Shannon+Core

 R Unit: Linear Equations and Their Graphs Audience: 9th Grade Resource Integrated Algebra and Geometry I || →Linear equations represent lines on a coordinate plane →Linear equations and their lines represent relationships →Analyze an equation and discuss the components that will effect the behaviors of the line that represents it || - There are several means to graphing a line -A //solution// is a coordinate that satisfies a linear equation -Given different input values come different output values -Points that have a relationship can be collinear; these create a line -Linear equations represent lines ||  -What does a //line// mean to you? -Describe what method you believe is most efficient for graphing linear equations? -How does slope relate to the collinear points that create the line? -Are all equations linear? Why or why not? -How might someone represent a linear relationship other than graphing? -Would you consider a linear relationship a pattern? || -  different methods to graphing an equation -//m// and //b// represent slope and y-intercept -different behaviors of slope -properties of x and y intercepts -a linear equation represents a line graphed on the coordinate plane - parent function of a linear equation is y=x -slope-intercept form is y=//m//x+//b// -given a point and slope how to write an equation of a line in slope intercept form -given a graph of a line, write a linear equation that represents that graph -given two points, write an equation of a line -slope formula -analyze an equation and determine the behavior of the graph || -Comprehension of how constants and coefficients relate to graphs by comparing and contrasting families of graphs -Comprehension of various representations of linear equations by analyzing equations to create tables and graphs -Analysis of horizontal and vertical lines by points on the coordinate plane, identifying patterns and relate to the equation of the line
 * Shannon Core
 * **//__Stage 1 – Desired Results __//** ||
 * **//__Established Goals: __//**
 * **//__Understandings: __//** 
 * **//__Essential Questions: __//**
 * **//__Students will know: __//**
 * <span style="font-size: 14pt; color: black; font-family: 'Arial','sans-serif'; text-decoration: none;">
 * //__<span style="font-size: 14pt; color: black; font-family: 'Arial','sans-serif';">Students will be able to demonstrate: __//**

