NEWARK PUBLIC SCHOOLS
Grade 8 Mathematics
CURRICULUM GUIDE
2010-2011
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
NEWARK PUBLIC SCHOOLS
ADMINISTRATION
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
The Office of Academic Services ©2010
Page 3
The Newark Public Schools
Subject: Mathematics
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 Office of Academic Services ©2010
Page 4
The Newark Public Schools
Subject: Mathematics
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
The Office of Academic Services ©2010
Page 5
The Newark Public Schools
Subject: Mathematics
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.
The Office of Academic Services ©2010
Page 6
The Newark Public Schools
Subject: Mathematics
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,
The Office of Academic Services ©2010
Page 7
The Newark Public Schools
Subject: Mathematics
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
The Office of Academic Services ©2010
Page 8
The Newark Public Schools
Subject: Mathematics
CURRICULUM COMMITTEE
Naga Madhuri Philkhana – Mathematics Coach (K-8)
Susana Monteiro – Teacher, Grade 8
The Office of Academic Services ©2010
Page 9
The Newark Public Schools
Subject: Mathematics
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
The Office of Academic Services ©2010
Page 10
The Newark Public Schools
Subject: Mathematics
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.
The Office of Academic Services ©2010
Page 11
The Newark Public Schools
Subject: Mathematics
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#0-13-366Lappan, 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
The Office of Academic Services ©2010
Page 12
The Newark Public Schools
Subject: Mathematics
Course Proficiencies
Upon successful completion of this course, students will:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
Identify Rational and Irrational Numbers
Use rational approximations of irrational numbers and be able to compare them by locating them on a number line.
Apply properties of exponents
Use the square root and cube root symbol to represent solutions
Use powers of 10 to represent large quantities or very small quantities
Perform operations using scientific notation for both whole numbers and decimals.
Use expressions involving more than one operation.
Choose appropriate measurement units
Substitute values for variables in order to evaluate algebraic expressions.
Comprehend the mechanics of simplifying expressions, including those containing one or more enclosures.
Identify the properties of integers, including negative numbers, in addition, perform accurately the basic operations involving them.
Solve equations including simple systems of linear, those containing fractions and/or enclosures as well as quadratics.
Show proficiency in writing English phrases in mathematical terms and be able to solve word problems of many types.
Simplify products and powers and evaluate algebraic expressions
Perform the four basic operations on polynomials, including the multiplication at sight of certain special products.
Apply factoring skills in specific algebraic situations.
Solve algebraic fractions.
Use Cartesian coordinates to graph a straight line and solve systems of linear equations graphically.
Apply the slope of a line and write the equation of a line given certain conditions.
Use and experiment with properties of transformations
Comprehend that a two-dimensional figure has congruency with different transformations
Appropriately integrate technology with the curriculum.
Relate mathematics education and career choice.
Students who complete this course successfully will be prepared to take Algebra I or Honors Algebra I.
The Office of Academic Services ©2010
Page 13
The Newark Public Schools
Subject: Mathematics
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
The Office of Academic Services ©2010
Page 14
The Newark Public Schools
Subject: Mathematics
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
The Office of Academic Services ©2010
Page 15
The Newark Public Schools
Subject: Mathematics
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
The Office of Academic Services ©2010
Page 16
The Newark Public Schools
Subject: Mathematics
Suggested Course Pacing
Unit
Books/Resources
Looking For Pythagoras
New Jersey ASK 8 Coach
I
Impact MathematicsCourse 3
Looking For Pythagoras
Semester I
II
Moving Straight Ahead
Thinking With
Mathematical Models
III
Say It With Symbols
Impact MathematicsCourse 3
Moving Straight Ahead
IV
Thinking With
Mathematical Models
Topics
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
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
Compare Unit Rate by analyzing functions 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
Solve systems of two linear equations in two variables algebraically
Setting up two-linear equations
#of Days
15
5
35
20
Say It With Symbols
The Office of Academic Services ©2010
Page 17
The Newark Public Schools
Unit
Books/Resources
Moving Straight Ahead
V
Thinking With
Mathematical Models
Semester II
Say It With Symbols
VI
Kaleidoscopes, Hubcaps
and Mirrors
NJ ASK 8 Math Coach
Buckle Down
ASK 7 Math Coach
Impact Mathematics Course
3-CD
Cord Bridges to Algebra
and Geometry-Learning
Context
Looking For Pythagoras
Filling & Wrapping
Data Distributions
VII
Samples & Populations
What Do You Expect?
Subject: Mathematics
Topics
Complete function tables by applying rules
Create graphs using input and output values of a table
Compare rates of change by analyzing functions in equation, table or graph form
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
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
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
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
#of Days
25
30
20
Total-150
The Office of Academic Services ©2010
Page 18
The Newark Public Schools
Subject: Mathematics
Domain 8.NS
The Number System
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)
1. (NPS-8NS,1) Students find values
of numerical expression by using
the order of operations or the
distributive property with [specify
level of accuracy].
How can we compare rational
numbers and what is their
significance?
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Investigation 4: Properties of
Operations (Accentuate the
Negative, St. Ed. pgs. 60-75)
Suggested Resources
CMP-Accentuate the Negative
Investigation 4
ACE questions, pgs. Stu. Ed.,
69-75.
Dealing Down Unit Project
(Accentuate the Negative, St. Ed.
Pg. 76)
Interactive Chip Model Activity
Integer Product Game Activity
(Student Express: Active Math,
Accentuate the Negative)
2. (CCSSI -8NS,1) Students
understand and use rational
numbers by representing them as a
quotient of two integers and/or as a
repeating or terminating decimal
with [specify level of accuracy].
