Download Grade 7 - Newark Public Schools

NEWARK PUBLIC SCHOOLS
MATHEMATICS – GRADE 7
CURRICULUM GUIDE
2010-2011
Newark Public Schools 2010-2011
Mathematics
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
Office of Academic Services©2010
2-2011
Newark Public Schools 2010-2011
Mathematics
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
Office of Academic Services©2010
3-2011
Newark Public Schools 2010-2011
Mathematics
TABLE OF CONTENTS
Title Page ........................................................................................................................................................................................................... 1
Board Members ................................................................................................................................................................................................. 2
Administration ................................................................................................................................................................................................... 3
Table of Contents .............................................................................................................................................................................................. 4
District Mission Statement ................................................................................................................................................................................ 5
District Goals and Guiding Principles ............................................................................................................................................................... 6
Curriculum Committee ...................................................................................................................................................................................... 8
Course Philosophy............................................................................................................................................................................................. 9
Course Description .......................................................................................................................................................................................... 10
Recommended Textbooks ............................................................................................................................................................................... 11
Course Proficiencies ........................................................................................................................................................................................ 13
Curriculum Units ............................................................................................................................................................................................. 14
Course Pacing .................................................................................................................................................................................................. 18
Standards, Goals, and Objectives .................................................................................................................................................................... 27
Appendix ......................................................................................................................................................................................................... 44
Office of Academic Services©2010
4-2011
Newark Public Schools 2010-2011
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
Office of Academic Services©2010
5-2011
Newark Public Schools 2010-2011
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.
Office of Academic Services©2010
6-2011
Newark Public Schools 2010-2011
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, fullservice “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.
Office of Academic Services©2010
7-2011
Newark Public Schools 2010-2011
Mathematics
CURRICULUM COMMITTEE
Michele Albruzzese, Math Coach
Lourdes M. Rocafort, Math Coach
Office of Academic Services©2010
8-2011
Newark Public Schools 2010-2011
Mathematics
Newark Public Schools
Mathematics – Grade 7
Course Philosophy
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.
Office of Academic Services©2010
9-2011
Newark Public Schools 2010-2011
Mathematics
Newark Public Schools
Mathematics – Grade 7
Course Description
Grade 7 Curriculum focuses on four important areas: (1) developing understanding of and applying proportional relationships; (2) developing
understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings
and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and
volume; (4) drawing inferences about populations based on samples. The course is designed to help students and teachers to develop mathematical
knowledge, understanding, and skill along with an awareness of and appreciation for the rich connections among mathematical strands and between
mathematics and other disciplines. It also reflects the information-processing capabilities of calculators and computers and the fundamental changes
such tools are making in the way people learn mathematics and apply their knowledge of problem-solving tasks. Mathematical vocabulary will be
strengthened and extended and opportunities will be given to apply these concepts in solving real, mathematical problems.
Office of Academic Services©2010
10-2011
Newark Public Schools 2010-2011
Mathematics
Recommended Textbooks/Resources
This curriculum is primarily based on:
Connected Mathematics 2
Lappan, Fey, Fitzgerald, Friel, Phillips (2009) Pearson Prentice Hall
Teacher Reference Texts:
Teacher’s Wraparound Edition
Lappan, Fey, Fitzgerald, Friel, Phillips (2009) Pearson Prentice Hall
Resources Recommended:
___________
(2009). Buckle Down New Jersey NJ ASK. Buckle Down Publishing. ISBN 0-7836-5299-2
Kaplan, Andrew. (2004). Math On Call. Houghton Mifflin Company. ISBN 10:0-669-5081 9-5
Kaplan, Jerome. (2010). New Jersey ASK Coach Grade 7.Triumph Learning, LLC. ISBN 13:978-1-58620-734-2
Neral, John T.( 2008). Barron’sNew Jersey Ask 7. Barron’s Educational Series, Inc. ISBN 13: 978-0-7641-3943-7
Rubenstein, Craine, Butts ( 2005). Integrated Mathematics.McDougald Little. ISBN 13: 978-0-618-07394-8
Online Resources:
http://www.math.newark.site.eboard.com
Figure This! (Math challenges for families of middle schoolers)
Annenberg/CPB K-12 Math and Science Project
Illuminations, part of NCTM
Office of Academic Services©2010
11-2011
Newark Public Schools 2010-2011
Mathematics
Recommended Textbooks/Resources
http://www.math.msu.edu/cmp
http://www.mathforum.org
http://wwwti.com/calc/docs/resources.html
Texas Instruments Calculator Resources for Educators
http:www.mathforum.org/sketchpad.html
Geometer’s Sketchpad Activities
http//www.2.eboard.com/eboard/servlet/boardservlet?
Balanced Mathematics: Middle School
http://www.math-play.com
Math-Play.com
http://www.3.eboard.com/eboard/servlet/boardservlet?
Math Exemplars I &II: 6-8
Office of Academic Services©2010
12-2011
Newark Public Schools 2010-2011
Mathematics
Course Proficiencies
Students will be able to…..
1. Use numbers in various forms to solve problems.
2. Reason proportionally in a variety of contexts using geometric and numerical reasoning, including scaling and solving proportions.
3. Compare numbers in a variety of ways, including differences, rates, ratios, and percents and choose when each comparison is appropriate.
4. Express rational numbers in equivalent forms.
5. Develop understanding and skill with all four arithmetic operations on rational numbers.
6. Use the order of operations to write, evaluate, and simplify numerical expressions.
7. Develop fluency with paper and pencil computation, calculators, mental calculation, and estimation; and choose among these when solving
problems.
8. Use the commutative and distributive properties to write equivalent numerical expressions.
9. Design and carry out data collection strategies to gather data to answer questions.
10. Organize, analyze, and interpret data to make predictions, construct arguments, and make decisions.
11. Use measures of center and spread to describe and compare data sets.
12. Read, create, and choose data representations (bar graphs, line plots, coordinate graphs, box-and-whisker plots, histograms, and stem-and-leaf
plot).
13. Find and interpret expected value.
14. Compute and compare the chances of various outcomes, including two-stage outcomes.
15. Categorize, define, and relate figures in a variety of representations.
16. Build and visualize three-dimensional figures from various two-dimensional representations and vice versa.
17. Recognize and use standard, essential geometric vocabulary.
18. Use scale factor and ratios to create similar figures or determine whether two or more shapes are similar or congruent.
19. Predict ways that similarity and congruence transformations affect lengths, angle measures, perimeters, areas, volume, and orientation.
20. Find area and perimeter of rectangles, parallelograms, triangles, circles, and irregular figures.
21. Find surface area and volume of rectangular solids, cylinders, and prisms as well as cones and spheres.
22. Use measurement concepts to solve problems.
23. Connect geometric concepts to concepts in other areas of mathematics.
24. Identify and use variables to describe relationships between quantitative variables in order to solve problems or make decisions.
