Experiencing+a+1-1+Math+Classroom

=__Consider the following questions as we go through the Immersion__= ==
 * 1) How is this classroom experience similar or different from what I have experienced and/or observed?
 * 2) How does my current role support such an environment at the district level? At the school level?
 * 3) What skill set is necessary for me to actively support administrators and teachers who work in these environments?
 * 4) How would an experience such as this be evaluated using current NC Teacher Standards (i.e. MCREL)?

=__Title of Lesson__= Exploring linear relationships

=__Overview__= The purpose of this immersion session is to provide participants with a lived-in experience of what it is like to learn in a technology-enabled math class. Today we are going to explore how to determine the optimal model for data that we are provided.

=__Standards__= The lesson is based upon the Common Core Standards: = = =__Essential Question__=
 * A-CED.2. Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
 * A-REI.1. Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
 * A-REI.10. Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).
 * How can real-world situations be examined through linear and non-linear relationships?

=__Learning Outcomes__=
 * The learner will be able to create slope and equation of a line from a model
 * The learner will be able to compare and contrast different relationships

=__Classroom Logistics__= All students have a laptop, desks are grouped in groups of four, projector in center of front board, Charging station in back right

=__Prior Content Knowledge__= Slope
 * Refers to the steepness, or grade, of a line
 * Slope represents the ratio of the vertical change to the horizontal change between two points on a line
 * Positive slope: Line goes upward as we look left to right
 * Negative slope: Line goes downward as we look left to right
 * Zero slope: Line that has no rise as we look left to right
 * Undefined slope: represented as a vertical line

=__Instructional Strategy/Activities (Lecture, workshop, etc.)__= Inquiry-based activities, small group collaboration, large group discussion

=__Methods of Assessment:__=
 * ===Activity 1===
 * While students are working, the teacher will circulate the classroom. He will listen to partner conversations and ask probing questions to explore what different students understand from the activity and how they built that understanding.
 * Upon completion, there will be a classroom sharing of how different groups solved the various problems. This will be shared and published along with classroom summary information.
 * ===Activity 2===
 * While students are working, the teacher will circulate the classroom. He will listen to partner conversations and ask probing questions to explore what different students understand from the activity and how they built that understanding.
 * Upon completion, there will be a classroom sharing of how different groups solved the various problems. This will be shared and published along with classroom summary information.
 * This assignment will also be given an assignment grade and individual feedback will be provided via email to each student about their responses.
 * ===Final Class Submission===
 * At the end of class, each student will be required to complete an exit ticket with the following two questions.
 * How do we recognize whether or not we are exploring a linear relationship?
 * In activity 1, two students found the same solution two different ways for when the candle completely burned out. Explain how the two solutions are connected.
 * Student 1 stated that he recognized that for every 20 minutes, the candle burned 5 inches. Since the candle was 20 inches tall, it would take four 20-minute increments to burn completely. 4x20 = 80 minutes
 * Student 2 stated that she had used the equation y=mx + b. She stated that since the candle started at 20 inches tall, it represented the y-interecept (b). She also recognized that for every 4 minutes that passed, the candled burned down 1 inch. This would lead to a slope of -1/4. Now since she knew the candle would end up at 0 inches tall, she used 0 = (-1/4)x + 20. She then used two step equations to find that it would take 80 minutes to burn completely out.
 * ===After class===
 * The teacher will review each group's responses to both Activity 1 and 2 to determine where there may be gaps in understanding. Grades and emails to each student discussing their work on Activity 2. The individual responses will lead to differentiated activities the following class.

Students, Continue to Immersion Activity 1

Observers, Click Here