Formative and Summative Assessments for High School Geometry Standard

Formative and Summative Assessments for a Geometry Standard

The standard I have chosen to write assessments for is a high school geometry standard: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. 

 A formative assessment is an evaluation of learning during a planned lesson while a summative assessment is an evaluation of learning at the end of a planned lesson.  A formative assessment is for both the student and the teacher and should reveal the students level of understanding.  A formative assessment enables a teacher to refine and or revise a lesson to ensure the standard is meet by each student in the classroom.  Formative assessments can be for a grade or not for a grade.  A summative assessment tests how much a student has learned at the end of the planned lesson.  A summative assessment could be a standardized chapter test or cumulative test, for a grade that demonstrates a student’s knowledge of a subject, and application of the knowledge learned.  Only future curriculum is affected with the data received from the summative assessment.

Formative Assessment #1:  For all five of my objective I would assign daily homework as a formative assessment to reinforce the concepts learned each day of class.  My homework assignments will be unique: 

Day 1 Objective 1 = 5 homework problems from the specific objective

Day 2 Objective 2 = 5 homework problems from Objective 2 and 3 homework problems from Objective 1

Day 3 Objective 3 = 5 homework problems from Objective 3 followed by 3 problems from Objective 2 and 2 problems from Objective 1; and so forth. 

Some high schools work on A/B 90 minute schedules and I would adjust my objectives and lesson and homework accordingly.  The goal of the formative assessment is the homework assignments will gradually build with each new objective to revisit and reinforce concepts learned until the standard and total lesson is completed.  As the amount of problems decrease when new objectives are introduced the complexity and critical thinking skills will increase challenging students to apply concepts, knowledge and work towards an excellent understanding of content, thoroughly identifying how topics are applied.

Formative Assessment #2:  Randomly choose students throughout the class time to state the Pythagorean Theorem. Every class during the week I would randomly choose 5 students (or total students in class divided by five or class days) – like a verbal pop quiz.  This would be a good verbal assessment of Objective 1 and have students commit to memory the Pythagorean Theorem which is used and applied in upper level mathematics classes. 

Performance Based Summative assessment #1: (5-10 minutes) Have students answer the following question to demonstrate their depth of understanding and coherence after all objectives have been covered: “How do you use trigonometric ratios to solve for a missing side or angle of a right triangle?” 

Performance Based Summative assessment #2: (5-10 minutes) Have students answer the following question to demonstrate their depth of understanding and coherence after all objectives have been covered: “Use the given image, angle C is a right angle, to find the value of sin A and cos B. What relationship does the ratios of sin A and cos B share? What is the value of tan A and tan B? "

 

Performance Based Summative assessments will be graded on a point system to show students level of learning and understanding:

(3) Superior – Shows thorough understanding of the concepts. Uses appropriate strategies to solve problems. Computations are correct. Written explanations are exemplary. Diagrams are accurate and appropriate. Goes beyond requirements of problem.

(2) Satisfactory with minor flaws – Shows understanding of the concepts. Uses appropriate strategies to solve problems. Computations are mostly correct. Written explanations are effective. Diagrams are mostly accurate and appropriate. Satisfies all requirements of problem.

(1) Nearly Satisfactory with serious flaws – Shows understanding of most of the concepts. May not use appropriate strategies to solve problems. Computations are mostly correct. Written explanations are satisfactory. Diagrams are mostly accurate and appropriate. Satisfies most requirements of the problem.

(0) Unsatisfactory – Shows little or no understanding of the concepts. May not use appropriate strategies to solve problems. Computations are incorrect. Written explanations are not satisfactory. Diagrams are not accurate or appropriate. Does not satisfy requirements of the problem.

The following are five objectives from the above standard:

Objective 1: Students in my geometry class will be able to define, show and solve the Pythagorean Theorem by the end of the class.

 Objective 2: Students in my geometry class will be able to recognize, comprehend and compute the converse of the Pythagorean Theorem and related theorems about obtuse and acute triangles by the end of class.

Objective 3: By the end of class my geometry students will be able to distinguish, identify and interpret the lengths of two sides of a 45-45-90 and 30-60-90 triangle when the length of the third side is known (given).

Objective 4: Student in my geometry class will be able to identify and explain tangent, sine and cosine ratios for an acute angle of a right triangle by the end of class time.

Objective 5. By the end of class, students in my geometry class will be able to solve right triangle problems by correct selection and use of the tangent, sine and cosine ratios.