Domain 8 - Newark Public Schools



NEWARK PUBLIC SCHOOLS

Grade 8 Mathematics

CURRICULUM GUIDE

2010-2011

NEWARK PUBLIC SCHOOLS

A D M I N I S T R A T I O N

2010-2011

Superintendent Dr. Clifford B. Janey

School Business Administrator Ms. Valerie Wilson

Chief of Staff Ms. Sadia White

Chief Academic Officer Mr. Roger Leon

Regional Superintendent XXXXXXXXXX

North Region

Regional Superintendent Dr. Dale Talbert

South Region

Regional Superintendent XXXXXXXXXXXX

East & Central Regions

Regional Superintendent Dr. Ronald Taylor

West Region

TABLE OF CONTENTS

Title Page 1

Board Members 2

Administration 3

Table of Contents 4

District Mission Statement 5

District Goals and Priorities 6

Curriculum Committee 9

Course Philosophy 10

Course Description 11

Recommended Textbooks 12

Course Proficiencies 13

Course Pacing 17

Curriculum Units 19

THE NEWARK PUBLIC SCHOOLS DISTRICT

MISSION STATEMENT

The Newark Public Schools District’s mission is to develop a productive citizen who is distinguished in all aspects of academic endeavors and willing to challenge the status quo in our society.  We are committed to ensuring that our policies and practices will prepare our students for a world that is increasingly diverse and knowledge driven. We expect our schools and classroom environments to be emotionally safe and intellectually challenging. We pledge to partner with parents, groups, and organizations that add support to the mission by changing hearts and minds to value education.

Dr. Clifford B. Janey

State District Superintendent

GOALS AND PRIORITIES

Great Expectations: 2009-13 Strategic Plan

OUR SHARED GOAL: PREPARING ALL STUDENTS FOR COLLEGE, WORK, AND CITIZENSHIP

Our youth need to be able to compete in an increasingly complex, competitive, and diverse world. Many of the best new jobs require not just a high school diploma but at least two years of college. We need to raise the bar, and we are. Our goals for 2013 are very challenging. Students need to be:

▪ Ready to learn by kindergarten. 80 percent of our students will be ready to learn by kindergarten, up from 64 percent in 2008–09.

▪ Reading and writing at grade level by the end of 3rd grade. 80 percent will be reading and writing by the end of 3rd grade, up from 40 percent in 2008–09.

▪ Ready for the middle grades. 80 percent of 5th graders will be proficient or above in language arts literacy and 85 proficient or above in math, up from 40 percent and 59 percent, respectively, in 2008–09.

▪ Ready for high school. 80 percent will be “on track for graduation,” up from 38 percent of freshmen who are on track to begin the 2009–10 school year.

▪ Ready for college or work. 80 percent will graduate, and 80 percent of graduates will enroll in college, up from 54 percent and 38 percent, respectively, in 2008–09.

GOALS AND PRIORITIES

Great Expectations: 2009-13 Strategic Plan

PRIORTIES

PRIORITY 1:. Ensure highly effective teachers and principals deliver strong curriculum, instruction, and assessment

▪ Strengthen and align curriculum with rigorous standards, ensuring that it is engaging, challenging, and consistently implemented.

▪ Create a highly effective professional development system for teachers and administrators that is more focused on delivering quality instruction and aligned to the learning needs of each student.

▪ Ensure there is a highly effective teacher in every classroom and a highly effective principal in every school by strengthening the preparation, recruitment, induction, evaluation, recognition, and compensation of effective teachers and principals.

PRIORITY 2: Build a system of great schools that serve students, their families, and the community

▪ Build an aligned, supportive Pre-K–grade 3 pipeline that ensures students are ready for kindergarten, reading by grade 3, and prepared to move forward.

▪ Transform the middle grades experience to ensure students are prepared for high school — academically, socially, and emotionally.

▪ Dramatically transform our high schools, building a system of themed, college and

▪ Career-oriented schools that ensure all students graduate prepared for college, work, and citizenship.

▪ Implement an aggressive strategy for turning around low-performing schools that includes reconstitution, external partnerships, full-service “community schools,” and other effective strategies.

PRIORITY 3: Ensure that schools are safe, welcoming, and working collaboratively with parents, families, and community partners to support student success

▪ Ensure that all students, parents, families, and community members are respected and all schools are safe and “family-friendly.”

▪ Actively work to help parents and families become more informed and involved.

▪ Expand and strengthen quality partnerships, including the “full-service community school” model to provide services,

PRIORITY 4: Improve our educational practice by creating an accountability system that promotes data-informed, effective, and efficient management and operations

▪ Reorganize central and regional offices, and streamline operations to strengthen support to schools and students.

▪ Create a culture of accountability that uses data to inform decision-making at every level in support of the district’s strategic priorities.

▪ Increase the transparency of how we make decisions and report on outcomes of our work together

CURRICULUM COMMITTEE

Naga Madhuri Philkhana – Mathematics Coach (K-8)

Susana Monteiro – Teacher, Grade 8

Newark Public Schools

Grade 8, Mathematics

Course Philosophy

Philosophy of Middle School Mathematics

By the end of eighth grade, each student will use his/her mathematics background to recognize their individual ability to grow into a successful and healthy adult.

Each student will think, write, read and speak the language of mathematics inside and outside of the classroom. These learned skills will be demonstrated by the student’s ability to problem solve with reason, insight, inventiveness and technical proficiency.

To develop versatile mathematics skills, each student will use prior knowledge to become an investigative, independent learner. The teacher will be the acting facilitator to guide, enhance and differentiate instruction. In addition, the teacher will ensure each student strengthens his/her mathematic skills and abilities.

Ultimately, each student will take his/her knowledge outside of the classroom walls to apply problem solving skills to solve real world situations and develop a successful future

Newark Public Schools

Eighth Grade Math

Course Description

This comprehensive course provides for the transition from elementary mathematics to algebra/geometry, while solidifying students’ grasp of arithmetic concepts and procedures. Emphasis is on the prerequisite skills and concepts for algebra, as well as problem-solving strategies. Students are guided through problem-solving processes to develop analytical skills. Extending the basic operations to operations with rational and irrational numbers eases the student’s transition to algebra. Simple equation-solving techniques and properties of operations are introduced. Students also explore exponential and quadratic functions. A student who is successful in this curriculum will be ready to take Algebra I as a ninth grader.

