Pennsauken Public Schools
Pennsauken School District
Curriculum Guide
Grade 6 Mathematics
(One Semester)
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Pennsauken Public Schools
Content Area: Mathematics
Course Title: 6th Grade Math
Grade Level: 6
Unit 1: Topics 1-4
Topic 1:
Topic 2:
Topic 3:
Topic 4:
Understand Num. and Alg. Expressions
Solve Equations and inequalities
Rational Number
Algebra: Coordinate Geometry
34 days
Unit 2: Topics 5+8
Topic 5: Patterns and Equations
Topic 8: Common Factors and Multiples
12 days
Unit 3: Topics 9-12
Topic 9:
Topic 10:
Topic 11:
Topic 12:
Ratio Concepts and Reasoning
Ratio Concepts: Rates
Ratio Concepts: Percents
Divide Fractions by Fractions
Date Created:
July 2015
Board Approved on:
41 days
August 2015
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Pennsauken Public Schools
Sixth Grade NJSLO Mathematics Pacing Guide for 2016-2017
Semester 1
Topic
Number
I-Ready
Title
Instructional
Period
Number of
Days
Readiness Testing
Sept 6-7, 2016
2
Algebra: Understand Numerical and Algebraic
Expressions
Sep 8-22, 2016
11
Benchmark - Topic 1 Assessment
Sep 23, 2016
1
Algebra: Solve Equations and Inequalities
Sep 26 - Oct 7,
2016
9
Benchmark - Topic 2 Assessment
Oct 10, 2016
1
3
Rational Numbers
Oct 11-18, 2016
5
4
Algebra: Coordinate Geometry
Oct 19-25, 2016
5
Online Benchmark Assessment
Oct 26-27, 2016
2
5
Algebra: Patterns and Equations
Oct 28 - Nov 4,
2016
6
8
Common Factors and Multiples
Nov 7-16, 2016
5
Benchmark - Topics 5 and 8 Assessment
Nov 17, 2016
1
Ratios Concepts and Reasoning
Nov 18-30, 2016
7
Benchmark - Topic 9 Assessment
Dec 1, 2016
1
Ratios Concepts: Rates
Dec 2-15, 2016
10
Benchmark - Topic 10 Assessment
Dec 16, 2016
1
Ratio Concepts: Percent
Dec 19 - Jan 4,
2017
8
Benchmark - Topic 11 Assessment
Jan 5, 2017
1
Divide Fractions by Fractions
Jan 9-24, 2017
11
Online Benchmark Assessment
Jan 25-26, 2017
2
1
2
1-4
9
10
11
12
1-12
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Pennsauken Public Schools
Pennsauken Public Schools
Grade Cluster:
6th
Course Description
This course is a required 6th grade mathematics course for all students. The students will be instructed for 84
minutes daily throughout the year.
Overarching Understanding(s) for the Course
Ratios and Proportional Relationships
● Understand ratio concepts and use ratio reasoning to solve problems.
The Number System
● Apply and extend previous understandings of multiplication and division to divide fractions by fractions
● Compute fluently with multi-digit numbers and find common factors and multiples.
● Apply and extend previous understandings of numbers to the system of rational numbers.
Expressions and Equations
● Apply and extend previous understandings of arithmetic to algebraic expressions.
● Reason about and solve one variable equations and inequalities.
● Represent and analyze quantitative relationships between dependent and independent variables.
Geometry
● Solve real-world and mathematical problems involving area, surface area, and volume.
Statistics and Probability
● Develop understanding of statistical variability.
● Summarize and describe distributions
st
21 Century Theme(s), Interdisciplinary Opportunities
21st Century Themes
● Global Awareness
○ Learning from and working collaboratively with individuals representing diverse cultures, religions
and lifestyles in a spirit of mutual respect and open dialogue in personal, work and community
contexts (Topics 4,8)
○ Understanding other nations and cultures, including the use of non-English languages (Topic 4)
● 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 (Topic 1,2,5,6,7,9,10,12,13,15 )
○ Investigate and analyze environmental issues, and make accurate conclusions about effective
solutions (Topics 1,2,5,6,7,9,10,)
Content Area:
Mathematics
Learning and Innovation Skills
● Creativity and Innovations
○ Think Creatively, Work Creatively with Others and Implement Innovations (Topics 8,14,16)
● Critical Thinking and Problem Solving
○ Reason Effectively, Use Systems Thinking, Make Judgements and Decisions, Solve Problems
(Topics 5, 7, 8, 10, 11, 12, 14)
● Communication and Collaboration
○ Communicate Clearly, Collaborate with Others (Topics 1, 2,3,4, 5,6, 7, 8,9,10, 11, 12,13, 14,
15,16)
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Life and Career Skills
● Initiative and Self-Direction
○ Manage goals and time, work independently, be self-directed learners (Topics 1,2,5,6,,10,13)
● Social and Cross Cultural Skills
○ Interact effectively with others, work effectively in diverse teams
(Topics1,2,3,4,5,6,7,8,9,10,12,13,15)
● Productivity and Accountability
○ Manage projects, produce results (Topics 8,13)
● Leadership and Responsibility
○ Guide and lead others, be responsible to others (Topics 6,12,15)
Technology Standards
Technology is integrated in each Topic of the enVisions 2016 Common Core resource book.
