Download 7th Grade Math Curriculum

Pennsauken Public School
Pennsauken School District
Curriculum Guide
Grade 7 Mathematics
(One Semester)
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Pennsauken Public School
Content Area: Mathematics
Course Title: Grade 7 CCSS
Grade Level: 7
Unit 1: The Number System
Module 1: Adding & Subtracting Integers
Module 2: Multiplying & Dividing Integers
Module 3: Rational Numbers
Unit 2: Ratios and Proportional
Relationships
Total Days: 20
Total Days: 10
Module 4: Rates & Proportionality
Module 5: Proportions & Percent
Unit 3: Expressions, Equations, and
Inequalities
Total Days: 11
Module 6: Expressions & Equations
Module 7: Inequalities
Unit 4: Geometry
Module 8: Modeling Geometric Figures
Module 9: Circumference, Area, & Volume
Total Days: 14
Unit 5: Statistics
Module 10: Random Samples & Populations
Module 11: Analyzing & Comparing Data
Total Days: 10
Unit 6: Probability
Module 12: Experimental Probability
Module 13: Theoretical Probability &
Simulations
Date Created:
June, 2016
Board Approved on:
Total Days: 13
August 2016
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Pennsauken Public School
Seventh Grade Mathematics Pacing Guide for 2016-2017
Module
Title
Instructional Period
Number
of Days
1
Adding and Subtracting Integers
Jan 30 - Feb 3, 2017
5
2
Multiplying and Dividing Integers
Feb 6-9, 2017
4
Benchmark
Feb 10-13, 2017
2
Rational Numbers
Feb 14-24, 2017
7
Benchmark Assessment: Unit 1
Feb 27-28, 2017
2
4
Rates and Proportionality
Mar 1-6, 2017
4
5
Proportions and Percents
Mar 7-10, 2017
4
Benchmark Assessment: Unit 2
Mar 13-14, 2017
2
6
Expressions and Equations
Mar 15-21, 2017
5
7
Inequalities
Mar 22-27, 2017
4
Online Benchmark Assessment: Unit 1-3
Mar 28-29, 2017
2
PARCC Adjustment
Mar 30-Apr 5, 2017
5
8
Modeling Geometric Figures
Apr 6-13, 2017
6
9
Circumference, Area and Volume
Apr 9-26, 2017
6
Benchmark Assessment: Unit 4
Apr 27-28, 2017
2
10
Random Samples and Populations
May 1-4, 2017
4
11
Analyzing and Comparing Data
May 5-10, 2017
4
Benchmark Assessment: Unit 5
May 11-12, 2017
2
Experimental Probability
May 15-19, 2017
5
3
12
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13
I-Ready
Theoretical Probability and Simulations
May 22-20, 2017
5
Online Benchmark Assessment: Unit 1-6
May 31-June 2, 2017
3
Growth Testing
June 5-6, 2017
2
Reteaching and Intervention
June 7-14, 2017
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Pennsauken Public Schools
Content Area:
Mathematics
Grade Cluster:
Course Description
7
This course is a required 7th grade mathematics course for all students. The students will be instructed for 74 minutes daily
throughout the semester.
In Grade 7, instructional time focuses on four critical 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; and (4) drawing inferences about
populations based on samples.
Overarching Understanding(s) for the Course
Ratios and Proportional Relationships
● Analyze proportional relationships and use them to solve real-world and mathematical problems.
The Number System
● Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
Expressions and Equations
● Use properties of operations to generate equivalent expressions.
● Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
Geometry
● Draw, construct and describe geometrical figures and describe the relationships between them.
● Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Statistics and Probability
● Use random sampling to draw inferences about a population.
● Draw informal comparative inferences about two populations.
● Investigate chance processes and develop, use, and evaluate probability models.