Recommended Textbooks/Resources

Teacher Reference Texts

Kaplan, J.D. (2008). New Jersey ASK8 Coach, Mathematics, Grade 8. New York: Triumph Learning. ISBN# 978-1-59823-723-8(SE)

Grace, et.al (2009). IMPACT Mathematics Course 3. Columbus, OH: Macmillan McGraw-Hill Glencoe. ISBN# 978-0-07-888708-6

Lappan, et. al. (2009). Data Distributions. Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366200-4

Lappan, et. al. (2009). Filling and Wrapping. Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366198-9

Lappan, et. al. (2009). Kaleidoscopes, Hubcaps, and Mirrors. Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366206-3

Lappan, et.al. (2009). Looking For Pythagoras. Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366202-0

Lappan, et. al. (2009). Moving Straight Ahead. Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366197-0

Lappan, et. al. (2009). Say It With Symbols. Upper Saddle River: Pearson-Prentice Hall ISBN#0-13-165682-1

Lappan, et. al. (2009). Samples and Populations. Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366-209-8

Lappan, et. al. (2009). Shapes of Algebra. Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366-

Lappan, et. al. (2009). Thinking With Mathematical Models. Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366201-2

Lappan, et. al. (2009). What Do You Expect? Upper Saddle River: Pearson-Prentice Hall. ISBN#0-13-366-144X

Further Resources Recommended

Brendel, J.T. (2009). New Jersey ASK 8 Math Test 2nd edition. Montvale, New Jersey: Barron’s Educational, Inc. ISBN#0-7641-4308-5

Course Proficiencies

Upon successful completion of this course, students will:

1. Identify Rational and Irrational Numbers

2. Use rational approximations of irrational numbers and be able to compare them by locating them on a number line.

3. Apply properties of exponents

4. Use the square root and cube root symbol to represent solutions

5. Use powers of 10 to represent large quantities or very small quantities

6. Perform operations using scientific notation for both whole numbers and decimals.

7. Use expressions involving more than one operation.

8. Choose appropriate measurement units

9. Substitute values for variables in order to evaluate algebraic expressions.

10. Comprehend the mechanics of simplifying expressions, including those containing one or more enclosures.

11. Identify the properties of integers, including negative numbers, in addition, perform accurately the basic operations involving them.

12. Solve equations including simple systems of linear, those containing fractions and/or enclosures as well as quadratics.

13. Show proficiency in writing English phrases in mathematical terms and be able to solve word problems of many types.

14. Simplify products and powers and evaluate algebraic expressions

15. Perform the four basic operations on polynomials, including the multiplication at sight of certain special products.

16. Apply factoring skills in specific algebraic situations.

17. Solve algebraic fractions.

18. Use Cartesian coordinates to graph a straight line and solve systems of linear equations graphically.

19. Apply the slope of a line and write the equation of a line given certain conditions.

20. Use and experiment with properties of transformations

21. Comprehend that a two-dimensional figure has congruency with different transformations

22. Appropriately integrate technology with the curriculum.

23. Relate mathematics education and career choice.

Students who complete this course successfully will be prepared to take Algebra I or Honors Algebra I.

Curriculum Units

Unit 1- Number Sense

▪ Rational Numbers through decimal representations an find the approximation

▪ Solve problems using ratios, proportions, and percents

▪ Use appropriate numerical operations to solve real-world problems using fractions

▪ Determine an irrational Numbers and find its equivalency

▪ Locating irrational numbers and locating them between two consecutive rational numbers.

Unit 2-Expressions and Equations (working with radical and integer exponents)

▪ Exponents

▪ Use root numbers and determine rational or irrational

▪ Use the root symbol to represent solutions to equations

▪ Evaluate common perfect squares and cubes

▪ Estimate and express large numbers

▪ Compare single digits numbers as scientific Notation

▪ Perform operations with scientific notation

▪ Choose appropriate units of measure for extremely large and small quantities

▪ Interpret scientific notation through the use of technology

▪ Compare Integers

Unit 3- Expressions and Equations (Evaluate Functions)

▪ Compare Unit Rate by analyzing functions given in the form of an equation, table, or graph

▪ Define linear functions by interpreting the linear equation in the form of y = mx +b

▪ Use functions to model relationships between two quantities

▪ Describe functional relationships between two quantities

▪ Solve for linear equations in one variable with one solution

▪ Evaluate and simplify equations

▪ Solve linear equations with rational number coefficients

▪ Find solutions to a system of two linear equations in two variables

▪ Locate the point of origin and the point of intersection on a graph

Unit 4- Analyze and Solve Linear Equations

▪ Solve systems of two linear equations in two variables algebraically

▪ Setting up two-linear equations

Unit 5-Functions

▪ Complete function tables by applying rules

▪ Create graphs using input and output values of a table

▪ Compare rates of change by analyzing functions in a form of an equation, table or graph

▪ Define linear functions by interpreting the equation y = mx +b

▪ Use function model relationships between two quantities

▪ Evaluating functions of x and y-values

▪ Describe functional relationships between two quantities

Unit 6- Geometry

▪ Verify properties of reflection, rotation, and translations

▪ Establish congruency between two 2-dimensional figures

▪ Identify similar figures by analyzing the sequence of transformations and/or dilations

▪ Generate geometric patterns

▪ Solve problems requiring calculations that involve various units of measurement

▪ Find surface area

▪ Explore the relation between area and perimeter

▪ Determine measures of angles

▪ Determine the measure of alternate interior and exterior, and interior and exterior angles.

▪ Apply the angle relationships formed by parallel lines

▪ Solve geometric problems by applying properties

▪ Construct nets for 2- and 3-dimensional figures

▪ Find proof for Pythagorean Theorem

▪ Find unknown side lengths for 2 and 3-dimensional figures

▪ Find the distance of coordinate points by applying the Pythagorean Theorem

Unit 7-Applying the Pythagorean Theorem

▪ Find the volume of cones, cylinders, spheres and prisms

▪ Find the volume of pyramids

▪ Find the surface area of cones, cylinders, spheres, prisms and pyramids

Unit 8-Statistics and Probability

▪ Construct a two way table using collected data

▪ Interpret and summarize data

▪ Determine data of line of best fit

▪ Solve problems in the context of bivariate measurement data

▪ Find patterns of bivariate data

▪ Find the probability of compound events

▪ Explore solutions to problems using the vertex edge

▪ Find the possibility of combinations

Suggested Course Pacing

| |Unit |Books/Resources |Topics |#of Days |

| |I |Looking For Pythagoras |Rational Numbers through decimal representations an find the approximation |15 |

|Semester I | |New Jersey ASK 8 Coach |Solve problems using ratios, proportions, and percents | |

| | |Impact Mathematics-Course 3 |Use appropriate numerical operations to solve real-world problems using fractions | |

| | | |Determine an irrational Numbers and find its equivalency | |

| | | |Locating irrational numbers and locating them between two consecutive rational numbers | |

| |II | |Exponents |5 |

| | |Looking For Pythagoras |Use root numbers and determine rational or irrational | |

| | | |Use the root symbol to represent solutions to equations | |

| | | |Evaluate common perfect squares and cubes | |

| | | |Estimate and express large numbers | |

| | | |Compare single digits numbers as scientific Notation | |

| | | |Perform operations with scientific notation | |

| | | |Choose appropriate units of measure for extremely large and small quantities | |

| | | |Interpret scientific notation through the use of technology | |

| | | |Compare Integers | |

| |III |Moving Straight Ahead |Compare Unit Rate by analyzing functions in the form of an equation, table, or graph |35 |

| | | |Define linear functions by interpreting the linear equation in the form of y = mx +b | |

| | |Thinking With Mathematical Models |Use functions to model relationships between two quantities | |

| | | |Describe functional relationships between two quantities | |

| | |Say It With Symbols |Solve for linear equations in one variable with one solution | |

| | | |Evaluate and simplify equations | |

| | |Impact Mathematics-Course 3 |Solve linear equations with rational number coefficients | |

| | | |Find solutions to a system of two linear equations in two variables | |

| | | |Locate the point of origin and the point of intersection on a graph | |

| |IV |Moving Straight Ahead |Solve systems of two linear equations in two variables algebraically |20 |

| | |Thinking With Mathematical Models |Setting up two-linear equations | |

| | |Say It With Symbols | | |

| |Unit |Books/Resources |Topics |#of Days |

|Semester II |V |Moving Straight Ahead |Complete function tables by applying rules |25 |

| | | |Create graphs using input and output values of a table | |

| | |Thinking With Mathematical Models |Compare rates of change by analyzing functions in equation, table or graph form | |

