symbols =, is not equal to, <, >, is less than or equal to, is greater than or equal to

Comparing and Ordering Decimals
Comparing and Ordering Fractions
Comparing and Ordering Integers
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions, and Decimals Greater Than 1
Real Number Line - Activity A
Real Number Line - Activity B
Treasure Hunter (Decimals on the Number Line)

N.3: use the concepts and vocabulary of prime numbers, factors (or divisors), multiples, common factors, common multiples, highest common factor, lowest common multiple, prime factorisation, including using product notation and the unique factorisation property

Factor Trees (Factoring Numbers)
Finding Factors with Area Models

N.4: use the four operations, including formal written methods, applied to integers, decimals, proper and improper fractions, and mixed numbers, all both positive and negative

Adding and Subtracting Integers
Adding and Subtracting Integers with Chips
Dividing Fractions
Dividing Mixed Numbers
Fractions Greater than One (Fraction Tiles)
Fractions with Unlike Denominators
Multiplying Decimals (Area Model)
Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Sums and Differences with Decimals

N.5: use conventional notation for the priority of operations, including brackets, powers, roots and reciprocals

Order of Operations
Simplifying Radical Expressions - Activity A

N.6: recognise and use relationships between operations including inverse operations

Function Machines 3 (Functions and Problem Solving)
Modeling and Solving Two-Step Equations
Solving Two-Step Equations

N.7: use integer powers and associated real roots (square, cube and higher), recognise powers of 2, 3, 4, 5 and distinguish between exact representations of roots and their decimal approximations

Square Roots

N.8: interpret and compare numbers in standard form A x 10 to the n power 1 is less than or equal to A < 10, where n is a positive or negative integer or zero

Unit Conversions

N.9: work interchangeably with terminating decimals and their corresponding fractions (such as 3.5 and 7/2 or 0.375 and 3\8)

Percents, Fractions, and Decimals

N.10: define percentage as ?number of parts per hundred?, interpret percentages and percentage changes as a fraction or a decimal, interpret these multiplicatively, express one quantity as a percentage of another, compare two quantities using percentages, and work with percentages greater than 100%

Percents and Proportions
Percents, Fractions, and Decimals
Real-Time Histogram
Time Estimation

N.11: interpret fractions and percentages as operators

Ordering Percents, Fractions and Decimals
Ordering Percents, Fractions, and Decimals Greater Than 1
Percents and Proportions

N.15: use a calculator and other technologies to calculate results accurately and then interpret them appropriately

Adding Real Numbers

N.16: appreciate the infinite nature of the sets of integers, real and rational numbers.

Comparing and Ordering Integers

A: Algebra

A.1: use and interpret algebraic notation, including:

A.1.1: ab in place of a × b

Multiplying Decimals (Area Model)

A.1.2: 3y in place of y + y + y and 3 × y

Multiplying Decimals (Area Model)

A.1.3: a² in place of a × a, a³ in place of a × a × a; a²b in place of a × a × b

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions

A.1.4: a/b in place of a ÷ b

No Alien Left Behind (Division with Remainders)

A.1.5: coefficients written as fractions rather than as decimals

Percents, Fractions, and Decimals

A.1.6: brackets

Order of Operations

A.3: understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors

Factor Trees (Factoring Numbers)
Finding Factors with Area Models
System of Two Quadratic Inequalities

A.4: simplify and manipulate algebraic expressions to maintain equivalence by:

A.4.2: multiplying a single term over a bracket

Chocomatic (Multiplication, Arrays, and Area)
Solving Equations By Graphing Each Side

A.4.3: taking out common factors

Factor Trees (Factoring Numbers)
Factoring Special Products
Finding Factors with Area Models
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c

A.6: model situations or procedures by translating them into algebraic expressions or formulae and by using graphs

Elevator Operator (Line Graphs)
Fourth-Degree Polynomials - Activity A
Point-Slope Form of a Line - Activity A
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Rational Functions

A.7: use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)

Modeling and Solving Two-Step Equations
Solving Equations By Graphing Each Side
Solving Two-Step Equations

A.8: work with coordinates in all four quadrants

City Tour (Coordinates)
Points in the Coordinate Plane - Activity A

A.9: recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane

Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line - Activity A
Quadratic and Absolute Value Functions
Quadratics in Factored Form
Quadratics in Polynomial Form - Activity A
Roots of a Quadratic
Slope-Intercept Form of a Line - Activity B

A.10: interpret mathematical relationships both algebraically and graphically

Elevator Operator (Line Graphs)

A.11: reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically

Defining a Line with Two Points
Elevator Operator (Line Graphs)
Slope - Activity B
Solving Equations By Graphing Each Side
Standard Form of a Line

A.12: use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations

Points in the Coordinate Plane - Activity A
Solving Linear Systems by Graphing
Systems of Linear Equations - Activity A

A.13: find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs

Function Machines 1 (Functions and Tables)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)

A.14: generate terms of a sequence from either a term-to-term or a position-to-term rule

Arithmetic and Geometric Sequences

A.15: recognise arithmetic sequences and find the nth term

Arithmetic Sequences
Arithmetic and Geometric Sequences

A.16: recognise geometric sequences and appreciate other sequences that arise.

