Math

Factors, fractions, decimals

Ratios, Rates, Percents

Expressions and Equations

Area, Surface Area, volume

Integers, number lines, coordinate planes

Statistical measures and Data Displays

Relationships:
Relationships allow students to identify and understand connections and associations between properties, objects, people and ideas- including the human community's connection with the world in which we live. Any change in relationships brings consequences-some of which may occur  on a small scale, while others may be far reaching, affecting large systems like human societies and the planet as a whole.

Relationships in MYP mathematics refers to the connections between quantities, properties or concepts and these connections may be expressed as models, rules or statements.

Relationships provide opportunities for students to explore patterns in the world around them. Connections between the student and mathematics in the real world are important developing deeper understanding.
 

Relationships:
Relationships allow students to identify and understand connections and associations between properties, objects, people and ideas- including the human community's connection with the world in which we live. Any change in relationships brings consequences-some of which may occur  on a small scale, while others may be far reaching, affecting large systems like human societies and the planet as a whole.

Relationships in MYP mathematics refers to the connections between quantities, properties or concepts and these connections may be expressed as models, rules or statements.

Relationships provide opportunities for students to explore patterns in the world around them. Connections between the student and mathematics in the real world are important developing deeper understanding.

Logic:
Logic is a method of reasoning and a system of principles used to build arguments and reach conclusions.

Logic in MYP mathematics is used as a process in making decisions about numbers, shapes, and variables. This system of reasoning provides students with a method for explaining the validity of their conclusions. Within the MYP, this should not be confused with the subfield of mathematics called symbolic logic.

Form:
Form is the shape and underlying structure of an entity or piece of work, including its organization, essential nature and external appearance. 

Form in MYP mathematics refers to the understanding that the underlying structure and shape of an entity is distinguished by its properties. Form provides opportunities for students to appreciate the aesthitic nature of the constructs used in a discipline.

Logic:
Logic is a method of reasoning and a system of principles used to build arguments and reach conclusions.

Logic in MYP mathematics is used as a process in making decisions about numbers, shapes, and variables. This system of reasoning provides students with a method for explaining the validity of their conclusions. Within the MYP, this should not be confused with the subfield of mathematics called symbolic logic.

Logic:
Logic is a method of reasoning and a system of principles used to build arguments and reach conclusions.

Logic in MYP mathematics is used as a process in making decisions about numbers, shapes, and variables. This system of reasoning provides students with a method for explaining the validity of their conclusions. Within the MYP, this should not be confused with the subfield of mathematics called symbolic logic.

Systems and simplification

Equivalence and models

Equivalence and justification

Models and space

Measurement and Quantity

Representation and Justification

Scientific and Technical Innovation

How do we understand the world in which we live? 

Students will explore the natural world and its laws; the interaction between people and the  natural world; how humans use their  understanding of scientific principles; the impact of scientific and technological advances on communities and environments; the impact of environments on human activity; how humans adapt environments to their needs.

Fairness and Development

What are the consequences of our common humanity?

Students will explore rights and responsibilities; the relationship between communities; sharing finite resources with other people and with other living things; access to equal opportunities; peace and conflict resolution

Possible explorations to develop

• Inequality, difference and inclusion

Scientific and Technical innovation

How do we understand the world in which we live? 

Students will explore the natural world and its laws; the interaction between people and the natural world; how humans use their understanding of scientific principles; the impact of scientific and technological advances on communities and environments; the impact of environments on human activity; how humans adapt environments to their needs

Identities and relationships

Who am I? Who are we?

Students will explore identity; beliefs and values; personal, physical, mental, social and spiritual health; human relationships including families, friends, communities and cultures; what it means to be human.

Possible explorations to develop 

• Competition and cooperation; teams, affiliation and leadership 

• Identity formation; self-esteem; status; roles and role models

Orientation of space and time

What is the meaning of “where” and “when”?

Students will explore personal histories; homes and journeys; turning points in humankind; discoveries; explorations and migrations of humankind; the relationships between, and the interconnectedness of, individuals and civilizations, from personal, local and global perspectives.

Possible exploration:

• Scale, duration, frequency and variability

Scientific and technical innovation

How do we understand the world in which we live?

