Objective: Students will investigate to apply rationalizing the denominator in a real-life context related to the energy consumption of light bulbs. Real-Life Scenario: A homeowner is trying to calculate the total cost of illuminating their house with energy-efficient light bulbs. The price of each bulb is based on a square root value in a foreign currency, so they need to rationalize the denominator to make comparisons in their home currency. Key Concepts Relationships: Exploring the relationships between mathematical expressions and their real-world implications, such as how energy costs relate to efficiency. Related Concepts Simplification: Understanding how simplification techniques, like rationalizing the denominator, make complex mathematical expressions more usable in practical applications. Modeling: Using mathematical models to represent and analyze real-world scenarios, like calculating energy costs. Global Context Scientific and Technical Innovation: The task explores how mathematical concepts, like rationalizing the denominator, can support innovations in energy efficiency and cost-saving strategies by making calculations more accessible and actionable. Statement of Inquiry Simplifying mathematical models allows us to make better predictions and understand relationships in realworld contexts, such as the relationship between energy consumption, efficiency, and cost.

Real-Life Math Investigation: Modeling Tides with Sinusoidal Functions (MYP Years 4-5) Product Description: Engage your IB MYP Mathematics students with this comprehensive investigation that explores the fascinating world of sinusoidal functions through real-life scenarios like tidal movements in a harbor. This ready-to-use task is designed for students in Years 4-5, helping them deepen their understanding of mathematical modeling, trigonometric functions, and real-world applications. What’s Included: Student Task Sheet: A well-structured investigation that guides students step by step through modeling tides using sinusoidal functions. The scenario is designed to be relatable and practical. Detailed Answer Key: Complete solutions with clear explanations for all tasks, ensuring teachers can quickly assess student work or guide students through the process. Graphing Instructions: Step-by-step guide on how to plot sinusoidal graphs related to the task, making it easy for students to visualize their solutions. Extension Task: A challenging bonus activity that pushes students to extend their thinking and apply their knowledge in a more complex scenario, encouraging critical thinking and deeper mathematical exploration. Criterion A, C, D Descriptors: Pre-written task-specific descriptors for IB MYP Criteria A (Knowing and Understanding), C (Communicating), and D (Applying Mathematics in Real-Life Contexts), making it easy for teachers to assess student performance using IB guidelines. Key Concepts and IB Framework: Key Concept: Relationships – Explore how mathematical relationships (such as those between time and tidal height) can model real-world phenomena. Related Concepts: Models, Approximation – Use mathematical models to approximate periodic real-life changes. Global Context: Scientific and Technical Innovation – Investigate how mathematical modeling supports scientific understanding of natural cycles. Statement of Inquiry: “How can mathematical models using sinusoidal functions help predict and understand periodic changes, such as tidal movements?”

Objective: Students will investigating how mathematical concepts of exponents and radicals apply to the design, resolution, and size of television screens. Context: Your goal is to develop a model that explains the relationships between screen size, resolution, and pixel density. Key Concept: Relationships This concept emphasizes the connections between mathematical rules and the technological systems they help us understand. It highlights how mathematics builds a relationship between abstract ideas like exponents and radicals and their practical applications in areas like screen resolution and viewing experience. Related Concepts: Models: Television technology is modeled using mathematical formulas that describe screen sizes, resolutions, and pixel densities. Understanding these models enables users to evaluate different options effectively. Approximation: Approximations of radicals and other complex calculations allow for practical decision-making when exact precision isn’t required, helping users choose technology that fits their needs. Global Context: Scientific and Technical Innovation This context explores how mathematical principles drive innovation in technology, particularly in understanding and improving television systems. The globalized nature of technology means that mathematical literacy enables individuals to assess innovations in a competitive, rapidly evolving market and select technologies that suit their personal and societal needs. Statement of Inquiry: Decision making process can be improved by using models to represent relationships. Criterion D: Applying Mathematics in Real-Life Contexts Criterion C: Communicating Including the task specific clarification, answer key . Recommended for MYP4 &5.

