Common Core Geometry Unpacked and Backwards

The Common Core State Standards are designed to get students ready for college and careers by helping them be critical thinkers.  Unpacking the standards set by the Common Core allows a teacher to develop a lesson plan that engages students to learn at a higher level by relating curriculum to real life application.  Backwards planning is a process where a teacher can create a learning experience to meet specific learning goals staring from the end result.  The teacher starts by identifying the objectives and learning standards required for students to meet or determining the end result of the lesson.  A list of skills and concepts that students need to master the specific learning objective follows.  Next a final test or assessment is designed that will determine students learned the objectives of the standard.  A series of lessons and projects are then designed to progressively move students to the complete understanding of the objective.  The teacher then decides how to assess the students at each step of the learning process for the unit.  Assessment can be in many forms, from a quiz, project or even verbal questions during class, allowing the teacher to determine if students are learning the material needed to be successful.  Finally the teacher can review and reflect on the lesson plan and make any changes or additions. 

Currently I am teaching a first and second semester online Geometry course through Oaks Christian Online School, but not a teacher in the traditional classroom.  The online course corresponds to the in class curriculum at Oaks Christian High School located in Westlake Village, CA and common core state standards are used.  I chose CCSS.Math.Content.HSG.SRT.C.8: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. High school students taking Geometry range from 9^th grade to 11^th grade.  I choose this standard because of the applications of right triangles, trigonometry and the best known and most useful theorem in mathematics, the Pythagorean Theorem. 

The following are goals or proficiencies I want students to achieve by the end of the unit: 

1.       Algebra review for this standard: Finding the square root and rationalizing the denominator.

2.       Understand and use mathematical vocabulary associated with this standard: Sine, Cosine, Tangent, Cosecant, Secant, Cotangent, Opposite, Adjacent, Hypotenuse. 

3.       State and Apply the Pythagorean Theorem and the Converse of the Pythagorean Theorem.

4.       Prove the Pythagorean Theorem.

5.       Know and apply the basic trigonometric functions defined by the angles of a right triangle.

6.       Use trigonometric functions to solve for an unknown length of a side of a right triangle.

 

 

I will use the following assessments to know students are meeting and understanding the standard:

1.     Assigned daily homework to reinforce concepts learned.  Students will have time to ask homework questions and receive feedback from homework assignment. Ability to call on a student who understood a problem to explain how they arrived at the solution. 

2.     Two to three quizzes prior to the test to assess student’s readiness and understanding of material.  All quiz grades below 70% can retake prior to the test for additional credit and support.

3.     Verbal questions throughout the class time, engaging the class to participate in the learning experience.

Learning experiences or activities I will use to help students meet the standard are as follows:

Student will design their own right triangle word problem and present to the class.  I will encourage students to design the problems as it relates to their own life.  For example:  I play golf and I could design a right triangle to find out how far I need to hit the golf ball or at what angle to the flag from a position on the golf course.   Students will submit their word problem with diagram using paper, poster board, or digital presentation; answer key provided on separate sheet of paper.

Words-Symbols-Models Project:  Students will write in words the trigonometric functions with specific ratio associated with that function, followed by the symbol represented by the specific function anda model to represent the function.  Students can present their work in google slides, Prezi, or presentation method of choice.  I would choose the top three presentations to present to the class and winning designs would receive a homework pass or first release from class for the week.

Students will work in groups of 2-3 on an applied word problem of my choice (involving sailing, gardening, painting, geography) using a right triangle and the Pythagorean theorem to determine the missing distance, find the Perimeter of the figure, Area of the figure, and cost analysis of project in word problem.  This will be an in class project.  Each group will make a drawing/ diagram labeling important parts.  On a separate page the group will present all math used for the drawing/diagram and in finding the cost of the perimeter/area of the project.