Activities from
www.education.ti.com
Rational Numbers
Decimal Defender App
Rational Number Rampage App
Fractions Number Line Fractions
to Decimal Form
3. (NPS-8NS,1) Students solve
problems by using rate with
[specify level of accuracy]
Investigation 3: Comparing and
Scaling Rates ( Comparing and
Scaling, St. ed., pgs. 33-39)
The Office of Academic Services ©2010
http://www.purplemath.com/m
odules/numtypes.htm
Comparing and Scaling, Stu.
Ed, Investigation 3
ACE Questions Pgs. 40-47
Page 19
The Newark Public Schools
Subject: Mathematics
Domain 8.NS
The Number System
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)
4. (NPS-8NS,1) Students solve
problems by using ratios,
proportions and/or percents with
[specify level of accuracy].
How can we compare rational
numbers and what is their
significance?
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Investigation 4: Making Sense of
Proportions ( Comparing and
Scaling, Stu. ed., pgs. 48-54)
Unit Project, “Paper
Pool”(Student Express: Active
Math, Comparing and Scaling)
Suggested Resources
Comparing and Scaling, Stu.
Ed, ACE Questions Pgs. 55-62
New Jersey ASK8 Coach
Lesson 3-Equivalent Rational
Numbers pgs. 29-33
Lesson 9-Solving Problems
Using Ratios, Rates,
Proportions, and Percents pgs.
57-62
http://www.purplemath.com/m
odules/ratio.htm
The Office of Academic Services ©2010
Page 20
The Newark Public Schools
Subject: Mathematics
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)
In what sense is an irrational
number knowable and how is
the number line useful for this
purpose?
5. (CCSSI-8NS, 1) Students
understand the meaning of
irrational numbers by finding that
their decimal equivalencies neither
terminate nor repeat with [specify
level of accuracy].
How and why is a real number
system evolved?
6. (CCSSI-8NS, 2) Students compare
the size of irrational numbers on a
number line diagram by making
rational approximations of
irrational numbers with [specify
level of accuracy].
7.
(CSSI-8NS, 2) Students make
better approximations of irrational
by positioning it between two
consecutive rational numbers with
[specify level of accuracy].
8. (CSSI-8NS, 2) Students conduct
operations with irrational numbers
without using calculator with
[specify level of accuracy]
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Irrational Numbers (Buckle
Down, lesson 1 pg. 5)
Analyzing the Wheel of
Theodorus (Looking For
Pythagoras, Stu. ed., pgs. 46-48)
Irrational Numbers
http://www.themathpage.com/are
al/irrational-numbers.htm
Line Up Cards Activity
http://regentsprep.org/Regents/ma
th/ALGEBRA/AOP1/Tcards.htm
Real Numbers TI 83
Plus Activity
Irrational Numbers on the
Computer – watch video
Simplify irrational numbers
http://www.edhelper.com/radicals
5.htm
Suggested Resources
Buckle Down
Definition: Looking for
Pythagoras, Pg. 48 & 68
Watch videos from website,
http://tulyn.com/8th-grademath/irrational-numbers
ACE Question # 45 Inv. 2
Looking For Pythagoras, Stu.
ed., pg 29
http://www.homeschoolmath.n
et/teaching/irrational_numbers.
php
www.education.ti.com
Watch videos from website,
http://www.onlinemathlearning
.com/rational-irrationalnumbers.html
For practice:
Inv. 2 ACE Ques: 7-35, 41, 44,
45, 49, 51, 52, 53 Stu. ed., pgs.
24-29. Inv.4 ACE Questions:
13-16, 27 pgs. 57-58
Page 21
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Strand 8.EE- Work with radicals and integer exponents
Essential Questions
Why is it necessary to follow
properties of integer exponents
in writing equivalent numerical
expression?
Why is
2 an irrational number?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
Types of Research Based
Activities and Assessments
that could illustrate Objectives
1. (CCSSI -8EE,1) Students generate Using Exponents (NJASK8
the equivalent numeric
Coach, pgs. 24-28)
expressions by applying the
Paul’s online notes
properties of integer exponents
http://tutorial.math.lamar.edu/Cla
with [specify level of accuracy].
sses/Alg/IntegerExponents.aspx
Interactive site on properties of
exponents
http://people.hofstra.edu/stefan_
Waner/realworld/tut_alg_review/f
ramesA_2.html
2
What is the relationship between
squares and square roots, cubes
and cube roots?
3
The Office of Academic Services ©2010
Suggested Resources
For Exponents
http://www.aaamath.com/grade
8.htm
(CCSSI -8EE, 2) Students
understand that 2 is an
irrational number by exploring
“Why is 2 an irrational number?”
with [specify level of accuracy].
Analyzing the Wheel of
Theodorus (Looking For
Pythagoras) pgs. 46-48
Looking For Pythagoras.
Why is 2 an irrational number?
http://www.math.utah.edu/~pa/ma Additional Practice and Skills
Workbook pgs. 41-44
th/q1.html
(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 accuracy]
http://math.pppst.com/roots.html
Inv. Squaring Off (Looking for
Pythagoras, pg. 43-46)
Square root and cube root
jeopardy
http://teachers.sduhsd.net/abrown/
Activities/Jeopardy/RootJeopardy
.htm
Looking For Pythagoras
Applications pgs. 25-28 #’s 3541, pgs. 29-30 #’s 43-46
Additional Practice and Skills
Workbook pgs. 31-34
Page 22
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Essential Questions
Strand 8.EE- Work with radicals and integer exponents
Instructional Objectives / Skills and
Types of Research Based
Benchmarks (CCSSIs)
Activities and Assessments
that could illustrate Objectives
4. (CCSSI -8EE, 2) Students
Activities from
evaluate square roots of common
www.eduationti.com
perfect squares and cube roots of
 Square Roots
common perfect cubes by
 Squares - Perfect or Not
factoring with [specify level of
 Perfect Squares and Roots
accuracy].