| | | |Define linear functions by interpreting the equation y = mx +b | |

| | |Say It With Symbols |Use function model relationships between two quantities | |

| | | |Evaluating functions of x and y-values | |

| | | |Describe functional relationships between two quantities | |

| |VI |Kaleidoscopes, Hubcaps and Mirrors | |30 |

| | |NJ ASK 8 Math Coach |Verify properties of reflection, rotation, and translations | |

| | |Buckle Down |Establish congruency between two 2-dimensional figures | |

| | |ASK 7 Math Coach |Identify similar figures by analyzing the sequence of transformations and/or dilations | |

| | |Impact Mathematics Course 3-CD |Generate geometric patterns | |

| | |Cord Bridges to Algebra and |Solve problems requiring calculations that involve various units of measurement | |

| | |Geometry-Learning Context |Find surface area | |

| | |Looking For Pythagoras |Explore the relation between area and perimeter | |

| | |Filling & Wrapping |Determine measures of angles | |

| | | |Find the volume of cones, cylinders, spheres and prisms | |

| | | |Find the volume of pyramids | |

| | | |Find the surface area of cones, cylinders, spheres, prisms and pyramids | |

| |VII | |Construct a two way table using collected data |20 |

| | |Data Distributions |Interpret and summarize data | |

| | | |Determine data of line of best fit | |

| | |Samples & Populations |Solve problems in the context of bivariate measurement data | |

| | | |Find patterns of bivariate data | |

| | |What Do You Expect? |Find the probability of compound events | |

| | | |Explore solutions to problems using the vertex edge | |

| | | |Find the possibility of combinations | |

Total-150

|Domain 8.NS |

|The Number System |

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|Strand 8.NS Number system includes positive, negative integers and rational numbers which are ratios of a number to a whole |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(NPS-8NS,1) Students find values of numerical expression |Investigation 4: Properties of Operations |CMP-Accentuate the Negative Investigation 4 |

| |by using the order of operations or the distributive |(Accentuate the Negative, St. Ed. pgs. 60-75) |ACE questions, pgs. Stu. Ed., 69-75. |

| |property with [specify level of accuracy]. | | |

| | |Dealing Down Unit Project (Accentuate the Negative, | |

| | |St. Ed. Pg. 76) | |

|How can we compare rational numbers and what is | | | |

|their significance? | |Interactive Chip Model Activity Integer Product Game| |

| |(CCSSI -8NS,1) Students understand and use rational |Activity (Student Express: Active Math, Accentuate | |

| |numbers by representing them as a quotient of two integers|the Negative) | |

| |and/or as a repeating or terminating decimal with [specify| | |

| |level of accuracy]. |Activities from education. | |

| |(NPS-8NS,1) Students solve problems by using rate with |Rational Numbers | |

| |[specify level of accuracy] |Decimal Defender App | |

| | |Rational Number Rampage App Fractions Number Line | |

| | |Fractions to Decimal Form | |

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| | |Investigation 3: Comparing and Scaling Rates ( | |

| | |Comparing and Scaling, St. ed., pgs. 33-39) |Comparing and Scaling, Stu. Ed, Investigation 3 |

| | | |ACE Questions Pgs. 40-47 |

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|Domain 8.NS |

|The Number System |

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|Strand 8.NS Number system includes positive, negative integers and rational numbers which are ratios of a number to a whole |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(NPS-8NS,1) Students solve problems by using ratios, |Investigation 4: Making Sense of Proportions ( |Comparing and Scaling, Stu. Ed, ACE Questions |

| |proportions and/or percents with [specify level of |Comparing and Scaling, Stu. ed., pgs. 48-54) |Pgs. 55-62 |

| |accuracy]. | | |

| | |Unit Project, “Paper Pool”(Student Express: Active |New Jersey ASK8 Coach Lesson 3-Equivalent |

| | |Math, Comparing and Scaling) |Rational Numbers pgs. 29-33 |

|How can we compare rational numbers and what is | | |Lesson 9-Solving Problems Using Ratios, Rates, |

|their significance? | | |Proportions, and Percents pgs. 57-62 |

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|Domain 8.NS |

|The Number System |

|Strand 8.NS - Know that there are numbers that are not rational, and approximate them by rational numbers |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CCSSI-8NS, 1) Students understand the meaning of |Irrational Numbers (Buckle Down, lesson 1 pg. 5) |Buckle Down |

| |irrational numbers by finding that their decimal | |Definition: Looking for Pythagoras, Pg. 48 & 68 |

|In what sense is an irrational number knowable |equivalencies neither terminate nor repeat with [specify |Analyzing the Wheel of Theodorus (Looking For |Watch videos from website, |

|and how is the number line useful for this |level of accuracy]. |Pythagoras, Stu. ed., pgs. 46-48) |

|purpose? |(CCSSI-8NS, 2) Students compare the size of irrational | |rs |

| |numbers on a number line diagram by making rational |Irrational Numbers | |

| |approximations of irrational numbers with [specify level | Question # 45 Inv. 2 Looking For Pythagoras,|

| |of accuracy]. |.htm |Stu. ed., pg 29 |

| |(CSSI-8NS, 2) Students make better approximations of | |

| |irrational by positioning it between two consecutive | |l_numbers.php |

|How and why is a real number system evolved? |rational numbers with [specify level of accuracy]. |Line Up Cards Activity | |

| |(CSSI-8NS, 2) Students conduct operations with irrational | |

| |numbers without using calculator with [specify level of |ards.htm | |

| |accuracy] | |Watch videos from website, |

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| | |Real Numbers TI 83 Plus Activity |ional-numbers.html |

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| | |Irrational Numbers on the Computer – watch video |For practice: |

| | | |Inv. 2 ACE Ques: 7-35, 41, 44, 45, 49, 51, 52, |

| | |Simplify irrational numbers |53 Stu. ed., pgs. 24-29. Inv.4 ACE Questions: |

| | | |13-16, 27 pgs. 57-58 |

|Domain 8.EE |

|Expressions and Equations |

|Strand 8.EE- Work with radicals and integer exponents |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CCSSI -8EE,1) Students generate the equivalent numeric |Using Exponents (NJASK8 Coach, pgs. 24-28) |For Exponents |

|Why is it necessary to follow properties of |expressions by applying the properties of integer |Paul’s online notes | |

|integer exponents in writing equivalent numerical|exponents with [specify level of accuracy]. | |

|expression? | |xponents.aspx | |

| | |Interactive site on properties of exponents | |

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| |(CCSSI -8EE, 2) Students understand that [pic] is an |t_alg_review/framesA_2.html | |

| |irrational number by exploring “Why is[pic]an irrational | | |

|Why is [pic]an irrational number? |number?” with [specify level of accuracy]. |Analyzing the Wheel of Theodorus (Looking For | |

| | |Pythagoras) pgs. 46-48 | |

| | |Why is [pic]an irrational number? | |

| |(CCSSI -8EE, 2) Students represent solutions to the | | |

| |equations of the form x2 = p and x3 = p, by using square | | |

| |root and cube root symbols with [specify level of | |Looking For Pythagoras. Additional Practice and |

| |accuracy] |Inv. Squaring Off (Looking for Pythagoras, pg. |Skills Workbook pgs. 41-44 |

|What is the relationship between squares and | |43-46) | |

|square roots, cubes and cube roots? | |Square root and cube root jeopardy |Looking For Pythagoras |

