Pennsylvania Standard 2.8.8 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 TaskFor 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 TaskAverage Height of Ball Bounces(drop height = 200 cm)Height of 1st bounce 153 cmHeight of 2nd bounce 110 cmHeight of 3rd bounce 86 cmHeight 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 TaskWas 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 TaskIf 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 WorkWhat 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 RubricAdvanced - 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 RubricBasic - Student shows basic understanding of a pattern.Below Basic - Response is incorrect or irrelevant.

The Assessment

Student A - ProficientStudent B - AdvancedStudent C - BasicStudent 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?