Center for Performance Assessment

Center for Performance Assessment

“Unwrapped,” Standards-Based
Performance Assessment Template (Short Version)

Identifying Information:

Grade Level: 6th grade - Math

Targeted Content Area(s): Number / Number Sense / Operations

Authors: Maria Prater, Mike Masloski, Rick Raach, Jeri Ernest

School, District, State, Phone and/or E-mail: Ridgewood Local School District

Overview:

Assessment Title: Number System and Operations

Summary of the entire performance assessment: Students will be introduced to exponents, prime factorizations, GCF and LCM, and orders of operations. Students will build models of exponents and create two-dimensional drawings of the models. They will create a factor tree diagram. Students will create a story that will enable them to identify the rules for orders of operation. Students will participate in a job fair.

Brief synopsis of each task:

Task 1: Students will build models of exponents using base ten blocks on graph paper.

Task 2: Students will create and demonstrate a family tree and prime factorization that relates to a prime factorization diagram.

Task 3: Students will compose a story that explains the acronym for the orders of operations and create a display that explains the rules for the order of operation.

Task 4: Students will research and demonstrate real life careers that utilize mathematical concepts or exponents, prime factorization, GCF, LCM and order of operations. Students will demonstrate one of these concepts by creating a presentation with a resume for a job fair.

Targeted Standard(s) and Indicator(s):

Full Text of Standard(s) and Indicators(s) in Main Content Area:

Number and Number Sense and Operation

6.1 Decompose and recompose whole numbers using factors and exponents and explain why “squared” means “second power” and “cubed” means “third power.”

6.2 Find and use the prime factorization of composite numbers. For example: a). use the prime factorization to recognize the greatest common factor (GCF); b)use the prime factorization to recognize the least common multiple (LCM); c) apply the prime factorization to solve problems and explain solutions.

6.6 Use the order of operations, including the use of exponents, decimals and rational numbers, to simplify numerical expressions.

Related Interdisciplinary Standard(s) and Indicators(s)

Reading Process 6.5

Reading Application (informational text) 6.5

Writing Process 6.5 , 6.10, 6.15

Writing Application 6.1

Research 6.1

Communication 6.2

“Unwrapping” Standard(s) and Indicator(s):

Grade-specific Standard(s) and Indicators Identified by Numbers/Letters:

Concepts: Need to Know About _____Number System / Operations

Exponents / factors

Second power (squared)

Cubed “third power”

Order of operations

Prime Factorization GCF and LCM

Skills: Be Able to Do

Decompose / recompose (whole numbers and factors)

Explain squared and cubed numbers

Find prime factorization

Use GCF and LCM

Apply prime factorization

Solve problems

Topics or Context: (What you will use to teach concepts and skills—particular unit, lessons, activities)

Text book, Buckle Down workbook, and teacher materials.

Big Ideas and Essential Questions:

Big Ideas Derived from “Unwrapped” Standard(s) and Indicator(s)

1. Exponents show how many times a base number occurs as a factor.

2. Prime factorization is a way of expressing a composite number as the product of prime numbers.

3. The largest common factor of two numbers is GCF, the smallest common multiple is LCM.

4. There are specific rules for the orders of operations.

Essential Questions to Guide Instruction and Assessment

1. How do exponents change the value of the base number? Give two examples.

2. Can’t you use prime factorizations with all numbers? (Create a factor tree with a number provided by the teacher.)

3. What are the orders of operations? Follow the rules to solve the following problem. 6+(15+2)x3 =

4. What is the difference between the GCF and LCM?

Engaging Scenario: Students will sort a collection of numbers which include perfect squares and perfect cubes. The numbers are:

49, 100, 25, 36, 144, 9, 8, 27, 64, 10, 38, 125, 343, 1000,

8000, 0, 1, 20, 50, 333

The Performance Assessment Tasks (Detailed) and Scoring Guides:

Task 1 (Complete Description)

Standards – Number and Number System

Indicators – 6.1

Question – How do exponents change the valve of the base number?

Content/Skill – exponent, explain, square, and cube

Application – Build physical models of exponents

Resources – Base ten blocks, overhead projector, transparency

Evidence – Creation of model

Task 1 – Scoring Guide (BLOCKS) (GRAPHS)

Exemplary:

When given nine sets of exponential numbers, students will build model blocks for eight out of the nine correctly.

When given nine sets of exponential numbers, students will draw models of exponents on graph paper for eight out of the nine correctly.

Proficient:

q Student will answer six or seven correctly using the base ten blocks.

q Student will answer six or seven correctly drawing models of exponents on graph paper.

Progressing:

q Student will answer four or five correctly using the base ten blocks.

q Student will draw four or five models of exponents on graph paper.

Not Yet Meeting Standard(s):

q Student will answer less than four correctly using the base ten blocks.

q Student drew less than four models of exponents on graph paper.

Peer Evaluation (Optional) ______

Self Evaluation ______

Teacher Evaluation ______

Comments:

Task 2 (Complete Description)

Standard – Number and Number System

Indicator – 6.2

Question – Why can’t you use prime factorization with all numbers?

Content/Skill – Find prime factorization

Application – Create and demonstrate a family and factor tree in comparison

Resources – Prior knowledge, book or movie for family tree, poster board, poster paper

Evidence – prime factorization and family tree diagrams

Task 2 – Scoring Guide

Exemplary:

q All Proficient Criteria Met PLUS:

Proficient:

Progressing:

Not Yet Meeting Standard(s):

Peer Evaluation (Optional) ______

Self Evaluation ______

Teacher Evaluation ______

Comments:

Task 3 (Complete Description)

Standards – Number and Number System

Indicators – 6.6

Question – What are the orders of operations?

Content/Skills – Identify specific rules of operation

Application – Write a story using the acronym for order of operations

Resources – Previously taught content, computer, word processor

Evidence – Display and story

Task 3 – Scoring Guide

Exemplary:

q All Proficient Criteria Met PLUS:

Proficient:

Progressing:

Not Yet Meeting Standard(s):

Peer Evaluation (Optional) ______

Self Evaluation ______

Teacher Evaluation ______

Comments:

Task 4 (Complete Description)

Task 4 – Scoring Guide

Exemplary:

q All Proficient Criteria Met PLUS:

Proficient:

Progressing:

Not Yet Meeting Standard(s):

Peer Evaluation (Optional) ______

Self Evaluation ______

Teacher Evaluation ______

Comments:

Teacher Reflections at Conclusion of Performance Assessment:

1. What worked? What didn’t?

2. What will I do differently next time?

3. What student work samples do I have for each task? What examples of proficiency (and exemplary) do I have for each task?

4. What field notes can I provide for other teachers who may use this performance assessment in the future?

Permission Granted to Duplicate for Instructional Purposes Only