21st Century Theme(s), Interdisciplinary Opportunities
21st Century Themes
● Global Awareness
○ Using 21st century skills to understand and address global issues (Module 8)
● Financial, Economic, Business, and Entrepreneurial Literacy
○
Knowing how to make appropriate personal economic choices (Module 5-6)
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○
Using entrepreneurial skills to enhance workplace productivity and career options. (Unit 2, Module 7)
● Environmental Literacy
○
○
○
Demonstrate knowledge and understanding of the environment and the circumstances and conditions
affecting it, particularly as relates to air, climate, land, food, energy, water and ecosystems. (Module 1-2, 1011)
Demonstrate knowledge and understanding of society’s impact on the natural world (e.g., population growth,
population development, resource consumption rate, etc.). (Module1-2, 10-11)
Investigate and analyze environmental issues, and make accurate conclusions about effective solutions. (Unit
5)
Learning and Innovation Skills
●
●
●
Creativity and Innovations
○ Think Creatively, Work Creatively with Others and Implement Innovations (Modules 1-13)
Critical Thinking and Problem Solving
○ Reason Effectively, Use Systems Thinking, Make Judgements and Decisions, Solve Problems (Modules 113)
Communication and Collaboration
○ Communicate Clearly, Collaborate with Others (Modules 1-13)
Life and Career Skills
●
●
●
●
●
Flexibility & Adaptability
○ Adapt to Change, Be Flexible (Modules 1-13)
Initiative and Self-Direction
○ Manage goals and time, work independently, be self-directed learners (Modules 1-13)
Social and Cross-Cultural Skills
○ Interact effectively with others, work effectively in diverse teams (Modules 1-13)
Productivity and Accountability
○ Manage projects, produce results (Modules 1-13)
Leadership & Responsibility
○ Guide and Lead Others, Be Responsible to Others (Modules 1-13)
Technology Standards
● Connecting the content knowledge to real-world applications and problem situations that enable students to
see how what they are learning connects with their lives and the world around them. The work that is asked
of students must be authentic work that is relevant and that mirrors real life.
● Emphasizing deep understanding of the learning by focusing on projects and problems that require students
to use the content knowledge in new ways and to extend their understanding through collaboration with
others.
● Helping students understand and monitor the thinking processes they are using by including metacognitive
activities that ask students to reflect on their use of thinking structures and the effectiveness of the thinking
strategies they employed.
● Using technology to help students access, analyze, organize and share what they are learning and allow
students to independently locate appropriate tools for the task.
● Engaging students in solving complex problems that require higher order thinking and application of
content and that result in new perspectives and solutions to problems.
● Providing opportunities for students to work collaboratively as they gather information, solve problems,
share ideas, and generate new ideas.
● Developing life and career skills by creating opportunities for students to become self-directed learners
who take responsibility for their own learning and who learn how to work effectively with others.
Desired Results
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Unit: #
1
Unit Name:
The Number System: Modules 1-3
Module 1: Adding and Subtracting Integers
Module 2: Multiplying and Dividing Integers
Module 3: Rational Numbers
New Jersey Core Curriculum State Standards:
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Number System
● Apply and extend previous understandings of operations with fractions.
○ 7.NS.A.1 Apply and extend previous understandings of addition and subtraction to add and
subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line
diagram.
○ 7.NS.A.1a Describe situations in which opposite quantities combine to make 0.
○ 7.NS.A.1b Understand p + q as the number located a distance |q| from p, in the positive or negative
direction depending on whether q is positive or negative. Show that a number and its opposite have
a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing real-world
contexts.
○ 7.NS.A.1c Understand p + q as the number located a distance |q| from p, in the positive or negative
direction depending on whether q is positive or negative. Show that a number and its opposite have
a sum of 0 (are additive inverses). Interpret sums of rational numbers by describging real-world
contexts.
○ 7.NS.A.1d Apply properties of operations as strategies to add and subtract rational numbers.
○ 7.NS.A.2 Apply and extend previous understandings of multiplication and division and of fractions
to multiply and divide rational numbers.
○ 7.NS.A.2a Understand that multiplication is extended from fractions to rational numbers by
requiring that operations continue to satisfy the properties of operations, particularly the distributive
property, leading to products such as (-1)(-1)=1 and the rules for multiplying signed numbers.
Interpret products of rational numbers by describing real-world contexts.