Students will explore the natural world and its laws; the interaction between people and the natural world; how humans use their understanding of scientific principles; the impact of scientific and technological advances on communities and environments; the impact of environments on human activity; how humans adapt environments to their needs.

Possible explorations to develop 

• Systems, models, methods; products, processes and 

solutions 

• Adaptation, ingenuity and progress

A mindset for globalization and sustainability is found through modeling and representing mathematical relationships.

Equivalent values expressed as fractions, decimals and percentages can be used to describe connections between quantities.

Using algebraic logic to justify equivalence helps us explore the world or The relationship between values can be used as a representation to analyze possible outcomes.

Models in various forms show relationships in space

Logic can be used to measure orientation in a space

Representing data visually helps justify logical decisions

A. Knowing and understanding

i. select appropriate mathematics when solving problems in both familiar

and unfamiliar situations

ii. apply the selected mathematics successfully when solving problems

iii. solve problems correctly in a variety of contexts. 

D. Applying math to real life

i. identify relevant elements of authentic real-life situations 

ii. select appropriate mathematical strategies when solving authentic real life situations 

iii. apply the selected mathematical strategies successfully to reach a solution 

iv. justify the degree of accuracy of a solution 

v. justify whether a solution makes sense in the context of the authentic real life situation.

A. Knowing and understanding

i. select appropriate mathematics when solving problems in both familiar

and unfamiliar situations

ii. apply the selected mathematics successfully when solving problems

iii. solve problems correctly in a variety of contexts.

B: Investigating Patterns

i. select and apply mathematical problem-solving techniques to discover

complex patterns

ii. describe patterns as general rules consistent with findings

iii. prove, or verify and justify, general rules.

C: Communicating

Students are expected to use correct mathematical thinking, language, and representation when communicating mathematical ideas both orally and written.

i. use appropriate mathematical language (notation, symbols and terminology) in both oral and written explanations

ii. use appropriate forms of mathematical representation to present information

iii. move between different forms of mathematical representation

iv. communicate complete, coherent and concise mathematical lines of reasoning

v. organize information using a logical structure.

A: Knowing and understanding

i. select appropriate mathematics when solving problems in both familiar and unfamiliar situations

ii. apply the selected mathematics successfully when solving problems

iii. solve problems correctly in a variety of contexts.

D: Applying mathematics in real  life contexts

i. identify relevant elements of authentic real-life situations 

ii. select appropriate mathematical strategies when solving authentic real life situations 

iii. apply the selected mathematical strategies successfully to reach a solution 

iv. justify the degree of accuracy of a solution 

v. justify whether a solution makes sense in the context of the authentic real life situation.

A: Knowing and understanding

i. select appropriate mathematics when solving problems in both familiar and unfamiliar situations

ii. apply the selected mathematics successfully when solving problems

iii. solve problems correctly in a variety of contexts.

C: Communicating

i. use appropriate mathematical language (notation, symbols and terminology) in both oral and written explanations

ii. use appropriate forms of mathematical representation to present information

iii. move between different forms of mathematical representation

iv. communicate complete, coherent and concise mathematical lines of reasoning

v. organize information using a logical structure.

D:Applying mathematics in real life:

i. identify relevant elements of authentic real-life situations

ii. select appropriate mathematical strategies when solving authentic real life situations

iii. apply the selected mathematical strategies successfully to reach a solution

iv. justify the degree of accuracy of a solution

v. justify whether a solution makes sense in the context of the authentic real life situation.

Self management: in order for students to apply mathematics in real life contexts students must learn to manage their time and tasks effectively.

Social skills: Collaboration, working effectively with others

Self management skills: students must be able to identify strengths and weaknesses of personal learning strategies (self-assessment)

Communication: Communication Skills I: Reading, writing and using language to gather and communicate information.

Thinking: Creativity and Innovation

Social: Collaboration, working effectively with others.

Self Management: organization skills, managing

Thinking skills: transfer and critical thinking

Communication

Research Skills: students must learn about information literacy and media literacy.

