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

Comparing and Ordering Decimals
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Percents, Fractions, and Decimals
Sums and Differences with Decimals
Toy Factory (Set Models of Fractions)
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

Using Algebraic Expressions

WM.DF.4: substitute values in expressions, rearrange and simplify expressions, and solve equations

Circles
Direct and Inverse Variation
Dividing Exponential Expressions
Equivalent Algebraic Expressions I
Equivalent Algebraic Expressions II
Exponents and Power Rules
Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Modeling the Factorization of ax²+bx+c
Modeling the Factorization of x²+bx+c
Multiplying Exponential Expressions
Operations with Radical Expressions
Order of Operations
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations II
Solving Equations on the Number Line

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

Arithmetic Sequences
Dividing Mixed Numbers
Fraction Garden (Comparing Fractions)
Function Machines 1 (Functions and Tables)
Geometric Sequences
Improper Fractions and Mixed Numbers
Modeling Decimals (Area and Grid Models)
Modeling Fractions (Area Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Points, Lines, and Equations

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

Absolute Value with Linear Functions
Addition and Subtraction of Functions
Arithmetic Sequences
Compound Interest
Distance-Time Graphs
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Linear Functions
Quadratics in Factored Form
Quadratics in Polynomial Form
Roots of a Quadratic
Slope-Intercept Form of a Line
Translating and Scaling Functions
Using Algebraic Expressions

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

Classifying Quadrilaterals
Compound Interest
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Algebraic Equations I
Solving Algebraic Equations II
Using Algebraic Equations
Using Algebraic Expressions

WM.RM: Reason mathematically

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)
Direct and Inverse Variation
Estimating Population Size
Percents and Proportions
Proportions and Common Multipliers

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

Absolute Value with Linear Functions
Solving Algebraic Equations I
Using Algebraic Expressions

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

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.

Biconditional Statements

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

Adding Whole Numbers and Decimals (Base-10 Blocks)
Comparing and Ordering Decimals
Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)
Subtracting Whole Numbers and Decimals (Base-10 Blocks)
Sums and Differences with Decimals
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
Integers, Opposites, and Absolute Values
Rational Numbers, Opposites, and Absolute Values

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

Chocomatic (Multiplication, Arrays, and Area)
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Operations with Radical Expressions

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 on the Number Line
Addition of Polynomials

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

Order of Operations

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

Dividing Polynomials Using Synthetic Division
Factor Trees (Factoring Numbers)
Function Machines 3 (Functions and Problem Solving)
Modeling One-Step Equations
Simplifying Algebraic Expressions I
Solving Two-Step Equations
Square Roots

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

Dividing Exponential Expressions
Exponents and Power Rules
Multiplying Exponential Expressions
Operations with Radical Expressions
Simplifying Radical Expressions
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
Unit Conversions 2 - Scientific Notation and Significant Digits

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

Modeling Decimals (Area and Grid Models)

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%

Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Real-Time Histogram
Time Estimation

N.11: interpret fractions and percentages as operators

Estimating Sums and Differences
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Toy Factory (Set Models of Fractions)

N.12: use standard units of mass, length, time, money and other measures, including with decimal quantities

Modeling Decimals (Area and Grid Models)
Modeling Whole Numbers and Decimals (Base-10 Blocks)

A: Algebra

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

A.1.1: ab in place of a × b

Multiplying with Decimals
Using Algebraic Expressions

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

Multiplying Fractions
Multiplying Mixed Numbers
Multiplying with Decimals
Using Algebraic Expressions

A.1.4: a/b in place of a ÷ b

Dividing Fractions
Dividing Mixed Numbers
Dividing Polynomials Using Synthetic Division
Using Algebraic Expressions

A.2: substitute numerical values into formulae and expressions, including scientific formulae

Compound Interest

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

Absolute Value Equations and Inequalities
Chocomatic (Multiplication, Arrays, and Area)
Comparing and Ordering Decimals
Compound Interest
Factor Trees (Factoring Numbers)
Finding Factors with Area Models
Linear Functions
Linear Inequalities in Two Variables
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II
Solving Equations on the Number Line
Solving Linear Inequalities in One Variable
Using Algebraic Equations

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

A.4.1: collecting like terms

Addition and Subtraction of Functions
Addition of Polynomials
Modeling the Factorization of ax²+bx+c
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

A.4.2: multiplying a single term over a bracket

Equivalent Algebraic Expressions II
Modeling the Factorization of x²+bx+c
Operations with Radical Expressions
Simplifying Algebraic Expressions I
Simplifying Algebraic Expressions II

A.4.3: taking out common factors

Equivalent Algebraic Expressions II
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
Operations with Radical Expressions
Simplifying Algebraic Expressions II

A.5: understand and use standard mathematical formulae; rearrange formulae to change the subject