○ 7.NS.A.2b Understand that integers can be divided, provided that the divisor is not zero, and every
quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then (p/q)=(-p)/q=p/(-q). Interpret quotients of rational numbers by describinng real-world contexts.
○ 7.NS.A.2c Apply properties of operations as strategies to multiply and divide rational numbers.
○ 7.NS.A.2d Convert a rational number to a decimal using long division; know that the decimal form
of a rational number terminates in 0s or eventually repeats.
○ 7.NS.A.3 Solve real-world and mathematical problems involving the four operations with rational
numbers.
Expressions and Equations
● Use properties of operations to generate equivalent expressions.
○ 7.EE.B.3 Solve multi-step real-life and mathematical problems posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically.
Apply properties of operations to calculate with numbers in any form; convert between forms as
appropriate; and assess the reasonableness of answers using mental computation and estimation
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strategies.
Essential Question(s)
● Module 1: How can you use addition and subtraction of integers to solve real-world problems?
● Module 2: How can you use multiplication and division of integers to solve real-world problems?
● Module 3: How can you use rational numbers to solve real-world problems?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Module 1: Adding and Subtracting Integers
The student will:
● Apply and extend previous understandings of addition and subtraction to add and subtract rational
numbers; represent addition and subtraction on a horizontal or vertical number line diagram. (1.1, 1.2, 1.3,
1.4)
● Understand p + q as the number located a distance |q| from p, in the positive or negative direction. (1.1,
1.2)
● Understand p + q as the number located a distance |q| from p, in the positive or negative direction
depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are
additive inverses). Interpret sums of rational numbers by describging real-world contexts. (1.3)
● Apply properties of operations as strategies to add and subtract rational numbers. (1.1, 1.4)
● Solve real-world and mathematical problems involving the four operations with rational numbers. (1.4)
● Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in
any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms as appropriate; and assess the
reasonableness of answers using mental computation and estimation strategies. (1.4)
Module 2:
The student will:
● Apply and extend previous understandings of multiplication and division and of fractions to multiply and
divide rational numbers. (2.1, 2.2)
● Understand that multiplication is extended from fractions to rational numbers by requiring that operations
continue to satisfy the properties of operations, particularly the distributive property, leading to products
such as (-1)(-1)=1 and the rules for multiplying signed numbers. Interpret products of rational numbers by
describing real-world contexts. (2.1, 2.3)
● Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers
(with non-zero divisor) is a rational number. (2.2)
● Apply properties of operations as strategies to multiply and divide rational numbers. (2.3)
● Solve real-world and mathematical problems involving the four operations with rational numbers. (2.2,
2.3)
● Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in
any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms as appropriate; and assess the
reasonableness of answers using mental computation and estimation strategies. (2.3)
Module 3:
The student will:
● Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers
(with non-zero divisor) is a rational number. If p and q are integers, then -(p/q)=(-p)/q=p/(-q). Interpret
quotients of rational numbers by describinng real-world contexts. (3.1, 3.5)
● Convert a rational number to a decimal using long division; know that the decimal form of a rational
number terminates in 0s or eventually repeats. (3.1)
● Describe situations in which opposite quantities combine to make 0. (3.2)
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● Understand p + q as the number located a distance |q| from p, in the positive or negative direction
depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are
additive inverses). Interpret sums of rational numbers by describing real-world contexts. (3.2)
● Apply properties of operations as strategies to add and subtract rational numbers. (3.2)
● Solve real-world and mathematical problems involving the four operations with rational numbers. (3.2,
3.6)
● Apply and extend previous understandings of addition and subtraction to add and subtract rational
numbers; represent addition and subtraction on a horizontal or vertical number line diagram. (3.3)
● Understand p + q as the number located a distance |q| from p, in the positive or negative direction
depending on whether q is positive or negative. Show that a number and its opposite have a sum of 0 (are
additive inverses). Interpret sums of rational numbers by describging real-world contexts. (3.3)
● Apply and extend previous understandings of multiplication and division and of fractions to multiply and
divide rational numbers. (3.4, 3.5)
● Understand that multiplication is extended from fractions to rational numbers by requiring that operations
continue to satisfy the properties of operations, particularly the distributive property, leading to products
such as (-1)(-1)=1 and the rules for multiplying signed numbers. Interpret products of rational numbers by
describing real-world contexts. (3.4)
● Apply properties of operations as strategies to multiply and divide rational numbers. (3.4, 3.5)
● Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in
any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of
operations to calculate with numbers in any form; convert between forms as appropriate; and assess the
reasonableness of answers using mental computation and estimation strategies. (3.6)
Assessment Evidence
Performance Task(s)
● Unit 1 Performance Task
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Go Math: Middle School Grade 7 will be used as the basic resource.