Information Literacy
● Access and Evaluate Information (Student e-book, Center games, Today’s Challenge, Visual Learning
Animation Plus, Animated Glossary, Math Tools, Another Look Homework Video, Interactive Math Story,
My Word Cards) 8.1.8.C.1
● Use and Manage Information
ICT (Information, Communications and Technology) Literacy
● Apply technology effectively (Center games, Math Tools, Student e-book) 8.1.8E.1
Unit:
1
.
Unit
Name:
Desired Results
Topics 1-4
Topic 1: Understand Numerical and Algebraic Expressions
Topic 2: Solve Equations and inequalities
Topic 3: Rational Numbers
Topic 4: Algebra: Coordinate Geometry
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
● Apply and extend previous understandings of arithmetic to algebraic expressions.
○ 6.EE.A1. Write and evaluate numerical expressions involving whole-number exponents.
○ 6.EE.A2. Write, read, and evaluate expressions in which letters stand for numbers.
■ Write expressions that record operations with numbers and with letters standing for
numbers.
■ Identify parts of an expression using mathematical terms (sum, term, product, factor,
quotient, coefficient); view one or more parts of an expression as a single entity.
■ Evaluate expressions at specific values of their variables. Include expressions that arise
from formulas used in real-world problems. Perform arithmetic operations, including those
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Pennsauken Public Schools
involving whole-number exponents, in the conventional order when there are no
parentheses to specify a particular order (Order of Operations).
○ 6.EE.A3 Apply the properties of operations to generate equivalent expressions
○ 6.EE.A4 Identify when two expressions are equivalent (i.e., when the two expressions name the
same number regardless of which value is substituted into them).
● Reason about and solve one-variable equations and inequalities
○ 6.EE.B5 Understand solving an equation or inequality as a process of answering a question: which
values from a specified set, if any, make the equation or inequality true? Use substitution to
determine whether a given number in a specified set makes an equation or inequality true.
○ 6.EE.B6 Use variables to represent numbers and write expressions when solving a real-world or
mathematical problem; understand that a variable can represent an unknown number, or, depending
on the purpose at hand, any number in a specified set.
○ 6.EE.B7 Solve real-world and mathematical problems by writing and solving equations of the form
x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
The Number System
● Apply and extend previous understandings of numbers to the system of rational numbers
○ 6.NS.C5. Understand that positive and negative numbers are used together to describe quantities
having opposite directions or values
○ 6.NS.C6. Understand a rational number as a point on the number line. Extend number line
diagrams and coordinate axes familiar from previous grades to represent points on the line and in
the plane with negative number coordinates.
■ Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the
number line; recognize that the opposite of the opposite of a number is the number itself.
■ Understand signs of numbers in ordered pairs as indicating locations in quadrants of the
coordinate plane; recognize that when two ordered pairs differ only by signs, the locations
of the points are related by reflections across one or both axes.
■ Find and position integers and other rational numbers on a horizontal or vertical number
line diagram; find and position pairs of integers and other rational numbers on a coordinate
plane.
○ 6.NS.C7 Understand ordering and absolute value of rational numbers.
■ Interpret statements of inequality as statements about the relative position of two numbers
on a number line diagram.
■ Write, interpret, and explain statements of order for rational numbers in real-world contexts.
■ Understand the absolute value of a rational number as its distance from 0 on the number
line; interpret absolute value as magnitude for a positive or negative quantity in a real-world
situation.
■ Distinguish comparisons of absolute value from statements about order.
