(Assessment of Learning) attainment of this outcome? Given a situation in context, students should be able to create arithmetic and geometric sequences and corresponding functions as models. Students should be able to judge the reasonableness of their models and determine solutions that accurately address the restrictions of a situation. (i.e. integer quantities) Prior Knowledge Needed to Support This Learning Students need to know: how to write an arithmetic and geometric sequence from a list of terms. how to write linear, exponential, and step functions from given data. By hand for straightforward data. By regression for more complicated situations. how to set up and solve a system of equation by graphing. Method for determining student readiness for the lesson How will evidence of student prior knowledge be determined? Students will demonstrate prior knowledge through warm up activities leading up to culminating activities. Students will be able to successfully write linear and exponential functions when given data. Students will be able to set up a system of equations. What will be done for students who are not ready for the lesson? Students who have not demonstrated the prerequisite skills will be able to perform introductory components, such as completing the scaffolding and developing the sequences early in the lesson. Teachers may elect to have students complete each of the tables in an exploration 1 and then use small group instruction to move students from the table to the sequence. Students will then have several opportunities for guided practice and eventually independent work in the lesson. Students with some knowledge of step functions will be able to move ahead in Exploration 2, but teachers may find that many students will need a brief reminder of range values for step functions and the meaning of the graph. Several visual explanations of step functions are available on graphingstories.com and take only 3 minutes to view. Exploration 3 will be new to most students. Solving systems of nonlinear functions will likely need intensive guidance to remind students of solution strategies similar to those for systems of linear functions. Learning Experience
For the “three friends” function, what is a realistic domain? Is all real numbers a good choice? Why or why not? How does the frequency of checking email affect the domain? What assumptions need to be made in order to create a continuous bandwidth function? Does this mean that the friends are continuously checking their email? Explain your answer. Is it possible to write a recursive or explicit rule for these continuous scenarios? Explain your answer. If this process were repeated with the 4 friend’s data what would be the similarities and the differences between what happened with the three friend’s data in problems 1-4? Exploration #3 Background The staff at Algebra2b.com has concluded their research study and is now ready to purchase servers to host videos. They decided that the most likely scenario for a viral video is “three friends checking email 5 times a day.” Exploration 3 Write the bandwidth function for this scenario. Use your work from pages 13 –15 and the table below to help you.
Complete the table below to illustrate this scenario. Day Email Recipients/ Views of the Video Required Bandwidth (MB) 0 3 396 0.1 9 1188 0.2 27 3564 0.3 81 10692 0.4 243 32076 0.5 729 96228 0.6 2187 288684 0.7 6561 866052 0.8 19683 2598156 0.9 59049 7794468 1 177147 23383404 Write a function to model this data in which bandwidth, B, is dependent on the days since the video was uploaded, d for this data. Create a graph on the grid below to communicate the bandwidth requirements for each day based on this data. If the pattern in the number of views of the video were to continue as described in problems 1-4 the data would be as shown. Notice to make it easier to compare the various scenarios, only the data for the actual whole number days has been included in this table.
The frequency of checking email defines a pattern that will determine the description of the domain. What assumptions need to be made in order to create a continuous bandwidth function? Does this mean that the friends are continuously checking their email? Explain your answer. Is it possible to write a recursive or explicit rule for these continuous scenarios? Explain your answer. If this process were repeated with the 4 friend’s data what would be the similarities and the differences between what happened with the three friend’s data in problems 1-4? Exploration #3/Answer Key Background The staff at Algebra2b.com has concluded their research study and is now ready to purchase servers to host videos. They decided that the most likely scenario for a viral video is “three friends checking email 5 times a day.” Exploration 3 Write the bandwidth function for this scenario. Use your work from pages 13 –15 and the table below to help you. The servers that Algebra2b.com will be purchasing are capable of handling 500 GB of traffic. Note that 1 GB = 1024 MB Complete the table below to help determine the number of 500GB servers needed. Day New email Recipients Required Bandwidth (MB) Servers Needed 0 3 0.2 0.4 0.6