Area of Triangles

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

Arithmetic Sequences
Geometric Sequences
Points, Lines, and Equations

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

Modeling One-Step Equations
Modeling and Solving Two-Step Equations
Solving Algebraic Equations II
Solving Equations on the Number Line
Solving Two-Step Equations

A.8: work with coordinates in all four quadrants

City Tour (Coordinates)
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Linear Functions
Point-Slope Form of a Line
Points in the Coordinate Plane
Points, Lines, and Equations
Slope

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

Arithmetic Sequences
Geometric Sequences

A.10: interpret mathematical relationships both algebraically and graphically

Absolute Value with Linear Functions
Quadratics in Polynomial Form

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

Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Slope-Intercept Form of a Line
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

Cat and Mouse (Modeling with Linear Systems)
Linear Functions
Point-Slope Form of a Line
Points, Lines, and Equations
Solving Equations by Graphing Each Side
Solving Linear Systems (Matrices and Special Solutions)
Solving Linear Systems (Slope-Intercept Form)

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

Arithmetic Sequences
Arithmetic and Geometric Sequences
Geometric Sequences

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

Arithmetic 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
Perimeters and Areas of Similar Figures
Points in the Coordinate Plane
Reading Topographic Maps
Similar Figures

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)

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

Beam to Moon (Ratios and Proportions)
Part-to-part and Part-to-whole Ratios

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)
Estimating Sums and Differences
Fraction Artist 1 (Area Models of Fractions)
Fraction Garden (Comparing Fractions)
Modeling Fractions (Area Models)
Part-to-part and Part-to-whole Ratios
Percents, Fractions, and Decimals
Proportions and Common Multipliers
Toy Factory (Set Models of Fractions)

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

Percents, Fractions, and Decimals

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

Compound Interest
Percent of Change
Percents and Proportions
Percents, Fractions, and Decimals
Polling: Neighborhood
Real-Time Histogram
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)
Perimeter and Area of Rectangles
Prisms and Cylinders
Pyramids and Cones

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

Area of Parallelograms
Area of Triangles
Chocomatic (Multiplication, Arrays, and Area)
Circumference and Area of Circles
Fido's Flower Bed (Perimeter and Area)
Perimeter and Area of Rectangles

GM.3: draw and measure line segments and angles in geometric figures, including interpreting scale drawings

Dilations

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

City Tour (Coordinates)
Classifying Quadrilaterals
Elevator Operator (Line Graphs)
Function Machines 2 (Functions, Tables, and Graphs)
Function Machines 3 (Functions and Problem Solving)
Parallelogram Conditions
Points in the Coordinate Plane
Special Parallelograms

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

Congruence in Right Triangles
Proving Triangles Congruent

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

Chords and Arcs
Circles
Classifying Quadrilaterals
Concurrent Lines, Medians, and Altitudes
Inscribed Angles
Parallelogram Conditions
Similarity in Right Triangles
Special Parallelograms
Triangle Angle Sum
Triangle Inequalities

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

Holiday Snowflake Designer
Reflections
Rock Art (Transformations)
Rotations, Reflections, and Translations
Similar Figures
Translations

GM.10: apply the properties of angles at a point, angles at a point on a straight line, vertically opposite angles

Investigating Angle Theorems
Triangle Angle Sum

GM.11: understand and use the relationship between parallel lines and alternate and corresponding angles

Triangle Angle Sum

GM.12: derive and use the sum of angles in a triangle and use it to deduce the angle sum in any polygon, and to derive properties of regular polygons

Isosceles and Equilateral Triangles
Polygon Angle Sum
Triangle Angle Sum

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

Circles
Classifying Quadrilaterals
Concurrent Lines, Medians, and Altitudes
Congruence in Right Triangles
Distance Formula
Isosceles and Equilateral Triangles
Parallelogram Conditions
Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Rock Art (Transformations)
Similar Figures
Similarity in Right Triangles
Special Parallelograms
Surface and Lateral Areas of Pyramids and Cones
Triangle Angle Sum
Triangle Inequalities

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

Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

GM.15: use the properties of faces, surfaces, edges and vertices of cubes, cuboids, prisms, cylinders, pyramids, cones and spheres to solve problems in 3-D

Surface and Lateral Areas of Pyramids and Cones

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

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

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

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

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

Compound Inequalities

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

Geometric Probability
Independent and Dependent Events
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
Mean, Median, and Mode
Reaction Time 1 (Graphs and Statistics)
Real-Time Histogram
Sight vs. Sound Reactions
Stem-and-Leaf Plots

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

Elevator Operator (Line Graphs)
Histograms
Mascot Election (Pictographs and Bar Graphs)
Reaction Time 1 (Graphs and Statistics)
Reaction Time 2 (Graphs and Statistics)
Stem-and-Leaf Plots