Communication skills

Unit 1 - Operations with Rationals

Unit 2 - Linear Comparison

Unit 3 - Equations and Inequalities

Unit 5 - Percents, Proportions, and Statistics

Unit 6 - Geometric Modeling and Measurement

Relationships

Relationships are the connections and associations between properties, objects, people and ideas— including the human community’s connections with the world in which we live. Any change in relationship brings consequences—some of which may occur on a small scale, while others may be far reaching, affecting large networks and systems such as human societies and the planetary ecosystem. 

Relationships in MYP mathematics refer to the connections between quantities, properties or concepts and these connections may be expressed as models, rules or statements. Relationships provide opportunities for students to explore patterns in the world around them. Connections between the student and mathematics in the real world are important in developing deeper understanding.

Logic

Logic is a method of reasoning and a system of principles used to build arguments and reach conclusions. Logic in MYP mathematics is used as a process in making decisions about numbers, shapes, and variables. This system of reasoning provides students with a method for explaining the validity of their conclusions. Within the MYP, this should not be confused with the subfield of mathematics called “symbolic logic.”

Relationships

Relationships allow students to identify and understand connections and associations between properties, objects, people and ideas—including the human community’s connections with the world in which we live. Any change in relationships brings consequences—some of which may occur on a small scale, while others may be far-reaching, affecting large systems like human societies and the planet as a whole.

Relationships in MYP mathematics refers to the connections between quantities, properties or concepts and these connections may be expressed as models, rules or statements. Relationships provide opportunities for students to explore patterns in the world around them. Connections between the student and mathematics in the real world are important in developing deeper understanding.

Relationships

Relationships are the connections and associations between properties, objects, people and ideas—including the human community’s connections with the world in which we live. Any change in relationship brings consequences—some of which may occur on a small scale, while others may be far reaching, affecting large networks and systems such as human societies and the planetary ecosystem.

Relationships in MYP mathematics refers to the connections between quantities, properties or concepts and these connections may be expressed as models, rules or statements. Relationships provide opportunities for students to explore patterns in the world around them. Connections between the student and mathematics in the real world are important in developing deeper understanding.

Form

Form in MYP mathematics refers to the understanding that the underlying structure and shape of an entity is distinguished by its properties. Form provides opportunities for students to appreciate the aesthetic nature of the constructs used in a discipline.

Simplification: The process of reducing to a less complicated form.

Quantity: An amount or number

Equivalence

Quantity: An amount or number

Models: Depictions of a real-life event using expressions, equations, or graphs.

Representation: The manner in which something is presented. 

Validity: Using well-founded, logical mathematics to come to a true and accurate conclusion or a reasonable interpretation of results.

Measurement: a method of determining quantity, capacity, or dimension using a defined unit.

Space: the frame of geometrical dimensions describing an entity.

Scientific and technical innovation

How do we understand the worlds in which we live?

Students will explore the natural world and its laws; the interaction between people and the natural world; how humans use their understanding of scientific principles; the impact of scientific and technological advances on communities and environments; the impact of environments on human activity; how humans adapt environments to their needs.

Possible explorations to develop:

• systems, models, methods

Fairness and Development

What are the consequences of our common humanity?

Students will explore rights and responsibilities; the relationship between communities; sharing finite resources with other people and with other living things; access to equal opportunities; peace and conflict resolution

Possible explorations to develop

• Inequality, difference and inclusion

Scientific and technical innovation

How do we understand the worlds in which we live?

Students will explore the natural world and its laws; the interaction between people and the natural world; how humans use their under- standing of scientific principles; the impact of scientific and technological advances on communities and environments; the impact of environments on human activity; how humans adapt environments to their needs.

Possible explorations to develop:

• processes and solutions

Scientific and technical innovation

How do we understand the worlds in which we live?

Students will explore the natural world and its laws; the interaction between people and the natural world; how humans use their under- standing of scientific principles; the impact of scientific and technological advances on communities and environments; the impact of environments on human activity; how humans adapt environments to their needs.

Possible explorations to develop: 

• Numbers, methods, real-world applications

Orientation in space and time:

Students will explore personal histories; homes and journeys; turning points in humankind; discoveries, explorations and migrations of human- kind; the relationships between, and the interconnectedness of individuals and civilizations, from personal, local and global perspectives.

Possible explorations to develop:

• scale, duration, frequency and variability

Modeling explorations of patterns between rational quantities provides connections to the real world.

