Mathematics

Unit 1: Number and operation

Duration

11 Weeks

Learner Profile Attributes

• Knowledgeable.
• Thinkers

Key Concept

• Form

Related Concept(s)

• Representation Systems

Global Context

• Orientation in Space and Time

Statement of Inquiry

Different systems and forms of representation develop as civilisations evolve and humans interact.

Summative Assessment Criteria

• Criterion A
• Criterion B

ATLs (Skills)

• S – Listen actively to other perspectives and ideas
• SM – Plan short and long term assignments; meet deadlines

Curriculum Standards

• B1.1 Rational Numbers read and represent whole numbers up to and including one million, using appropriate tools and strategies, and describe various ways they are used in everyday life.
• B1.2 Rational Numbers read and represent integers, using a variety of tools and strategies, including horizontal and vertical number lines.
• B1.3 Rational Numbers compare and order integers, decimal numbers, and fractions, separately and in combination, in various contexts.
• B1.4 Fractions, Decimals, and Percents read, represent, compare, and order decimal numbers up to thousandths, in various contexts.
• B1.5 Fractions, Decimals, and Percents round decimal numbers, both terminating and repeating, to the nearest tenth, hundredth, or whole number, as applicable, in various contexts.
• B1.6 Fractions, Decimals, and Percents describe relationships and show equivalences among fractions and decimal numbers up to thousandths, using appropriate tools and drawings, in various contexts.
• B2.1 Properties and Relationships use the properties of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and whole number percents, including those requiring multiple steps or multiple operations.
• B2.2 Math Facts understand the divisibility rules and use them to determine whether numbers are divisible by 2, 3, 4,5, 6, 8,9, and 10.
• B2.3 Mental Math use mental math strategies to calculate percents of whole numbers, including 1%, 5%, 10%, 15%, 25%, and 50%, and explain the strategies used.
• B2.4 Addition and Subtraction represent and solve problems involving the addition and subtraction of whole numbers and decimal numbers, using estimation and algorithms.
• B2.5 Addition and Subtraction add and subtract fractions with like and unlike denominators, using appropriate tools, in various contexts.
• B2.6 Multiplication and Division represent composite numbers as a product of their prime factors, including through the use of factor trees.
• B2.7 Multiplication and Division represent and solve problems involving the multiplication of three-digit whole numbers by decimal tenths, using algorithms.
• B2.8 Multiplication and Division represent and solve problems involving the division of three-digit whole numbers by decimal tenths, using appropriate tools, strategies, and algorithms, and expressing remainders as appropriate.
• B2.9 Multiplication and Division multiply whole numbers by proper fractions, using appropriate tools and strategies.
• B2.10 Multiplication and Division divide whole numbers by proper fractions, using appropriate tools and strategies.
• B2.11 Multiplication and Division represent and solve problems involving the division of decimal numbers up to thousandths by whole numbers up to 10, using appropriate tools and strategies.
• B2.12 Multiplication and Division solve problems involving ratios, including percents and rates, using appropriate tools and strategies.

Unit 2： Patterns and Equations

Duration

9 Weeks

Learner Profile Attributes

• Inquirers
• Thinkers

Key Concept

• Logic

Related Concept(s)

• Generalisation
• Models
• Patterns

Global Context

• Scientific and Technical Innovation

Statement of Inquiry

A logical process helps to model and generalise patterns in the natural world.

Summative Assessment Criteria

• Criterion C
• Criterion D

ATLs (Skills)

• SM – Consider content – What did I learn about today?
• SM – Consider content – What don’t I understand yet?
• SM – Consider content – What questions do I have now?
• T – Draw reasonable conclusions and generalizations

Curriculum Standards

• C1.1 Patterns identify and describe repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and specify which growing patterns are linear
• C1.2 Patterns create and translate repeating, growing, and shrinking patterns using various representations, including tables of values, graphs, and, for linear growing patterns, algebraic expressions and equations
• C1.3 Patterns determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns
• C1.4 Patterns create and describe patterns to illustrate relationships among whole numbers and decimal numbers
• C2.1 Variables and Expressions add monomials with a degree of 1 that involve whole numbers, using tools
• C2.2 Variables and Expressions evaluate algebraic expressions that involve whole numbers and decimal tenths
• C2.3 Equalities and Inequalities solve equations that involve multiple terms and whole numbers in various contexts, and verify solutions
• C2.4 Equalities and Inequalities solve inequalities that involve two operations and whole numbers up to 100, and verify and graph the solutions
• C3.1 Coding Skills solve problems and create computational representations of mathematical situations by writing and executing efficient code, including code that involves conditional statements and other control structures
• C3.2 Coding Skills read and alter existing code, including code that involves conditional statements and other control structures, and describe how changes to the code affect the outcomes and the efficiency of the code
• F. Financial Literacy

Unit 3： Geometry and Measurements

Duration

9 Weeks

Learner Profile Attributes

• Thinkers

Key Concept

• Form

Related Concept(s)

• Measurement

Global Context

• Personal and Cultural Expression

Statement of Inquiry

Artistry and creativity are enhanced through an understanding of how measurement helps to define forms.