●
●
●
●
●
●
●
●
●
●
(F) Are You Ready?
(F) Daily Lesson Quiz
(F) Your Turn
(F) Essential Question Check-In
(S) Module Quiz: Ready to Go On?
(S) Module Assessment Readiness
(S) Unit Assessment Readiness
(S) Module Quiz
(S) Unit 1 Benchmark
(S) Unit 1 Performance Task
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Differentiation:
Ongoing Intervention: During a Lesson
Readiness Materials: Are You Ready? (Before each topic)
Prevent Misconceptions: Explore Activity, Examples, Your Turn
Error Intervention (If...Then…): Guided Practice
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Strategic Intervention: At the End of a Lesson
Independent Practice
Lesson Quiz
Ready to Go On? (At the end of Unit)
Assessment Readiness (Assigned with a Topic Test)
Study Guide (Assigned with Unit Test)
Assessment Readiness (Assigned with a Unit Test)
Performance Tasks (At the end of Unit)
Personal Math Trainer
Digital Math Tools
Leveled Homework and Practice
Leveled Quizzes and Tests
Intensive Intervention As needed ANYTIME
Intervention Lesson: Guided instruction and practice or independent practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
Desired Results
Unit:
#
2
Unit Name:
Ratios and Proportional Relationships: Modules 4-5
Module 4: Rates & Proportionality
Module 5: Proportions & Percent
New Jersey Core Curriculum State Standards:
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Ratios & Proportional Relationships
● Analyze proportional relationships and use them to solve real-world and mathematical problems.
○ 7.RP.A.1 Compute unit rates associated with ratios of fractions, including ratios of lengths,
areas, and other quantities measured in like or different units.
○ 7.RP.A.2a Decide whether two quantities are in a proportional relationship, e.g., by testing for
equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is
a straight line through the origin.
○ 7.RP.A.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations,
diagrams, and verbal descriptions of proportional relationships.
○ 7.RP.A.2c Represent proportional relationships by equations.
○ 7.RP.A.2d Explain what a point (x, y) on the graph of a proportional relationship means in terms
of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
○ 7.RP.A.3 Use proportional relationships to solve multistep ratio and percent problems.
Expressions and Equations
● Use properties of operations to generate equivalent expressions.
○ 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can
shed light on the problem and how the quantities in it are related.
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Pennsauken Public School
○ 7.EE.B.3 Solve multi-step real-life and mathematical probelms posed with positive and negative
rational numbers in any form (whole numbers, fractions, and decimals), using tools
strategicially. Apply properties of operations to calculate with numbers in any form; convert
between forms as appropriate; and assess the reasonableness of answers using mental
computation and estimation strategies.
Essential Question(s)
● Module 4: How can you use rates and proportionality to solve real-world problems?
● Module 5: How can you use proportions and percent to solve real-world problems?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Module 4: Rates & Proportionality
The student will:
● Compute unit rates associated with ratios of fractions, including ratios of lengths, areas, and other
quantities measured in like or different units. (4.1)
● Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in
a table or graphing on a coordinate plane and observing whether the graph is a straight line through the
origin. (4.2, 4.3)
● Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal
descriptions of proportional relationships. (4.2, 4.3)
● Represent proportional relationships by equations. (4.2)
● Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation,
with special attention to the points (0, 0) and (1, r) where r is the unit rate. (4.3)
● Use proportional relationships to solve multistep ratio and percent problems. (4.3)
Module 5: Proportions & Percent
The student will:
● Use proportional relationships to solve multistep ratio and percent problems. (5.1, 5.2, 5.3)
● Understand that rewriting an expression in different forms in a problem context can shed light on the
problem and how the quantities in it are related. (5.2)
● Solve multi-step real-life and mathematical probelms posed with positive and negative rational numbers
in any form (whole numbers, fractions, and decimals), using tools strategicially. Apply properties of
operations to calculate with numbers in any form; convert between forms as appropriate; and assess the
reasonableness of answers using mental computation and estimation strategies. (5.2, 5.3)
Assessment Evidence
Performance Task(s)
● Unit 2 Performance Task
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Go Math: Middle School Grade 7 will be used as the basic resource.