Reasoning (logic) about the equivalence of quantities provides access to understanding of differences.

Connections between quantities are discovered through modeling processes and solutions

Through the use of numbers, methodologies and real-world applications, relationships between representations can be validated.

Measurement of dimensional space, through scale and variability, allows for understanding of structures and shapes (form).

Criteria A – Knowing and Understanding Students must know and understand the concepts and skills of the prescribed framework in mathematics.

Criteria C – Communicating Students are expected to use correct mathematical thinking, mathematical language, and representation when communicating mathematical ideas both orally and written.

Criteria D – Applying Math to Real Life Context Students are expected to transfer mathematical knowledge into real-world situations, apply problem-solving strategies, and draw valid conclusions.

Criteria C – Communicating Students are expected to use correct mathematical thinking, mathematical language, and representation when communicating mathematical ideas both orally and written.

Criteria A – Knowing and Understanding Students must know and understand the concepts and skills of the prescribed framework in mathematics.

Criteria A – Knowing and Understanding Students must know and understand the concepts and skills of the prescribed framework in mathematics.

Criteria B – Investigating Patterns Through investigation students become risk-takers, inquirers, and critical thinkers.

Classroom test with groups in real-life situations.

Criteria D – Applying Math to Real Life Context Students are expected to transfer mathematical knowledge into real-world situations, apply problem-solving strategies, and draw valid conclusions.

Communication

Skill Indicators:

Take effective notes in class

Organize and depict information logically

Use and interpret a range of discipline-specific terms and symbols

Self Management

Skill Indicators:

Keep and use a weekly planner for assignments

Set goals that are challenging and realistic

Keep an organized and logical system of information files/notebooks

Self Management:

Skill Indicators:

Develop new skills, techniques, and strategies for effective learning

Demonstrate flexibility in the selection and use of learning strategies

Focus on the process of creating by imitating the work of others

Thinking

Skill Indicators:

Practise visible thinking strategies and techniques

Apply existing knowledge to generate new ideas, products or processes

Create novel solutions to authentic problems

Social

Skill Indicators:

Listen actively to other perspectives and ideas

Encourage everyone to contribute

Give and receive meaningful feedback

Take responsibility for one’s own actions

Thinking

Skill Indicators:

Propose and evaluate a variety of solutions

Identify obstacles and and challenges

Evaluate evidence and arguments

Test generalizations and conclusions

Research

Skill Indicator:

Present information in a variety of formats and platforms

Process data and report results

Collect and analyze data to identify solutions and make informed decisions

Thinking

Skill Indicator:

Intepret data

Identify trends and forecast possibilities

Draw reasonable conclusions and generalizations

Communication

Skill Indicators:

Use and interpret a range of discipline-specific terms and symbols

Understand and use mathematical notation

Paraphrase accurately and concisely

Self Management

Skill Indicators:

Mindfulness awareness

Self Motivation

Resilience

Add and subtract integers and rational numbers.

Apply properties of operations as strategies to perform operations with rational numbers.

Solve problems involving the four operations with rational numbers.Multiply and divide rational numbers.

Apply properties of operations as strategies to perform operations with rational numbers.

Convert a rational number to a decimal using long division.

Solve problems involving the four operations with rational numbers.

Add, subtract, factor, and expand linear expressions with rational coefficients.

Understand that rewriting expressions in different forms can show how the quantities are related.

Solve two-step equations. Compare algebraic solutions to arithmetic solutions.

Solve two-step inequalities involving integers and rational numbers.

Understand representative samples (random samples) and populations.Use proportionality to solve multistep percent problems. Solve percent problems involving percents of increase and decrease, and simple interest.

Compare fractions, decimals, and percents.

Use samples to draw inferences about populations.

Compare two populations from random samples using measures of center and variability.Find unit rates associated with ratios of fractions, areas, and other quantities in like or different units.

Decide whether two quantities are proportional using ratio tables and graphs.

Identify the constant of proportionality in tables, graphs, equations, diagrams, and verbal descriptions.

Represent proportional relationships with equations.

Use proportionality to solve multistep ratio problems.

Use scale drawings to compute actual lengths and areas and reproduce a scale drawing at a different scale.

