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.

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.