●
●
●
●
●
●
●
●
(F) Are You Ready?
(F) Daily Lesson Quiz
(F) Your Turn
(F) Essential Question Check-In
(S) Module Quiz: Ready to Go On?
(S) Module Assessment Readiness
(S) Unit Assessment Readiness
(S) Module Quiz
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Pennsauken Public School
● (S) Unit 2 Benchmark
● (S) Unit 2 Performance Task
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Differentiation:
Ongoing Intervention: During a Lesson
Readiness Materials: Are You Ready? (Before each topic)
Prevent Misconceptions: Explore Activity, Examples, Your Turn
Error Intervention (If...Then…): Guided Practice
Strategic Intervention: At the End of a Lesson
Independent Practice
Lesson Quiz
Ready to Go On? (At the end of Unit)
Assessment Readiness (Assigned with a Topic Test)
Study Guide (Assigned with Unit Test)
Assessment Readiness (Assigned with a Unit Test)
Performance Tasks (At the end of Unit)
Personal Math Trainer
Digital Math Tools
Leveled Homework and Practice
Leveled Quizzes and Tests
Intensive Intervention As needed ANYTIME
Intervention Lesson: Guided instruction and practice or independent practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
Desired Results
Unit:
#
3
Unit Name:
Expressions, Equations, and Inequalities: Modules 6-7
Module 6: Expressions and Equations
Module 7: Inequalities
New Jersey Core Curriculum State Standards:
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Expressions and Equations
● Use properties of operations to generate equivalent expressions.
○ 7.EE.A.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear
expressions with rational coefficients.
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Pennsauken Public School
○ 7.EE.A.2 Understand that rewriting an expression in different forms in a problem context can
shed light on the probelm and how the quantities in it are related.
○ 7.EE.B.4 Use variables to represent quantities in a real-world or mathematical problem, and
construct simple equations and inequalities to solve problems by reasoning about the quantities.
○ 7.EE.B.4a Solve word problems leading to equations of the form px + q = r, where p, q, and r
are specific rational numbers. Compare an algebraic solution to an arithmetic solution,
identifying the sequence of the operations used in each approach.
○ 7.EE.B.4b Solve word problems leading to inequalities of the form px + q > r or px + q < r,
where p, q, and r are specific rational numbers. Graph the solution set of the inequality and
interpret it in the context of the problem.
Essential Question(s)
● Module 6: How can you use algebraic expressions and equations to solve real-world problems?
● Module 7: How can you use inequalities to solve real-world problems?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Module 6: Expressions and Equations
The student will:
● Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with
rational coefficients. (6.1)
● Understand that rewriting an expression in different forms in a problem context can shed light on the
probelm and how the quantities in it are related. (6.1)
● Use variables to represent quantities in a real-world or mathematical problem, and construct simple
equations and inequalities to solve problems by reasoning about the quantities. (6.2, 6.3, 6.4)
● Solve word problems leading to equations of the form px + q = r, where p, q, and r are specific rational
numbers. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the
operations used in each approach. (6.4)
Module 7: Inequalities
The student will:
● Use variables to represent quantities in a real-world or mathematical problem, and construct simple
equations and inequalities to solve problems by reasoning about the quantities. (7.2)
● Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are
specific rational numbers. Graph the solution set of the inequality and interpret it in the context of the
problem. (7.1, 7.3)
Assessment Evidence
Performance Task(s)
● Unit 3 Performance Task
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Go Math: Middle School Grade 7 will be used as the basic resource.