Square Roots (Looking For
Pythagoras) pgs. 39-42
Suggested Resources
For evaluating squares & cubes
http://www.aaamath.com/grade
8.htm
Impact Mathematics
Inv. 4-Exponent Laws and
Scientific Notation pgs. 156158
5. (CPI-8EE, 3) Students estimate
and express large 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.
 http://www.purplemath.com/
modules/exponent3.htm
 http://www.factmonster.com/i
pka/A0876783.html
www.purplemath.com/
www.factmonster.com/
6. (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].
http://www.purplemath.com/mod
ules/exponent3.htm
www.purplemath.com/
The Office of Academic Services ©2010
Page 23
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Strand 8.EE- Work with radicals and integer exponents
Essential Questions
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
7. (CPI-8EE, 4) Students use and
perform operations with numbers
expressed in scientific notation
and decimal notation by complying
the rules of operations with integer
exponents used with specified
Types of Research Based
Activities and Assessments
that could illustrate Objectives
http://www.purplemath.com/mod
ules/exponent3.htm
Powers. Roots, Exponents, and
Scientific Notation (Preparing for
the New Jersey GEPA Grade 8)
Suggested Resources
For Scientific Notation
http://www.aaamath.com/grade
8.htm
Preparing for the New Jersey
GEPA Grade 8
levels of accuracy.
8.
(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].
http://www.purplemath.com/mod
ules/exponent3.htm
9.
(CPI-8EE, 4) Students interpret
technology generated scientific
notation by applying the rules of
operations with [specify level of
accuracy].
Perform operations with numbers
expressed in scientific notation using
The Office of Academic Services ©2010
www.anus.astro.umd.edu
Interactive website
http://janus.astro.umd.edu/astro/sc www.csgnetwork.com
inote/
Decimal to Scientific notation
converter
http://www.csgnetwork.com/dect
osncalc.html
Page 24
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Strand 8.EE- : Understand the connections between proportional relationships, lines and linear equations
Essential Questions
Why are graphs important when
trying to find relationships in a
desired situation?
How can real-world situations
be modeled using graphs and
functions?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
1. ( CCSSI -8EE, 5) Students
interpret unit rate as the slope of
the graph by generating a graph
showing proportional relationship
between two variables with
[specify level of accuracy]
2. ( CCSSI -8EE, 5) Students
compare two different
proportional relationships by
analyzing the proportional
relationships; one represented as a
graph and the other as an equation
with [specify level of accuracy].
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Linear Changes
Slope Review - Learning Check
quiz
Walking Marathon (Moving
Straight Ahead) pgs 5-6
Raising Money (Moving Straight
Ahead) pgs. 8-9
Climbing stairs (Moving Straight
ahead) pgs
Waling Rates and Linear
Relationships (Moving Straight
Ahead pgs 6-7
Suggested Resources
www.education.ti.com
Moving Straight Ahead
Applications #’s 6a-d, 13 pgs.
14-16 Connections #’s 20a-c
pg. 18
Additional Practice and Skills
Workbook 83-86
Additional Practice and Skills
Workbook 83-86
Moving Straight Ahead
Inv. 1, Problem 1.3 , 1.4-Using
the Walkathon Money
Applications #’s 1d, 3g-I, 4a,
4c, 7a, 9, 10, 12e pgs. 12-15
Page 25
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Strand 8.EE- : Understand the connections between proportional relationships, lines and linear equations
Essential Questions
Why are graphs important when
trying to find relationships in a
desired situation?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
3. ( CCSSI-8EE, 6) Students derive
the equation y= mx for a line that
passes through the origin, and y =
mx + b for a line intercepts the
vertical axis at b by finding the
slope and y-intercept with
[specify level of accuracy]
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Using Linear Relationships
(Moving Straight Ahead) pgs 8-9
Crossing the Line (Moving
Straight Ahead)
Linear Models and Equations
(Thinking With Mathematical
Models) pgs. 24-32
Suggested Resources
Thinking With Mathematical
Models
Inv. 2-Linear Models and
Equations, Problems 2.1-2.4
pgs. 37-51
ACE questions pgs.33-46
Additional Practice and Skills
Workbook 83-86
How can real-world situations
be modeled using graphs and
functions?
The Office of Academic Services ©2010
Page 26
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Strand 8.EE- : Analyze and solve linear equations and pairs of simultaneous linear equations.
Essential Questions
How are algebraic expressions
used for solving real world
problems?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
1. ( CCSSI -8EE, 7a) Students solve
linear equations in one variable
with one solution by using exact
reasoning methods and
approximation with [specify level
of accuracy].
2. ( CCSSI -8EE, 7a) Students
evaluate and simplify the
equations in one variable by using
the symbolic method with
[specify level of accuracy].
How does writing and solving
equations and systems of
equations help solve complex
problems graphically and
algebraically?