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences
Pattern Finder

RP: Ratio, proportion and rates of change

RP.2: use scale factors, scale diagrams and maps

Building Topographic Maps
Dilations
Reading Topographic Maps

RP.3: express one quantity as a fraction of another, where the fraction is less than 1 and greater than 1

Fraction Artist 1 (Area Models of Fractions)
Fraction Artist 2 (Area Models of Fractions)

RP.4: use ratio notation, including reduction to simplest form

Part-to-part and Part-to-whole Ratios
Polling: Neighborhood

RP.5: divide a given quantity into two parts in a given part:part or part:whole ratio; express the division of a quantity into two parts as a ratio

Part-to-part and Part-to-whole Ratios
Polling: Neighborhood

RP.6: understand that a multiplicative relationship between two quantities can be expressed as a ratio or a fraction

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Proportions and Common Multipliers

RP.7: relate the language of ratios and the associated calculations to the arithmetic of fractions and to linear functions

Beam to Moon (Ratios and Proportions)
Linear Functions
Part-to-part and Part-to-whole Ratios
Polling: Neighborhood
Slope-Intercept Form of a Line - Activity B

RP.8: solve problems involving percentage change, including: percentage increase, decrease and original value problems and simple interest in financial mathematics

Percent of Change
Percents and Proportions
Polling: Neighborhood
Real-Time Histogram
Simple and Compound Interest
Time Estimation

RP.9: solve problems involving direct and inverse proportion, including graphical and algebraic representations

Direct and Inverse Variation

RP.10: use compound units such as speed, unit pricing and density to solve problems.

Household Energy Usage

GM: Geometry and measures

GM.1: derive and apply formulae to calculate and solve problems involving: perimeter and area of triangles, parallelograms, trapezia, volume of cuboids (including cubes) and other prisms (including cylinders)

Area of Parallelograms
Area of Triangles
Balancing Blocks (Volume)
Parallelogram Conditions
Prisms and Cylinders - Activity A
Segment and Angle Bisectors

GM.2: calculate and solve problems involving: perimeters of 2-D shapes (including circles), areas of circles and composite shapes

Area of Triangles
Circles: Circumference and Area
Fido's Flower Bed (Perimeter and Area)
Minimize Perimeter
Perimeter and Area of Rectangles

GM.4: derive and use the standard ruler and compass constructions (perpendicular bisector of a line segment, constructing a perpendicular to a given line from/at a given point, bisecting a given angle); recognise and use the perpendicular distance from a point to a line as the shortest distance to the line

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

GM.5: describe, sketch and draw using conventional terms and notations: points, lines, parallel lines, perpendicular lines, right angles, regular polygons, and other polygons that are reflectively and rotationally symmetric

Classifying Triangles
Constructing Parallel and Perpendicular Lines
Holiday Snowflake Designer
Quilting Bee (Symmetry)
Reflections
Rotations, Reflections and Translations

GM.6: use the standard conventions for labelling the sides and angles of triangle ABC, and know and use the criteria for congruence of triangles

Classifying Triangles
Congruence in Right Triangles
Proving Triangles Congruent
Segment and Angle Bisectors
Triangle Inequalities

GM.7: derive and illustrate properties of triangles, quadrilaterals, circles, and other plane figures [for example, equal lengths and angles] using appropriate language and technologies

Area of Parallelograms
Chords and Arcs
Inscribed Angles
Parallelogram Conditions
Segment and Angle Bisectors
Triangle Inequalities

GM.8: identify properties of, and describe the results of, translations, rotations and reflections applied to given figures

Classifying Triangles
Parallelogram Conditions
Reflections
Rock Art (Transformations)
Rotations, Reflections and Translations
Special Parallelograms
Translations

GM.9: identify and construct congruent triangles, and construct similar shapes by enlargement, with and without coordinate grids

Congruence in Right Triangles
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures - Activity A

GM.13: apply angle facts, triangle congruence, similarity and properties of quadrilaterals to derive results about angles and sides, including Pythagoras? Theorem, and use known results to obtain simple proofs

Congruence in Right Triangles
Distance Formula - Activity A
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard
Similar Figures - Activity A

GM.14: use Pythagoras? Theorem and trigonometric ratios in similar triangles to solve problems involving right-angled triangles

Distance Formula - Activity A
Perimeters and Areas of Similar Figures
Pythagorean Theorem - Activity B
Pythagorean Theorem with a Geoboard

P: Probability

P.1: record, describe and analyse the frequency of outcomes of simple probability experiments involving randomness, fairness, equally and unequally likely outcomes, using appropriate language and the 0-1 probability scale

Probability Simulations
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

P.2: understand that the probabilities of all possible outcomes sum to 1

Spin the Big Wheel! (Probability)

P.3: enumerate sets and unions/intersections of sets systematically, using tables, grids and Venn diagrams

Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Toy Factory (Set Models of Fractions)

P.4: generate theoretical sample spaces for single and combined events with equally likely, mutually exclusive outcomes and use these to calculate theoretical probabilities.

Compound Independent Events
Compound Independent and Dependent Events
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability

S: Statistics

S.1: describe, interpret and compare observed distributions of a single variable through: appropriate graphical representation involving discrete, continuous and grouped data; and appropriate measures of central tendency (mean, mode, median) and spread (range, consideration of outliers)

Box-and-Whisker Plots
Describing Data Using Statistics
Mean, Median and Mode
Movie Reviewer (Mean and Median)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions

S.2: construct and interpret appropriate tables, charts, and diagrams, including frequency tables, bar charts, pie charts, and pictograms for categorical data, and vertical line (or bar) charts for ungrouped and grouped numerical data

Describing Data Using Statistics
Elevator Operator (Line Graphs)
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)

S.3: describe simple mathematical relationships between two variables (bivariate data) in observational and experimental contexts and illustrate using scatter graphs.

Geometric Probability - Activity A
Probability Simulations
Scatter Plots - Activity A
Spin the Big Wheel! (Probability)
Theoretical and Experimental Probability