●
●
●
●
●
●
●
●
●
(F) Are You Ready?
(F) Daily Lesson Quiz
(F) Your Turn
(F) Essential Question Check-In
(S) Module Quiz: Ready to Go On?
(S) Module Assessment Readiness
(S) Unit Assessment Readiness
(S) Module Quiz
(S) Unit 3 Benchmark
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● (S) Unit 3 Performance Task
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Differentiation:
Ongoing Intervention: During a Lesson
Readiness Materials: Are You Ready? (Before each topic)
Prevent Misconceptions: Explore Activity, Examples, Your Turn
Error Intervention (If...Then…): Guided Practice
Strategic Intervention: At the End of a Lesson
Independent Practice
Lesson Quiz
Ready to Go On? (At the end of Unit)
Assessment Readiness (Assigned with a Topic Test)
Study Guide (Assigned with Unit Test)
Assessment Readiness (Assigned with a Unit Test)
Performance Tasks (At the end of Unit)
Personal Math Trainer
Digital Math Tools
Leveled Homework and Practice
Leveled Quizzes and Tests
Intensive Intervention As needed ANYTIME
Intervention Lesson: Guided instruction and practice or independent practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
Desired Results
Unit:
#
4
Unit Name:
Geometry: Modules 8-9
Module 8: Modeling Geometric Figures
Module 9: Circumference, Area, and Volume
New Jersey Core Curriculum State Standards:
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Geometry
● Draw, construct, and describe geometrical figures and describe the relationships between them.
○ 7.G.A.1 Solve problems involving scale drawings of geometric figures, including computing
actual lengths and areas from a scale drawing and reproducing a scale drawing at a different
scale.
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○ 7.G.A.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with
given conditions. Focus on constructing triangles from three measures of angles or sides,
noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
○ 7.G.A.3 Describe two-dimensional figures that result from slicing three-dimensional figures, as
in plane sections of right rectangular prisms and right rectangular pyramids.
● Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
○ 7.G.B.4 Know the formulas for the area and circumference of a circle and use them to solve
problems; give an informal derivation of the relationship between the circumference and area of
a circle.
○ 7.G.B.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a
multi-step problem to write and solve simple equations for an unknown angle in a figure.
○ 7.G.B.6 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.
Essential Question(s)
● Module 8: How can you use proportions to solve real-world geometry problems?
● Module 9: How can you apply geometry concepts to solve real-world problems?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Module 8: Modeling Geometric Figures
The student will:
● Solve problems involving scale drawings of geometric figures, including computing actual lengths and
areas from a scale drawing and reproducing a scale drawing at a different scale. (8.1)
● Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given
conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the
conditions determine a unique triangle, more than one triangle, or no triangle. (8.2)
● Describe two-dimensional figures that result from slicing three-dimensional figures, as in plane sections
of right rectangular prisms and right rectangular pyramids. (8.3)
● Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to
write and solve simple equations for an unknown angle in a figure. (8.4)
Module 9:
The student will:
● Know the formulas for the area and circumference of a circle and use them to solve problems; give an
informal derivation of the relationship between the circumference and area of a circle. (9.1, 9.2)
● Solve real-world and mathematical problems involving area, volume and surface area of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. (9.3, 9.4,
9.5)
Assessment Evidence
Performance Task(s)
● Unit 4 Performance Task
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Go Math: Middle School Grade 7 will be used as the basic resource.
●
●
●
●
●
(F) Are You Ready?
(F) Daily Lesson Quiz
(F) Your Turn
(F) Essential Question Check-In
(S) Module Quiz: Ready to Go On?