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Crossing the Line (Moving
straight ahead) pgs 25-26
Walking to Win (Moving straight
ahead) pgs. 24-25
Tiling Pools, Thinking in
Different Ways, The Community
Pool Problem, and Diving In (Say
It With Symbols) pgs 19-43
Suggested Resources
Moving Straight Ahead
Investigation 2 Problem 2.2
Crossing the Line pgs. 49-50
Moving Straight Ahead:
Investigation2 Problem 2.1:
Walking to win pgs. 41-46
Applications #’s 1
Say It With Symbols:
Investigation 1-Equivalent
expression Problems 1.1-1.4
pgs. 19-43
Page 27
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Strand 8.EE- : Analyze and solve linear equations and pairs of simultaneous linear equations.
Essential Questions
How are algebraic expressions
used for solving real world
problems?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
3. ( CCSSI -8EE, 7b) Students solve
linear equations with rational
number coefficients including
equations whose solutions require
expanding expressions by using
distributive property and
combining like terms with
[specify level of accuracy].
How does writing and solving
equations and systems of
equations help solve complex
problems graphically and
algebraically?
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Connecting, Tables, Graphs and
Equations (Moving Straight
Ahead) pgs. 29-30
Graphs of Linear Equations (Say
it With Symbols) pgs, 24-25
Many Ways to Reach Goal (Say
It With Symbols) pgs. 37-38
Many Ways to Reach a Goal (Say
It With /Symbols)
Suggested Resources
Moving Straight Ahead: Inv. 2
Problem 2.4-Connecting
Tables, Graphs, and Equations
pgs. 55-57
Applications #’s 15-28
Extensions #’s 40-41
Say It With Symbols:
Inv. 1-Equivalent expression
Inv. 2-Linear Equations and
inequalities pgs. 39-42
Applications #1-2 pg. 30 #1322
Inv. 3- Equations With Two or
More Variables Problem 3.1Many Ways to Reach a Goal
pgs. 55-60
Moving Straight Ahead:
Investigation 2 Problem 2.1:
Walking to win pgs. 41-46
Connections #’s 29-34
Extensions # 42
Page 28
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Strand 8.EE- : Analyze and solve linear equations and pairs of simultaneous linear equations.
Essential Questions
How are algebraic expressions
used for solving real world
problems?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
4. (CCSSI -8EE, 8a) Students find
solutions to a system of two linear
equations in two variables by
locating the point of intersection
that satisfies both of the equations
simultaneously with [specify level
of accuracy]
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Say It With Symbols:
Linear Inequalities pgs. 26-27
Solving Linear Inequalities pgs.
28-29
Connecting y = mx + b and ax
+by = c pgs. 39-40
Intersecting of Lines pgs.
Suggested Resources
Say It With Symbols
Inv. 2-Linear Equations and
inequalities Problem 2.2Linear Inequalities pgs. 43-46
Applications #3-7 pg. 31
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. 6568
How does writing and solving
equations and systems of
equations help solve complex
problems graphically and
algebraically?
The Office of Academic Services ©2010
Page 29
The Newark Public Schools
Subject: Mathematics
Domain 8.EE
Expressions and Equations
Strand 8.EE- : Analyze and solve linear equations and pairs of simultaneous linear equations.
Essential Questions
How are algebraic expressions
used for solving real world
problems?
How does writing and solving
equations and systems of
equations help solve complex
problems graphically and
algebraically?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
5. ( CCSSI -8EE, 8b) Students solve
systems of two linear equations in
two variables algebraically, and
estimate solutions by graphing the
equations with [specify level of
accuracy]
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].
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Solving Equations Using Tables
and Graphs (Moving straight
Ahead) pgs. 46-48
Exploring Equality (Moving
straight Ahead) pgs. 48-51
From Pouches to Variables
(Moving straight Ahead) pgs. 5253
Solving Linear Equations
(Moving straight Ahead) pgs.5354
Suggested Resources
Moving Straight Ahead
Investigations 3: Solving
Equations Problem 3.1-Solving
Equations Using Tables and
Graphs pgs. 67-70
Problem 3.2-Exploring
Equality
Pgs. 71-78
Say It with Symbols:
Investigation 2-combining
Expressions
Moving Straight Ahead
Investigations 3: Solving
Equations Problem 3.30- From
Pouches to Variables pgs. 7980
Problem 3.4-solving Linear
Equations pgs. 81-84
Page 30
The Newark Public Schools
Subject: Mathematics
Domain 8.F
Functions
Strand 8.F – Define, evaluate, and compare functions.
Essential Questions
How are functions applied to
solve complex algebraic
problems?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
Types of Research Based
Activities and Assessments
that could illustrate Objectives
1. ( CCSSI -8F, 1) Students
Walking Rates (Moving Straight
complete a function table by a
Ahead pgs. 5-6)
applying a rule with [specify level Raising money (Moving straight
of accuracy]
Ahead pgs. 8-9)
Suggested Resources
Moving Straight Ahead
Investigation 1: Walking Rates
Problem 1.1 Walking
Marathons pgs 5- 6
Applications
Connections #24a-b
Algebra tools to draw graphs,
tables (Prentice Hall, Student
Express, Active Math)
2. ( CCSSI -8F, 1) Students create a
graph by using the input and
output values of a table as ordered
pairs of a graph with [specify
level of accuracy]
The Office of Academic Services ©2010
Walking Rates and Linear
Relationships (Moving Straight
Ahead pgs. 6-7)
Raising Money (Moving Straight
Ahead pgs. 8-9)
Moving Straight Ahead
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
Page 31
The Newark Public Schools
Subject: Mathematics
Domain 8.F
Functions
Strand 8.F – Define, evaluate, and compare functions.
