Summary on Unpacking the Standards and Backwards mapping

Summary on Unpacking Standards and Backwards Mapping Relating to High School Geometry

“Understanding and Applying Standards “is the current course I am studying in my online course program Teach-Now to become a qualified and certified secondary mathematics teacher.  In this unit I studied methods of planning a lesson based on a common core standard I selected based on subject specific area.  I chose Geometry and picked two standards that relate to each other: CCSS.Math.Content.HSG.SRT.C.7 - Explain and use the relationship between the sine and cosine of complementary angles and CCSS.Math.Content.HSG.SRT.C.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.  I learned what it means to unpack a standard, identify the big idea and essential questions, and backwards mapping as it relates to how a teacher designs a lesson based on a specific standard.

 

Unpacking the Standard

Providing students with clear and concise learning objectives is what I learned the main goal of unpacking the standard.  Standard based instruction, like the Common Core State Standard Initiative, helps the teacher in planning for specific key content in a lesson, implementing the key content each student is required to master and assessing each students understanding and application of key concepts of the standard.  To gain full knowledge of the two standards I chose I used the unpacking method on the standard “Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.”  First I identified the verb(s) used in the standard to know what the students need to be able to do to meet the key concepts of the material.  Next I identified the noun(s) used in the standard to for the concepts or what students will know by the end of the unit.  I also noted the context that related the noun and the verb in the standard.  The unpacking phase ends with rewriting the standard in a broken down method that addresses all the requirements and key concepts.  I can now recognize and fully understand the learning goals students need to successfully achieve the standard.  Unpacking a standard gives clarity, continuity, alignment and integration of the desired concepts to be taught.   

 

The Big Idea

Once a standard is unpacked, the Big Idea, or main learning goals will emerge.  Some standards have multiple Big Idea’s which is why unpacking is key in identifying all key concepts students need to master from the standard.  It is important not to add any requirements and to highlight the expectations your desire from the unpacked standard.  Once the Big Idea emerges the teacher can design projects and learning strategies based on each goal.  Big Ideas lead to big learning!

Backward Design Process

Backward design process for a standard begins with identifying the end result or what you want your students to know and apply before you design a lesson plan.  Once the end goal(s) are identified the teacher determines the best assessment for the goal(s).  Now the lesson plan and teaching activities are designed.  A list of concepts, skills and knowledge is needed called learning objectives that students need to demonstrate by the end of the unit or standard.  The assessment plan the teacher chooses evaluate and measure how much each student has learned and if the student can apply the learning objectives successfully.  The teacher can make a formative assessment of the lesson plan in which changes to the lesson can be made to better accommodate the learning needs of the class.  The Backward design process is an effective tool in planning standard based lessons for successful learning. 

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. 

 

Consequences in the Classroom

After the class has acknowledge the rules and procedures the next step is to announce the consequences of following and not following these agreed upon rules.  Consequences should be both positive and negative and established in the first week of class and addressed routinely and frequently over the class year.  Without consequences rules and procedures are meaningless and have no standing with the students.  Consequences must be used in an appropriate way with a mindset of enhancing the learning environment and maintaining and managing a successful classroom. 

Example of positive consequences:  Algebra 2 class of twenty students - Using the "I do it / We do it / You do it together / You do it alone" method, after  I do the example problems on the smart board the students are to work on three specific problems as a class for the We Do It part of the lesson.  Raising hands and participating quietly is crucial for a positive and productive learning environment for all students.  This part of the lesson requires me to remain in the front of the room and guide the students through the problems while having students interact to solve the problems.  Each student that raises their hand I will reply with verbal comments like: "Thank you for raising your hand and following the class rules, what is your question?", "Excellent choice being quiet and waiting to be called on 'students name' what do you think the next step is in solving this problem?".  Using non verbal responses by smiling at students working quietly and giving them a thumbs up when they are sitting quietly waiting for the class to finish as a whole is another way to respond to students in a positive and appreciative way.  For students that demonstrate an excellence of upholding the rules and procedures of the classroom I will send a note home to the parent(s) or guardian acknowledging the students excellent behavior and diligent work in the classroom. 

Example of negative consequences:  Algebra 2 class of twenty students - Using the "I do it / We do it / You do it together / You do it alone" method, while I am demonstrating the "I do it" part of the lesson a student is talking and disrupting the learning - first the student is met with concerned eye contact.  If the behavior continues I will use the students name remaining calm and positive with comments like: "Student name please respect the classroom rules and hold your conversation or comments for after class."; "Verbal warning Students name"; "Just a reminder to the class that being silent is necessary for all students learning, right Students name!".  I would monitor this student during the class time by keeping a close proximity having watchful eye (withitness).  If a student is unable to contain and control breaking the rules and procedures of the class I would initiate a three strike rule: three verbal warnings results in parent/guardian phone call or email. 

A coogle diagram of positive and negative consequences follows:

https://drive.google.com/open?id=100lwQqw-bu68gz4yBmyr6l8tkNxwcdNK

https://coggle.it/diagram/WgUvluojMQABDQqi/f57975feaf72fa3ecc475c43ee482a13341461d584cc4df65dc4a5ad91492f3a