The purpose of the task is to connect properties of fractional exponents with ordering of real numbers. One can place the numbers on the number line to emphasize this.
Thunder Jalili, University of Utah answers the question: What are the facts about health risks and cheese?
Grant and Russell Kohler, engineers and dairy farmers answer the question: What do technology, engineering, and math have to do with cheese?
Michelle Culumber, Weber State University answers the question: What is the difference between white and blue molds in cheese?
John Armstrong, Weber State University answers the question: What role does physics play in cheese making?
Jess Perrie, graduate student in cheese chemistry, Utah State University answers the question: Why are there so many different cheddar cheeses?
Craig Oberg, Weber State University answers the question: Why do raw milk cheeses produce a wider variety of flavor?
Although this task is fairly straightforward, it is worth noticing that it does not explicitly tell students to look for intersection points when they graph the circle and the line. Thus, in addition to assessing whether they can solve the system of equations, it is assessing a simple but important piece of conceptual understanding, namely the correspondence between intersection points of the two graphs and solutions of the system.
This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment. The point so constructed is called the circumcenter of the triangle.
This task assesses a student's ability to use the addition rule to compute a probability and to interpret a probability in context.
In this lesson, students will first be introduced to adding two constant functions graphically to develop an understanding of how to add two functions together. Next students will add a constant function to a linear function and discover how that translates the graph of the linear function. Students will also begin building the connection between the graphical sums and algebraic sums. Students will be exposed to adding two linear functions together graphically before function notation is introduced. Students will also be exposed to adding a constant and exponential function together as exponential functions are a key function type in Secondary Math 1. Lastly, students will be challenged with adding a linear function and quadratic function together. Students will make the connection that adding a linear function and quadratic function together will result in a quadratic function.
The primary purpose of this problem is to rewrite simple rational expressions in different forms to exhibit different aspects of the expression, in the context of a relevant real-world context (the fuel efficiency of of a car). Indeed, the given form of the combined fuel economy computation is useful for direct calculation, but if asked for an approximation, is not particularly helpful.
This task gives students an opportunity to work with exponential functions in a real world context involving continuously compounded interest. They will study how the base of the exponential function impacts its growth rate and use logarithms to solve exponential equations.
This problem is intended to reinforce the geometric interpretation of distance between complex numbers and midpoints as modulus of the difference and average respectively.
This task is preliminary to F-LE Compounding Interest with a 5% Interest Rate which further develops the relationship between e and compound interest.
This task develops reasoning behind the general formula for balances under continuously compounded interest. While this task itself specifically addresses the standard (F-BF), building functions from a context, a auxiliary purpose is to introduce and motivate the number e, which plays a significant role in the (F-LE) domain of tasks.
This task asks students to perform computations involving complex numbers using the given information.
In this video segment you’ll discover how using concentric circles can help you determine how much paint is needed to cover the deck of a carousel.
The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.
This task presents a real world application of finite geometric series. The context can lead into several interesting follow-up questions and projects. Many drugs only become effective after the amount in the body builds up to a certain level. This can be modeled very well with geometric series.