Draw geometric shapes with given conditions, focusing on triangles.

Solve problems involving the area and circumference of a circle. Understand pi and its estimates.

Use facts about supplementary, complementary, vertical, and adjacent angles.

Solve real-world and mathematical problems involving area of two-dimensional objects.

Chapter 1:Equations

Chapter 2&3: Geometry

Chapter 4: Linear equations

Chapter 5: Solving systems of equations

Chapter 6: Data, Analysis, and Displays

Chapter 7: Functions

Chapter 8

8.E.E: Expressions and Equations 

• Understand the connections between proportional relationships, lines, and linear equations. 

• Analyze and solve linear equations and pairs of simultaneous linear equations.

8.G: Geometry

• Understand congruence and similarity using physical models, transparencies, or geometry software.

Major: 8.EE.B.5, 8.EE.B.6, 8.F.B.4

• Graph linear equations.

• Find and interpret the slope of a line.

• Graph proportional relationships.

• Graph linear equations in slope-intercept form.

• Graph linear equations in standard form.

• Write equations of lines in slope-intercept form.

• Write equations of lines in point-slope form.

• 8.EE.C: Analyze and solve linear equations and pairs of simultaneous linear equations.

• 8.EE.B: Understand the connections between proportional relationships, lines, and linear equations.

• Represent systems of equations graphically and algebraically.

• Solve systems of equations using graphing, substitution, and elimination methods

• Interpret and use the solutions to real-world problems involving systems of equations.

8.SP: Statistics and Probability 

• Investigate patterns of association in bivariate data.

8.F: Functions

• Define, evaluate, and compare functions.

• Use functions to model relationships between quantities. 

Major: 8.F.A.1, 8.F.A.2, 8.F.A.3, 8.F.A.4, 8.F.A.5

• Understand the concept of a function.

• Represent functions in a variety of ways.

• Use functions to model linear relationships.

• Understand differences between linear and nonlinear functions.

• Use graphs of functions to describe relationships between quantities.

Supporting: 8.SP.A.1, 8.SP.A.2, 8.SP.A.3, 8.SP.A.4

Logic

Change, Time, place, and space

Connection

Connection

Equivalence: State of being identically equal or interchangeable, applied to statements, quantities or expressions

Representation: Manner in which something is presented

Space:  The frame of geometric dimensions describing an entity

Change:  A variation in size, amount, or behavior

Systems:  Groups of interrelated elements

Representations:  The manner in which something is presented

Systems: Groups of interrelated elements

Patterns: Sets of numbers or objects that follow a specific order or rule

Scientific and Technical Innovation:

Models, Processes and Solutions

Orientation in Space in Time:

Migration, Scale, Turning Points (history/space/shapes)

Globalization and Sustainability:

Interconnectedness

Globalization and Sustainability:

• Exploration: Understanding how systems of equations can model global economic issues and sustainable solutions, such as resource allocation, environmental impact analysis, and fair trade practices.

Modeling uses a logical process involving organizing and balancing to find solutions to equations

Exploring how objects change and  move through space and the fluctuations of direction and size

Using algebraic representations (linear equations) to model and analyze consistent patterns of change in real-world situations, revealing the underlying connections between variables through linear equations

Solving systems of equations to model real-world problems helps us understand the intersections of variables and their solutions

A: Knowing and Understanding: 

i. select appropriate mathematics when solving problems in both familiar and unfamiliar situations

ii. apply the selected mathematics successfully when solving problems

iii. solve problems correctly in a variety of contexts.

Recognize and use mathematical ideas, terminology, and symbols.

• Example: Students should understand that to "undo" multiplication by a number, you divide by that number. For instance, if 3x=12

• 3x = 12, 

• dividing both sides by 3 gives x=4

• x = 4.

Criterion C. Communicating: 

i. use appropriate mathematical language (notation, symbols and terminology) in both oral and written explanations

ii. use appropriate forms of mathematical representation to present information

iii. move between different forms of mathematical representation

iv. communicate complete and coherent mathematical lines of reasoning

v. organize information using a logical structure

Use appropriate mathematical language, notation, and forms of representation.