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Pennsauken Public School
●
●
●
●
●
(S) Module Assessment Readiness
(S) Unit Assessment Readiness
(S) Module Quiz
(S) Unit 4 Benchmark
(S) Unit 4 Performance Task
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Differentiation:
Ongoing Intervention: During a Lesson
Readiness Materials: Are You Ready? (Before each topic)
Prevent Misconceptions: Explore Activity, Examples, Your Turn
Error Intervention (If...Then…): Guided Practice
Strategic Intervention: At the End of a Lesson
Independent Practice
Lesson Quiz
Ready to Go On? (At the end of Unit)
Assessment Readiness (Assigned with a Topic Test)
Study Guide (Assigned with Unit Test)
Assessment Readiness (Assigned with a Unit Test)
Performance Tasks (At the end of Unit)
Personal Math Trainer
Digital Math Tools
Leveled Homework and Practice
Leveled Quizzes and Tests
Intensive Intervention As needed ANYTIME
Intervention Lesson: Guided instruction and practice or independent practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
Desired Results
Unit:
#
5
Unit Name:
Statistics: Modules 10-11
Module 10: Random Samples and Populations
Module 11: Analyzing and Comparing Data
New Jersey Core Curriculum State Standards:
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Statistics and Probability
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Pennsauken Public School
● Use random sampling to draw inferences about a population.
○ 7.SP.A.1 Understand that statistics can be used to gain information about a population by
examining a sample of the population; generalizations about a population from a sample are
valid only if the sample is representative of that population. Understand that random sampling
tends to produce representative samples and support valid inferences.
○ 7.SP.A.2 Use data from a random sample to draw inferences about a population with an
unknown characteristic of interest. Generate multiple samples (or simulated samples) of the
same size to gauge the variation in estimates or predictions.
● Draw informal comparative inferences about two populations.
○ 7.SP.B.3 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.
○ 7.SP.B.4 Use measures of center and measures of variability for numerical data from random
samples to draw informal comparative inferences about two populations.
Ratios & Proportional Relationships
● Analyze proportional relationships and use them to solve real-world and mathematical problems.
○ 7.RP.A.2c Represent proportional relationships by equations.
Essential Question(s)
● Module 10: How can you use random samples and populations to solve real-world problems?
● Module 11: How can you solve real-world problems by analyzing and comparing data?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Module 10: Random Samples and Populations
The student will:
● Understand that statistics can be used to gain information about a population by examining a sample of
the population; generalizations about a population from a sample are valid only if the sample is
representative of that population. Understand that random sampling tends to produce representative
samples and support valid inferences. (10.1, 10.2)
● Use data from a random sample to draw inferences about a population with an unknown characteristic
of interest. Generate multiple samples (or simulated samples) of the same size to gauge the variation in
estimates or predictions. (10.2, 10.3)
● Represent proportional relationships by equations. (10.2)
Module 11: Analyzing and Comparing Data
The 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. (11.1, 11.2, 11.3)
● Use measures of center and measures of variability for numerical data from random samples to draw
informal comparative inferences about two populations. (11.1, 11.2, 11.3)
Assessment Evidence
Performance Task(s)
● Unit 5 Performance Task
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Go Math: Middle School Grade 7 will be used as the basic resource.
● (F) Are You Ready?
● (F) Daily Lesson Quiz
● (F) Your Turn
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Pennsauken Public School
●
●
●
●
●
●
●
(F) Essential Question Check-In
(S) Module Quiz: Ready to Go On?
(S) Module Assessment Readiness
(S) Unit Assessment Readiness
(S) Module Quiz
(S) Unit 5 Benchmark
(S) Unit 5 Performance Task
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Differentiation:
Ongoing Intervention: During a Lesson
Readiness Materials: Are You Ready? (Before each topic)
Prevent Misconceptions: Explore Activity, Examples, Your Turn
Error Intervention (If...Then…): Guided Practice
Strategic Intervention: At the End of a Lesson
Independent Practice
Lesson Quiz
Ready to Go On? (At the end of Unit)
Assessment Readiness (Assigned with a Topic Test)
Study Guide (Assigned with Unit Test)
Assessment Readiness (Assigned with a Unit Test)
Performance Tasks (At the end of Unit)
Personal Math Trainer
Digital Math Tools
Leveled Homework and Practice
Leveled Quizzes and Tests
Intensive Intervention As needed ANYTIME
Intervention Lesson: Guided instruction and practice or independent practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
Desired Results
Unit:
#
6
Unit Name:
Probability: Modules 12-13
Module 12: Experimental Probability
Module 13: Theoretical Probability and Simulations
New Jersey Core Curriculum State Standards:
Mathematical Practices
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
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Pennsauken Public School
8. Look for and express regularity in repeated reasoning.
Statistics and Probability
● Investigate chance processes and develop, use, and evaluate probability models.