In this task, you will step into the role of an engineer tasked with optimizing the design of a blender blade. The blade can be modeled as a sector of a circle, and your goal is to use mathematical concepts to determine the most efficient blade design based on the arc length, perimeter, and area of the sector. Key Concept: Relationship: Explores the interconnection between variables, objects, or concepts. In this context, it looks at how the geometric properties of sectors (arc length, perimeter, and area) relate to real-world design applications like blender blade efficiency. Related Concepts: Approximation: Involves estimating values or simplifying complex models to make calculations more manageable. In this task, students approximate the real-world performance of blades using geometric models. Models: Representations of real-world phenomena. The circular sectors in this task are mathematical models representing blender blades, which are used to analyze and optimize their design. Global Context: Globalization and Sustainability: Focuses on how interconnected systems, like the global economy or environmental sustainability, impact design and resource use. In this investigation, the design of efficient blender blades can be tied to energy consumption and sustainable production methods, emphasizing the need for efficient, durable, and environmentally conscious designs. Statement of Inquiry: “Understanding the relationship between mathematical models and real-world approximations allows us to optimize product design, promoting efficiency and sustainability in a globalized economy.” Including the task specific clarification, answer key . Recommended for MYP4 &5.

In this investigation, students take on the role of a meteorologist analyzing rainfall data collected over a period of time. The task requires students to model the relationship between time and rainfall using linear equations, enhancing their understanding of how mathematical concepts can apply to real-world problems, such as weather prediction. Key Concepts Patterns: Understanding patterns helps identify relationships in data, such as the linear relationship between time and rainfall. Relationships: Exploring how one variable affects another, specifically how time influences the amount of rainfall. Change: Analyzing how rainfall accumulates over time and how it can affect the environment and society. Related Concepts Function: The equation of a straight line represents a functional relationship between time and rainfall. Data Representation: Understanding how to collect, represent, and interpret data through graphs and tables. Modeling: Using mathematical models to predict future outcomes based on historical data. Global Context Scientific and Technical Innovation: This global context involves understanding how scientific data and mathematical modeling can be applied to real-world problems, such as predicting weather patterns and preparing for natural events. Statement of Inquiry How can mathematical models, represented by linear equations, help us understand and predict real-world phenomena such as rainfall patterns? This structure emphasizes how mathematical thinking is vital for understanding and managing personal finances, encouraging students to apply their knowledge to everyday contexts. Available as a PDF due to intricate formatting. For an editable Microsoft Word file or Google Doc, please request it after purchase. Please share the receipt for confirmation.

IB MYP Key Concept: Relationships: The task explores the relationship between time and the amount of water left in the washing machine. It also focuses on the behavior of the rational function as it approaches certain values, showing how changes in one variable (time) impact another (water volume). Related Concepts: Model: The rational function serves as a mathematical model that simulates a real-world process (draining water from a washing machine). Change: The task explores how the quantity of water changes over time and how this change is represented in the graph of the rational function. Global Context: Scientific and Technical Innovation: This task connects to understanding scientific principles (like the rate of change in processes) and how mathematical modeling helps us understand real-world technical systems, such as household appliances. Statement of Inquiry: Mathematical models help us understand and represent changes in real-world systems over time, allowing us to predict and analyze behaviors such as water drainage in technological devices.

IB MYP task based on constructing and substituting algebraic expressions in the context of travel tickets. This task aligns with Criterion D (Applying mathematics in real-life contexts) strands Construct Algebraic Expressions Substitute Values Analyze and Interpret Reflection Criterion D: Applying Mathematics in Real-life Contexts Strand D1: Identify relevant elements of authentic real-life situations. Understand the ticket types, base prices, and discount structures. Strand D2: Select appropriate mathematical strategies. Use algebra to create expressions that represent ticket pricing with discounts. Strand D3: Apply the selected mathematical strategies correctly. Substitute values into your expressions to calculate total costs accurately. Strand D4: Discuss results considering the context. Analyze which ticket combination offers the best value and reflect on discount effects. Reflection on ATL Skill: Transfer After completing the task, students can reflect on their use of transfer skills with questions such as: How did the mathematical concepts I learned in class help me solve a real-world problem involving ticket pricing? Can I think of other areas or subjects where understanding discounts and constructing algebraic expressions might be useful? How can I apply the strategies I used in this task to other situations outside of mathematics? By integrating transfer skills into this task, students are encouraged to recognize the wide applicability of their learning, fostering a deeper understanding and appreciation of the relevance of mathematics in everyday life.