25. Construct tables, graphs, symbolic expressions and verbal descriptions and use them to describe and predict pattern of change in variables.
26. Connect equations to problem situations.
27. Use language of mathematics to express mathematical ideas by communicating their mathematical thinking to peers, teachers, and
others through written and oral expressions.
28. Analyze and evaluate the mathematical thinking and strategies of others.
Office of Academic Services©2010
13-2011
Newark Public Schools 2010-2011
Mathematics
Curriculum Units
Unit I: Computing with Decimals and Percents
Lesson 1 Decimals
1.1 Estimating with Decimals
1.2 Adding and Subtracting Decimals
1.3 Using Fractions to Add and Subtract Decimals
1.4 Decimal Sum and Difference Algorithms
Lesson 2 Multiplication of Decimals
2.1 Finding Missing Factors and Decimal Products
2.2 Factor-Product Relationship
Lesson 3 Division of Decimals
3.1 Exploring Dividing Decimals (Use knowledge of computations with fractions, place value and inverse relationship
between multiplication and division)
3.2 Representing Fractions as Decimals (Terminating or Repeating)
Lesson 4 Percents
4.1 Using percents in estimating or computing taxes, tips, and discounts
4.2 Finding what percent one number is of another number
Lesson 5 Problem Solving using decimals and percents
Problem Solving Focus:
Power Writing Focus:
Work backwards / Guess and check
Problem Writing: Have students write a story problem that involves rational numbers.
Unit II: Integers and Rational Numbers
Lesson 1 Positive and Negative Numbers
1.1 Using positive and negative numbers in applied settings
1.2 Comparing and Ordering Rational Numbers
1.3 Using Number Line to add and subtract rational numbers
Lesson 2 Computations with Rational Numbers
2.1 Addition and Subtraction of Positive and Negative Numbers
2.2 Multiplication and Division of Positive and Negative Numbers
2.3 Coordinate Graphing with Positive and Negative Coordinates to All Four Quadrants
Lesson3
Properties of Operations
3.1 Order of Operations
3.2 The Distributive Property and Subtraction
Office of Academic Services©2010
14-2011
Newark Public Schools 2010-2011
Problem Solving Focus:
Power Writing Focus:
Mathematics
Computation of rational numbers to solve mathematical and real-world problems.
Explanations: Have students explain how they solve a problem. Then, let students write a “how to”
piece for another student. (Burns, 2004; Fortescue, 1994; Brandenburg, 2002; Evans, 1984)
Unit III: Understanding Similarity
Lesson 1 Enlarging and Reducing Shapes
1.1 Introduction to Similarity
1.2 Comparing Similar Figures
1.3 Corresponding Sides and Angles
Lesson 2 Similar Figures
2.1 The use of algebraic rules to produce similar figures on a coordinate grid
2.2 The role multiplication plays in similarity relationships
2.3 Relationships of angles, side lengths, perimeters, and areas of similar polygons
Lesson 3 Similar Polygons
3.1 Construction of quadrilaterals and triangles from smaller, congruent figures
3.2 Relationship between scale factor and area and scale factors less than 1
3.3 The use of scale factor to make similar shapes and find missing measures in similar figures
Lesson 4 Similarity and Ratios
4.1 Ratios within Similar Parallelograms and Similar Triangles
4.2 Using Similarity to Find Measurements
Lesson 5 Using similar Triangles and Rectangles
5.1 The use of shadows and mirrors to estimate the height of real-world object
5.2 Solving problems using the concepts of similar triangles and similar quadrilaterals
Problem Solving Focus:
Power Writing Focus:
Draw a picture / Look for a Pattern
Definitions: Have students write “mathematical definitions” in their own terms. (Burns, 1995)
Unit IV: Ratio, Proportion, and Percent
Lesson 1 Making Comparisons
1.1 Exploring Ratios and Rates
1.2 Analyzing Comparison Statements
1.3 Writing Comparison Statements
Lesson 2 Comparing Ratios, Percents, and Fractions
2.1 Developing Comparison Strategies
2.2 Finding Equivalent Ratios
Lesson 3 Comparing and Scaling Rates
Office of Academic Services©2010
15-2011
Newark Public Schools 2010-2011
Lesson 4
Mathematics
3.1 Making and Using a Rate Table
3.2 Finding Rates
3.3 Unit Rates and Equations
Proportions
4.1 Setting Up and Dividing Proportions
4.2 Applications of Proportions ( The use of ratios and scaling up or scaling down to find the missing value in a
proportion.)
4.3 Strategies for Solving Proportions
Problem Solving Focus: Guess and check / Work backwards / Make a Table, Graph, and Equations
Power Writing Focus: Cubing: A writing strategy that “allows students to examine a problem from six viewpoints”. Prompts
can be written on a cube and modified to meet learning objective. Students will share informal responses with their classmates.
(Pugalee, DiBiase & Wood, 1999)
Unit V: Introduction to Algebra
Lesson 1 Variables, Tables, and Coordinate Graphs
1.1 Making, Interpreting, and Reading Data from Tables
1.2 Making, Interpreting, and Reading Data from Graphs
Lesson 2 Analyzing Graphs and Tables
2.1 Making and Analyzing a Table and a Graph
2.2 Interpreting Graphs
Lesson 3 Rules and Equations
3.1 Equations with One Operation
3.2 Equations with Two Operations
3.3 Writing Equations to Represent Varied Situations
Lesson 4 Graphing Calculator
4.1 Making and Using Graphical Representations on a Graphing Calculator
4.2 Using a Graphing Calculator to Support Problem Solving
Problem Solving Focus:
Power Writing Focus:
Find a Pattern / Write a Number Sentence
Problem Writing: Have student write a math problem using the skills they have learned in class.
Unit VI: Data Analysis
Lesson 1 Measures of Central Tendency (Mean, Median, Mode, Range, and Quartiles)
Lesson 2 Organizing Data and Choosing a Graph
2.1 Graphs (bar graphs, line graphs, circle graphs)
2.2 Displaying and Interpreting Data
Office of Academic Services©2010
16-2011
Newark Public Schools 2010-2011
Mathematics
Lesson 3
Lesson 4
Box-and-Whisker Plots
Scatter Plots
4.1 Correlation and Trend lines
Lesson 5 Sampling
Lesson 6 Venn Diagrams
Lesson 7 Vertex-Edge Graphs
Problem Solving Focus:
Power Writing Focus:
Draw a Picture / Make a List
Problem Writing: Write a step-by-step explanation on how to represent data using appropriate
graphs.