○ 6.NS.C8 Solve real-world and mathematical problems by graphing points in all four quadrants of
the coordinate plane. Include use of coordinates and absolute value to find distances between points
with the same first coordinate or the same second coordinate.
Ratio and Proportional Reasoning
● Understand ratio concepts and use ratio reasoning to solve problems
○ 6.RP.A1 Understand the concept of a ratio and use ratio language to describe a ratio relationship
between two quantities.
Geometry
● Solve real world and mathematical problems involving area, surface area, and volume
○ 6.G.A3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates
to find the length of a side joining points with the same first coordinate or the same second
coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
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Essential Question(s)
● Topic 1: What are expressions and how can they be written and evaluated?
● Topic 2: What procedures can be used to solve equations and inequalities?
● Topic 3: What are integers and rational numbers? How can you compare and order rational numbers?
● Topic 4: How are points graphed on a coordinate plane?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 1: Algebra: Understand Numerical and Algebraic Expressions
The student will:
● Write and evaluate numbers with whole-number exponents. (1-1)
● Use the order of operations to evaluate numerical expressions. (1-2)
● Use variables to write algebraic expressions. (1-3)
● Identify parts of an expression. (1-4)
● Evaluate algebraic expressions using substitution (1-5)
● Write equivalent expressions. (1-6)
● Simplify algebraic expressions by combining like terms. (1-7)
● Identify equivalent algebraic expression. (1-8)
● Use formulas to solve problems. (1-9)
● Solve problems by using structure to analyze algebraic expressions . (1-10)
Topic 2: Algebra: Solve Equations and Inequalities
The students will:
● Use substitution to find solutions. (2-1)
● Identify equivalent expressions and use the properties of equality to write equivalent equations. (2-2)
● Use inverse relationships and properties of equality to solve one-step addition and subtraction equations.(23)
● Use inverse relationships and properties of equality to solve one-step multiplication and division equations.
(2-4)
● Inverse relationships and properties of equality can be used to solve equations with fractions and mixed
numbers.(2-5)
● Write inequalities to describe mathematical or real-world situations. (2-6)
● Describe solutions to an inequality and represents them on a number line.(2-7)
● Use equations to make sense of problems and persevere in solving them. (2-8)
Topic 3: Rational Numbers
The student will:
● Use positive and negative integers. (3-1)
● Find and position rational numbers on a number line. (3-2)
● A number to the right of another on the number line is the greater number. (3-3)
● Interpret absolute value and real world situations. (3-4)
● Make sense of quantities and relationships in problem situations. (3-5)
Topic 4: Algebra: Coordinate Geometry
The students will:
● Identify and graph points with integer coordinates on the coordinate plane.( 4-1)
● Identify and graph points with rational number coordinates on the coordinate plane.
(4-2)
● Use absolute value to find distances between points with the same first coordinate or the same second
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coordinate on the coordinate plane. (4-3)
● Solve problems that involve finding side length's of polygons on the coordinate plane.
(4-4)
● Construct arguments using previously learned concepts and skills, such as finding distances on the
coordinate plane. (4-5)
Assessment Evidence
Performance Task(s)
● Topic 1 Performance Assessment p.77-78 in Volume 1 Student Book
● Topic 2 Performance Assessment p.137-138 in Volume 1 Student Book
● Topic 3 Performance Assessment p. 179-180 in Volume 1 Student Book
● Topic 4 Performance Assessment p. 221-222 in Volume 1 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Envisions Common Core 2016 will be used as the basic resource.
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(F) Questions in the Visual Learning Animation Plus
(F) Questions to use with the Visual Learning Bridge
(F) Do You Understand? Convince Me!
(F)Guided Practice
(F) Quick Checks
(S) Topic Assessment 1 pages 73-76 in Volume 1 Student Book
(S) Topic Assessment 2 pages 135-136 in Volume 1 Student Book
(S) Topic Assessment 3 pages 177-178 in Volume 1 Student Book
(S) Topic Assessment 4 pages 219-220 in Volume 1 Student Book
(S) After a group of Topics Cumulative/Benchmark Assessment via Scantron.