Objective: Students will apply their understanding of constructing and substituting into algebraic expressions to solve real-world problems related to motorbike performance and fuel efficiency. Scenario: You are a mechanical engineer working for a motorbike manufacturing company. Your team is developing a new model, the TurboMax 5000. You need to calculate various performance metrics to ensure the motorbike is fuel-efficient and has good acceleration.

Knowledge questions: How can calculus be used to inform both theory-led and data-led modeling approaches in understanding complex phenomena? Theory-led vs. Data-led Modeling: Harnessing Knowledge for Predictive Relationships

The following points are discussed with evidences First-order knowledge questions: What are the various ways language impacts the understanding of mathematical concepts? How do mathematical symbols contribute to the precision and clarity of mathematical communication? In what ways does linguistic variation influence the acquisition of mathematical knowledge across different cultures? How does the use of different languages affect the interpretation and application of mathematical principles? What role does symbolic representation play in simplifying complex mathematical ideas? Second-order knowledge questions: To what extent does linguistic diversity in mathematics contribute to a deeper appreciation of cultural perspectives in mathematical reasoning? How can standardized mathematical symbols bridge language barriers and facilitate global mathematical collaboration? How does the interpretation of mathematical symbols differ based on cultural and linguistic contexts? How might the development of a universal mathematical language enhance the communication and understanding of mathematical concepts worldwide?

In contemplating the role of mathematics in understanding the universe, one must navigate a complex landscape of philosophical inquiry, scientific discovery, and cognitive theory. The proposition that mathematics might not merely describe the universe but represent the fundamental language or logical system employed by the brain to interact with reality challenges conventional notions about the nature of mathematics and its relationship to the cosmos.

This worksheet structure should help students practice applying the binomial theorem, understanding binomial coefficients, and exploring related concepts

Trigonometry worksheets are designed to reinforce understanding of these concepts through practice problems of varying difficulty levels.

Exam-style questions on complex numbers in the IB Mathematics curriculum often cover a range of topics, testing both theoretical understanding and problem-solving skills. Here are some typical types of questions you might encounter.

IB AA HL & SL Revision worksheet Integral calculus This worksheet focuses on Calculus describes rates of change between two variables and the accumulation of limiting areas. Understanding these rates of change and accumulations allow us to model, interpret and analyze realworld problems and situations. Calculus helps us to understand the behaviour of functions and allows us to interpret the features of their graphs Command Terms: Show that : Obtain the required result (possibly using information given) without the formality of proof. “Show that” questions do not generally require the use of a calculator. Find:Obtain an answer showing relevant stages in the working

Revision worksheet Differentiation

Curriculum: IB DP Unit: Calculus Subject: Mathematics Concepts: Integration by substitution Resource: Worksheet

How do we choose the axioms underlying mathematics? Is this an act of faith? “Mathematics is the language with which God wrote the Universe” – Galileo TOK concepts: perspectives and evidence.

What do we know about rational functions? - This routine helps us to activate our prior knowledge about rational functions, which are functions that can be expressed as a ratio of two polynomials. What are the key features of rational functions? - This routine helps us to identify the important characteristics of rational functions, such as asymptotes, intercepts, and the behavior of the function as the input variable approaches positive or negative infinity. How do reciprocal functions relate to rational functions? - This routine helps us to make connections between rational functions and their reciprocal functions, which are functions that can be expressed as 1 over the original function. What is the general form of a reciprocal function? - This routine prompts us to recall the general form of a reciprocal function, which is y = 1/x. How do the graphs of rational and reciprocal functions differ? - This routine encourages us to compare and contrast the graphs of rational and reciprocal functions, noting similarities and differences in their behavior. What real-world situations can be modeled using rational and reciprocal functions? - This routine prompts us to think about real-world scenarios that can be described using these types of functions, such as the spread of disease or the movement of celestial bodies. What are some common misconceptions about rational and reciprocal functions? - This routine helps us to identify common misunderstandings or errors that people may have when working with these functions. What strategies can we use to solve problems involving rational and reciprocal functions? - This routine prompts us to think about problem-solving techniques, such as graphing or algebraic manipulation, that can be used to analyze and solve problems involving these functions. How can we apply our understanding of rational and reciprocal functions in other contexts? - This routine encourages us to reflect on the broader applications of our knowledge, such as in fields like engineering, economics, or physics.