Carson

=Common Core Resources= 1. [] This website shows standards for each of the content areas as well as information about the standards and what states have adopted the standards.

2. [] This website shows the common core standards associated with North Carolina and gives information on how NC is adapting to the standards.

3. [] This website has many pdfs that give advice and tools to help support teachers in their interaction with the new common core standards

4. [] This website shows the support and concerns that nctm has about the common core standards and mathematics

5. [] This link opens a powerpoint that goes through the implementation plan for the common core standards in New Hanover County

6. [] This website gives applications and support for alignment into the new common core standards.

7. [] This Website Aligns current state standards with Common Core State Standards so teachers can identify gaps between the current curriculum and expectations of the Common Core State Standards.

8. [] This website has example lesson plans for mathematics and other subjects that are aligned with the new standards

9.[] Provides tools and support for teachers when transfering over to common core standards

10. [] This webside provides videos to help teachers with any questions they may have about the common core standards

11. [] This website allows you to create lesson plans and align them with the common core standards.

**Leadership Lesson Plan** **Graphing Quadratic Functions** **Solving Quadratic Functions by Graphing**
 * Lesson Follow Up For Chapter 5.1, 5.2**

Students solved systems of equations by graphing.
 * Prerequisites:** Students identified and manipulated graphs of functions.


 * Objectives:**
 * Learners will be able to graph quadratic functions.
 * Learners will be able to find and interpret the maximum and minimum values of quadratic functions.
 * Learners will be able to solve quadratic equations by graphing.
 * Learners will be able to estimate solutions of quadratic equations by graphing.


 * Summary:** Students will represent quadratic functions as a table, with a graph, and with an equation. They will compare data and move between each representation. In the activity students encounter data that comes in different forms that are a result of a egg launch contest done by another class. Students will work in groups to complete each part of the activity and focus on each representation as a individual and as a whole group.


 * Materials:** Activity Sheet, Graphing Calculator

**BEFORE** Warm Up: 2. Graph the function by using the equation. 14-x2 = -6x + 23
 * Teacher Actions:** Teacher will post a warm up for students to complete as they enter the classroom. Homework will be checked at this time and a couple minutes will be taken for any homework questions.
 * 1) Graph the function by using the table. Label each point.
 * X ||  1  ||  2  ||  3  ||  4  ||  5  ||
 * f(x) ||  4  ||  1  ||  0  ||  1  ||  4  ||
 * Are there any similarities or differences between these two graphs?
 * If so what are they?
 * Students Actions:** Students will come into the classroom and begin the warm up. They will have their homework out on their desks to be checked for completeness and effort. The Students may ask any questions about the homework.

**DURING**
 * Teacher Actions**: The teacher will hand out the Egg Launch Contest activity sheet. The teacher will have the students read the first two paragraphs of the activity sheet to start with.


 * What happens to the height of the egg as the distance from the starting line increases?
 * The students will then be told to read the third paragraph and describe the shape described by the equation given. What kind of equation is it?

The fourth paragraph will be read and the students will be asked what they know about the flight path of team C.

After introducing each team to the students the teacher will ask each group of students to make a hypothesis of which team they believe will win the height contest as well as distance contest.

The teacher will then allow the class to work in their groups to complete each part of the activity sheet. Students may ask questions about any calculator issues but are encouraged to use their peers in their groups to answer any mathematical questions about the activity.


 * Student Actions:** Students will work together in groups to complete and answer all questions in the activity sheet. Student will use multiple representations of quadratic functions to describe a winner based on the results from the egg launch contest.

**AFTER**
 * Teacher Actions:** The teacher will bring the students back together as a whole to answer questions about the activity.


 * How did each representation (table, graph, equation) of the data help you better understand a quadratic function?
 * What information can you obtain from each of the representations?
 * Do negative leading coefficients have any effect on the equations graphs?
 * What ways were you able to find the maximum height of each of the graphs?
 * Is their any type of symmetry in the graphs?
 * Which team one the contests and why do you think that team won?
 * Was your beginning hypothesis correct?

For homework students will be asked to come up with another type of real world activity that would fit the same concept of quadratic functions.


 * Student Actions:** Students will come back together as a whole and have a discussion and answer all of the teacher’s questions to have a better understanding of the activity as well as the material.


 * Assessment:** The teacher will assess the students on the activity worksheet and on how the students answer questions in the classroom discussion. Did the students work well together as a group? Did they complete the activity sheet and how well did they understand the activity to answer the questions asked during the discussion?


 * Standards:**
 * < HS.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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ||


 * < HS.F.IF.1. ||< 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. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. ||

a. Graph linear and quadratic functions and show intercepts, maxima, and minima.
 * < Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

d. (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

e. Graph exponential and logarithmic functions, showing intercept and end behavior, and trigonometric function ||