Round 1: Programming, Free Play, Yammer
Students can collaborate, share, get support, and discuss their programming as they are participating in the coding activities, games, and lessons. Students can free play in programming games such as CodeCombat, Hour of Code Games, and Tynker. Yammer allows for file sharing, polling, and communication among students and teacher.
Round 2: Constitutional Law, Conduct an Interview, Video Recorder
To learn about and explore constitutional law, students can carry out an interview with a peer, teacher, or an expert in person or on the internet. This interview can be videotaped to be edited, shared, and analyzed by the class. Discussions about the questions and answers in the interview can be used to further examine the topic of constitutional law and transition into other issues.
Round 3: Digital Citizenship, Minute Write, Wiki
A minute write on digital citizenship completed by students can also be posted on the class wiki to be shared. Students preconceived notions, background, and experiences are shared through the minute write activity and then shared with others and the class through the wiki. This provides a great launching point for discussion and research into digital citizenship.
Round 4: Engineering, Brainstorming, Padlet
Platforms such as Padlet, Google Keep, and Trello provide a collaborative space for class brainstorming. For the task of engineering a product, students can brainstorm with each other in these, and other platforms. This creates a digital record of the brainstorming process, and students can return to their notes throughout the research and product creation.
Round 5: Self-Regulation, Team-Based Learning, iMovie
Students can create an iMovie with their team to demonstrate self-regulation in different reenacted scenarios. Research into self-regulation will be completed by students to create a script that students can relate to. Visual cues provide more connections for students to learn and remember self-regulation techniques.
TPACK Lesson Plan
Title: Polynomial Division
Summary: In this lesson students will use area models to reverse the process of multiplication to perform polynomial division. They will work out area model “puzzles” to learn the process of division and then create an instructional video.
Primary Core Goals/Outcomes:
A-APR.2. Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
A-APR.6. Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.
Intended Learning Outcomes: Students will use polynomial division to find factors of polynomials.
This lesson will be more student-centered as it is a discovery activity completed in small groups that build upon their prior knowledge with the teacher as a facilitator and guide. Students should develop similar conclusions and understandings about the process of polynomial division (convergent learning) based on of their prior experiences of working with polynomial operations (more relevant background knowledge with polynomials needed). Since this is more of an introductory exercise, students will be building more surface-level comprehension of the concept than deeper knowledge.
With the time spent in class (about 50 minutes) and homework assignment (about 30 minutes), this plan will take a moderate about of time (duration) and will lead into further lessons which use polynomial division to determine the real and complex roots of a polynomial in factored form. Materials needed include a recording device such as an iPad or Chromebook, calculators, and writing supplies. Overall this less will be more structured as students use puzzles and problems to practice to learn the fixed division process but given more flexibility and creative freedom when creating the instructional video.
TPACK Activity Types:
“Consider” activity type: Discuss (collaborative group work), recognize a pattern (steps to divide polynomials), investigate a concept (polynomial division)
“Practice” activity type: Solve a puzzle (area model with blanks to demonstrate polynomial division process), do computation (division), do practice (practice dividing polynomials)
“Interpret” activity type: Interpret a representation (explain the steps of polynomial division from an area model)
“Produce” activity type: Describe a concept mathematically (polynomial division), produce a representation (division with area models)
“Apply” activity type: Take a test (summative assessment at end of unit)
“Evaluate” activity type: Test a solution (with graphing calculator)
“Create” activity type: Create a product (instructional video)
Assessment Plan: Formative assessment will be through observation, questioning, completion of puzzles, practice problems, and video creation. Summative assessment will be through a mid unit quiz and unit test.
Used by the Teacher: Polynomial division puzzles and practice problems, assessments, and questioning prompts.
Used by the Students: Polynomial division puzzles and practice problems, answers for checking work, and writing supplies.
Used by the Teacher: Interactive whiteboard for discussions and support, device to view and evaluate student created videos, and an optional learning management system to give feedback (such as Edmodo or Schoology).
Used by the Students:
Video creation software (Doceri or Screencastify) and device for recording such as an iPad, Chromebook, or computer, and graphing calculator (online such as Desmos or handheld such as TI-84).
Warm up – Students will complete practice problems involving polynomial multiplication which requires them to use their background knowledge from Algebra 1. This warm-up can be done with Socrative or Kahoot to give students immediate feedback and as a formative assessment.
Launch – Class discussion and review of how multiplication and division are inverses of each other, how using the factored form of a polynomial can give the roots of the graph, and how limited our graphing calculator is in giving the roots as it only gives real roots in decimal form. Polynomial division can convert a standard form of a polynomial into factored form, giving the exact real and complex roots. This analysis and discussion will be conducted using the interactive whiteboard and graphing calculators.
Explore – Students will complete the polynomial division puzzles with their teams, filling in the blanks by working backward and using their background knowledge of how to multiply polynomials using area models. As they work, the teacher will observe, question, and have students check answers to assess their progress informally. Once they have completed the problems and understood the division process, students will use their devices to create an instructional video (similar to Khan Academy videos) to explain the process of dividing polynomials with an area model. They have the option to be as creative as they like with the media and to work in pairs.
Closure – Once the students are finished creating their videos, they will watch at least one of the other couple’s video and give them feedback. This feedback can be provided through a Google app (such as Docs, Forms, or Keep) or Peergrade and should be on the clarity, detailedness, creativity, and correctness of the video. Feedback is shared in a class discussion with any misunderstanding or extensions examined. Summative assessments will be a pencil and paper mid unit quiz and an end of unit test.