-Comprehension of how slope and the y-intercept relate to an equation of a line by analyzing graphs on the coordinate plane || || <span style="font-size: 12pt; font-family: 'Times New Roman','serif';">1. Discuss the relationship between the slope of a line and its collinear points 2. Given an equation of a line, how can you determine its behavior on a graph? 3. How do you know if a point is collinear to the line given the equation of a line? 4. Describe one method you would use to graph a linear relationship. 5. What is a parent function? 6. What do all //y//-intercepts have in common with one another? Why? Does this hold true for //x//-intercepts? Justify your answer with mathematical support. 7. The following equation represents the total cost for cell phone usage of a Verizon customer. y=.40x + 59.99 where x represents the usage in minutes over the plan allowance of 200 minutes and there is a plan charge of $59.99. Find the total cost (y) when this customer talks for 200 minutes, 300 minutes and 520 minutes. Graph your findings. || <span style="font-size: 12pt; color: black; font-family: 'Times New Roman','serif';">-quizzes; exit cards; do nows; tests containing exercises that assess method <span style="font-size: 12pt; font-family: 'Times New Roman','serif';"> || || <span style="font-size: 12pt; color: black; font-family: 'Times New Roman','serif';">1. Investigating lines and the points that create them Plot the given points; What is the relationship between these points (collinear)? How many points do you think lie on this line? Describe the line. Teacher will provide a linear equation (the one that represents the line above). Students will graph the equation. Set up x/y chart. What do you notice (lines are the same)? Do you think there is a relationship between equations and lines? What evidence do you have to support this? 2. Investigate slope. Given an equation, graph and discuss the relationship between each point. Students will be given different equations and they should discuss in groups of three their graphs and equations. Groups will be determined by teacher. Each member of the group will have an equation that represents a different family of linear equations. One will be the parent. Relationships between lines and the //y// axis. Relationship between given equations and the lines they create regarding their slope. Discuss slope formula. Students will use graphing calculators to input linear equations and use as a tool to discuss slope. 3. Given an equation, investigate different lines and their y-intercepts. Relate to their equations. 4. Discuss //x// and //y// intercepts. 5. Investigate slope intercept form y=//m//x+//b//. When an equation is written in slope intercept form, behaviors of the graph can be determined. 6. Investigate the two methods learned for graphing a linear relationship. Discuss your answer with your neighbor. 7. How can you prove a linear relationship does not exist given three points? Support your answer by creating an example. 8. Given an equation in slope intercept form, what do the //x// and //y// represent? 9. Given an equation of a line, how can I determine at what point the line crosses the //x// axis? The //y// axis? 10. Investigate different families of linear equations and their graphs; relating back to parent function. 11. Given an equation, not in slope intercept form, discuss methods of graphing. 12. Writing equations of lines given graphs. 13. Writing equations of lines given information other than a graph or slope and y-intercept. 14. Relating linear equations and their graphs to real-life situation (ie phone bills; pond depth and rainfall; etc). || Reflection: I really like this format. Although it takes some time to create "essential questions" it ends up making the entire process easier and more efficient. It is a wonderful way to organize thoughts and put everything in perspective. I think the biggest difficulty I had was creating the "essential questions." I think I may have been trying to reinvent the wheel...my own fault. I was a bit confused on whether or not the lesson activities were supossed to be more spelled out than they are in my plans. I like how the end goal is always in front of me. This way of planning constantly reinforces what it is I want my students to be able to understand by the end of the lesson/unit. It is very easy to get lost in irrelevant details as opposed to just focusing on what it is I want to get across. I think this is a wonderful way of planning.
 * **//__<span style="font-size: 14pt; color: black; font-family: 'Arial','sans-serif';">Stage 2- Assessment Evidence __//**<span style="font-size: 24pt; color: black; font-family: 'Arial','sans-serif';">
 * **//__<span style="font-size: 14pt; color: black; font-family: 'Arial','sans-serif';">Performance Tasks: __//**
 * **//__<span style="font-size: 14pt; color: black; font-family: 'Arial','sans-serif';">Other Evidence: __//**
 * **//__<span style="font-size: 14pt; color: black; font-family: 'Arial','sans-serif';">Stage 3 – Learning Plans __//**<span style="font-size: 24pt; color: black; font-family: 'Arial','sans-serif';">
 * **//__<span style="font-size: 14pt; color: black; font-family: 'Arial','sans-serif';">Learning Activities: __//**

Shannon,I think that you did a great job of sorting through all of the objectives of this unit. It is the biggest unit of the year in Algebra 1 with many different concepts embedded in it. My favorite activity was number 2. The study of functions and the transformations are such a major part of Algebra 2, precalculus, and math that I enjoyed that you focused in on it. I think that graph shifting and the effects of changing slope and the intercepts are often overlooked in some schools and I think it is a shame. There are some great geometry sketchpad activities that are similar to your group activity where you graph a family of functions and take note of the changes (if your school has the software).

I thought you did a very thorough and excelent job. Jim Memory

Shannon, I think your EQ are great! In terms of performance assessments, in what other ways beyond tests and orally sharing can kids demonstrate their knowledge of the content? Further, how can they transfer this knowledge of slope and intercept to a practical situation? (i.e. You are a commander of an air squadron and are planning an attack route on the enemy who is at a certain degree. Plot the course for the attack.) Or, how can various levels of understanding be shown beyond giving back the formulas? BB

Shannon, I really like your real life application question on the verizon phone plans. I think it really connects with the kids and allows them to see a real life scenario using math. I was re-reading your objectives and noticed that there was a lot of comprehension objectives being made. Is there anyway you can use higher level objectives like synthesis or analysis more then comprehension? You're questions indicated a lot of synthesis and higher level thinking. Maybe you need to just reword your objectives. Frank