Essential Questions
How are functions applied to
solve complex algebraic
problems?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
Types of Research Based
Activities and Assessments
that could illustrate Objectives
3. ( CCSSI -8F, 2) Students compare
the rate of change by analyzing
Using the Walkathon Money
functions given in the form of an
(Moving Straight Ahead pgs. 10equation, a table and a graph with 11)
[specify level of accuracy].
Virtual Bridge Experiment
(Thinking with Mathematical
models, Prentice Hall, Student
Express, Active Math)
4. ( 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].
The Office of Academic Services ©2010
Getting Started with the TINavigator™ System: Phone Card
Linear Changes
Raising Money (Moving Straight
Ahead pgs 8-9)
Suggested Resources
Moving Straight Ahead
Investigation 1.4-Using the
Walkathon Money Problem
1.4- Recognizing Linear
Relationships pgs. 10-11
Applications #’s 2, 3a, 3f
Algebra tools to draw graphs,
tables (Prentice Hall, Student
Express, Active Math)
Moving Straight Ahead
Inv.1 Problem 1.3- Using
Linear Relationships pgs 8-9
Applications #’s 3g-I, 4a
Page 32
The Newark Public Schools
Subject: Mathematics
Domain 8.F
Functions
Strand 8.F – Use functions to model relationships between quantities.
Essential Questions
How are functions applied to
solve complex algebraic
problems?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
Types of Research Based
Activities and Assessments
that could illustrate Objectives
1. ( CCSSI -8F, 2) Students compare
the rate of change by analyzing
Using the Walkathon Money
functions given in the form of an
(Moving Straight Ahead pgs. 10equation, a table and a graph with 11)
[specify level of accuracy].
2. ( 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].
The Office of Academic Services ©2010
Getting Started with the TINavigator™ System: Phone Card
Linear Changes
Raising Money (Moving Straight
Ahead pgs 8-9)
Suggested Resources
Moving Straight Ahead
Investigation 1.4-Using the
Walkathon Money Problem
1.4- Recognizing Linear
Relationships pgs. 10-11
Applications #’s 2, 3a, 3f
Moving Straight Ahead
Inv.1 Problem 1.3- Using
Linear Relationships pgs 8-9
Applications #’s 3g-I, 4a
Page 33
The Newark Public Schools
Subject: Mathematics
Domain 8.G
Geometry
Strand 8.G –Understand congruence and similarity using physical models, transparencies, or geometry software
Essential Questions
How are transformations and
dilations conducted and/or
useful in geometric situations in
real world?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
1. (CPI-8G, 1) Students verify the
properties of rotation, reflection
and translation by conducting
experiments with [specify level
of accuracy]
2. (CPI-8G, 2) Students establish
congruency between two 2dimensional figures by
conducting rotations, reflections
and translations and describing
the sequence of transformations
used with [specify level of
accuracy]
How is similarity and
congruency useful in real-life
mathematical situations across
the disciplines?
3. (CPI-8G, 3) Students describe
dilations, rotations, reflections
and translations of two
dimensional figures by using
coordinates with [specify level of
accuracy].
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Inv. 2 Symmetry
Transformations (Kaleidoscopes,
Hubcaps and Mirrors, pgs 27-33)
Geometers Sketch Pad Activity
Dilations in the Plane
Exploring Transformations
REAL LIFE, REAL WORLD
Activity - Architecture
"Fishing for Points"-Transformations Using Lists
Kaleidoscopes, Hubcaps and
Mirrors, Inv. 3: Exploring
Congruence (pgs. 48-50)
Matching Game- Properties of
Congruent Triangles (pg. 51)
Inv. 4 Applying Congruence and
Symmetry (pgs.65-69)
Geometers Sketch Pad Activity
Suggested Resources
Kaleidoscopes, Hubcaps and
Mirrors
Geometer Sketch Pad
Activities
District Math e-board
Hubcap Maker,
Transformational Tool,
Prentice Hall, Student Express,
Active Math
Kaleidoscopes, Hubcaps and
Mirrors, Inv.5: Transforming
coordinates by use of Geometers
Sketch Pad.
The Office of Academic Services ©2010
Page 34
The Newark Public Schools
Subject: Mathematics
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)
4. (CPI-8G, 4) Students identify
similar figures by analyzing the
sequence of transformations
and/or dilations that demonstrate
the similarity between them with
[specify level of accuracy].
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Geometer Sketch Pad Activity
Suggested Resources
District Math e-board
Page 35
The Newark Public Schools
Subject: Mathematics
Domain 8.G
Geometry
Strand 8.NPS –Iterations/Measurements
Essential Questions
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
1. (NPS-8G) Students generate
geometric patters by using
iterative procedures with [specify
level of accuracy].
2. (NPS-8G) Students solve
problems requiring calculations
that involve different units of
measurement within a
measurement system by using
conversion formulas with [specify
level of accuracy].
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Fractals (New Jersey ASK 8
Coach) pgs. 142-147
Converting Measurements (New
Jersey ASK 8 Coach) pgs. 148151
Approximate Equivalent
Measures (New Jersey ASK 8
Coach) pgs. 152-155
3. (NPS-8G) Students solve
problems that involve finding
surface area by generating and
applying the surface area formula
with [specify level of accuracy].
Finding Surface Area and
Volume (New Jersey ASK 8
Coach) pgs176-184
4. (NPS-8G) Students explore the
relationship between area and
perimeter by changing one of the
two measurements [specify level
of accuracy].