Unit VII: Probability and Discrete Mathematics
Lesson 1 Theoretical Probability
Lesson 2 Simple Events
Lesson 3 Compound Events
3.1 Independent Events
3.2 Dependent Events
3.3 Mutually Exclusive Events
Lesson 4 Experimental Probability
Lesson 5 Expected Value
5.1 Binomial Probability
Lesson 6 Counting Techniques
6.1 Tree Diagrams
Lesson 7 Fundamental Counting Principle
7.1 Tables
7.2 Organized Lists
Lesson 8 Arrangements
8.1 Combinations
8.2 Permutations
Problem Solving Focus:
Power Writing Focus:
Use Logical Reasoning
Explanations: Have students explain how they solve a problem. Then, let students write a “how to”
piece for another student. (Burns, 2004; Fortescue, 1994; Brandenburg, 2002; Evans, 1984)
Office of Academic Services©2010
17-2011
Newark Public Schools 2010-2011
Mathematics
Suggested Course Pacing
Mathematics Grade 7
CONTENT: SEMESTER ONE
NUMBER OF DAYS
UNIT I: Computing with Decimals and Percents
Lesson 1 Decimals
1.1 Estimating with Decimals
1.2 Adding and Subtracting Decimals
1.3 Using Fractions to Add and Subtract Decimals
1.4 Decimal Sum and Difference Algorithms
Mathematical Reflections
Assessment: Check Up #1
Multiplication of Decimals
2.1 Finding Missing Factors and Decimal Products
2.2 Multiplying Decimals
2.3 Factor-Product Relationship
Mathematical Reflections
Lesson 3 Division of Decimals
3.1 Dividing Decimals
3.2 Fractions as Decimals (Terminating/Repeating Decimals)
Mathematical Reflections
Assessment Check Up #2
Lesson 4 Percents
4.1 Using Percents to estimate or compute taxes, tips, and discounts
4.2 Finding What percent One Number Is of Another Number
Mathematical Reflections
Lesson 5 Problem Solving Using Decimals and Percents
Power Writing Focus: Extended Power Writing Paragraph
Assessments: Unit Test ( Review Included)
Unit Project
Focus: Detailed Power Writing Paragraph
TOTAL # OF DAYS
1
1
1
1
½
1
Lesson 2
1
1
1
½
2
1
½
1
2
2
½
2
1
2
23
UNIT II: Integers and Rational Numbers
Lesson 1 Positive and Negative Numbers
Office of Academic Services©2010
18-2011
Newark Public Schools 2010-2011
CONTENT: SEMESTER ONE
1.1 Using Positive and Negative Numbers in Applied Settings
1.2 Comparing and Ordering Positive and Negative Numbers
1.3 Using Number Line and Chip Models
Mathematical Reflections
Assessment: Check Up # 1
Lesson 2 Computations with Rational Numbers
2.1 Addition and Subtraction of Positive and Negative Numbers
2.2 Multiplication and Division of Positive and Negative Numbers
2.3 Coordinate Graphing with Positive & Negative Coordinates to All Four Quadrants
Mathematical Reflections
Assessment: Partner Quiz
Lesson 3 Properties of Operations
3.1 Order of Operations
3.2 The Distributive Property and Subtraction
Mathematical Reflections
Assessment: Check Up # 2
Power Writing Focus: Extended Power Writing Paragraph
Assessments: Self Assessment
Unit Test ( Review Included)
Unit Project
Focus: Detailed Power Writing Paragraph
TOTAL # OF DAYS
UNIT III: Understanding Similarity
Lesson 1
Enlarging and Reducing Shapes
1.1 Introduction to Similarity
1.2 Comparing Similar Figures
1.3 Corresponding Sides and Angles
Mathematical Reflections
Lesson 2 Similar Figures
2.1 The Use of Algebraic Rules to Produce Similar Figures on a Coordinate Grid
2.2 The Role Multiplication Plays in Similarity Relationships
2.3 Relationships of angles, side lengths, perimeters, and areas of similar polygons
Mathematical Reflections
Assessment: Check Up #1
Office of Academic Services©2010
Mathematics
NUMBER OF DAYS
1
1
1
½
1
2
2
2
½
1
2
2
½
1
Take Home
1
1
19½
1
1
1
½
2
1
2
½
1
1
19-2011
Newark Public Schools 2010-2011
CONTENT: SEMESTER ONE
Lesson 3 Similar Polygons
3.1 Construction of Quadrilaterals and Triangles from smaller, congruent figures
3.2 Relationship between Scale factor and area and scale factors less than 1
3.3 The Use of Scale Factor to Make Similar Shapes & Find Missing Measures in
Similar Figures
Mathematical Reflections
Assessment: Partner Quiz
Lesson 4 Similarity and Ratios
4.1 Ratios Within Similar Parallelograms and Similar Triangles
4.2 Using Similarity to Find Measurements
Mathematical Reflections
Assessment: Check Up #2
Lesson 5 Reflections, Rotations, Translations, and Dilations on a Coordinate Plane
Lesson 6 Combining Transformations
Mathematical Reflections
Assessment: Check Up # 3
Lesson 7 Using Similar Triangles and Rectangles
5.1 The Use of Shadows and Mirrors to Estimate the Height of real-world object
5.2 Problem solving involving similar triangles and similar quadrilaterals
Mathematical Reflections
Power Writing Focus: Cubing
Assessments: Self Assessment
Unit Test (Review included)
Unit Project
Focus: Math Essays
TOTAL # OF DAYS
Office of Academic Services©2010
Mathematics
NUMBER OF DAYS
2
2
½
1
2
2
½
1
2
2
½
1
1
1
½
Take Home
1
1
32
20-2011
Newark Public Schools 2010-2011
Mathematics
CONTENT: SEMESTER ONE
UNIT IV: Ratio, Proportion, and Percent
Lesson 1 Making Comparison
1.1 Exploring Ratios and Rates
1.2 Analyzing Comparison Statements
1.3 Writing Comparison Statements
Mathematical Reflections
Lesson 2 Comparing Ratios, Percents, and Fractions
2.1 Developing Comparison Strategies
2.2 Finding Equivalent Ratios
Mathematical Reflections
Assessment: Check Up #1
NUMBER OF DAYS
1
1
1
½
1
1
½
1
TOTAL # OF DAYS
Office of Academic Services©2010
7
MID-TERM EXAM
1
SUBTOTAL
82½
21-2011
Newark Public Schools 2010-2011
Mathematics
CONTENT: SEMESTER TWO
Continue Unit IV: Ratio, Proportion , and Percent
Lesson 3
Lesson 4
NUMBER OF DAYS
Comparing and Scaling Rates
3.1 Making and Using a Rate Table
3.2 Finding Rates
3.3 Unit Rates and Equations
Mathematical Reflections
Assessment: Partner Quiz
Proportions
4.1 Setting Up and Dividing Proportions
4.2 Finding Missing Value in a Proportion
4.3 Problem Solving Involving Proportions
Mathematical Reflections
2
2
2
½
1
1
1
2
½
Power Writing Focus: Guided Response Strategy ( Students are required to rewrite problems
in their own words, come up with a plan for solving it, solve, and
analyze their strategy.)
