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 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.

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.