| | | pgs. 25-28 #’s 35-41, pgs. 29-30 |

| | |dy/RootJeopardy.htm |#’s 43-46 |

| | | |Additional Practice and Skills Workbook pgs. |

| | | |31-34 |

|Domain 8.EE |

|Expressions and Equations |

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|Strand 8.EE- Work with radicals and integer exponents |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CCSSI -8EE, 2) Students evaluate square roots of common |Activities from |For evaluating squares & cubes |

| |perfect squares and cube roots of common perfect cubes by |Square Roots | |

| |factoring with [specify level of accuracy]. |Squares - Perfect or Not |Impact Mathematics |

| | |Perfect Squares and Roots |Inv. 4-Exponent Laws and Scientific Notation |

| |(CPI-8EE, 3) Students estimate and express large |Square Roots (Looking For Pythagoras) pgs. 39-42 |pgs. 156-158 |

| |quantities by writing numbers in the form of a single | | |

| |digit times an integer power of 10 with [specify level of | | |

| |accuracy]. |Writing numbers from standard form to scientific | |

| | |notation. | |

| |(CPI-8EE, 3) Students determine how many times one number | | |

| |is larger than the other by comparing two numbers written | | |

| |in the form of a single digit times an integer power of 10| | |

| |with [specify level of accuracy]. | | |

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|Domain 8.EE |

|Expressions and Equations |

|Strand 8.EE- Work with radicals and integer exponents |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CPI-8EE, 4) Students use and perform operations with | |For Scientific Notation |

| |numbers expressed in scientific notation and decimal | | |

| |notation by complying the rules of operations with |Powers. Roots, Exponents, and Scientific Notation |Preparing for the New Jersey GEPA Grade 8 |

| |integer exponents used with specified levels of accuracy. |(Preparing for the New Jersey GEPA Grade 8) | |

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| |(CPI-8EE, 4) Students use scientific notation and choose | | |

| |units of appropriate size for measurements of very large | | |

| |or very small quantities by determining if the selection | | |

| |is apt to the given problem with [specify level of | | |

| |accuracy]. | | |

| |(CPI-8EE, 4) Students interpret technology generated | | |

| |scientific notation by applying the rules of operations | | |

| |with [specify level of accuracy]. | | |

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| | |Perform operations with numbers expressed in | |

| | |scientific notation using |anus.astro.umd.edu |

| | |Interactive website | |

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| | |Decimal to Scientific notation converter | |

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|Domain 8.EE |

|Expressions and Equations |

|Strand 8.EE- : Understand the connections between proportional relationships, lines and linear equations |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |( CCSSI -8EE, 5) Students interpret unit rate as the slope|Linear Changes |education. |

|Why are graphs important when trying to find |of the graph by generating a graph showing proportional |Slope Review - Learning Check quiz |Moving Straight Ahead |

|relationships in a desired situation? |relationship between two variables with [specify level of |Walking Marathon (Moving Straight Ahead) pgs 5-6 |Applications #’s 6a-d, 13 pgs. 14-16 Connections|

| |accuracy] |Raising Money (Moving Straight Ahead) pgs. 8-9 |#’s 20a-c pg. 18 |

| | |Climbing stairs (Moving Straight ahead) pgs |Additional Practice and Skills Workbook 83-86 |

| | | |Additional Practice and Skills Workbook 83-86 |

| |( CCSSI -8EE, 5) Students compare two different | | |

| |proportional relationships by analyzing the proportional |Waling Rates and Linear Relationships (Moving | |

| |relationships; one represented as a graph and the other as|Straight Ahead pgs 6-7 |Moving Straight Ahead |

| |an equation with [specify level of accuracy]. | |Inv. 1, Problem 1.3 , 1.4-Using the Walkathon |

|How can real-world situations be modeled using | | |Money |

|graphs and functions? | | |Applications #’s 1d, 3g-I, 4a, 4c, 7a, 9, 10, |

| | | |12e pgs. 12-15 |

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|Domain 8.EE |

|Expressions and Equations |

|Strand 8.EE- : Understand the connections between proportional relationships, lines and linear equations |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |( CCSSI-8EE, 6) Students derive the equation y= mx for a |Using Linear Relationships (Moving Straight Ahead) |Thinking With Mathematical Models |

| |line that passes through the origin, and y = mx + b for a |pgs 8-9 |Inv. 2-Linear Models and Equations, Problems |

| |line intercepts the vertical axis at b by finding the |Crossing the Line (Moving Straight Ahead) |2.1-2.4 pgs. 37-51 |

|Why are graphs important when trying to find |slope and y-intercept with [specify level of accuracy] |Linear Models and Equations (Thinking With |ACE questions pgs.33-46 |

|relationships in a desired situation? | |Mathematical Models) pgs. 24-32 |Additional Practice and Skills Workbook 83-86 |

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|How can real-world situations be modeled using | | | |

|graphs and functions? | | | |

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|Domain 8.EE |

|Expressions and Equations |

|Strand 8.EE- : Analyze and solve linear equations and pairs of simultaneous linear equations. |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |( CCSSI -8EE, 7a) Students solve linear equations in one |Crossing the Line (Moving straight ahead) pgs 25-26|Moving Straight Ahead Investigation 2 Problem |

| |variable with one solution by using exact reasoning | |2.2 Crossing the Line pgs. 49-50 |

| |methods and approximation with [specify level of | | |

|How are algebraic expressions used for solving |accuracy]. | | |

|real world problems? | | | |

| |( CCSSI -8EE, 7a) Students evaluate and simplify the | | |

| |equations in one variable by using the symbolic method | | |

| |with [specify level of accuracy]. | | |

| | |Walking to Win (Moving straight ahead) pgs. 24-25 |Moving Straight Ahead: Investigation2 Problem |

| | |Tiling Pools, Thinking in Different Ways, The |2.1: Walking to win pgs. 41-46 |

| | |Community Pool Problem, and Diving In (Say It With |Applications #’s 1 |

| | |Symbols) pgs 19-43 |Say It With Symbols: |

| | | |Investigation 1-Equivalent expression Problems |

| | | |1.1-1.4 pgs. 19-43 |

|How does writing and solving equations and | | | |

|systems of equations help solve complex problems | | | |

|graphically and algebraically? | | | |

| | | | |

| | | | |

| | | | |

|Domain 8.EE |

|Expressions and Equations |

|Strand 8.EE- : Analyze and solve linear equations and pairs of simultaneous linear equations. |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |( CCSSI -8EE, 7b) Students solve linear equations with |Connecting, Tables, Graphs and Equations (Moving |Moving Straight Ahead: Inv. 2 Problem |

| |rational number coefficients including equations whose |Straight Ahead) pgs. 29-30 |2.4-Connecting Tables, Graphs, and Equations |

| |solutions require expanding expressions by using |Graphs of Linear Equations (Say it With Symbols) |pgs. 55-57 |

|How are algebraic expressions used for solving |distributive property and combining like terms with |pgs, 24-25 |Applications #’s 15-28 |

|real world problems? |[specify level of accuracy]. |Many Ways to Reach Goal (Say It With Symbols) pgs. |Extensions #’s 40-41 |

| | |37-38 |Say It With Symbols: |

| | |Many Ways to Reach a Goal (Say It With /Symbols) |Inv. 1-Equivalent expression Inv. 2-Linear |