Summative Assessment Criteria

• Criterion A
• Criterion B

ATLs (Skills)

• T – Design improvements to existing machines, media, and technologies
• T – Make connections between subject groups and disciplines

Curriculum Standards

• E1.1 Geometric Reasoning create lists of the geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry
• E1.2 Geometric Reasoning construct three-dimensional objects when given their top, front, and side views
• E1.3 Location and Movement plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another
• E1.4 Location and Movement describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations
• E2.1 The Metric System measure length, area, mass, and capacity using the appropriate metric units, and solve problems that require converting smaller units to larger ones and vice versa
• E2.2 Angles use a protractor to measure and construct angles up to 360°, and state the relationship between angles that are measured clockwise and those that are measured counterclockwise
• E2.3 Angles use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures
• E2.4 Area and Surface Area determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas
• E2.5 Area and Surface Area create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas
• E2.6 Area and Surface Area determine the surface areas of prisms and pyramids by calculating the areas of their two-dimensional faces and adding them together

Unit 4 ：Data Management

Duration

7 Weeks

Learner Profile Attributes

• Inquirers
• Thinkers

Key Concept

• Relationships

Related Concept(s)

• Representation
• Justification

Global Context

• Identities and Relationships

Statement of Inquiry

Being able to represent relationships effectively can help justify characteristics and trends in communities.

Summative Assessment Criteria

• Criterion C
• Criterion D

ATLs (Skills)

• R – Communicate information and ideas effectively to multiple audiences using a variety of media and formats
• T – Identify trends and forecast possibilities

Curriculum Standards

• D1.1 Data Collection and Organization describe the difference between discrete and continuous data, and provide examples of each
• D1.2 Data Collection and Organization collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals
• D1.3 Data Visualization select from among a variety of graphs, including histograms and broken-line graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs
• D1.4 Data Visualization create an infographic about a data set, representing the data in appropriate ways, including in tables, histograms, and broken-line graphs, and incorporating any other relevant information that helps to tell a story about the data
• D1.5 Data Analysis determine the range as a measure of spread and the measures of central tendency for various data sets, and use this information to compare two or more data setsD1.6 Data Analysis analyse different sets of data presented in various ways, including in histograms and broken-line graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisionsD2.1 Probability use fractions, decimals, and percents to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisionsD2.2 Probability determine and compare the theoretical and experimental probabilities of two independent events happening

Unit 1: Number: Human Explorations

Duration

9 Weeks

Learner Profile Attributes

• Inquirers
• Knowledgeable

Key Concept

• Form

Related Concept(s)

• Quantity
• Representation

Global Context

• Orientation in Space and Time

Statement of Inquiry

Being able to represent different forms of quantities has helped humans explore and describe our planet.

Summative Assessment Criteria

• Criterion A
• Criterion D

ATLs (Skills)

• T – Identify trends and forecast possibilities
• R – Use memory techniques to develop long term memory

Curriculum Standards

• B1.1 Rational Numbers represent and compare whole numbers up to and including one billion, including in expanded form using powers of ten, and describe various ways they are used in everyday life
• B1.2 Rational Numbers identify and represent perfect squares, and determine their square roots, in various contexts
• B1.3 Rational Numbers read, represent, compare, and order rational numbers, including positive and negative fractions and decimal numbers to thousandths, in various contexts
• B1.4 Fractions, Decimals, and Percents use equivalent fractions to simplify fractions, when appropriate, in various contexts
• B1.5 Fractions, Decimals, and Percents generate fractions and decimal numbers between any two quantities
• B1.6 Fractions, Decimals, and Percents round decimal numbers to the nearest tenth, hundredth, or whole number, as applicable, in various contexts
• B1.7 Fractions, Decimals, and Percents convert between fractions, decimal numbers, and percents, in various contexts
• B2.1 Properties and Relationships use the properties and order of operations, and the relationships between operations, to solve problems involving whole numbers, decimal numbers, fractions, ratios, rates, and percents, including those requiring multiple steps or multiple operations
• B2.2 Math Facts understand and recall commonly used percents, fractions, and decimal equivalents
• B2.3 Mental Math use mental math strategies to increase and decrease a whole number by 1%, 5%, 10%, 25%, 50%, and 100%, and explain the strategies used
• B2.4 Addition and Subtraction use objects, diagrams, and equations to represent, describe, and solve situations involving addition and subtraction of integers
• B2.5 Addition and Subtraction add and subtract fractions, including by creating equivalent fractions, in various contexts
• B2.6 Multiplication and Division determine the greatest common factor for a variety of whole numbers up to 144 and the lowest common multiple for two and three whole numbers
• B2.7 Multiplication and Division evaluate and express repeated multiplication of whole numbers using exponential notation, in various contexts
• B2.8 Multiplication and Division multiply and divide fractions by fractions, using tools in various contexts
• B2.9 Multiplication and Division multiply and divide decimal numbers by decimal numbers, in various contexts
• B2.10 Multiplication and Division identify proportional and non-proportional situations and apply proportional reasoning to solve problems

Unit 2: Algebraic Expressions and Equations

Duration

9 Weeks

Learner Profile Attributes

• Thinkers
• Balanced

Key Concept

• Form

Related Concept(s)

• Simplification
• Equivalence

Global Context

• Scientific and technical innovation

Statement of Inquiry

Producing equivalent forms through simplification can help to clarify, solve, and create puzzles and tricks.

