Pennsylvania Standard B Algebra and Functions Discover and generalize patterns, including linear, exponential and simple quadratic relationships.

Step 1: Evidence to Excellence Process Why study patterns?

What is the intent of the standard?  Identify the essential understandings.  What prior knowledge and understandings must students have in order to achieve this standard by grade 8?

Achieving the Standard  Identify and describe the lessons/activities used to equip students with the needed knowledge and skills to achieve understanding?  What would be acceptable as evidence that students understand?

Step 2: The Task Analyze a task which addresses the standard

The Task For Tiffany and Miguel's science fair project, they dropped the same ball from a height of 200 centimeters 20 times. Each time they dropped the ball, they measured how high it bounced on its first four bounces. The following table gives the average of their measurements.

The Task Average Height of Ball Bounces (drop height = 200 cm) Height of 1st bounce153 cm Height of 2nd bounce110 cm Height of 3rd bounce 86 cm Height of 4th bounce 63 cm

The Questions A. Using the grid in your answer booklet, draw a graph showing the data in the table. Be sure to label the axes. B.Predict the height of the 5th bounce.

The Questions C. Describe the pattern that can be used to predict the height of the bounce.

The Task  Was the language of the task clear?  Does the task provide an opportunity for students to have a relevant and meaningful experience that actively engages them in constructing their own knowledge?

The Task  Does the task stimulate higher order thinking and discussion? Explain.  Did the task provide students an opportunity to work with significant ideas and relationships that are included in the standard?

The Task If you would have given this task, what evidence would you use to determine if the student understood the content of the lesson?

Step 3: Student Work Analyze the student work samples and provide their assessment of each sample of work.

Student Work  What is the evidence that the student used good thinking and reasoning skills in completing the task?  How does the student connect the mathematics they were learning to the real world?

Student Work  What is the evidence that the student achieved the goal of the task?  How would you assess the work?  Which pieces of student work achieve the understandings intended in the standard?

The Rubric Advanced - Student shows complete understanding of a number pattern by correctly identifying extensions and describing the pattern graphically, verbally, and algebraically. Proficient - Student shows general understanding of a pattern by identifying extensions and describing the pattern graphically, verbally and algebraically with only minor errors.

The Rubric Basic - Student shows basic understanding of a pattern. Below Basic - Response is incorrect or irrelevant.

The Assessment Student A - Proficient Student B - Advanced Student C - Basic Student D - Below Basic

Step 4: The Assessment Does the assessment fairly reflect the objectives of the task? Based on the student work that you saw, and what you read and understood of the assessment, do you agree or disagree with the assessment of the task?

Step 5: The Reflection How can the task be improved? How can the assessment of the work be improved?

The Reflection What additional evidence is needed to make this a more complete picture of student understanding of the concepts addressed? What interventions should be considered to help students who do not yet understand the concepts?

The Reflection As a result of looking at the student's work, are there things you will consider in your classroom in making assignments and in assessing student work?

The Reflection If you would have given this task, what evidence would you use to determine if the student understood the content of the lesson? Does the task stimulate higher order thinking and discussion? Explain.

The Reflection Did the task provide students an opportunity to work with significant ideas and relationships that are included in the standard?