Square tiles activities: Constant
Area Activity, Constant Perimeter
Activity
The Office of Academic Services ©2010
Suggested Resources
New Jersey ASK 8 Coach
Fractals pgs. 142-147
New Jersey ASK 8 Coach
Converting Measurements pgs.
148-151
Approximate Equivalent
Measures pgs. 152-155
New Jersey ASK 8 Coach
Finding Surface Area and
Volume pgs.176-184
Page 36
The Newark Public Schools
Subject: Mathematics
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)
1. (NPS-8G) Students determine the
measures of angles by identifying
supplementary, complementary
and vertical angles with [specify
level of accuracy].
2. (CPI-8G, 5) Students understand
interior, exterior angles, alternate
interior and alternate exterior
angles by exploring special angle
relationships formed when a set
of parallel lines are intersected by
a transversal with [specify level
of accuracy].
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Impact Mathematics: Lesson 2.2Angle Relationships, Inv.1Supplementary , Complementary
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
Skills Practice: Leveled Lesson
Resources P. 16, Teacher Edition
Pg. 87B
Impact Mathematics: Lesson 2.2Angle Relationships,
Investigation 2-Parallel Lines Cut
By a Transversal, pages 91-93 On
Your Own Exercises 7-10, 12
Suggested Resources
Impact Mathematics, Teacher
Edition
Impact Mathematics, Teacher
Works CD Lesson 2.2
Impact Mathematics, Teacher
Edition
Impact Mathematics, Teacher
Works CD Lesson 2.2
Page 37
The Newark Public Schools
Subject: Mathematics
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)
3. (CPI-8G, 5) Students solve real
life mathematical problems by
applying the angle relationships
formed when a set of parallel
lines are intersected by a
transversal with [specify level of
accuracy].
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Impact Mathematics Teacher
Edition: Leveled Lesson
Resources- Problem Solving
Practice on angle relationships.
pg 87B
Assessment:
Quick Quiz Problems 1-10, page
95, Impact Mathematics Teacher
Edition
Suggested Resources
Impact Mathematics Teacher
Edition: Leveled Lesson
Resource
Page 38
The Newark Public Schools
Subject: Mathematics
Domain 8.G
Geometry
Strand 8.G –Geometric properties
Essential Questions
How do geometric properties
help in solving problems and
make sense of phenomena?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
1. (NPS-8G) Students solve
geometric problems by applying
properties of polygons with
[specify level of accuracy].
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Polygons (Cord Bridges to
Algebra and Geometry-Learning
context)
Similar Polygons (New Jersey
ASK 8 Coach)
How are 3-D figures generated
from 2-D figures?
2.
(NPS-8G) Students construct 2dimensional nets for 3dimensional objects by unfolding
3-D paper models with [specify
level of accuracy].
The Office of Academic Services ©2010
Suggested Resources
Cord Bridges to Algebra and
Geometry-Learning context
Lesson 10.5-Polygons pgs.
555-562
New Jersey ASK 8 Coach
Lesson 15-Similar
Polygons94-98
Lesson 17-Using Scale
Drawings pgs 106-110
Shapes and Properties Activities
(Teaching Student-Centered
Mathematics Grades 5-8) pgs.
187-188
Teaching Student-Centered
Mathematics Grades 5-8
Shapes and Properties
Activities pgs. 187-188
Three-Dimensional Figures (New
Jersey ASK 8 Coach) pgs. 111116
New Jersey ASK 8
Coach Three-Dimensional
Figures pgs. 111-116
Page 39
The Newark Public Schools
Subject: Mathematics
Domain 8.G
Geometry
Strand 8.G –Understand and apply the Pythagorean Theorem
Essential Questions
What is the importance of
Pythagorean Theorem in
solving real life mathematical
situations?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
Types of Research Based
Activities and Assessments
that could illustrate Objectives
1. (CPI-8G, 6) Students find proof to
the Pythagorean Theorem by
The Pythagorean Theorem
establishing an area model with
A Proof of the Pythagorean
[specify level of accuracy].
Theorem (Looking For
Pythagoras) pgs. 31-32
Proof of the Pythagorean
Theorem using Transformations
Interactive Pythagoras
(Prentice Hall, Student Express,
Active Math)
2. (CPI-8G, 6) Students find proof
to the converse of the
Pythagorean Theorem by solving
the equation/formula for the
values of a or b with [specify
level of accuracy].
The Office of Academic Services ©2010
A Proof of the Pythagorean
Theorem (Looking For
Pythagoras) pg. 33-34
The Pythagorean Theorem And
Classifying Triangles
Suggested Resources
Looking for Pythagoras
Investigation 3-The
Pythagorean Theorem
Problem 3.1-The Pythagorean
Theorem pgs. 51-56
Applications #’s 1-14 pgs. 3840
www.education.ti.com
Additional Practice Problems
pgs. 35-40
Looking for Pythagoras
Inv. 3-The Pythagorean
Theorem
Problem 3.2-A Proof of the
Pythagorean Theorem pgs. 5760
Connections #’s 18-23, 26
www.education.ti.com
Additional Practice Problems
pgs. 35-40
Page 40
The Newark Public Schools
Subject: Mathematics
Domain 8.G
Geometry
Strand 8.G –Understand and apply the Pythagorean Theorem
Essential Questions
What is the importance of
Pythagorean Theorem in
solving real life mathematical
situations?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
3. (CPI-8G, 7) Students find the
unknown side lengths of right
triangles in two- and/or threedimensional figures within reallife mathematical situations with
[specify level of accuracy].
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Measuring the Egyptian Way
(Looking For Pythagoras) pgs.