Summative Assessment Criteria

• Criterion B
• Criterion C

ATLs (Skills)

• C – Make inferences and draw conclusions
• T – Apply existing knowledge to generate new ideas, products or processes

Curriculum Standards

• C1.1 Patterns identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing patterns on the basis of their constant rates and initial values
• C1.2 Patterns create and translate repeating, growing, and shrinking patterns involving whole numbers and decimal numbers using various representations, including algebraic expressions and equations for linear growing patterns
• C1.3 Patterns determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in repeating, growing, and shrinking patterns involving whole numbers and decimal numbers, and use algebraic representations of the pattern rules to solve for unknown values in linear growing patterns
• C1.4 Patterns create and describe patterns to illustrate relationships among integers
• C2.1 Variables and Expressions add and subtract monomials with a degree of 1 that involve whole numbers, using tools
• C2.2 Variables and Expressions evaluate algebraic expressions that involve whole numbers and decimal numbers
• C2.3 Equalities and Inequalities solve equations that involve multiple terms, whole numbers, and decimal numbers in various contexts, and verify solutions
• C2.4 Equalities and Inequalities solve inequalities that involve multiple terms and whole numbers, and verify and graph the solutions
• C3.1 Coding Skills solve problems and create computational representations of mathematical situations by writing and executing efficient code, including code that involves events influenced by a defined count and/or sub-program and other control structures
• C3.2 Coding Skills read and alter existing code, including code that involves events influenced by a defined count and/or sub-program and other control structures, and describe how changes to the code affect the outcomes and the efficiency of the code

Unit 3: 2D and 3D Geometry

Duration

9 Weeks

Learner Profile Attributes

• Communicators
• Reflective

Key Concept

• Relationships

Related Concept(s)

• Generalisation
• Measurement

Global Context

• Orientation in Space and Time

Statement of Inquiry

Generalising relationships between measurements can help explore the formation of human and natural landscapes.

Summative Assessment Criteria

• Criterion A
• Criterion B

ATLs (Skills)

• T – Apply skills and knowledge in unfamiliar situations
• C – Make effective summary notes for studying

Curriculum Standards

• E1.1 Geometric Reasoning describe and classify cylinders, pyramids, and prisms according to their geometric properties, including plane and rotational symmetry
• E1.2 Geometric Reasoning draw top, front, and side views, as well as perspective views, of objects and physical spaces, using appropriate scales
• E1.3 Location and Movement perform dilations and describe the similarity between the image and the original shape
• E1.4 Location and Movement describe and perform translations, reflections, and rotations on a Cartesian plane, and predict the results of these transformations
• E2.1 The Metric System describe the differences and similarities between volume and capacity, and apply the relationship between millilitres (mL) and cubic centimetres (cm³) to solve problems
• E2.2 The Metric System solve problems involving perimeter, area, and volume that require converting from one metric unit of measurement to another
• E2.3 Circles use the relationships between the radius, diameter, and circumference of a circle to explain the formula for finding the circumference and to solve related problems
• E2.4 Circles construct circles when given the radius, diameter, or circumference
• E2.5 Circles show the relationships between the radius, diameter, and area of a circle, and use these relationships to explain the formula for measuring the area of a circle and to solve related problems
• E2.6 Volume and Surface Area represent cylinders as nets and determine their surface area by adding the areas of their parts
• E2.7 Volume and Surface Area show that the volume of a prism or cylinder can be determined by multiplying the area of its base by its height, and apply this relationship to find the area of the base, volume, and height of prisms and cylinders when given two of the three measurements

Unit 4: Data and Probability

Duration

9 Weeks

Learner Profile Attributes

• Thinkers
• Communicators

Key Concept

• Logic

Related Concept(s)

• Models
• Quantity

Global Context

• Identities and Relationships

Statement of Inquiry

Modeling the relationship between quantities can help us make informed decisions.

Summative Assessment Criteria

• Criterion C
• Criterion D

ATLs (Skills)

• T – Evaluate and manage risks
• C – Organize and depict information logically

Curriculum Standards

• D1.1 Data Collection and Organization identify situations involving one-variable data and situations involving two-variable data, and explain when each type of data is needed.
• D1.2 Data Collection and Organization collect continuous data to answer questions of interest involving two variables, and organize the data sets as appropriate in a table of values.
• D1.3 Data Visualization select from among a variety of graphs, including scatter plots, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs.
• D1.4 Data Visualization create an infographic about a data set, representing the data in appropriate ways, including in tables and scatter plots, and incorporating any other relevant information that helps to tell a story about the data.
• D1.5 Data Analysis use mathematical language, including the terms “strong”, “weak”, “none”, “positive”, and “negative”, to describe the relationship between two variables for various data sets with and without outliers.
• D1.6 Data Analysis analyze different sets of data presented in various ways, including in scatter plots and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions.
• D2.1 Probability solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams.
• D2.2 Probability determine and compare the theoretical and experimental probabilities of multiple independent events happening and of multiple dependent events happening.

Unit 1: Number and operation

Duration

9 Weeks

Learner Profile Attributes

• Thinkers
• Communicators

Key Concept

• Form

Related Concept(s)

• Quantity
• Representation
• Simplification

Global Context

• Orientation in Space and Time

Statement of Inquiry

Representing and simplifying quantities in different forms can help explore discoveries and developments.

