DAy 1 activitY:
List of Materials/Resources Required by Student:
-Computer or tablet to participate in lesson (my school provides laptops to students)
-Wi-fi or internet access
-Pencil & Paper for notes
-Access to Desmos, Weebly, Geogebra applet, Youtube, and Nearpod.
-Smart phone, digital camera, or scanner for homework (Students can arrive in the morning and use my equipment to post homework and watch videos)
Activity Rational: I am opening with a review of solving systems of linear equations graphically and algebraically for student recollection. Because tomorrow we will deal with discussing complex and irrational solutions, the next opener will focus on solving quadratic equations in various forms (standard, vertex, and factored). Today we will focus on solving sytems with integer ordered pair solutions to keep with introduction. The activity will have students using Desmos to solve linear/quadratic systems visually first, but the intersection of points. From here, students will watch a video that teaches (reminds of solving quadratic equations with the Zero Product Property) to solve solutions algebraically. The video will also connect both methods of solving. At the end, students will need to demonstrate lesson comprehension and understanding with a ticket out the door problem. This lesson uses technology for discovery and to see connections between solving in different manners. It directly aligns to CCGPS standards outlined for the unit.
Mathematical Practices developed in the unit:
-Use of graphs of linear and quadratic functions to solve a system of equations.
-Use of finding the roots of a quadratic formula to solve a system of equations.
-The ability to model different solution methods and connect them to each other.
-Understanding how to solve more complicated system of equations, and understanding why a system has 2 solutions (today) or no solutions (next lesson) through graphic and algebraic representation.
Connection between technology and the learning objective:
-Desmos: Students will find how to quickly solve systems of linear equations graphically and also be able to discover how the algebraic solution steps work.
-Nearpod presentation: Allows the teacher to collect student responses and assessment during class as well as keep the class on task/pace. The teacher can use the technology to help in the classroom teaching while aiding students who may fall behind. The teacher can also use student responses to facilitate classroom discussion.
-Youtube video: Used to teach a segment of the unit with examples. This will allow the teacher time to help students and student groups more one on one in the classroom as well as help students who missed the class.
-Weebly: Used to collect homework results and provide homework to students. This allows students to submit questions and the teacher to quickly understand if students are ready to move on.
Teacher Guidelines:
The teacher should use the following Nearpod slideshow:
https://app.nearpod.com/#/?pin=C41182B8FCA1002298BC6383DF79DE44-0
Some editing may be needed for collecting the homework assignment on the last slide. The teacher should be able to follow along (answer details below) and facilitate discussion based on student response and assessment throughout the lesson.
List of Materials/Resources Required by Teacher:
-Computer or tablet to participate in lesson (my school provides laptops to students)
-Additional laptops or devices for students to use if they do not have them
-A smart board or projector to display results in front of the class as well as on personal devices (as you may need to pull up desmos or write something out further)
-Access to Youtube videos (test if your school blocks youtube)
-Wi-fi or internet access
-Pencil & Paper to provide to students
-Access to Desmos, Weebly, Youtube, and Nearpod on your machine (directions and troubleshooting can be found directly at each app site)
-Smart phone, digital camera, or scanner for students to hand in homework if you are collecting through weebly
-Teacher answers and guidelines below
-Printouts of activity questions if you do not want to use the Nearpod lesson.
Anticipated Student Actions/Potential Difficulties/Misconceptions:
Warm-up: Students may not remember how to solve these, so some suggestions on graphing and setting the equations equal to each other to solve for x might be needed. Students might also confuse solving for quadratics and not realize to isolate the x. Students might need a reminder of how to solve for the dependent variable and connect to what this means in terms of both expressions. I anticipate most students will be able to solve this one and discuss different implications. Some students will not understand why we can graph both equations and interpret them as the solution. Tell them to plug in the x values in both equations and see what the output is. Discuss that.
Task 1: Students might have issue with remembering how to find key features to graph or finding where the points intersect. Perhaps suggest that they make the table. I think students will factor and find roots, but may forget how to find vertex form. one with 1 solution with a horizontal line at the vertex (as only a vertical line can cross a parabola once and that is not a function). This should be discussed.
Some students may have factoring issues from the previous unit still. They need to practice or find other methods to solve.
Challenge students by introducing inequalities and having them think about ways to interpret them (by defining domain as an answer).
Homework: I do not anticipate students will have issues with the homework if they paid attention to today's lesson. They can refer to their notes and look up solutions (definitions as well). Tomorrow they will have more issues when we don't have nice integers in the mix. We will practice more in class tomorrow and take questions on the homework assignment.
Students may have issues with the technology or loads on the computer. Try to establish a system to be notified of these issues. If need be, have a few laptops with the apps loaded on them so students can continue working and class time is not wasted. Students can also work in groups and share computers if too many issues arise.
It is important to point out that a vertical line is not a function and describe why.
Ask students what real world situations they might be able to model off of this type of system of equations!
I do not anticipate a lot of misconception as the lesson is pretty guided by the teacher and has nice clean solutions.
If you can stretch this activity, discuss inequalities with these functions as well. Do they actually make sense? How could they make sense?
Questions to pose to students:
I have outlined some good questions in my youtube homework video for the next lesson, questions for students have been incorporated into the presentation and outlined in the teacher guide below. You could ask what other real world applications could these expressions help with.
Sequencing of student responses:
I would suggest doing algebra common errors first, then looking at the correct solutions with algebra. They focus on the graphing solutions and tying the two together.
Assessments:
-Informal assessments are incorporated into the Nearpod and have been outlined in the teacher guide below. You can also see who is in the application and following along as you go.
-A formal assessment and homework activity has been outlined and provided in the Nearpod as well as in the teacher guidelines below.
| day1teacherfile.docx |