| | | |Equations and inequalities pgs. 39-42 |

| | | |Applications #1-2 pg. 30 #13-22 |

| | | |Inv. 3- Equations With Two or More Variables |

| | | |Problem 3.1- Many Ways to Reach a Goal pgs. |

| | | |55-60 |

| | | |Moving Straight Ahead: Investigation 2 Problem |

| | | |2.1: Walking to win pgs. 41-46 |

|How does writing and solving equations and | | |Connections #’s 29-34 |

|systems of equations help solve complex problems | | |Extensions # 42 |

|graphically and algebraically? | | | |

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| | | | |

| | | | |

|Domain 8.EE |

|Expressions and Equations |

|Strand 8.EE- : Analyze and solve linear equations and pairs of simultaneous linear equations. |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |4. (CCSSI -8EE, 8a) Students find solutions to a system of|Say It With Symbols: |Say It With Symbols |

| |two linear equations in two variables by locating the |Linear Inequalities pgs. 26-27 |Inv. 2-Linear Equations and inequalities |

| |point of intersection that satisfies both of the equations|Solving Linear Inequalities pgs. 28-29 |Problem 2.2-Linear Inequalities pgs. 43-46 |

|How are algebraic expressions used for solving |simultaneously with [specify level of accuracy] |Connecting y = mx + b and ax +by = c pgs. 39-40 |Applications #3-7 pg. 31 |

|real world problems? | |Intersecting of Lines pgs. |Problem 2.3- Solving linear Inequalities pgs. |

| | | |47-50 |

| | | |Inv.3-Equations With Two or More Variables |

| | | |Problem 3.2 Connecting y = mx + b and ax +by = |

| | | |c pgs. 61-64 |

| | | |Problem 3.3- Connecting y = mx + b and ax +by =|

| | | |c pgs. 65-68 |

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| | | | |

|How does writing and solving equations and | | | |

|systems of equations help solve complex problems | | | |

|graphically and algebraically? | | | |

| | | | |

| | | | |

| | | | |

|Domain 8.EE |

|Expressions and Equations |

|Strand 8.EE- : Analyze and solve linear equations and pairs of simultaneous linear equations. |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |5. ( CCSSI -8EE, 8b) Students solve systems of two linear |Solving Equations Using Tables and Graphs (Moving |Moving Straight Ahead |

| |equations in two variables algebraically, and estimate |straight Ahead) pgs. 46-48 |Investigations 3: Solving Equations Problem |

| |solutions by graphing the equations with [specify level of|Exploring Equality (Moving straight Ahead) pgs. |3.1-Solving Equations Using Tables and Graphs |

|How are algebraic expressions used for solving |accuracy] |48-51 |pgs. 67-70 |

|real world problems? | | |Problem 3.2-Exploring Equality |

| | | |Pgs. 71-78 |

| | | |Say It with Symbols: Investigation 2-combining |

| | | |Expressions |

| |6. (CCSSI -8EE, 8c) Students solve real-world mathematical| | |

| |problems by setting up two linear equations in two | | |

| |variables and determine the point of intersection of the | | |

| |two lines by graphing with [specify level of accuracy]. | |Moving Straight Ahead |

| | | |Investigations 3: Solving Equations Problem |

| | |From Pouches to Variables (Moving straight Ahead) |3.30- From Pouches to Variables pgs. 79-80 |

|How does writing and solving equations and | |pgs. 52-53 |Problem 3.4-solving Linear Equations pgs. 81-84|

|systems of equations help solve complex problems | |Solving Linear Equations (Moving straight Ahead) | |

|graphically and algebraically? | |pgs.53-54 | |

| | | | |

|Domain 8.F |

|Functions |

|Strand 8.F – Define, evaluate, and compare functions. |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |( CCSSI -8F, 1) Students complete a function table by a |Walking Rates (Moving Straight Ahead pgs. 5-6) |Moving Straight Ahead |

| |applying a rule with [specify level of accuracy] |Raising money (Moving straight Ahead pgs. 8-9) |Investigation 1: Walking Rates |

| | | |Problem 1.1 Walking Marathons pgs 5- 6 |

|How are functions applied to solve complex | | |Applications |

|algebraic problems? | | |Connections #24a-b |

| | | | |

| |( CCSSI -8F, 1) Students create a graph by using the input| |Algebra tools to draw graphs, tables (Prentice |

| |and output values of a table as ordered pairs of a graph | |Hall, Student Express, Active Math) |

| |with [specify level of accuracy] | | |

| | | | |

| | |Walking Rates and Linear Relationships (Moving | |

| | |Straight Ahead pgs. 6-7) |Moving Straight Ahead |

| | |Raising Money (Moving Straight Ahead pgs. 8-9) |Inv.1: Walking Rates |

| | | |Problem. 1.2 Walking Rates and Linear |

| | | |Relationships pgs. 6-7 |

| | | |Problem 1.3 Raising Money pgs. 8-9 |

| | | |Applications #’s 3c-e, 4b |

| | | |Connections # 23, 25a-b, |

| | | |Extensions 30c-d |

| | | | |

|Domain 8.F |

|Functions |

|Strand 8.F – Define, evaluate, and compare functions. |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |( CCSSI -8F, 2) Students compare the rate of change by | |Moving Straight Ahead |

| |analyzing functions given in the form of an equation, a |Using the Walkathon Money (Moving Straight Ahead |Investigation 1.4-Using the Walkathon Money |

| |table and a graph with [specify level of accuracy]. |pgs. 10-11) |Problem 1.4- Recognizing Linear Relationships |

|How are functions applied to solve complex | | |pgs. 10-11 |

|algebraic problems? | |Virtual Bridge Experiment (Thinking with |Applications #’s 2, 3a, 3f |

| | |Mathematical models, Prentice Hall, Student | |

| | |Express, Active Math) |Algebra tools to draw graphs, tables (Prentice |

| |( CCSSI -8F, 3) Students define a linear function by | |Hall, Student Express, Active Math) |

| |interpreting the equation y = mx + b whose graph is a | | |

| |straight line with [specify level of accuracy]. | | |

| | | | |

| | | | |

| | |Getting Started with the TI-Navigator™ System: |Moving Straight Ahead |

| | |Phone Card |Inv.1 Problem 1.3- Using Linear Relationships |

| | | |pgs 8-9 |

| | |Linear Changes |Applications #’s 3g-I, 4a |

| | |Raising Money (Moving Straight Ahead pgs 8-9) | |

|Domain 8.F |

|Functions |

|Strand 8.F – Use functions to model relationships between quantities. |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |( CCSSI -8F, 2) Students compare the rate of change by | |Moving Straight Ahead |

| |analyzing functions given in the form of an equation, a |Using the Walkathon Money (Moving Straight Ahead |Investigation 1.4-Using the Walkathon Money |

| |table and a graph with [specify level of accuracy]. |pgs. 10-11) |Problem 1.4- Recognizing Linear Relationships |

|How are functions applied to solve complex | | |pgs. 10-11 |

|algebraic problems? | | |Applications #’s 2, 3a, 3f |

| | | | |

| | | | |

| |( CCSSI -8F, 3) Students define a linear function by | | |

| |interpreting the equation y = mx + b whose graph is a | | |

| |straight line with [specify level of accuracy]. | | |

| | | | |

| | | | |

| | |Getting Started with the TI-Navigator™ System: |Moving Straight Ahead |

| | |Phone Card |Inv.1 Problem 1.3- Using Linear Relationships |

| | | |pgs 8-9 |

| | |Linear Changes |Applications #’s 3g-I, 4a |

| | |Raising Money (Moving Straight Ahead pgs 8-9) | |

|Domain 8.G |

|Geometry |

|Strand 8.G –Understand congruence and similarity using physical models, transparencies, or geometry software |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs)|Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CPI-8G, 1) Students verify the properties of rotation, |Inv. 2 Symmetry Transformations (Kaleidoscopes, | |

