Welcome to Austin Smith's Mini Lessons. The goal of these mini lessons is to utilize technology to engage, enhance, and extend learning. The three mini lessons will pull from the following standards:
ISTE Standards for Students
1. Creativity and innovation
Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
a. Apply existing knowledge to generate new ideas, products, or processes
b. Create original works as a means of personal or group expression
c. Use models and simulations to explore complex systems and issues
d. Identify trends and forecast possibilities
2. Communication and collaboration
Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.
a. Interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media
b. Communicate information and ideas effectively to multiple audiences using a variety of media and formats
c. Develop cultural understanding and global awareness by engaging with learners of other cultures
d. Contribute to project teams to produce original works or solve problems
3. Research and information fluency
Students apply digital tools to gather, evaluate, and use information.
a. Plan strategies to guide inquiry
b. Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media
c. Evaluate and select information sources and digital tools based on the appropriateness to specific tasks
d. Process data and report results
4. Critical thinking, problem solving, and decision making
Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.
a. Identify and define authentic problems and significant questions for investigation
b. Plan and manage activities to develop a solution or complete a project
c. Collect and analyze data to identify solutions and/or make informed decisions
d. Use multiple processes and diverse perspectives to explore alternative solutions
5. Digital citizenship
Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
a. Advocate and practice safe, legal, and responsible use of information and technology
b. Exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity
c. Demonstrate personal responsibility for lifelong learning
d. Exhibit leadership for digital citizenship
6. Technology operations and concepts
Students demonstrate a sound understanding of technology concepts, systems, and operations.
a. Understand and use technology systems
b. Select and use applications effectively and productively
c. Troubleshoot systems and applications
d. Transfer current knowledge to learning of new technologies
Students demonstrate creative thinking, construct knowledge, and develop innovative products and processes using technology.
a. Apply existing knowledge to generate new ideas, products, or processes
b. Create original works as a means of personal or group expression
c. Use models and simulations to explore complex systems and issues
d. Identify trends and forecast possibilities
2. Communication and collaboration
Students use digital media and environments to communicate and work collaboratively, including at a distance, to support individual learning and contribute to the learning of others.
a. Interact, collaborate, and publish with peers, experts, or others employing a variety of digital environments and media
b. Communicate information and ideas effectively to multiple audiences using a variety of media and formats
c. Develop cultural understanding and global awareness by engaging with learners of other cultures
d. Contribute to project teams to produce original works or solve problems
3. Research and information fluency
Students apply digital tools to gather, evaluate, and use information.
a. Plan strategies to guide inquiry
b. Locate, organize, analyze, evaluate, synthesize, and ethically use information from a variety of sources and media
c. Evaluate and select information sources and digital tools based on the appropriateness to specific tasks
d. Process data and report results
4. Critical thinking, problem solving, and decision making
Students use critical thinking skills to plan and conduct research, manage projects, solve problems, and make informed decisions using appropriate digital tools and resources.
a. Identify and define authentic problems and significant questions for investigation
b. Plan and manage activities to develop a solution or complete a project
c. Collect and analyze data to identify solutions and/or make informed decisions
d. Use multiple processes and diverse perspectives to explore alternative solutions
5. Digital citizenship
Students understand human, cultural, and societal issues related to technology and practice legal and ethical behavior.
a. Advocate and practice safe, legal, and responsible use of information and technology
b. Exhibit a positive attitude toward using technology that supports collaboration, learning, and productivity
c. Demonstrate personal responsibility for lifelong learning
d. Exhibit leadership for digital citizenship
6. Technology operations and concepts
Students demonstrate a sound understanding of technology concepts, systems, and operations.
a. Understand and use technology systems
b. Select and use applications effectively and productively
c. Troubleshoot systems and applications
d. Transfer current knowledge to learning of new technologies
GSE Analytic Geometry Content Standards
Unit 2: Right Triangle Trigonometry
Define trigonometric ratios and solve problems involving right triangles
MGSE9-12.G.SRT.6
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
MGSE9-12.G.SRT.7
Explain and use the relationship between the sine and cosine of complementary angles.
MGSE9-12.G.SRT.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Define trigonometric ratios and solve problems involving right triangles
MGSE9-12.G.SRT.6
Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
MGSE9-12.G.SRT.7
Explain and use the relationship between the sine and cosine of complementary angles.
MGSE9-12.G.SRT.8
Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Principles of Inquiry-Based Learning
- Authenticity
The first element of strong inquiry is an authentic learning task where students are engaged in work that is worthy of their time and attention, is personally relevant to them and deeply connected to the world in which they live. The development of authentic learning tasks for students means first and foremost situating learning in rich places and contexts (think: topics, topos, topographies) where curriculum outcomes can brought to life with real world connections, stories and relevance. - Understanding
The challenge for educators is to make use of the engagement that is made possible through authentic, hands-on learning in ways that develop deep understanding of the subject at hand. - Performances
In addition to emphasizing deep understanding of concepts, inquiry provides opportunities for students to engage in, wrestle with and ultimately improve their own ideas and the ideas of their peers. - Assessment
Strong assessment practices must be woven into the continual practices of an effective learning environment, and this is especially true in an inquiry-based study. It is assessment practices that form the bridge between the learning goals and the tasks, making clear to students and teachers what should be learned. - Technology
Technology allows both teachers and students immediate access to current information, statistics and data on a given topic. As finding information is one of the most regular activities students use digital technologies for developing critical information literacy skills is of the utmost importance. - Expertise
When students are engaged in authentic, real world tasks, issues or problems, a natural outcome will be developing connections with experts as part of the learning process. - Success
Another of the key principles behind inquiry-based teaching is involving students in the design and management of the learning, allowing for the development of goal setting, task-management, appreciation of different perspectives and group work skills. - Citizenship
The final element of strong, inquiry-based learning involves creating space in the learning for students to consider their citizenship activities in the communities they participate in, be it their classroom, school, local community, city, country or beyond.
Target Audience
The target audience is a high school mathematics (Analytic Geometry) class. These consists of 9th and 10th graders.