Summative Assessment Criteria

• Criterion A
• Criterion D

ATLs (Skills)

• T – Make connections between subject groups and disciplines
• C – Make inferences and draw conclusions

Curriculum Standards

• B1.1 Rational and Irrational Numbers represent and compare very large and very small numbers, including through the use of scientific notation, and describe various ways they are used in everyday life.
• B1.2 Rational and Irrational Numbers describe, compare, and order numbers in the real number system (rational and irrational numbers), separately and in combination, in various contexts.
• B1.3 Rational and Irrational Numbers estimate and calculate square roots, in various contexts.
• B1.4 Fractions, Decimals, and Percents use fractions, decimal numbers, and percents, including percents of more than 100% or less than 1%, interchangeably and flexibly to solve a variety of problems.
• B2.1 Properties and Relationships use the properties and order of operations, and the relationships between operations, to solve problems involving rational numbers, ratios, rates, and percents, including those requiring multiple steps or multiple operations.
• B2.2 Math Facts understand and recall commonly used square numbers and their square roots.
• B2.3 Mental Math use mental math strategies to multiply and divide whole numbers and decimal numbers up to thousandths by powers of ten, and explain the strategies used.
• B2.4 Addition and Subtraction add and subtract integers, using appropriate strategies, in various contexts.
• B2.5 Addition and Subtraction add and subtract fractions, using appropriate strategies, in various contexts.
• B2.6 Multiplication and Division multiply and divide fractions by fractions, as well as by whole numbers and mixed numbers, in various contexts.
• B2.7 Multiplication and Division multiply and divide integers, using appropriate strategies, in various contexts.
• B2.8 Multiplication and Division compare proportional situations and determine unknown values in proportional situations, and apply proportional reasoning to solve problems in various contexts.

Unit 2: Patterns & equations

Duration

9 Weeks

Learner Profile Attributes

• Knowledgeable
• Thinkers

Key Concept

• Relationships

Related Concept(s)

• Change
• Models
• Representations

Global Context

• Globalisation and Sustainability

Statement of Inquiry

Representing patterns of change as relationships can help determine the impact of human decision-making on the environment.

Summative Assessment Criteria

• Criterion B
• Criterion C
• Criterion D

ATLs (Skills)

• T – Identify trends and forecast possibilities
• R – Locate, organize, analyze, synthesize, and ethically use information from a variety of courses and media (including digital social media and online networks)

Curriculum Standards

• C1.1 Patterns identify and compare a variety of repeating, growing, and shrinking patterns, including patterns found in real-life contexts, and compare linear growing and shrinking patterns on the basis of their constant rates and initial values.
• C1.2 Patterns create and translate repeating, growing, and shrinking patterns involving rational numbers using various representations, including algebraic expressions and equations for linear growing and shrinking patterns.
• C1.3 Patterns determine pattern rules and use them to extend patterns, make and justify predictions, and identify missing elements in growing and shrinking patterns involving rational numbers, and use algebraic representations of the pattern rules to solve for unknown values in linear growing and shrinking patterns.
• C1.4 Patterns create and describe patterns to illustrate relationships among rational numbers.
• C2.1 Variables and Expressions add and subtract monomials with a degree of 1, and add binomials with a degree of 1 that involve integers, using tools.
• C2.2 Variables and Expressions evaluate algebraic expressions that involve rational numbers.
• C2.3 Equalities and Inequalities solve equations that involve multiple terms, integers, and decimal numbers in various contexts, and verify solutions.
• C2.4 Equalities and Inequalities solve inequalities that involve integers, and verify and graph the solutions.
• C3.1 Coding Skills solve problems and create computational representations of mathematical situations by writing and executing code, including code that involves the analysis of data in order to inform and communicate decisions.
• C3.2 Coding Skills read and alter existing code involving the analysis of data in order to inform and communicate decisions, and describe how changes to the code affect the outcomes and the efficiency of the code.

Unit 3: Geometry and Measurement

Duration

9 Weeks

Learner Profile Attributes

• Thinkers

Key Concept

• Form

Related Concept(s)

• Measurement

Global Context

• Personal and Cultural Expression

Statement of Inquiry

Artistry and creativity are enhanced through an understanding of how measurement helps to define forms.

Summative Assessment Criteria

• Criterion A
• Criterion B

ATLs (Skills)

• T – Design improvements to existing machines, media, and technologies
• T – Make connections between subject groups and disciplines

Curriculum Standards

• E1.1 Geometric Reasoning: Create lists of the geometric properties of various types of quadrilaterals, including the properties of the diagonals, rotational symmetry, and line symmetry.
• E1.2 Geometric Reasoning: Construct three-dimensional objects when given their top, front, and side views.
• E1.3 Location and Movement: Plot and read coordinates in all four quadrants of a Cartesian plane, and describe the translations that move a point from one coordinate to another.
• E1.4 Location and Movement: Describe and perform combinations of translations, reflections, and rotations up to 360° on a grid, and predict the results of these transformations.
• E2.1 The Metric System: Measure length, area, mass, and capacity using the appropriate metric units, and solve problems that require converting smaller units to larger ones and vice versa.
• E2.2 Angles: Use a protractor to measure and construct angles up to 360°, and state the relationship between angles that are measured clockwise and those that are measured counterclockwise.
• E2.3 Angles: Use the properties of supplementary angles, complementary angles, opposite angles, and interior and exterior angles to solve for unknown angle measures.
• E2.4 Area and Surface Area: Determine the areas of trapezoids, rhombuses, kites, and composite polygons by decomposing them into shapes with known areas.
• E2.5 Area and Surface Area: Create and use nets to demonstrate the relationship between the faces of prisms and pyramids and their surface areas.
• E2.6 Area and Surface Area: Determine the surface areas of prisms and pyramids by calculating the areas of their two-dimensional faces and adding them together.