Assessments: Self Assessment
Unit Test (Review Included)
Unit Project
Focus: Explanations (Have students write a “how to” piece for another student)
TOTAL # OF DAYS
Office of Academic Services©2010
Take Home
1
2
15
22-2011
Newark Public Schools 2010-2011
CONTENT: SEMESTER TWO
Mathematics
NUMBER OF
DAYS
UNIT V: Introduction to Algebra
1
Lesson 1
Extending Patterns
1
½
Lesson 2
Properties of Rational Numbers
Mathematical Reflections
Lesson 3
Writing and Evaluating Expressions
Lesson 4
Simplifying Expressions by Combining Like Terms
Mathematical Reflections
Assessment: Check Up # 1
Lesson 5
Variables, Tables, and Coordinate Graphs
1.1 Making, Interpreting, and Reading Data from Tables
1.2 Making, Interpreting, and Reading Data from Graphs
Mathematical Reflections
1
1
½
Lesson 6
Analyzing Graphs and Tables
2.1 Making and Analyzing a Table and a Graph
2.2 Interpreting Graphs
Mathematical Reflections
Assessment: Check Up #2
1
1
½
1
1
Lesson 7
Functional Relationships
Mathematical Reflections
Lesson 8
Drawing Graphs of Functions
Mathematical Reflections
Assessment: Check Up #2
Lesson 5
Rules and Equations
3.1 Equations with One Operations
Office of Academic Services©2010
2
½
1
2
½
2
½
1
1
1
23-2011
Newark Public Schools 2010-2011
Lesson 6
Mathematics
3.2 Equations with Two Operations
3.3 Writing Equations to Represent Varied Situations
Mathematical Reflections
Assessment: Partner Quiz
2
½
1
Graphing Calculator
4.1 Making and Using Graphical Representations on a Graphing Calculator
4.2 Using a Graphing Calculator to Support Problem Solving
Mathematical Reflections
1
1
½
Assessments: Self Assessment
Unit Test ( Review included)
Take Home
1
Power Writing Focus: Detailed Power Writing Paragraph
TOTAL # OF DAYS
28
UNIT VI: Data Analysis
Lesson1
Measures of Central Tendency (Mean, Median, Mode, Range, Quartiles)
Mathematical Reflections
Assessment: Check Up # 1
2
½
1
Lesson 2
Organizing Data and Choosing a Graph
2.1 Graphs ( Bar Graphs, Line Graphs, Circle Graphs)
2.2 Displaying and Interpreting Data
Mathematical Reflections
2
2
½
Lesson 3
Box-and-Whisker Plots
Mathematical Reflections
2
½
Lesson 4
Scatter Plots
4.1 Correlation and Trend Lines
Mathematical Reflections
Assessment: Partner Quiz
2
½
1
Office of Academic Services©2010
24-2011
Newark Public Schools 2010-2011
Mathematics
Lesson 5
Sampling
Mathematical Reflections
2
½
Lesson 6
Venn Diagrams
Mathematical Reflections
1
½
Lesson 7
Vertex-Edge Graphs
Mathematical Reflections
2
½
Assessments: Self Assessment
Unit Test ( Review Included)
Unit Project
Power writing Focus: Problem Writing ( Have students write math problems using the skill
that is being learned in class.)
TOTAL # OF DAYS
Take Home
1
1
22½
UNIT VII: Probability and Discrete Mathematics
Lesson 1
Theoretical Probability
Mathematical Reflections
1
½
Lesson 2
Simple Events
Mathematical Reflections
Assessment: Check Up #1
1
½
1
Lesson 3
Compound Events
3.1 Independent Events
3.2 Dependent Events
3.3 Mutually Exclusive Events
Mathematical Reflections
1
1
1
½
Experimental Probability
1
Lesson 4
Office of Academic Services©2010
25-2011
Newark Public Schools 2010-2011
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Mathematics
Mathematical Reflections
Assessment: Partner Quiz
½
1
Expected Value
5.1 Binomial Probability
Mathematical Reflections
1
½
Counting Techniques
6.1 Tree Diagrams
Mathematical Reflections
1
½
Fundamental Counting Principle
7.1 Tables
7.2 Organized Lists
Mathematical Reflections
1
1
½
Arrangements
8.1 Combinations
8.2 Permutations
Mathematical Reflections
2
2
½
Assessments: Self Assessment
Unit Test ( Review included)
Unit Project
Take Home
1
1
Power Writing Focus: Troubleshooting ( Have students explain their errors)
TOTAL # OF DAYS
22
FINAL EXAM
Office of Academic Services©2010
2
SUBTOTAL
88.5
TOTAL
171
26-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.RP
Ratios and Proportional Relationships
CCSSI Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Essential Questions
Instructional Objectives / Skill and
Benchmarks (CCSSI standards)
How can we use ratios,
proportions and percents to
solve real-world and
mathematical problems?
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
1. (CCSSI 7.RP.1) Students will use ratios
to compute unit rates, including ratios of
lengths, areas and other quantities, using
like or different units (specify level of
accuracy).
Technology On Sale (Comparing &
Scaling, page 55)
2. (CCSSI 7.RP.2a) Students will determine
whether two quantities are in a
proportional relationship to test for
equivalency in a table or on a graph
(specify level of accuracy).
Ratios within Similar
Parallelograms (Stretching &
Shrinking, pages 77-78)
3. (CCSSI 7.RP.2b,c) Students will identify
the constant of proportionality using
tables, graphs, equations, diagrams, and
verbal descriptions of proportional
relationships (specify level of accuracy).
4. (CCSSI 7.RP.2d) Students will explain
what a point (x, y) on the graph of a
proportional relationship means to
identify the point of origin (0, 0) and the
unit rate (1, r) (specify level of
accuracy).