| |reflection and translation by conducting experiments with|Hubcaps and Mirrors, pgs 27-33) | |

|How are transformations and dilations conducted |[specify level of accuracy] |Geometers Sketch Pad Activity | |

|and/or useful in geometric situations in real |(CPI-8G, 2) Students establish congruency between two 2- |Dilations in the Plane | |

|world? |dimensional figures by conducting rotations, reflections |Exploring Transformations | |

| |and translations and describing the sequence of |REAL LIFE, REAL WORLD Activity - Architecture |Kaleidoscopes, Hubcaps and Mirrors |

| |transformations used with [specify level of accuracy] |"Fishing for Points"-- Transformations Using Lists |Geometer Sketch Pad Activities |

| |(CPI-8G, 3) Students describe dilations, rotations, | | |

| |reflections and translations of two dimensional figures |Kaleidoscopes, Hubcaps and Mirrors, Inv. 3: |District Math e-board |

| |by using coordinates with [specify level of accuracy]. |Exploring Congruence (pgs. 48-50) | |

| | |Matching Game- Properties of Congruent Triangles |Hubcap Maker, Transformational Tool, Prentice |

| | |(pg. 51) |Hall, Student Express, Active Math |

| | |Inv. 4 Applying Congruence and Symmetry (pgs.65-69)| |

| | |Geometers Sketch Pad Activity | |

|How is similarity and congruency useful in | | | |

|real-life mathematical situations across the | |Kaleidoscopes, Hubcaps and Mirrors, Inv.5: | |

|disciplines? | |Transforming coordinates by use of Geometers Sketch| |

| | |Pad. | |

|Domain 8.G |

|Geometry |

|Strand 8.G –Understand congruence and similarity using physical models, transparencies, or geometry software |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CPI-8G, 4) Students identify similar figures by analyzing| | |

| |the sequence of transformations and/or dilations that |Geometer Sketch Pad Activity |District Math e-board |

| |demonstrate the similarity between them with [specify | | |

| |level of accuracy]. | | |

|Domain 8.G |

|Geometry |

|Strand 8.NPS –Iterations/Measurements |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(NPS-8G) Students generate geometric patters by using |Fractals (New Jersey ASK 8 |New Jersey ASK 8 Coach Fractals pgs. 142-147 |

| |iterative procedures with [specify level of accuracy]. |Coach) pgs. 142-147 | |

| |(NPS-8G) Students solve problems requiring calculations | | |

| |that involve different units of measurement within a | |New Jersey ASK 8 Coach Converting Measurements |

| |measurement system by using conversion formulas with |Converting Measurements (New Jersey ASK 8 Coach) |pgs. 148-151 |

| |[specify level of accuracy]. |pgs. 148-151 |Approximate Equivalent Measures pgs. 152-155 |

| |(NPS-8G) Students solve problems that involve finding |Approximate Equivalent Measures (New Jersey ASK 8 | |

| |surface area by generating and applying the surface area |Coach) pgs. 152-155 | |

| |formula with [specify level of accuracy]. | | |

| |(NPS-8G) Students explore the relationship between area | |New Jersey ASK 8 Coach |

| |and perimeter by changing one of the two measurements | |Finding Surface Area and Volume pgs.176-184 |

| |[specify level of accuracy]. |Finding Surface Area and Volume (New Jersey ASK 8 | |

| | |Coach) pgs176-184 | |

| | | | |

| | | | |

| | | | |

| | |Square tiles activities: Constant Area Activity, | |

| | |Constant Perimeter | |

| | |Activity | |

|Domain 8.G |

|Geometry |

|Strand 8.G –Understand congruence and similarity using physical models, transparencies, or geometry software |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(NPS-8G) Students determine the measures of angles by |Impact Mathematics: Lesson 2.2- Angle |Impact Mathematics, Teacher Edition |

| |identifying supplementary, complementary and vertical |Relationships, Inv.1-Supplementary , Complementary |Impact Mathematics, Teacher Works CD Lesson 2.2|

| |angles with [specify level of accuracy]. |and Vertical Angles, pg. 87-90 | |

| | |On Your Own Exercises 1-6, 11, 13-22 | |

| | |Enrichment: Leveled Lesson Resources P. 18, Teacher| |

| | |Edition Pg. 87B | |

| | |Intervention: Leveled Lesson Resources P. 15, | |

| | |Teacher Edition Pg. 87B | |

| |(CPI-8G, 5) Students understand interior, exterior angles,|Skills Practice: Leveled Lesson Resources P. 16, | |

| |alternate interior and alternate exterior angles by |Teacher Edition Pg. 87B | |

| |exploring special angle relationships formed when a set of| | |

| |parallel lines are intersected by a transversal with |Impact Mathematics: Lesson 2.2- Angle | |

| |[specify level of accuracy]. |Relationships, Investigation 2-Parallel Lines Cut | |

| | |By a Transversal, pages 91-93 On Your Own Exercises| |

| | |7-10, 12 | |

| | | | |

| | | | |

| | | |Impact Mathematics, Teacher Edition |

| | | |Impact Mathematics, Teacher Works CD Lesson 2.2|

| | | | |

|Domain 8.G |

|Geometry |

|Strand 8.G –Understand congruence and similarity using physical models, transparencies, or geometry software |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CPI-8G, 5) Students solve real life mathematical problems|Impact Mathematics Teacher Edition: Leveled Lesson |Impact Mathematics Teacher Edition: Leveled |

| |by applying the angle relationships formed when a set of |Resources- Problem Solving Practice on angle |Lesson Resource |

| |parallel lines are intersected by a transversal with |relationships. pg 87B | |

| |[specify level of accuracy]. |Assessment: | |

| | |Quick Quiz Problems 1-10, page 95, Impact | |

| | |Mathematics Teacher Edition | |

| | | | |

|Domain 8.G |

|Geometry |

|Strand 8.G –Geometric properties |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(NPS-8G) Students solve geometric problems by applying |Polygons (Cord Bridges to Algebra and |Cord Bridges to Algebra and Geometry-Learning |

|How do geometric properties help in solving |properties of polygons with [specify level of accuracy]. |Geometry-Learning context) |context |

|problems and make sense of phenomena? | | |Lesson 10.5-Polygons pgs. 555-562 |

| |(NPS-8G) Students construct 2-dimensional nets for |Similar Polygons (New Jersey ASK 8 Coach) |New Jersey ASK 8 Coach |

| |3-dimensional objects by unfolding 3-D paper models with | |Lesson 15-Similar Polygons94-98 |

|How are 3-D figures generated from 2-D figures? |[specify level of accuracy]. | |Lesson 17-Using Scale Drawings pgs 106-110 |

| | | | |

| | | | |

| | | |Teaching Student-Centered Mathematics Grades |

| | |Shapes and Properties Activities |5-8 |

| | |(Teaching Student-Centered Mathematics Grades 5-8) |Shapes and Properties Activities pgs. 187-188 |

| | |pgs. 187-188 | |

| | | |New Jersey ASK 8 |

| | |Three-Dimensional Figures (New Jersey ASK 8 Coach) |Coach Three-Dimensional Figures pgs. 111-116 |