36-37
Stopping Sneaky Sally (Looking
For Pythagoras) pgs. 49-50
Finding Distances (Looking for
Pythagoras) p. 35
4. (CPI-8G, 8) Students find the
distance between two points in
the coordinates system by
applying the Pythagorean
Theorem with [specify level of
accuracy]
The Office of Academic Services ©2010
Lesson 12- The Pythagorean
Theorem (New Jersey ASK 8
Coach) pgs. 77-81
Suggested Resources
Looking For Pythagoras
Inv. 3- The Pythagorean
Theorem
P.3.4-Measuring The Egyptian
Way pgs. 36-37
Application #’s 15-17 pg40
Connection # 25 pg. 42
Inv.4-Using The Pythagorean
Theorem, P.4.2-Stopping
Sneaky Sally, pgs. 79-82
Application #’s 3-5 p. 53
Connections #’s 24-25 p. 57
Additional Practice Problems
pgs. 35-40
Investigation 3-The
Pythagorean Theorem
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. 6567
Page 41
The Newark Public Schools
Subject: Mathematics
Domain 8.G
Geometry
Essential Questions
How will applying appropriate
measurement concepts, tools,
and formulas help solve
geometric problems efficiently?
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
1. (CPI-8G, 9) Students find the
volume of cones to solve realworld situations and
mathematical problems by
exploring and applying the
formula with [specify level of
accuracy].
2. (CPI-8G, 9) Students find the
volume of cylinders to solve realworld situations and
mathematical problems by
exploring and applying the
formula with [specify level of
accuracy].
3. CPI-8G, 9) Students find the
volume of spheres to solve realworld situations and
mathematical problems by
exploring and applying the
formula with [specify level of
accuracy].
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Finding the Volume of Other
Prisms (Filling and Wrapping
pgs. 32-33
Cones and Cylinders, Pyramids
and Cubes pgs. 50-52
Finding the Volumes of
Cylinders
(Filling & Wrapping) pgs 34-35
Making a New Juice Container
(Filling & Wrapping) p. 37
Comparing Spheres and
Cylinders (Filling and Wrapping)
pgs. 48-50
Melting Ice Cream (Filling and
Wrapping) pgs. 52-53
Suggested Resources
Filling & Wrapping
Inv.3 Problem 3.1 p.57-60
Investigation 4 Problem 4.2
p.83-86, Problem 4.3 p.87-90
Applications #’s 7, 10d, 11b,
15, pgs. 38-41
Filling & WrappingInv. 3, Problem 3.2 p.61-64
and Problem 3.4 p. 69-72
Investigation 4 Problem 4.3
p.87-90
Applications #’s 1a, 2, 3, 7,
10c, 11a, 14, 15, 17a, 22, 24,
26 pgs. 38-43, Connections #’s
27-29, 33 pgs 44 & 46
Mathematical Reflections p.
47 2b & 3
Filling & WrappingInv. 4 Problem 4.1 p.79-82 &
Problem 4.3 p.87-90
Applications #’s 2, 10e, 11c
pgs. 38-41, Connections #’s
27-29, 31-33 pgs 44-46
Page 42
The Newark Public Schools
Subject: Mathematics
Domain 8.G
Geometry
Essential Questions
How will applying appropriate
measurement concepts, tools,
and formulas help solve
geometric problems efficiently?
Instructional Objectives / Skills
and Benchmarks (CCSSIs)
1. (NPS-8G9) Students explore
the formula for finding volume
of prisms and solve
mathematical problems in realworld situations by applying the
formula with [specify level of
accuracy].
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Finding the Volume of Other
Prisms (Filling and Wrapping
pgs. 32-33
Melting Ice Cream (Filling and
Wrapping) pgs. 52-53
2. (NPS-8G) Students explore the Cones, Cylinders, pyramids and
formula for finding volume of
Cubes (Filling and Wrapping) p.
pyramids and solve
50
mathematical problems in realworld situations by applying the
formula with [specify level of
accuracy].
3. (NPS-8G) Students explore the
Making cylinders and Prisms
formula for finding surface area
from Nets (Filling and
of prisms and solve
Wrapping) pgs 35-36
mathematical problems in realworld situations by applying the
formula with [specify level of
accuracy]
The Office of Academic Services ©2010
Suggested Resources
Filling & Wrapping
Inv. 3 Problem 3.1 pgs. 57-60
Inv. 4 Problem 4.3 p.52-53
Applications #’s 1, 7, 10c,
11a, 15, 31-32 pgs. 38-45,
Connections #’s 27-29, 31-33
pgs 44-46 Mathematical
Reflections #1 p. 47
Filling & Wrapping- Inv. 4
Problem 4.2 pgs. 50
Applications #’s 13, 16, 17,
22 pgs. 55-57 Extensions #
33, 35 pgs. 59-60
Filling & Wrapping- Inv. 3
Problem 3.3 p.67-68
Applications #’s 15, 18 pgs.
40-41
Interactive Activities,
(Filling and Wrapping,
Prentice Hall, Student
Express, Grade 7, Active
Math)
Page 43
The Newark Public Schools
Subject: Mathematics
Domain 8.G
Geometry
Essential Questions
How will applying appropriate
measurement concepts, tools,
and formulas help solve
geometric problems efficiently?
Instructional Objectives / Skills
and Benchmarks (CCSSIs)
4. (NPS-8G) Students explore the
formula for finding surface area
of cylinder and solve
mathematical problems in realworld situations by applying the
formula with [specify level of
accuracy].