Office of Academic Services©2010
Time, Rate, and Distance
(Comparing & Scaling, pages 57-58)
Ratios Within Similar Triangles
(Stretching & Shrinking, page 81)
Finding Missing Parts
(Stretching & Shrinking, page 85)
Finding and Using Rates (Moving
Straight Ahead page 6)
Suggested Resources
Comparing & Scaling
 Investigation 3
pages 56 & 60
 ACE Questions,
pages 69-72
Additional Practice & Skills
Workbook pages 39, 41, 43, 46-52
Stretching & Shrinking
 Investigation 4,
pages 78, 82, 86
 ACE Questions,
pages 87-89
Moving Straight Ahead
 Investigation 1.1
pages 16-18
Additional Practice & Skills
Workbook, pages 31-34
Integrated Algebra,
pages 303 - 305
27-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.RP
Ratios and Proportional Relationships
CCSSI Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Essential Questions
What kinds of questions can
be answered using
proportional reasoning?
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
5.
(CCSSI – 7.RP.3) Students will solve
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
multi-step ratio and percent problems
using proportional thinking (specify level
of accuracy).
Suggested Resources
NJ ASK Coach
Pages 42-43, 48-49
NJASK Coach Jumpstart
Barron’s NJ ASK 7, pages 29-34
Math on Call
Pages 424 - 454
Math at Hand
Pages 424 - 454
6.
(NPS 7.RP) Given a set of data, students
will write, analyze, and use comparative
statements to make judgments and
choices about quantitative comparisons
with (specify level of accuracy)
Office of Academic Services©2010
Analyzing Comparison Statements
(Comparing & Scaling, pg. 7)
Writing Comparison Statements
(Comparing & Scaling, pg. 9)
Comparing & Scaling
 Investigation 1, Problems
1.2 & 1.3, pgs. 19-26
 ACE Questions, pg. 11
#4,5,7; pg. 16 # 36-41
28-2011
Measuring UP
People’s Education, Inc.
Newark Public Schools 2010-2011
Mathematics
Domain 7.RP
Ratios and Proportional Relationships
CCSSI Cluster: Analyze proportional relationships and use them to solve real-world and mathematical problems.
Essential Questions
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
Types of Research Based
Activities and Assessments
that could illustrate
Texas Instrument
Activities:
Objectives
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Office of Academic Services©2010
Are You Normal Size?
Banquet Meal
Can You Walk 3 Miles Per
Hour?
Two Friends' Methods
Creating Word Problems
Smart Shoppers
Exemplars
Charmin® Choices
Dense Rocks
Double Dilemma
Fat Intake
Gears
Newspaper Advertisements
Olympic Trophy Design
Raisins
Sneakers
The Great Kayak
Expedition
Gum-dilly-icious!
Suggested Resources
http://www.math.newark.site.eboard.
com
http://www.mth.msu.edu/cmp
http://www.mathforum.org
Texas Instruments Calculator
Resources for Educators
Geometer's_Sketchpad_Activities
Balanced Mathematics: Middle
School
Math-Play.com
29-2011
Newark Public Schools 2010-2011
Mathematics
Domain7.NS
The Number System
CCSSI Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.
Essential Questions
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
What makes a computational
strategy both effective and
efficient?
1. (CCSSI 7.NS.1a) Student will
communicate a clear understanding of
how to add and subtract rational numbers
utilizing a number line (specify level of
accuracy).
2. (CCSSI 7.NS.1b,c) On a number line
students will demonstrate and model
situations which a number and its
opposite (additive inverse) have a sum of
zero (specify level of accuracy).
3. (CCSSI 7.NS.1d) Students will choose
strategies to add and subtract opposite
numbers using properties of operations
to solve real world and mathematical
problems (specify level of accuracy) .
4. (CCSSI 7.NS.2a) Students will multiply
rational numbers using the Distributive
Property for Multiplication (specify level
of accuracy).
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Playing Math
Fever
(Accentuate the Negative, pages 1517)
From Sauna to Snowbank
(Accentuate the Negative, pages 2124)
What’s the Change? (Accentuate the
Negative, pages 25-27)
In the Chips (Accentuate the
Negative, pages 29-31)
Introducing Subtraction of Integers (
Accentuate the Negative, pages 4144)
The “+/-“ Connection (Accentuate
the Negative, pages 45-47)
Coordinate Graphing (Accentuate
the Negative, pages 53-55)
Introducing Multiplication of
Integers (Accentuate the Negative,
pages 63-68)
Office of Academic Services©2010
Suggested Resources
Accentuate the Negative (TG)
 Investigation 1,
pages 17-32
 Investigation 2,
pages 41-56
 Investigation 3,
pages 63-80
 Investigation 4,
pages 87-98
 ACE Questions, pages 3335, 57-61, 81-85, 99-102
Additional Practice & Skills
Workbook, pages 58 - 82
Math on Call, pages, 46-47
New Jersey Ask Coach Grade 7,
pages 50-80 & 71
Measuring Up, pages 2-15
Barron’s NJ Ask 7, pages 1-5, 18-29
Lesson 9, pgs. 38-42
30-2011
Newark Public Schools 2010-2011
Mathematics
Domain7.NS
The Number System
CCSSI Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational numbers.
Essential Questions
How do operations affect
numbers?
How do negative and
positive numbers help in
describing real world
situations?
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
5. (CCSSI 7.NS.2a) Student will compile
rules for multiplying signed numbers to a
interpret products of rational numbers;
describing real-world contexts (specify
level of accuracy).
6. (CCSSI 7.NS.2b) Student will compile
rules for dividing signed numbers to
interpret quotients of rational numbers
describing real-world contexts (specify
level of accuracy).
7. (CCSSI 7NS.2c) Students will choose
strategies to multiply and divide opposite
numbers, using properties of operations
to solve real world and mathematical
problems (specify level of accuracy).
8. (CCSSI 7NS.2d) Student will convert
rational numbers to repeating or
terminating decimals using long division
(specify level of accuracy),
Office of Academic Services©2010
Types of Research Based
Activities and Assessments
that could illustrate
IntroducingObjectives
Division of Integers
(Accentuate the Negative, pgs.73-76
Playing the Integer Product Game
(Accentuate the Negative, pgs.77-80)
Order of Operations (Accentuate the
Negative, pgs. 87-90)
Distributing Operations
(Accentuate the Negative, pgs.91-94)
Suggested Resources
http://www.math.newark.site.eboard.
com
Figure This! (Math challenges for
families of middle schoolers)
Annenberg/CPB K-12 Math and
Science Project
Illuminations, part of NCTM
The Distributive Property and
Subtraction
(Accentuate the Negative, pgs.95-98
Texas Instrument Activities:
 Absolute Values
 Adding Integers - A
Modeling Approach
 Division of Integers
 Integers
 Mining with Fours
 Multiplication of Integers
31-2011
Newark Public Schools 2010-2011
Mathematics
Domain7.NS
The Number System
CCSSI Cluster: Apply and extend previous understandings of operations with fractions to add, subtract, multiply and divide rational
Essential Questions
What information and
strategies would you use to
solve multi-step word
problem?