| | |pgs. 111-116 | |

|Domain 8.G |

|Geometry |

|Strand 8.G –Understand and apply the Pythagorean Theorem |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CPI-8G, 6) Students find proof to the Pythagorean Theorem| |Looking for Pythagoras |

| |by establishing an area model with [specify level of |The Pythagorean Theorem |Investigation 3-The Pythagorean Theorem |

| |accuracy]. |A Proof of the Pythagorean Theorem (Looking For |Problem 3.1-The Pythagorean Theorem pgs. 51-56 |

|What is the importance of Pythagorean Theorem in | |Pythagoras) pgs. 31-32 |Applications #’s 1-14 pgs. 38-40 |

|solving real life mathematical situations? | | |education. |

| | |Proof of the Pythagorean Theorem using |Additional Practice Problems pgs. 35-40 |

| | |Transformations | |

| | | | |

| | |Interactive Pythagoras | |

| |(CPI-8G, 6) Students find proof to the converse of the |(Prentice Hall, Student Express, Active Math) | |

| |Pythagorean Theorem by solving the equation/formula for | |Looking for Pythagoras |

| |the values of a or b with [specify level of accuracy]. | |Inv. 3-The Pythagorean Theorem |

| | | |Problem 3.2-A Proof of the Pythagorean Theorem |

| | | |pgs. 57-60 |

| | |A Proof of the Pythagorean Theorem (Looking For |Connections #’s 18-23, 26 |

| | |Pythagoras) pg. 33-34 |education. |

| | | |Additional Practice Problems pgs. 35-40 |

| | | | |

| | | | |

| | |The Pythagorean Theorem And Classifying Triangles | |

|Domain 8.G |

|Geometry |

|Strand 8.G –Understand and apply the Pythagorean Theorem |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| | (CPI-8G, 7) Students find the unknown side lengths of |Measuring the Egyptian Way (Looking For Pythagoras)|Looking For Pythagoras |

| |right triangles in two- and/or three-dimensional figures |pgs. 36-37 |Inv. 3- The Pythagorean Theorem |

| |within real-life mathematical situations with [specify |Stopping Sneaky Sally (Looking For Pythagoras) pgs.|P.3.4-Measuring The Egyptian Way pgs. 36-37 |

|What is the importance of Pythagorean Theorem in |level of accuracy]. |49-50 |Application #’s 15-17 pg40 |

|solving real life mathematical situations? | | |Connection # 25 pg. 42 |

| | | |Inv.4-Using The Pythagorean Theorem, |

| | |Finding Distances (Looking for Pythagoras) p. 35 |P.4.2-Stopping Sneaky Sally, pgs. 79-82 |

| | | |Application #’s 3-5 p. 53 |

| |(CPI-8G, 8) Students find the distance between two points | |Connections #’s 24-25 p. 57 |

| |in the coordinates system by applying the Pythagorean | |Additional Practice Problems pgs. 35-40 |

| |Theorem with [specify level of accuracy] |Lesson 12- The Pythagorean Theorem (New Jersey ASK |Investigation 3-The Pythagorean Theorem |

| | |8 Coach) pgs. 77-81 |Pr.3.3-Finding Distances p. 35 |

| | | |Connections # 24 pg. 42 |

| | | |Extension #’s 27-35 pgs. 43-44 |

| | | |New Jersey ASK 8 Math Coach |

| | | |Additional Practice Problems pgs. 35-40 |

| | | |Looking Back and Looking Ahead- Unit Review |

| | | |pgs. 65-67 |

|Domain 8.G |

|Geometry |

| |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs)|Types of Research Based Activities and Assessments |Suggested Resources |

| | |that could illustrate Objectives | |

| |(CPI-8G, 9) Students find the volume of cones to solve |Finding the Volume of Other Prisms (Filling and |Filling & Wrapping |

| |real-world situations and mathematical problems by |Wrapping pgs. 32-33 |Inv.3 Problem 3.1 p.57-60 |

| |exploring and applying the formula with [specify level of|Cones and Cylinders, Pyramids and Cubes pgs. 50-52 |Investigation 4 Problem 4.2 p.83-86, Problem |

| |accuracy]. | |4.3 p.87-90 |

|How will applying appropriate measurement |(CPI-8G, 9) Students find the volume of cylinders to | |Applications #’s 7, 10d, 11b, 15, pgs. 38-41 |

|concepts, tools, and formulas help solve |solve real-world situations and mathematical problems by | | |

|geometric problems efficiently? |exploring and applying the formula with [specify level of|Finding the Volumes of Cylinders |Filling & Wrapping- |

| |accuracy]. |(Filling & Wrapping) pgs 34-35 |Inv. 3, Problem 3.2 p.61-64 and Problem 3.4 p. |

| | |Making a New Juice Container (Filling & Wrapping) |69-72 |

| |CPI-8G, 9) Students find the volume of spheres to solve |p. 37 |Investigation 4 Problem 4.3 p.87-90 |

| |real-world situations and mathematical problems by | |Applications #’s 1a, 2, 3, 7, 10c, 11a, 14, 15,|

| |exploring and applying the formula with [specify level of| |17a, 22, 24, 26 pgs. 38-43, Connections #’s |

| |accuracy]. | |27-29, 33 pgs 44 & 46 Mathematical Reflections|

| | | |p. 47 2b & 3 |

| | | | |

| | | |Filling & Wrapping- |

| | |Comparing Spheres and Cylinders (Filling and |Inv. 4 Problem 4.1 p.79-82 & Problem 4.3 |

| | |Wrapping) pgs. 48-50 |p.87-90 |

| | |Melting Ice Cream (Filling and Wrapping) pgs. 52-53|Applications #’s 2, 10e, 11c pgs. 38-41, |

| | | |Connections #’s 27-29, 31-33 pgs 44-46 |

|Domain 8.G |

|Geometry |

| |

|Essential Questions |Instructional Objectives / Skills and Benchmarks |Types of Research Based Activities and Assessments|Suggested Resources |

| |(CCSSIs) |that could illustrate Objectives | |

| |(NPS-8G9) Students explore the formula for finding |Finding the Volume of Other Prisms (Filling and |Filling & Wrapping |

| |volume of prisms and solve mathematical problems in |Wrapping pgs. 32-33 |Inv. 3 Problem 3.1 pgs. 57-60 |

| |real-world situations by applying the formula with |Melting Ice Cream (Filling and Wrapping) pgs. |Inv. 4 Problem 4.3 p.52-53 |

| |[specify level of accuracy]. |52-53 |Applications #’s 1, 7, 10c, 11a, 15, 31-32 |

|How will applying appropriate measurement | | |pgs. 38-45, Connections #’s 27-29, 31-33 pgs |

|concepts, tools, and formulas help solve |(NPS-8G) Students explore the formula for finding volume| |44-46 Mathematical Reflections #1 p. 47 |

|geometric problems efficiently? |of pyramids and solve mathematical problems in | | |

| |real-world situations by applying the formula with | |Filling & Wrapping- Inv. 4 Problem 4.2 pgs. 50|

| |[specify level of accuracy]. | |Applications #’s 13, 16, 17, 22 pgs. 55-57 |

| | |Cones, Cylinders, pyramids and Cubes (Filling and |Extensions # 33, 35 pgs. 59-60 |

| |(NPS-8G) Students explore the formula for finding |Wrapping) p. 50 |Filling & Wrapping- Inv. 3 Problem 3.3 p.67-68|