Unit 4: Data Management

Duration

7 Weeks

Learner Profile Attributes

• Inquirers
• Thinkers

Key Concept

• Relationships

Related Concept(s)

• Representation
• Justification

Global Context

• Identities and Relationships

Statement of Inquiry

Being able to represent relationships effectively can help justify characteristics and trends in communities.

Summative Assessment Criteria

• Criterion C
• Criterion D

ATLs (Skills)

• R – Communicate information and ideas effectively to multiple audiences using a variety of media and formats
• T – Identify trends and forecast possibilities

Curriculum Standards

• D1.1 Data Collection and Organization: Describe the difference between discrete and continuous data, and provide examples of each.
• D1.2 Data Collection and Organization: Collect qualitative data and discrete and continuous quantitative data to answer questions of interest about a population, and organize the sets of data as appropriate, including using intervals.
• D1.3 Data Visualization: Select from among a variety of graphs, including histograms and broken-line graphs, the type of graph best suited to represent various sets of data; display the data in the graphs with proper sources, titles, and labels, and appropriate scales; and justify their choice of graphs.
• D1.4 Data Visualization: Create an infographic about a data set, representing the data in appropriate ways, including in tables, histograms, and broken-line graphs, and incorporating any other relevant information that helps to tell a story about the data.
• D1.5 Data Analysis: Determine the range as a measure of spread and the measures of central tendency for various data sets, and use this information to compare two or more data sets.
• D1.6 Data Analysis: Analyze different sets of data presented in various ways, including in histograms and broken-line graphs and in misleading graphs, by asking and answering questions about the data, challenging preconceived notions, and drawing conclusions, then make convincing arguments and informed decisions.
• D2.1 Probability solve various problems that involve probability, using appropriate tools and strategies, including Venn and tree diagrams
• D2.2 Probability determine and compare the theoretical and experimental probabilities of multiple independent events happening and of multiple dependent events happening

Unit 1: Number Sense

Duration

14 Weeks

Learner Profile Attributes

• Thinkers
• Communicators

Key Concept

• Logic

Related Concept(s)

• Approximation
• Quantity
• Representation
• Simplification

Global Context

• Scientific and Technical Innovation

Statement of Inquiry

• Representing numbers in different forms to simplify them can help us to understand human-made systems.

Summative Assessment Criteria

• Criterion A
• Criterion B
• Criterion C
• Criterion D

ATLs (Skills)

• C – Use appropriate forms of writing for different purposes and audiences
• SM – Use appropriate strategies for organizing complex information
• T – Apply skills and knowledge in unfamiliar situations

Curriculum Standards

• SL & EL
  – substitute into and evaluate algebraic expressions involving exponents
  – describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three
  – derive, through the investigation and examination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents;
  – extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents
  – simplify numerical expressions involving integers and rational numbers, with and without the use of technology;*
  – solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion;*
  – relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations;
  – add and subtract polynomials with up to two variables , using a variety of tools;
  – multiply a polynomial by a monomial involving the same variable, using a variety of tools;
  – expand and simplify polynomial expressions involving one variable, using a variety of tools;
  – solve first-degree equations, including equations with fractional coefficients, using a variety of tools and strategies;
  – rearrange formulas involving variables in the first degree, with and without substitution;
  – solve problems that can be modelled with first-degree equations, and compare algebraic methods to other solution methods.
  Logarithms
  1.     Convert between exponential and logarithmic form: rational bases
  2.     Evaluate logarithms
  3.     Change of base formula
  4.     Identify properties of logarithms
  5.     Product property of logarithms
  6.     Quotient property of logarithms
  7.     Power property of logarithms
  Financial Literacy: F2
  1.     Describe linear and exponential growth and decay
  2.     Exponential growth and decay: word problems
  3.     Compound interest: word problems
  4.     Continuously compounded interest: word problems

Unit 2: Statistics – A Whole Range of Things

Duration

8 Weeks

Learner Profile Attributes

• Thinkers
• Inquirers

Key Concept

• Relationships

Related Concept(s)

• Representation
• Quantity

Global Context

• Globalisation and Sustainability

Statement of Inquiry

• How quantities are represented can help to establish underlying relations and trends in the population.