Instructional Objectives / Skills
and Benchmarks (CCSSI
standard)
9. (CCSSI 7NS.3) Students will add,
subtract, multiply, and divide rational
numbers to solve real-world
problems(specify level of accuracy).
10. (NPS 7.NS) Students use equivalent
representations of numbers such as fractions,
decimals, and percents to develop estimation
strategies with (specify level of accuracy).
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Exemplars:
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Baffling Bacteria
Cavity-Less Caper
Frugal Freda's Fruit Foray
LA to NY
Newspaper Advertisements
Variable Dilemma
Winning the Megabucks
Ski Pass Possibilities
Estimating with Decimals (Bits &
Pieces III, pgs. 6-7)
Estimation (Explore ASK 7
Mathematics, pg. 45)
Suggested Resources
The Math Forum (Swarthmore
College)
Mathematics Internet Sites
Texas Instruments Calculator
Resources for Educators
Geometer's_Sketchpad_Activities
Bits & Pieces III
 Investigation 1, Problem 1.1,
pgs. 19-20
 ACE Questions, pg. 13 #1-7
Explore ASK 7 Mathematics, Lesson
10, pgs. 43-44
11. (NPS 7.NS) Students will compare and
order numbers of all named types with
(specify level of accuracy).
NJ ASK Coach 7, pgs. 38-39
Barron’s NJ ASK 7, pgs. 19-22
Project:
Dealing Down Report
(Accentuate the Negative,
pages 105-106)
Office of Academic Services©2010
32-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.EE
Expressions and Equations
CCSSI Cluster: Use properties of operations to generate equivalent expressions.
Essential Questions
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
1. (CCSSI 7.EE.1) Students will apply
properties of operations as strategies to
add, subtract, factor, and expand linear
expressions with rational coefficients
with (specify level of accuracy).
What makes mathematical
expressions and equations
both effective and efficient?
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Variable , Tables,
and Coordinate
Graphs (Variable &Patterns, pgs.514)
Analyzing Graphs and Tables
(Variable &Patterns, pgs. 30-34)
Rules and Equations (Variable
&Patterns, pgs 49-54)
Calculators Tables and Graph
(Variable &Patterns, pgs. 64-71)
2. (CCSSI 7.EE.2) Students will rewrite
expressions to clarify problems and show
how quantities are related with (specify
level of accuracy).
Walking Rates and Linear
Relationships (Moving Straight
Ahead, pgs. 19-24)
Raising Money (Moving Straight
Ahead, pgs. 25-30)
Using the Marathon Money (Moving
Straight Ahead, pgs. 31-34)
Suggested Resources
Variables and Patterns
 Investigation 1
pages 15 - 36
 Ace Questions
pages 37 - 43
 Investigation 2
pages 45-58
 Ace Questions
pages 59-67
 Investigation 3
pages 68-80
 Ace Questions
pages 81-85
 Investigation 4
pages 89-98
 Ace Questions
pages 99-105
Additional Practice & Skills
Workbook, pages 1-20
Math Exemplars II: 6-8
Texas Instruments
Office of Academic Services©2010
33-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.EE
Expressions and Equations
CCSSI Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Essential Questions
How are algebraic and
numerical expressions used
to represent and solve realworld situations?
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
3. (CCSSI 7.EE.3) Using properties of
operations, students will solve multistep real-life and mathematical
problems involving positive and
negative rational numbers in various
forms (specify level of accuracy).
4. (CCSSI 7.EE.4) Students will
convert positive and negative
rational numbers in various forms
and assess the reasonableness of
their answers by using mental
computation and estimation
strategies (specify level of accuracy).
5. (CCSSI 7.EE.4) Students will
construct simple equations and
inequalities to solve problems using
variables to represent quantities in
real-world or mathematical problems
(specify level of accuracy).
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Texas Instrument
Activities:
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Adding Up The Operations
CDs Anyone?
Concrete Algebra:
Equation Builder
Creating Word Problems
Expanding Space Station
Function Junction
Inequalities
The Best Cell Phone Plan
Rent a Video Game
Exemplar:

Math Team Fundraiser
Suggested Resources
Moving Straight Ahead
 Investigation 1.2, 1.3, & 1.4
pages 19-34
 Ace Questions
pages 35-40
http://www.math.newark.site.eboard.
com
Figure This! (Math challenges for
families of middle schoolers)
Annenberg/CPB K-12 Math and
Science Project
Illuminations, part of NCTM
The Math Forum (Swarthmore
College)
Mathematics Internet Sites
Office of Academic Services©2010
34-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.EE
Expressions and Equations
CCSSI Cluster: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Essential Questions
Why are mathematical
rules necessary?
Instructional Objectives
/ Skills and
Benchmarks (CCSSI standards)
6. (CCSSI 7.EE.4a) Students will solve
word problems using equation forms
px + 2 = r and p(x + q) = r (specify
level of accuracy).
7. (CCSSI 7.EE.4a) Student will
compare an algebraic solution to an
arithmetic solution identifying the
sequence of the operations used in
each approach (specify level of
accuracy).
Why are equations and
inequalities useful?
8. (CCSSI 7.EE.4b) Students will
solve, graph and interpret word
problems to illustrate inequalities
using the form px + q > r or px + q <
r (specify level of accuracy).
Office of Academic Services©2010
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
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Exemplars:
Checkerboard Dilemma
Swinging Time
Math Team Fundraiser
Games:
Algebraic Expressions
Millionaire
One-Step Equation Game
7th Grade Algebra Jeopardy
Project:
Wasted Water
Experiment(Moving Straight Ahead,
pages 123-125)
Suggested Resources
Barron’s NJ ASK 7, pgs. 11-123
NJ ASK Coach 7, Lesson 27, pgs. 188194
Texas Instruments Calculator
Resources for Educators
Geometer's_Sketchpad_Activities
Balanced Mathematics: Middle
School
Math-Play.com.
35-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.G
Geometry
CCCSI Cluster: Draw, construct, and describe geometrical figures and describe the relationship between them.
Essential Questions
How can figures be
represented and compared
using geometric attributes?
Instructional Objectives / Skills
and Benchmarks (CCCSI
standards)
1. (CCSSI 7.G.1) Given drawings of
various geometric figures, students will
accurately compute actual lengths and
areas of the original figures then
reproduce a scale drawing of the figures
(specify level of accuracy).
2. (CCSSI 7.G.2) Given a set of conditions,
students will use various tools (freehand,
ruler, protractor and technology) to draw
geometric figures (specify level of
accuracy).
3. (CCSSI 7.G.2) Students will accurately
construct triangles from three measures
of angles or sides and classify them as
unique triangles, more than one triangle,
or no triangle (specify level of accuracy).