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate Objectives
Making cylinders and Prisms
from Nets (Filling and
Wrapping) pgs 35-36
Interactive Activity, “Virtual
Cylinder”, (Filling and
Wrapping, Prentice Hall, Student
Express, Grade 7, Active Math)
Suggested Resources
Filling & Wrapping- Inv. 3
Problem 3.3 p.67-68
Applications #’s 1b, 4-6, 12,
14c, 17b, 18, 22 pgs. 39-42
Interactive Activities
Filling and Wrapping,
Prentice Hall, Student
Express, Grade 7, Active
Math
Page 44
The Newark Public Schools
Subject: Mathematics
Domain 8.SP
Statistics and Probability
Strand 8.SP: - Investigate patterns of association in bivariate data
Essential Questions
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
1. (CPI-8SP, 1) Students construct a
scatter plot by using bivariate
measurement data with [specify
level of accuracy].
What is the use of data
organizers (graphs, tables
etc.) in making predictions
and conjectures in real
world problems?
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Two kinds of Variability (Data
Distributions) pgs. 13-15
2. (CPI-8SP, 1) Students interpret and
describe scatter plots by
investigating patterns of association
between two variables with [specify
level of accuracy].
Relating Two Variables
(Samples and Populations)
Are Quality Ratings and Prices
Related p. 62
3. (CPI-8SP, 2) Students determine
closeness of data to the lines of best
fit by exploring scatter plots that
suggest linear association of two
quantities with [specify level of
accuracy].
Variability in Categorical Data
(Data Distributions) pgs. 7-11
4. (CPI-8SP, 3) Students solve
problems in the context of bivariate
measurement data by interpreting
the slope and the intercept with
[specify level of accuracy].
The Office of Academic Services ©2010
Use Data tools to develop
scatter plots ( Prentice Hall,
Student Express, Active Math)
Ti Graphing Calculator
Activities
ACE questions, Additional
Practice, Question Bank
(Samples and Populations)
Suggested Resources
Data Distributions
Inv. 1-Making Sense of
Variability
Problem 1.4-Two Kinds of
Variability pgs. 13-15
Application #’s 12-13 p. 20
Connection #’s 19-23pgs. 2326
Inv. 4- Relating Two
Variables
Problem 4.1-Are Quality
Ratings and Prices Related
pgs.96-98
Applications #1
Connections #’s 4-8
Data Distributions
Investigation 1-Making Sense
of Variability
Problem 1.1- Variability in
Categorical Data pgs 6-8
Application #’s1 & 12
Connections #’s 14-15 pg.21
Page 45
The Newark Public Schools
Subject: Mathematics
Domain 8.SP
Statistics and Probability
Strand 8.SP: - Investigate patterns of association in bivariate data
Essential Questions
Instructional Objectives / Skills and
Benchmarks (CCSSIs)
5. (CPI-8SP, 4) Students find patterns
of association in bivariate
categorical data by displaying
frequencies and relative frequencies
in a two-way table with [specify
level of accuracy].
What is the use of data
organizers (graphs, tables
etc.) in making predictions
and conjectures in real
world problems?
6. (CPI-8SP, 4) Students construct a
two way table using the data
collected from the same subjects
with [specify level of accuracy]
7. (CPI-8SP, 4) Students interpret and
summarize data in a two way table
by observing the patterns in the
categorical variables with [specify
level of accuracy]
The Office of Academic Services ©2010
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Solving Archeological Mystery
(Samples and Populations) pgs.
47-50
Suggested Resources
Investigation 3-Solving RealWorld Problems
Problem 3.1-solvign an
archaeological Mystery pgs.
76-81
Investigation 4- Relating Two
Relating Two Variables
Variables
(Samples and Populations)
Problem 4.1-Are Quality
Are Quality Ratings and Prices
Ratings and Prices Related
Related p. 62
pgs.96-98
Writing an Equation to Describe Applications #1
A Relationship pgs. 63-65
Connections #’s 4-8
Human Development Index and Problem 4.2-Writing an
Life Expectancies pgs. 66-68
Equation to Describe A
Relationship pgs. 99-102
Applications #2
Connections #9, 27-30
Problem 4.3-Human
Development Index and Life
Expectancies pgs. 103-106
Applications- #3
Connections #31-35
Extension #36
Page 46
The Newark Public Schools
Subject: Mathematics
Domain 8.SP
Statistics and Probability
Strand 8.SP: - Probability and Vertex Edge Graphs
Essential Questions
What are the real life
practical implications of
theories of probability
Instructional Objectives / Skills
and Benchmarks (CCSSIs)
Suggested Resources
Types of Research Based
Activities and Assessments
that could illustrate Objectives
1. (CCSSI-8,1) Students determine
Red and Blue is a Winner (What What do you Expect?
probability of compound events
do You Expect?) pgs. 7-8
Problem 1.2-Red and Blue is
by using tree diagram/ area
a Winner pgs. 23-26
model/ multiplication principle
Playing the Multiplication Game Applications #’s 3-10 pgs.
with [specify level of accuracy]
(What Do You Expect?) p.9
Connections #’s 20-22 pgs.
Extensions # 29 p.
Problem 1.3-Playing The
Multiplication Game pgs.272. (CCSSI-8,1) Students explore
32
solutions to practical problems by
Applications #’s 11-13 pgs.
using vertex edge graphs with
Connections #’s 23-28 pgs.
[specify level of accuracy]
Extensions #’s 30-33pgs.
How can visual tools such as
networks (vertex-edge
graphs) be used to answer
questions?
The Office of Academic Services ©2010
Page 47