• Example: Clearly explain the steps to solve for variable, from simple one-step equations and multistep equations

• Check answers by plugging them and reporting if the result is true or false.
 

A: Knowing and Understanding: 

i. select appropriate mathematics when solving problems in both familiar and unfamiliar situations

ii. apply the selected mathematics successfully when solving problems

iii. solve problems correctly in a variety of contexts.

• Example:  Students should understand the various types of transformations for various shapes

B: Investigating Patterns 

i. select and apply mathematical problem-solving techniques to discover complex patterns

ii. describe patterns as relationships and/or general rules consistent with findings

iii. verify and justify relationships and/or general rules.

A: Knowing and Understanding

Students must know and understand the concepts and skills of linear equations and how x an y variables represent coordinates in graphs.

B: Investigating Patterns

Through investigation 

Students become critical thinkers when they perform tasks that show the interconnectedness between a dot or tile pattern, an x/y table, a rule (linear equation) and a line graph in four quadrants.

C: Communicating

Students are expected to use correct mathematical thinking, mathematical language, and representation when communicating mathematical ideas both orally and written.

D: Applying Mathematics in Real Life Contexts

Students are expected to transfer mathematical knowledge into real-world situations, apply problem-solving strategies, and draw valid conclusions.

• Word problems transferred to a table and graph (Food sales, employment, businesses, gaming)

A: Knowing and Understanding:

Apply mathematical concepts to solve problems:

• Solve systems of equations using various methods such as graphing, substitution, and elimination.

• Apply these methods to solve real-world problems involving multiple variables, such as predicting outcomes based on given constraints.

C. Communicating:

Use appropriate mathematical language, notation, and forms of representation:

• Clearly explain the steps taken to solve systems of equations using different methods.

• Use graphs, tables, and written explanations to show and interpret solutions.

•

A: Knowing and Understanding

Students must know and understand the concepts and skills of linear equations and how x an y variables represent coordinates in graphs.

B: Investigating Patterns

Through investigation 

Students become critical thinkers when they perform tasks that show the interconnectedness between a dot or tile pattern, an x/y table, a rule (linear equation) and a line graph in four quadrants.

C: Communicating

Students are expected to use correct mathematical thinking, mathematical language, and representation when communicating mathematical ideas both orally and written.

D: Applying Mathematics in Real Life Contexts

Students are expected to transfer mathematical knowledge into real-world situations, apply problem-solving strategies, and draw valid conclusions.

A: Knowing and Understanding

Students must know and understand the concepts and skills of linear equations and how x an y variables represent coordinates in graphs.

B: Investigating Patterns

Through investigation 

Students become critical thinkers when they perform tasks that show the interconnectedness between a dot or tile pattern, an x/y table, a rule (linear equation) and a line graph in four quadrants.

C: Communicating

Students are expected to use correct mathematical thinking, mathematical language, and representation when communicating mathematical ideas both orally and written.

D: Applying Mathematics in Real Life Contexts

Students are expected to transfer mathematical knowledge into real-world situations, apply problem-solving strategies, and draw valid conclusions.

Organization: Use appropriate strategies to organize complex information.

Organization:

Give clear and specific directions to change an object's position on a coordinate plane

Transfer Skills:

Relate an objects orientation in space to colonial voyages and oceanic feets

Relate orientation in space to the organized structure of atoms and compounds.

Communication:  Express what the linear equation is trying to present including the meaning of the slope and the meaning of the y-intercept

Transfer Skills:  Relate linear equations and proportional reasoning to a variety of real-world examples 

Media Literacy Skills:  Locate, organize, analyze, synthesize, and ethically use information from a variety of sources and media

Critical Thinking:

• Analyzing: Break down complex systems of equations into simpler steps to solve them effectively. Recognize patterns and connections between different equations.

• Evaluating: Assess different methods (graphing, substitution, elimination) to determine which is the most efficient for solving a particular system.

• Reflecting: After solving, review and reflect on the solutions to ensure accuracy and understand the reasoning behind each step.
 

Solving one, two, and multistep equations by using inverse operations and keeping the equation balanced.

Transformations:  Translations, Reflections, Rotations, and Dilations (Scale Factor)

Connections between models, tables, equations, and line graphs in different contexts