4. (CCSSI 7.G.3) Students will accurately
describe two-dimensional figures that
result from slicing three-dimensional
figures using right rectangular prisms
and right rectangular pyramids (specify
level of accuracy).
Office of Academic Services©2010
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Solving a Mystery
(Stretching &
Shrinking, pages 15-17)
Stretching a Figure (Stretching &
Shrinking, pages 19-24)
Scaling Up and Down (Stretching &
Shrinking, pages 25-27)
Drawing Wumps (Stretching &
Shrinking, pages 33-37)
Hats Off to the Wumps (Stretching &
Shrinking, pages 39-42)
Mouthing Off and Nosing Around
(Stretching & Shrinking pages 4348)
Rep-Tile Quadrilaterals (Stretching
& Shrinking, pages 55-60)
Rep-Tile Triangles (Stretching
&Shrinking , pages 61-64)
Suggested Resources
Stretching & Shrinking (TG)
 Investigation 1,
pages 14-28
 ACE Questions,
pages 12-19 (SP)
 Investigation 2,
pages 32-48
 ACE Questions,
pages 28-36 (SP)
 Investigation 3, pages 54-68
 ACE Questions, pages 44-56
(SP)
Filling & Wrapping (TG)
 Problems 5.2 & 5.3,
pages 101-108
 ACE Questions,
pages 67-74 (SP)
Additional Practice & Skills
Workbook, pages 21-38, 136-138
36-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.G
Geometry
CCSSI Cluster: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Essential Questions
How do the dimensions of a
geometric figure affect area,
surface area, and volume?
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
5. (CCSSI 7.G.4) Using formulas for the
area and circumference of a circle,
student will accurately solve real-life and
mathematical problems (specify level of
accuracy)
6. (CCSSI 7.G.4) Using mathematical and
logical arguments, students will compare
and contrast the relationship between the
area and circumference of a circle
(specify level of accuracy).
How do geometric
relationships help to solve
problems and/or make sense
of phenomena?
7. (CCSSI 7.G.5) Using facts about
supplementary, complementary, vertical,
and adjacent angles, students will write
equations and solve multi-step problems
to find an unknown angle in a figure
(specify level of accuracy).
8. (CCSSI 7.G.6) Using various strategies,
students will accurately solve real-world
and mathematical problems involving
area, volume and surface area of two and
three-dimensional objects composed of
triangles, quadrilaterals, polygons, cubes,
and right prisms (specify level of
accuracy).
Office of Academic Services©2010
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Scale Factors
& Similar Shapes
Suggested Resources
Math at Hand, pages 293-312
(Stretching & Shrinking, pgs. 65-68)
Scaling Up the Compost Box (Filling
& Wrapping, pages 101-104)
Building Model Ships (Filling &
Wrapping, pages 105-108)
Texas Instrument Activities:
 Proportional Flag
 What's the Scale?
 Area Patterns
 Building a Garden Fence
 Geometric Swimming Pools
 Going Around in Circles
 Slam Dunk!
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Exemplars:
Fences for Grazing
Olympic Trophy Design
Stained Glass
John's Field
Packing Predicament
Rectangular Box vs. Cube
Project:
Shrinking or Enlarging Pictures
(Stretching & Shrinking, pages 106-107)
Math on Call, pages 328-377
Buckle Down, pages 122-133
Barron’s NJ ASK 7, pages 59-110
http://www.math.newark.site.eboard.
com
Figure This! (Math challenges for
families of middle schoolers)
Annenberg/CPB K-12 Math and
Science Project
Illuminations, part of NCTM
The Math Forum (Swarthmore
College)
Mathematics Internet Sites
Texas Instruments Calculator
Resources for Educators
Geometer's_Sketchpad_Activities
Balanced Mathematics: Middle
School
37-2011
Newark Public Schools 2010-2011
Mathematics
Domain7. SP
Statistics and Probability
CCSSI Cluster: Use random sampling to draw inferences about a population
Essential Questions
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
What is the best way to
collect, organize, interpret,
and display data to get
desired information?
1. (CCSSI 7.SP.1) Students will articulate
how statistics can be used to gain
information and make valid inferences
about a population by examining a
representative sampling of that
population (specify level of accuracy).
What strategies work best to
predict outcomes?
2. (CCSSI 7.SP.2) Students will estimate,
predict, and infer information about a
population by using data from a random
sample and gauge how far off the
estimation or prediction is to generate
multiple samples of the same size
(specify level of accuracy).
3. (CCSSI 7.SP.3) Student will informally
assess the degree of visual overlap of
two numerical data distributions with
similar variabilities, measuring the
difference between the centers by
expressing it as a multiple of a measure
of variability (specify level of accuracy).
Office of Academic Services©2010
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Guessing Answers
(What Do You Expect, pages 79-82)
Ortonville
(What Do You Expect, pages 83-86)
A Baseball Series (What Do You
Expect, pages 89-90)
Variability in Categorical Data
(Data Distributions, pages 20-24)
Variability in Numerical Counts
(Data Distributions, pages 25-28)
Variability in Numerical
Measurements (Data Distributions,
pages 29-32)
Suggested Resources
What do You Expect?
 Investigation 4, pages 78-90
 ACE Questions, pages 54-59
(SP)
Data Distributions
 Investigation 1, pages 19-36
 ACE Questions, pages 16-26
(SP)
Additional Practice & Skills
Workbook, pages 139-155, 156-163,
164-166,
Barron’s NJ ASK 7, pg. 135
NJ ASK Coach 7 Lesson 7, pgs. 139-143
Two Kinds of Variability
(Data Distributions, pages 33-36)
38-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.SP
Statistics and Probability
CCSSI Cluster: Draw informal comparative inferences about two populations.
Essential Questions
What is the purpose of data
displays and statistical
measures?
Instructional Objectives
/ Skills and
Benchmarks (CCSSI standards)
4.
(CCSSI 7.SP.4) Student will develop
informal comparative inferences about
two populations by using measures of
center and variability for numerical data
(specify level of accuracy).
5. (CCSSI 7.SP.5) Students will use
probability to make a decision by
interpreting the chances of an event
occurring as a number between 0 and
1(specify level of accuracy). A
probability near 0 indicates an unlikely
occurrence, ½ indicates neither likely
nor unlikely, and near 1 a likely
occurrence.
6. (CCSSI 7.SP.6) After collecting data on
a chance event and observing its longrun relative frequency, students will
estimate and predict the frequency the
event will occur (specify level of
accuracy).
