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Trigonometry is covered over three units in my Precalculus class. In the first unit we work on graphing trigonometry and trigonometric functions.  The second trigonometry unit includes such topics of angles of depression and elevation, identities and the law of sines and cosines. The final trig unit works with vectors.  

Students who have come out of Algebra 2 are familiar with the basic trigonometric functions.  This unit is primarily review and a great place for an open-ended project that taps into students’ creativity. 
Ancient Rome is an era rich with lasting legacies in architecture, government and more.  One often overlooked legacy of Ancient Rome is the technological advances that occurred even as the empire expanded.  
There are lots of ways to approach the science and technology.  If you are short on time, you can grab a video (this is one from study.com).   But if you have time, it is a worth while investment to have students engage in one or more activities.  I set up 5 stations for students to investigate.  Typically, students will complete 2 - 3 of the stations.  

The stations are:

Wouldn’t it be great if every topic could be highly engaging?  Or if you had time and creativity to “play” with topics?  It would. In reality, time is scarce.  Furthermore, and I hope it's not just me, some topics are just not that inspiring.  

 Graphing exponential functions is one of those, somewhat uninspiring.  It’s in the curriculum, so we learn it but I have yet to find a truly creative approach to them.  After completing our notes, students need to practice. To make it just a little more fun than a problem set, students use digital task cards. 

 Benefits of digital task cards: 

Ancient Greece is a unit rich with fascinating topics - major changes in governmental structures, architecture and art whose influence and style are still used today, city development, literary themes that have been replayed in literature and novels for centuries, and of course, philosophical thought.  Our approach is shaped by the themes of the year and the maturity and interests of the students.  I ascribe to the school of thought that supports reaching high, and when possible, we include at least one day on the big three philosophers: Socrates, Aristotle, and Plato.  The scope of this first lesson is divided into four parts: primary source readings, background and discussion, and activities.

 Readings:  primary sources are the way to go if my students can handle it. I often choose readings from each philosopher that generally approach the same topic, because this provides a good basis for comparison. 

  • Socrates:  so, Socrates is interesting because of course there are no primary sources for Socrates.  What we attribute to his writings were actually not written by him. Our knowledge of what Socrates thought is through Plato's dialogues.  Plato was the witness of Socrates' teachings.  Sections of The Republic describe Socrates' beliefs and views on government.
  • Plato:  there are lots of choices for Plato.  I like Plato's cave allegory which is found in Republic VII.  Students complete the reading and sort out what they think is happening and then we continue the discussion and analysis in the next two parts of the lesson.
  • Aristotle: excerpts from Aristotle's A Treatise on Government have long-term value as this set of writings is arguably one of the most influential political thought texts, even today.

Background and Discussion:  The primary sources present their own challenges but can be difficult for students to understand.  I provide a 2-page summary of each philosopher that includes background on their lives and key ideas.  Often this is a homework assignment, so they are prepared for hands-on classwork on day 2. 

 Activities:  Five activities to help students work with the material are provided.  I give students a choice of two or three to complete.  I require one involving government and the philosophers.  Students compare the viewpoints of each Socrates, Plato and Aristotle on government. Students follow their analysis of the philosophers with their own viewpoints on government.  Depending on the number of activities each student completes this can take 1-2 class periods.  


 Analysis:  On the final day we wrap up our study of thought from Ancient Greece with a Socratic discussion.  It seems only fitting.  For those less familiar with the how-to of Socratic Method, Teachhub.com has a good outline here.  Although this is where we conclude our formal study of these philosophers, the ideas we have read, discussed, and analyzed will be revisited for much of the year (and hopefully, as students go on in their studies).



This is part of a series of posts on teaching topics in World History.  Topics include:
  • Ancient Mesopotamia
  • Ancient Egypt
  • China
  • Ancient Greece
  • Ancient Rome
  • The Middle Ages in Europe
  • Medieval Japan
  • The Renaissance
  • The Age of Exploration

Social Sundays is a bi-weekly post sharing tips, ideas, resources, and products for teaching social studies.  If you have questions or think there is something I should share, you can leave me a message in the comments below or at the store in the question and answer section.  
 Systems of equations is a great, open-ended math topic to work with.  Over the years, I have developed multiple assessment projects for systems of equations.  I like to give students choice of projects.  Here's a brief introduction to 5 project to use in your own classroom:

The roaring 20s is a fantastic era to get U.S. history students thinking about a division of experiences and viewpoints.  While known as the "roaring 20s" and often portrayed as an era of parties, there was also a large portion of the United States that was living in poverty already and who were not living the "high life."  There was an ideological divide in the United States.  It was further exacerbated by policies and technology of the day.  

We study the clashing ideologies, inequity and changes.  One of the major topics to explore this division is immigration and nativism.  This topic is especially salient to my students and to modern times.

We started Unit 2: Polynomials in PreCalculus.  Quadratic functions go fast, as this is the third time they have seen them.  I would like to say that I get super creative for Quadratic Functions.  I would, but I don't.  We fly through them focusing on factoring, solving, and graphing. I spend more time in this unit on the concepts which I find can be challenging - zeros of polynomial functions, polynomial division, and graphing rational functions.

China is a challenging topic for me.   I often feel like I am learning the material just ahead of the students and wish I knew more.  There just never seems to be enough time.  Instead, our journey through China is one of mutual inquiry and discovery.  We look at the cyclical nature of the 11,000 period of China we study as well as how similar cycles continue today.

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I am a research policy advocate, educator, curriculum developer, author, PhD, amateur chef and of course, ultra marathon runner. I am deeply passionate about helping every student have the best opportunity to find their passions and develop their skills.

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