Learning Map

Here is my Learning Map for Assignment 1B. I know that the assignment says to use the map we made in TED 632, but that was over a year ago for me and I didn't like it, so I made a new one. I used the last week of school that I taught, where my Integrated II students were getting a jump on Integrated III/Precalculus topics. I had some difficulty coming up with the real world applications, because polynomials tend to be a bit abstract for these students. Though it didn't go into any of these real world applications, one that we often talk about is roller coasters. polynomials can be written to represent the same of roller coasters to help designers and physicists accurately create safe and fun coasters. 

Day of the Week	Day 1	Day 2	Day 3	Day 4	Day 5
Essential Question	When we add functions, do we still have a function? Of the same degree? What about when we multiply functions?	Do we have to factor (x+1) raised to the 6 five times?	How can we determine the end behavior of a function without graphing it using technology?	If you are given one of the roots of a polynomial, how can you find the other roots?	What information can be found about polynomials when given one feature?
Standard	A.APR.5- Understand that polynomials for a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.	A.APR.5- Know and apply the Binomial Theorem for the expansion of (x+y)^n in powers of z and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.	F.IF.4- For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship...	A.APR.3- Identify zeros polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.	F.IF.7- Graph functions expressed symbolically and show key features of the graph, by hand in simple cases… C. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
Relevance	Students will be able to combine two functions and determine how the relationship changes.	This serves as an introduction to multiplicity and will save students time with writing a function in standard form.	Students can determine if a relationship is increasing or decreasing over time.	Students will be able to find all the solutions to any polynomial of any degree.	Students will finally be able to find all aspects of the polynomial relationship which will help them fully graph and understand them.
Real World Application	Students can look at more than one relationship at once. For example, if f(x) = the amount of money that you make per month and g(x) = your monthly expenses, then (f – g)(x) = the amount of money left over each month.	The binomial expansion can be used in many situations, because it is mostly a tool to quickly multiply functions. A real world application could involve probability. If you were flipping a coin four times, and we made heads x and tails y, the function of (x+y)^4 could give us information about the probability of getting heads or tails a certain number of times.	The main real world application of end behavior will be to determine in a relationship (like money made)  will increase forever, decrease forever, or level out.	If you let the ground have a height of 0, then the roots of a function would represent the time at which an object hits the ground. For example a quadratic polynomial would represent the following situation: A ball is thrown straight up, from 3m above the ground, with a velocity of 14m/s, when does it hit the ground?	Creating a better graph of the function would allow us to determine more about the following situation: A ball is thrown straight up, from 3m above the ground, with a velocity of 14m/s. The roots would tell us when it hits the ground, the y-intercept would determine its initial height, the end behavior would determine whether it falls forever, and the maximum would determine how high the ball gets.
Purpose for Learning	Students will be prepared to multiply functions to get another function, as a polynomial written in standard form.	Students will be able to write functions in standard form without needing to foil several times. They will also understand multiplicity, which will help them graph functions more accurately.	Students will be able to graph the end behavior of a function as well as determine how the function grows or decays over time, which is a foundation for learning limits.	Students will be able to show that they can apply the Fundamental Theorem of Algebra as well as divide polynomials to help graph polynomials by hand.	Students will begin to understand the connection between features of a polynomial, including how they affect the graph and zeros.