Types of Research
Based
Activities and Assessments
that could illustrate
Objectives
The Mean as
an Equal Share ( Data
Distributions, pages 46-50)
The Mean as a Balance Point in a
Distribution (Data Distributions,
pages 51-54)
Suggested Resources
Data Distributions
 Investigation 2, pages 46-66
 ACE Questions, pages 44-53
(SP)
Repeated Values in a Distribution
(Data Distributions, pages 55-60)
Median and Mean and Shapes of
Distributions (Data Distributions,
pages 61-66)
Matching Colors (What Do You
Expect? pages 18-22)
Red and Blue Is a Winner
(What do You Expect? pages 23-26)
Playing the Multiplication Game
(What Do You Expect? pages 27-32)
Office of Academic Services©2010
39-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.SP
Statistics and Probability
CCSSI Cluster: Investigate chance processes and develop, use, and evaluate probability models.
Essential Questions
How can data representation
influence conclusions?
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
7. (CPI 7.SP.7) Students will find
probabilities of events, compare
probabilities, observe frequencies and
explain possible discrepancies by
developing probability models (specify
level of accuracy).
8. (CPI 7.SP.7a) Students will determine the
probability of events by developing a
uniform probability model by assigning
equal probability to all outcomes
(specify level of accuracy).
9. (CPI 7.SP.7b) Students will develop a
probability model (which may not be
uniform) by observing frequencies in
data generated from a chance process
(specify level of accuracy).
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Making Purple
(What Do You
Expect? pages 38-42)
Choosing Paths (What Do You
Expect,pgs 43 – 48)
What Do Finding the Best
Arrangement (What Do You Expect?
pages 49-54)
Barron’s NJ ASK 7, Lesson 4, pg.
154-156
What Do You Expect?
 Investigations 1- 3. pages
18-72
 ACE Questions, pages 43-48
(SP)
http://www.math.newark.site.eboard.
com
Figure This! (Math challenges for
families of middle schoolers)
Annenberg/CPB K-12 Math and
Science Project
Exemplars:
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Office of Academic Services©2010
Suggested Resources
Illuminations, part of NCTM
Winning the Megabucks
What Does Mother Nature
Have Planned for My
Birthday?
Ski Pass Possibilities
The Math Forum (Swarthmore
College)
Mathematics Internet Sites
40-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.SP
Statistics and Probability
CCSSI Cluster: Investigate chance processes and develop, use, and evaluate probability models.
Essential Questions
How do compound events
affect probability?
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
10. (CPI 7.SP.8) Students will find
probabilities of compound events by
using organized lists, tables, tree
diagrams, and simulations (specify level
of accuracy).
11. (CPI 7.SP.8a) Students will determine the
probability of a simple event by
calculating the fraction of outcomes in
the sample space for which the simple
event occurs (specify level of accuracy).
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
One-and-One
Free-Throws (What
Do You Expect? pages 63-64)
Finding Expected Value (What do
You Expect? pages 65-68)
Choosing Play Plans (What Do You
Expect?) pages 69-72
Suggested Resources
Texas Instruments Calculator
Resources for Educators
Geometer's_Sketchpad_Activities
Balanced Mathematics: Middle
School
Math-Play.com.
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12. (NPS 7.SP) Students determine the total
number of possibilities for various events
by using permutations and combinations
to calculate outcomes with (specify level
of proficiency)
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13. (NPS 7.SP) Students will present,
interpret, and analyze data by organizing
information in appropriate types of
graphs with (specify level of proficiency)
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Texas Instruments:
Active Wear - Adventure
10
A Wet Welcome
Box Plots: How Many Pairs
of Socks
Calculator Controlled
Robots - Mission 5: Game
Spinner
Hat Trick
How Much Water Can Abe
Hold?
Keeping Up with the
Joneses
Barron’s NJ ASK 7 pgs. 143-162
NJ ASK Coach 7 218-271
Project:
The Carnival Game (What Do You
Expect? pages 96-104
Office of Academic Services©2010
41-2011
Newark Public Schools 2010-2011
Mathematics
Domain 7.SP
Statistics and Probability
CCSSI Cluster: Investigate chance processes and develop, use, and evaluate probability models.
Essential Questions
Instructional Objectives / Skills
and Benchmarks (CCSSI
standards)
How can experimental and
theoretical probabilities be
used to make predictions or
draw conclusions?
14. (CCSSI 7.SP.8b) Students will determine
the probability of compound events by
calculating the fraction of outcomes in
the sample space for which the
compound event occurs (specify level of
accuracy).
15. (CCSSI 7.SP.8c) Students will generate
frequencies for compound events by
designing and using a simulation to
estimate the probability of the event
(specify level of accuracy).
Types of Research Based
Activities and Assessments
that could illustrate
Objectives
Representing
Survey Data
(Data Distributions, pages 99-102)
Are Steel Coasters Faster than Wood
Coasters? (Data Distributions,
pages 103-114)
Suggested Resources
Data Distributions
 Investigation 4, pages 99114
 ACE Questions, pages 78-84
Additional Practice & Skills
Workbook, pages 171-173
Measuring Up, chapter 4, pages 120155
Barron’s NJ ASK 7, chapter 4, pages
139-162
I Play Math Games.com
Nick's Mathematical Puzzles
Office of Academic Services©2010
42-2011
Newark Public Schools 2010-2011
Mathematics
Appendix
Mathematics Resources – Grade 7
Texas Instruments
Exemplars
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Absolute Values
Adding Integers - A Modeling Approach
Division of Integers
Integers
Mining with Fours
Multiplication of Integers
Are You Normal Size?
Banquet Meal
Can You Walk 3 Miles Per Hour?
Two Friends' Methods
Creating Word Problems
Smart Shoppers
Adding Up The Operations
CDs Anyone?
Concrete Algebra: Equation Builder
Creating Word Problems
Expanding Space Station
Function Junction
Inequalities
The Best Cell Phone Plan
Rent a Video Game
Proportional Flag
What's the Scale?
Area Patterns
Building a Garden Fence
Geometric Swimming Pools
Going Around in Circles
Slam Dunk!
Baffling Bacteria
Cavity-Less Caper
Frugal Freda's Fruit Foray
LA to NY
Newspaper Advertisements
Variable Dilemma
Winning the Megabucks
Ski Pass Possibilities
Charmin® Choices
Dense Rocks
Double Dilemma
Fat Intake
Gears
Newspaper Advertisements
Olympic Trophy Design
Raisins
Sneakers
The Great Kayak Expedition
Gum-dilly-icious!
Math Team Fundraiser
Fences for Grazing
Olympic Trophy Design
Stained Glass
John's Field
Packing Predicament
Rectangular Box vs. Cube
Winning the Megabucks
What Does Mother Nature Have Planned for My Birthday?
Ski Pass Possibilities
Writing Resources
http://www.thewritingsite.org/articles/vol2num2a.asp
Office of Academic Services©2010
43-2011