Summative Assessment Criteria

• Criterion A
• Criterion C
• Criterion D

ATLs (Skills)

• S – Practice empathy
• S – Building consensus
• S – Make fair and equitable decisions
• R – Collect, record and verify data
• R – Make connections between various sources of information

Curriculum Standards:

• All Data strands – D Linear Relations
  – interpret the meanings of points on scatter plots or graphs that represent linear relations, including scatter plots or graphs in more than one quadrant ;
  – pose problems, identify variables, and formulate hypotheses associated with relationships between two variables;
  – design and carry out an investigation or experiment involving relationships between two variables, including the collection and organization of data, using appropriate methods, equipment, and/or technology and techniques;
  – describe trends and relationships observed in data, make inferences from data, compare the inferences with hypotheses about the data, and explain any differences between the inferences and the hypotheses
  – construct tables of values, graphs, and equations, using a variety of tools, to represent linear relations derived from descriptions of realistic situations
  – construct tables of values, scatter plots, and lines or curves of best fit as appropriate, using a variety of tools, for linearly related and non-linearly related data collected from a variety of sources;
  – identify, through investigation, some properties of linear relations,and apply these properties to determine whether a relation is linear or non-linear;
  – compare the properties of direct variation and partial variation in applications, and identify the initial value
  – determine the equation of a line of best fit for a scatter plot, using an informal process
  – determine values of a linear relation by using a table of values, by using the equation of the relation, and by interpolating or extrapolating from the graph of the relation
  – describe a situation that would explain the events illustrated by a given graph of a relationship between two variables
  – determine other representations of a linear relation, given one representation
  – describe the effects on a linear graph and make the corresponding changes to the linear equation when the conditions of the situation they represent are varied

Unit 3: Geometry and Measurement

Duration

7 Weeks

Learner Profile Attributes

• Caring

Key Concept:

• Form

Related Concept(s)

• Models
• Space

Global Context

• Orientation in Space and Time

Statement of Inquiry

• Representing transformed objects and studying their form helps enjoy their creativity in space.

Summative Assessment Criteria

• Criterion A
• Criterion B

ATLs (Skills):

• C – Understand and use mathematical notation
• T – Create novel solutions to complex problems
• T – Apply existing knowledge to generate new ideas, products or processes

Curriculum Standards

• All Geometry and Measurment E
  Analytic Geometry
  – determine, through investigation, the characteristics that distinguish the equation of a straight line from the equations of nonlinear relations
  – identify, through investigation, the equation of a line in any of the forms y = mx + b, Ax + By + C = 0, x = a, y = b;
  – express the equation of a line in the form y = mx + b, given the form Ax + By + C = 0
  – determine, through investigation, various formulas for the slope of a line segment or a line, and use the formulas to determine the slope of a line segment or a line;
  – identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b;
  – determine, through investigation, connections among the representations of a constant rate of change of a linear relation
  – identify, through investigation, properties of the slopes of lines and line segments, using graphing technology to facilitate investigations, where appropriate.
  – graph lines by hand, using a variety of techniques
  – determine the equation of a line from information about the line
  – describe the meaning of the slope and y-intercept for a linear relation arising from a realistic situation , and describe a situation that could be modelled by a given linear equation
  – identify and explain any restrictions on the variables in a linear relation arising from a realistic situation
  – determine graphically the point of intersection of two linear relations, and interpret the intersection point in the context of an application
  Measurement and Geometry
  – determine the maximum area of a rectangle with a given perimeter by constructing a variety of rectangles, using a variety of tools, and by examining various values of the area as the side lengths change and the perimeter remains constant
  – determine the minimum perimeter of a rectangle with a given area by constructing a variety of rectangles, using a variety of tools, and by examining various values of the side lengths and the perimeter as the area stays constant;
  – identify, through investigation with a variety of tools, the effect of varying the dimensions on the surface area [or volume] of square-based prisms and cylinders, given a fixed volume [or surface area];
  – explain the significance of optimal area, surface area, or volume in various applications;
  – pose and solve problems involving maximization and minimization of measurements of geometric shapes and figures
  – relate the geometric representation of the Pythagorean theorem and the algebraic representation a2 + b2 = c2;
  – solve problems using the Pythagorean theorem, as required in applications;
  – solve problems involving the areas and perimeters of composite two-dimensional shapes;
  – develop, through investigation, the formulas for the volume of a pyramid, a cone, and a sphere
  – determine, through investigation, the relationship for calculating the surface area of a pyramid
  – solve problems involving the surface areas and volumes of prisms, pyramids, cylinders, cones, and spheres, including composite figures
  – determine, through investigation using a variety of tools, and describe the properties and relationships of the interior and exterior angles of triangles, quadrilaterals, and other polygons, and apply the results to problems involving the angles of polygons
  – determine, through investigation using a variety of tools, and describe some properties of polygons, and apply the results in problem solving;
  – pose questions about geometric relationships, investigate them, and present their findings, using a variety of mathematical forms
  – illustrate a statement about a geometric property by demonstrating the statement with multiple examples, or deny the statement on the basis of a counter-example, with or without the use of dynamic geometry software
  Geometry and Measurement: E2
  1.     Convert between radians and degrees
  2.     Radians and arc length
  3.     Quadrants
  4.     Coterminal and reference angles
  5.     Find trigonometric ratios using right triangles
  6.     Find trigonometric ratios using the unit circle
  7.     Find trigonometric ratios using reference angles

Unit 4: How to Use Algebraic Expressions to Generalise Relationships

Duration

7 Weeks

Learner Profile Attributes

• Knowledgeable
• Reflective

Key Concept

• Relationships

Related Concept(s)

• Equivalence
• Pattern
• Representation

Global Context

• Scientific and Technical Innovation

Statement of Inquiry

• Discovering relationships in patterns and studying equivalence between representations can lead to better models.

