In this course, you will be introduced to basic algebraic operations and concepts, as well as the structure and use of algebra. Topics include linear inequalities and graphing, exponents, polynomials, and rational expressions. You will study basic algebraic operations and concepts, as well as the structure and use of algebra. This includes solving algebraic equations, factoring algebraic expressions, working with rational expressions, and graphing linear equations. You will apply these skills to solve real-world problems (word problems). Each unit will have its own application problems, depending on the concepts you have been exposed to. This course is also intended to provide you with a strong foundation for intermediate algebra and beyond. It will begin with a review of some math concepts formed in pre-algebra, such as ordering operations and simplifying simple algebraic expressions, to get your feet wet. You will then build on these concepts by learning more about functions, graphing of functions, evaluation of functions, and factorization. You will spend time on the rules of exponents and their applications in distribution of multiplication over addition/subtraction.
Students will work on the rate_of_change_investigation in pairs. Students will take the first few minutes with their partner to understand the problem (MP1) The goal is for each pair to make a poster on chart paper that shows their thinking about how fast each of these bike riders was traveling on their journey to the top of the volcano. Students can use the diagram on the worksheet as well as the questions to focus their thinking and identify pertinent information to include on their posters.
The most important part of this investigation is that students determine how long it will take Cliantha to reach the top because she is riding at a constant rate. Most students will base this on the launch information. Five hours is a pretty good estimate for how long it will take to reach the end of the 38-mile trail. If that is their estimate then (5, 38) would be the coordinates of point B. With this in mind, students can use a ruler (MP5) to determine the coordinates of points A and C. They can use proportional reasoning to determine what portion of the 5 and 38 each point is located at. Approximate locations could be (2, 26) for point A and (3, 13) for point C.
Students can use their approximations to justify (MP3) a story for each of the three bike riders. In doing this students will develop the concept of slope as a rate of change. Students will make connections between the steepness of a line and the rate of change that it represents.