| |surface area of prisms and solve mathematical problems | |Applications #’s 15, 18 pgs. 40-41 |

| |in real-world situations by applying the formula with | |Interactive Activities, |

| |[specify level of accuracy] | |(Filling and Wrapping, Prentice Hall, Student |

| | | |Express, Grade 7, Active Math) |

| | | | |

| | | | |

| | | | |

| | |Making cylinders and Prisms from Nets (Filling and| |

| | |Wrapping) pgs 35-36 | |

| | | | |

| | | | |

|Domain 8.G |

|Geometry |

| |

|Essential Questions |Instructional Objectives / Skills and Benchmarks |Types of Research Based Activities and Assessments|Suggested Resources |

| |(CCSSIs) |that could illustrate Objectives | |

| |(NPS-8G) Students explore the formula for finding |Making cylinders and Prisms from Nets (Filling and|Filling & Wrapping- Inv. 3 Problem 3.3 p.67-68|

| |surface area of cylinder and solve mathematical problems|Wrapping) pgs 35-36 |Applications #’s 1b, 4-6, 12, 14c, 17b, 18, 22|

| |in real-world situations by applying the formula with | |pgs. 39-42 |

| |[specify level of accuracy]. |Interactive Activity, “Virtual Cylinder”, | |

|How will applying appropriate measurement | |(Filling and Wrapping, Prentice Hall, Student |Interactive Activities |

|concepts, tools, and formulas help solve | |Express, Grade 7, Active Math) |Filling and Wrapping, Prentice Hall, Student |

|geometric problems efficiently? | | |Express, Grade 7, Active Math |

|Domain 8.SP |

|Statistics and Probability |

|Strand 8.SP: - Investigate patterns of association in bivariate data |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and |Suggested Resources |

| | |Assessments that could illustrate Objectives | |

| |(CPI-8SP, 1) Students construct a scatter plot by using |Two kinds of Variability (Data |Data Distributions |

| |bivariate measurement data with [specify level of accuracy]. |Distributions) pgs. 13-15 |Inv. 1-Making Sense of Variability |

| |(CPI-8SP, 1) Students interpret and describe scatter plots by| |Problem 1.4-Two Kinds of Variability pgs. |

| |investigating patterns of association between two variables | |13-15 |

| |with [specify level of accuracy]. | |Application #’s 12-13 p. 20 |

| |(CPI-8SP, 2) Students determine closeness of data to the |Relating Two Variables (Samples and Populations) |Connection #’s 19-23pgs. 23-26 |

| |lines of best fit by exploring scatter plots that suggest |Are Quality Ratings and Prices Related p. 62 | |

| |linear association of two quantities with [specify level of | |Inv. 4- Relating Two Variables |

| |accuracy]. | |Problem 4.1-Are Quality Ratings and Prices |

| |(CPI-8SP, 3) Students solve problems in the context of |Variability in Categorical Data |Related pgs.96-98 |

|What is the use of data organizers |bivariate measurement data by interpreting the slope and the |(Data Distributions) pgs. 7-11 |Applications #1 |

|(graphs, tables etc.) in making |intercept with [specify level of accuracy]. | |Connections #’s 4-8 |

|predictions and conjectures in real world| |Use Data tools to develop scatter plots ( | |

|problems? | |Prentice Hall, Student Express, Active Math) |Data Distributions |

| | | |Investigation 1-Making Sense of Variability |

| | |Ti Graphing Calculator Activities |Problem 1.1- Variability in Categorical Data |

| | | |pgs 6-8 |

| | |ACE questions, Additional Practice, Question Bank|Application #’s1 & 12 |

| | |(Samples and Populations) |Connections #’s 14-15 pg.21 |

| | | | |

|Domain 8.SP |

|Statistics and Probability |

|Strand 8.SP: - Investigate patterns of association in bivariate data |

|Essential Questions |Instructional Objectives / Skills and Benchmarks (CCSSIs) |Types of Research Based Activities and |Suggested Resources |

| | |Assessments that could illustrate Objectives | |

| |(CPI-8SP, 4) Students find patterns of association in |Solving Archeological Mystery (Samples and |Investigation 3-Solving Real-World Problems |

| |bivariate categorical data by displaying frequencies and |Populations) pgs. 47-50 |Problem 3.1-solvign an archaeological Mystery |

| |relative frequencies in a two-way table with [specify level | |pgs. 76-81 |

| |of accuracy]. | | |

| |(CPI-8SP, 4) Students construct a two way table using the | |Investigation 4- Relating Two Variables |

| |data collected from the same subjects with [specify level of | |Problem 4.1-Are Quality Ratings and Prices |

| |accuracy] |Relating Two Variables (Samples and Populations) |Related pgs.96-98 |

| | |Are Quality Ratings and Prices Related p. 62 |Applications #1 |

| |(CPI-8SP, 4) Students interpret and summarize data in a two |Writing an Equation to Describe A Relationship |Connections #’s 4-8 |

| |way table by observing the patterns in the categorical |pgs. 63-65 |Problem 4.2-Writing an Equation to Describe A |

|What is the use of data organizers |variables with [specify level of accuracy] |Human Development Index and Life Expectancies |Relationship pgs. 99-102 |

|(graphs, tables etc.) in making | |pgs. 66-68 |Applications #2 |

|predictions and conjectures in real world| | |Connections #9, 27-30 |

|problems? | | |Problem 4.3-Human Development Index and Life |

| | | |Expectancies pgs. 103-106 |

| | | |Applications- #3 |

| | | |Connections #31-35 |

| | | |Extension #36 |

|Domain 8.SP |

|Statistics and Probability |

|Strand 8.SP: - Probability and Vertex Edge Graphs |

|Essential Questions |Instructional Objectives / Skills and Benchmarks |Types of Research Based Activities and Assessments|Suggested Resources |

| |(CCSSIs) |that could illustrate Objectives | |

|What are the real life practical implications|(CCSSI-8,1) Students determine probability of compound |Red and Blue is a Winner (What do You Expect?) |What do you Expect? |

|of theories of probability |events by using tree diagram/ area model/ multiplication|pgs. 7-8 |Problem 1.2-Red and Blue is a Winner pgs. |

| |principle with [specify level of accuracy] | |23-26 |

| | |Playing the Multiplication Game (What Do You |Applications #’s 3-10 pgs. |

| |(CCSSI-8,1) Students explore solutions to practical |Expect?) p.9 |Connections #’s 20-22 pgs. |

| |problems by using vertex edge graphs with [specify level| |Extensions # 29 p. |

| |of accuracy] | |Problem 1.3-Playing The Multiplication Game |

| | | |pgs.27-32 |

| | | |Applications #’s 11-13 pgs. |

| | | |Connections #’s 23-28 pgs. |

| | | |Extensions #’s 30-33pgs. |

| | | | |

|How can visual tools such as networks | | | |

|(vertex-edge graphs) be used to answer | | | |

|questions? | | | |

| | | | |

-----------------------

NEWARK PUBLIC SCHOOLS ADVISORY BOARD MEMBERS

2010-2011

Mr. Shavar Jeffries, Chairperson

Ms. Barbara King, Vice Chairperson

Ms. Ivan Lamourt

Mr. Marques-Aquil Lewis

Ms. Eliana Pintor

Mr. Juan Rivera

Ms. Arelis Romero

Ms. Shanique L. Davis-Speight

Ms. Nakia J. White

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