Summative Assessment Criteria

• Criterion A
• Criterion C

ATLs (Skills)

• C – Organize and depict information logically
• T – Gather and organize relevant information to formulate an argument

Curriculum Standards

– substitute into and evaluate algebraic expressions involving exponents.
– describe the relationship between the algebraic and geometric representations of a single-variable term up to degree three.
–  derive, through the investigation and exam- ination of patterns, the exponent rules for multiplying and dividing monomials, and apply these rules in expressions involving one and two variables with positive exponents.
– extend the multiplication rule to derive and understand the power of a power rule, and apply it to simplify expressions involving one and two variables with positive exponents.
–  simplify numerical expressions involving integers and rational numbers, with and without the use of technology
– solve problems requiring the manipulation of expressions arising from applications of percent, ratio, rate, and proportion
– relate their understanding of inverse operations to squaring and taking the square root, and apply inverse operations to simplify expressions and solve equations.
– add and subtract polynomials with up to two variables
– multiply a polynomial by a monomial involving the same variable
– expand and simplify polynomial expressions involving one variable
– solve first-degree equations, including equations with fractional coefficients, using a variety of tools
– rearrange formulas involving variables in the first degree, with and without substi- tution
– solve problems that can be modelled with first-degree equations, and compare alge- braic methods to other solution methods
Factorization: C5
1.     Factor monomials
2.     Factor quadratics
3.     Factor quadratics using algebra tiles
4.     Factor using a quadratic pattern
5.     Factor by grouping
6.     Factor sums and differences of cubes
7.     Factor polynomials
Sequences and Series: C6
1.     Find terms of a sequence
2.     Find terms of a recursive sequence
3.     Identify a sequence as explicit or recursive
4.     Find a recursive formula
5.     Find recursive and explicit formulas
6.     Convert a recursive formula to an explicit formula
7.     Convert an explicit formula to a recursive formula
8.     Convert between explicit and recursive formulas
9.     Introduction to sigma notation
10.  Identify arithmetic and geometric series
11.  Find the sum of a finite arithmetic or geometric series
12.  Introduction to partial sums
13.  Partial sums of arithmetic series
14.  Partial sums of geometric series
15.  Convergent and divergent geometric series
16.  Find the value of an infinite geometric series

Unit 1: How Do I Show That? An Introduction to Functions

Duration

13 Weeks

Learner Profile Attributes

• Inquirers

Key Concept

• Form

Related Concept(s)

• Representation
• Systems

Global Context

• Scientific and Technical Innovation (systems, models)

Statement of Inquiry

• Different forms of representation can explain how technological advances affect society.

Summative Assessment Criteria

• Criterion A
• Criterion B
• Criterion C
• Criterion D

ATLs (Skills)

• SM – Plan short and long term assignments, meet deadlines:
• R – Make connections between various sources of information:
• R – Create references and citations:
• T – Draw reasonable conclusions and generalisations:
• T – Create original works and ideas; use existing works and ideas in new ways

Curriculum Standards:

• Rational Functions:
  1. Rational functions: asymptotes and excluded values
  2. Solve rational equations
  3. Check whether two rational functions are inverse
• Exponential and Logarithmic Functions HL:
  1. Domain and range of exponential and logarithmic functions
  2. Evaluate exponential functions
  3. Match exponential functions and graphs
  4. Solve exponential equations by rewriting the base
  5. Solve exponential equations using common logarithms
  6. Solve logarithmic equations I
  7. Solve logarithmic equations II
  8. Identify linear and exponential functions
  9. Exponential functions over unit intervals
• Trigonometric Functions HL:
  1. Find properties of sine functions
  2. Write equations of sine functions from graphs
  3. Write equations of sine functions using properties
  4. Graph sine functions
  5. Find properties of cosine functions
  6. Write equations of cosine functions from graphs
  7. Write equations of cosine functions using properties
  8. Graph cosine functions
  9. Graph sine and cosine functions
• Quadratic Relations of the Form y = ax² + bx + c:
  1. Collect data that can be represented as a quadratic relation, from experiments using appropriate equipment and technology, or from secondary sources; graph the data and draw a curve of best fit, if appropriate, with or without the use of technology.
  2. Determine, through investigation with and without the use of technology, that a quadratic relation of the form y = ax² + bx + c (a ≠ 0) can be graphically represented as a parabola, and that the table of values yields a constant second difference.
  3. Identify the key features of a graph of a parabola, and use the appropriate terminology to describe them.
  4. Compare, through investigation using technology, the features of the graph of y = x² and the graph of y = 2^x, and determine the meaning of a negative exponent and of zero as an exponent.
  5. Identify, through investigation using technology, the effect on the graph of y = x² of transformation.
  6. Explain the roles of a, h, and k in y = a(x – h)² + k, using the appropriate terminology to describe the transformations, and identify the vertex and the equation of the axis of symmetry.
  7. Sketch, by hand, the graph of y = a(x – h)² + k by applying transformations to the graph of y = x².
  8. Determine the equation, in the form y = a(x – h)² + k, of a given graph of a parabola.
  9. Expand and simplify second-degree polynomial expressions, using a variety of tools and strategies.
  10. Factor polynomial expressions involving common factors, trinomials, and differences of squares, using a variety of tools and strategies.
  11. Determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts of the graph of the corresponding quadratic relation, expressed in the form y = a(x – r)(x – s).
  12. Interpret real and non-real roots of quadratic equations, through investigation using graphing technology, and relate the roots to the x-intercepts of the corresponding relations.
  13. Express y = ax² + bx + c in the form y = a(x – h)² + k by completing the square in situations involving no fractions, using a variety of tools.
  14. Sketch or graph a quadratic relation whose equation is given in the form y = ax² + bx + c, using a variety of methods.
  15. Explore the algebraic development of the quadratic formula.
  16. Solve quadratic equations that have real roots, using a variety of methods.
  17. Determine the zeros and the maximum or minimum value of a quadratic relation from its graph or from its defining equation.
  18. Solve problems arising from a realistic situation represented by a graph or an equation of a quadratic relation, with and without the use of technology.