○ 7.SP.C.5 Understand that the probability of a chance event is a number between 0 and 1 that
expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A
probability near 0 indicates an unlikely event, a probability around ½ indicates an event that is
neither unlikely nor likely, and a probability near 1 indicates a likely event
○ 7.SP.C.6 Approximate the probability of a chance event by collecting data on the chance
process that produces it and observing its long-run relative frequency, and predict the
approximate relative frequency given the probability.
○ 7.SP.C.7 Develop a probability model and use it to find probabilities of events. Compare
probabilities from a model to observed frequencies; if the agreement is not good, explain
possible sources of the discrepancy.
○ 7.SP.C.7a Develop a uniform probability model by assigning equal probability to all outcomes,
and use the model to determine probabilities of events.
○ 7.SP.C.7b Develop a probability model (which may not be uniform) by observing frequencies
in data generated from a chance process.
○ 7.SP.C.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and
simulation.
○ 7.SP.C.8a Understand that, just as with simple events, the probability of a compound event is
the fraction of outcomes in the sample space for which the compound event occurs.
○ 7.SP.C.8b Represent sample spaces for compound events using methods such as organized lists,
tables and tree diagrams. For an event described in everyday language (e.g., “rolling double
sixes”), identify the outcomes in the sample space which compose the event.
○ 7.SP.C.8c Design and use a simulation to generate frequencies for compound events.
Essential Question(s)
● Module 12: How can you use experimental probability to solve real-world problems?
● Module 13: How can you use theoretical probability to solve real-world problems?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Module 12: Experiemental Probability
The student will:
●
Module 13: Theoretical Probability and Simulations
The student will:
● Develop a probability model and use it to find probabilities of events. Compare probabilities from a
model to observed frequencies; if the agreement is not good, explain possible sources of the
discrepancy. (13.1)
● Develop a uniform probability model by assigning equal probability to all outcomes, and use the model
to determine probabilities of events. (13.1, 13.3)
● Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.
(13.2, 13.4)
● Understand that, just as with simple events, the probability of a compound event is the fraction of
outcomes in the sample space for which the compound event occurs. (13.2)
● Represent sample spaces for compound events using methods such as organized lists, tables and tree
diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the
outcomes in the sample space which compose the event. (13.2)
● Approximate the probability of a chance event by collecting data on the chance process that produces it
and observing its long-run relative frequency, and predict the approximate relative frequency given the
probability. (13.3)
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Pennsauken Public School
● Design and use a simulation to generate frequencies for compound events. (13.4)
Assessment Evidence
Performance Task(s)
● Unit 6 Performance Task
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Go Math: Middle School Grade 7 will be used as the basic resource.
●
●
●
●
●
●
●
●
●
●
(F) Are You Ready?
(F) Daily Lesson Quiz
(F) Your Turn
(F) Essential Question Check-In
(S) Module Quiz: Ready to Go On?
(S) Module Assessment Readiness
(S) Unit Assessment Readiness
(S) Module Quiz
(S) Unit 6 Benchmark
(S) Unit 6 Performance Task
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Differentiation:
Ongoing Intervention: During a Lesson
Readiness Materials: Are You Ready? (Before each topic)
Prevent Misconceptions: Explore Activity, Examples, Your Turn
Error Intervention (If...Then…): Guided Practice
Strategic Intervention: At the End of a Lesson
Independent Practice
Lesson Quiz
Ready to Go On? (At the end of Unit)
Assessment Readiness (Assigned with a Topic Test)
Study Guide (Assigned with Unit Test)
Assessment Readiness (Assigned with a Unit Test)
Performance Tasks (At the end of Unit)
Personal Math Trainer
Digital Math Tools
Leveled Homework and Practice
Leveled Quizzes and Tests
Intensive Intervention As needed ANYTIME
Intervention Lesson: Guided instruction and practice or independent practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
GoMath, Houghton Mifflin Harcourt, 2014
19