Blendeman - 2C
2.4 solve optimization problems involving polynomial, simple rational, and exponential functions drawn from a variety of applications, including those arising from real-world situations.
2.5 solve problems arising from real-world applications by applying a mathematical model and the concepts and procedures associated with the derivative to determine mathematical results, and interpret and communicate the results.
For these expectations students need to take their prior knowledge of derivatives and apply that knowledge to real world application problems. Students may be faced with a problem and then have to decode what that problem is asking them to do. From the information that they are given they would have to create and apply a mathematical model that will allow them to solve the problem.
Example: A farmer has 2400 ft of fencing and wants to fence off a rectangular field that borders a straight river. He needs no fencing along the river. What are the dimensions of the field that has the largest area?
This example gives students an idea of how the concepts that they are learning in the course can be applied to real world situations. The problem does not provide the students with the needed mathematical model, but gives them all the needed information to create a model that will help them solve the problems. Students have to recognize that this is an optimization question dealing with maximizing an area.
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As a math teacher, I answer the following question at least once a week: “Am I going to use this in my life?” The first thing that comes to my mind is: “You will use math to pay your taxes, take your car to a mechanic, compare the number of hours worked and your paycheck”, among others. “When a topic connects to what students like to do, engagement deepens as they willingly spend time thinking, dialoguing, and creating ideas in meaningful ways. Making learning contextual to real-world experiences is a key learning technique with differentiating for student interests.” (McCarthy, 2014). Knowing the interests of my students is essential for them in order to master the material being covered in class. In addition, this gives me the opportunity to create a differentiating classroom. A few months ago I talked with the administration in my school and I let them know that my desire is that students have the opportunity to go to college or university to complete a degree,
She decided that in allowing her 6th grade math class to work the school’s supply store would allow the students to apply real life situation to what they are studying in class. The students are responsible for opening the store, operating cash box, and closing the store. In what they learn in class, they applied to the store. In this particular unit they are working on sales tax and percentage.
It also requires the student to understand approaches to problem solutions utilized by other students and being able to provide peer feedback. Students should be introduced to the use of mathematics to: organize data, solve problems applicable to their life, and understand the world around them. This approach makes the subject both interesting and enjoyable. The use of these strategies is addressed in the next standard “#4 Model with mathematics” (Academics), which helps the student to make connections, surpass procedural knowledge and gain a conceptual understanding of a
Student B demonstrates mathematical strengths in the explanation of both solutions of the area and perimeter, although one of the formula used was incorrect. Mathematical strength was also displayed in the actual multiplication 5x2x5x2=100, and addition 5+2+5+2=14 cm, failing to include the units of measurement
Construct viable arguments and critique the reasoning of others- it’s important for students to be able to explain and be able to discuss the process into which they believe a problem should be solved this demonstrates the students understanding on the concept. They should be able to clarify and answer any questions that arise about the problem once again displaying a deeper understanding then just being able to memorize formulas/steps and solving a problem.
This is one unit in a yearlong 6th grade math course. In this unit, the students will learn about expressions and equations. Students will learn how letters stand for numbers, and be able to read, write, and evaluate expressions in which these letters take the place of numbers. In this unit, students will learn how to identify parts of an expression using various new terms. They will learn to solve both one- and two-step equations. Students will be able to distinguish between dependent and independent variables. They will be able to identify the dependent and independent variables of equations and in turn, be able to graph them. Various activities to be completed inside and outside of the classroom will be used to show
Standard: A1.4. Linear functions, equations, and inequalities (Algebra) Students understand that linear functions can be used to model situations involving a constant rate of change. They build on the work done in middle school to solve sets of linear equations and inequalities in two variables, learning to interpret the intersection of the lines as the solution. While the focus is on solving equations, students also learn graphical and numerical methods for approximating solutions to equations. They use linear functions to analyze relationships, represent and model problems, and answer questions. These algebraic skills are applied in other Core Content areas across high school courses.
-The student will find details to formulate a plan to determine and justify the solution of the given mathematical word problem.
Exact optimisation method is the optimisation method that can guarantee to find all optimal solutions. In principle, the optimality of generated solution can be proofed mathematically. Therefore, exact optimisation is also termed as mathematical optimisation. However, exact optimisation approach is impractical usually. The effort of solving an optimisation problem by exact optimisation grows polynomially with the problem size. For example, to solve a problem by brute force approach, the execution time increases exponentially respect to the dimensions of the problem.