Unit 2: How Do They Measure Up? Geometry & Trigonometry

Duration

10 Weeks

Learner Profile Attributes

• Thinkers

Key Concept

• Logic

Related Concept(s)

• Space
• Generalization

Global Context

• Personal and Cultural Expression: Beauty

Statement of Inquiry

• Logic can guide us from approximation to generalization and increase our appreciation of the aesthetic.

Summative Assessment Criteria

• Criterion A
• Criterion B

ATLs (Skills)

• T – Apply existing knowledge to generate new ideas, products or processes:
• T – Consider ideas from multiple perspectives:
• T – Analyse complex concepts and projects into their constituent parts and synthesize them to create new understanding

Curriculum Standards

• Trigonometry
  – verify, through investigation, the properties of similar triangles
  – describe and compare the concepts of similarity and congruence;
  – solve problems involving similar triangles in realistic situations
  – determine, through investigation, the relationship between the ratio of two sides in a right triangle and the ratio of the two corresponding sides in a similar right triangle, and define the sine, cosine, and tangent ratios
  – determine the measures of the sides and angles in right triangles, using the primary trigonometric ratios and the Pythagorean theorem;
  – solve problems involving the measures of sides and angles in right triangles in reallife applications, using the primary trigonometric ratios and the Pythagorean theorem.
  – explore the development of the sine law within acute triangles
  – explore the development of the cosine law within acute triangles
  – determine the measures of sides and angles in acute triangles, using the sine law and the cosine law
  – solve problems involving the measures of sides and angles in acute triangles.

Unit 3: A World of Difference: Function Transformations (IDU Science & I&S)

Duration

8 Weeks

Learner Profile Attributes

• Thinkers

Key Concept

• Relationships

Related Concept(s)

• Patterns
• Validity

Global Context

• Orientation in Space and Time (Civilization and Social Histories, Natural and Human Landscapes and Resources)

Statement of Inquiry

• Change over time can create significant impact on sustainability and relationships between quantities.

Summative Assessment Criteria

• IDU Criteria
• Criterion C
• Criterion D

ATLs (Skills)

• C – Understand and use mathematical notation
• T – Propose and evaluate a variety of solutions
• T – Identify obstacles and challenges
• T – Identify trends and forecast possibilities

Curriculum Standards

• Transformations:
  1. Translations: graphing the image
  2. Translations: find the coordinates
  3. Translations: writing the formula
  4. Reflections: graphing the image
  5. Reflections: finding the coordinates
  6. Rotations: graphing the image
  7. Rotations: finding the coordinates
  8. Classifying congruence transformations
  9. Compositions of congruence transformations
  10. Dilations: graphing the image
  11. Dilations: scale factors
  12. Dilations and parallel lines
• Two-dimensional vectors (EL):
  1. Find the magnitude of a vector
  2. Find the direction angle of a vector
  3. Find the component form of a vector
  4. Find the component form of a vector from its magnitude and direction angle
  5. Find a unit vector
  6. Add and subtract vectors
  7. Multiply a vector by a scalar
  8. Find the magnitude or direction of a vector scalar multiple
  9. Find the magnitude and direction of a vector sum
  10. Linear combinations of vectors
  11. Graph a resultant vector using the triangle method
  12. Graph a resultant vector using the parallelogram method

Unit 4: What Are the Chances? Probability

Duration

6 Weeks

Learner Profile Attributes

• Thinkers

Key Concept

• Logic

Related Concept(s)

• Models
• Approximation

Global Context

• Globalization and sustainability: consumption, conservation, scarcity

Statement of Inquiry

• Probabilistic models can approximate real-world consumption patterns and models.

Summative Assessment Criteria

• Criterion A (if time permits)

ATLs (Skills)

• R – Collect, record and verify data:
• R – Access information to be informed and inform others:
• T – Interpret data:
• T – Evaluate and manage risk

Curriculum Standards

• Probability:
  1. Introduction to probability
  2. Calculate probabilities of events
  3. Combinations and permutations (EL)
  4. Find probabilities using combinations and permutations (EL)
  5. Find probabilities using two-way frequency tables
  6. Identify independent events
  7. Find conditional probabilities (EL)
  8. Independence and conditional probability
  9. Find conditional probabilities using two-way frequency tables
  10. Find probabilities using the addition rule