(PBL) Topic 1: Lesson Opener, Lessons 1-4 and 1-9
(PBL) Topic 2: Lesson Opener, Lessons 2-4 and 2-8
(PBL) Topic 3: Lesson Opener, Lessons 3-2 and 3-5
(PBL) Topic 4: Lesson Opener, Lessons 4-2 and 4-5
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
Prevent Misconceptions: During the Learning Bridge
Error Intervention (If...Then…): During Guided Practice
Reteaching Set: Before Independent Practice
Learning Aids Online: In Practice Buddy during lesson practice
Higher Order Thinking problems: In lesson practice
Strategic Intervention: At the End of a Lesson
Intervention Activity: Teacher time with struggling students
Reteach to Build Understanding: Guided reteaching
Center Game: In the On-Level and Advanced Activity Centers
Math and Science Activity: In the On-Level and Advanced Activity Center
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Pennsauken Public Schools
Problem-Solving Reading Activity: In the On-Level and Advanced Activity Center
Digital Math Tools Activity: In the Technology Center
Online Math Games: In the Technology Center
Leveled Homework and Practice: Within differentiated assignments
Learning Aids Online: In Practice Buddy during homework and practice
Intensive Intervention As needed ANYTIME
Intervention Lesson: Two pages of guided instruction and practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
Visual Learning Animation Plus: For use anytime to refresh understanding
Online Math Games: For use anytime for more reinforcement
Learning Aids Online: In Practice Buddy for use anytime
Fluency sub skills practice: For use anytime
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Pennsauken Public Schools
Desired Results
Topics 5+8
Topic 5: Patterns and Equations
Topic 8: Common Factors and Multiples
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
● Apply and extend previous understandings of arithmetic to algebraic expressions
○ 6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers.
■ Evaluate expressions at specific values of their variables. Include expressions that arise
from formulas used in real-world problems. Perform arithmetic operations, including
those involving whole-number exponents, in the conventional order when there are no
parentheses to specify a particular order (Order of Operations).
● Reason about and solve one-variable equations and inequalities
○ 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the
form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
● Represent and analyze quantitative relationships between dependent and independent variables.
○ 6.EE.9 Use variables to represent two quantities in a real-world problem that change in
relationship to one another; write an equation to express one quantity, thought of as the
dependent variable, in terms of the other quantity, thought of as the independent variable.
Analyze the relationship between the dependent and independent variables using graphs and
tables, and relate these to the equation.
Number System
● Compute fluently with multi-digit numbers and find common factors and multiples.
○ 6.NS.2. Fluently divide numbers using the standard algorithm.
○ 6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the standard
algorithm for each operation.
○ 6.NS.4. Find the greatest common factor of two whole numbers less than or equal to 100 and
the least common multiple of two whole numbers less than or equal to 12. Use the distributive
property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a
sum of two whole numbers with no common factor.
Essential Question(s)
● Topic 5: How can equations be written? What patterns can be found in tables of values? How are
equations that can relate real-world quantities graphed?
● Topic 6: How are quotients of multi-digit numbers found?
● Topic 7: How can you fluently add, subtract, multiply and divide decimals?
● Topic 8: How can you find common factors and multiples of numbers?
Unit:
2
Unit Name:
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 5: Algebra: Patterns and Equations
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Pennsauken Public Schools
The students will:
● Identify dependent and independent variables. (5-1)
● Analyze the relationships between variables by using tables and write equations to represent the
relationships. (5-2)
● Analyze the relationships between variables by using tables and write equations to represent the
relationship. (5-3)
● Graph linear equations on a coordinate plane. (5-4)
● Graph linear equations involving more than one operation. (5-5)
● Use math models to represent and solve problems involving previously learned concepts and skills.(5-6)
Topic 8:Common Factors and Multiples
The students will:
● Identify prime and composite numbers, and write the prime factorization of a number. (8-1)
● Find the greatest common factor of two whole numbers. (8-2)
● Find the least common multiple of two whole numbers. (8-3)
● Critique the reasoning of others using what is known about factors and multiples. (8-4)
Assessment Evidence
Performance Task(s)
● Topic 5 Performance Assessment p.269-270 in Volume 1 Student Book
● Topic 8 Performance Assessment p.421-422 in Volume 1 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Envisions Common Core 2016 will be used as the basic resource.
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(F) Questions in the Visual Learning Animation Plus
(F) Questions to use with the Visual Learning Bridge
(F) Do You Understand? Convince Me!
(F)Guided Practice
(F) Quick Checks
(S) Topic Assessment 5 pages 267-268 in Volume 1 Student Book
(S) Topic Assessment 6 pages 313-314 in Volume 1 Student Book
(S) Topic Assessment 7 pages 383-384 in Volume 1 Student Book
(S) Topic Assessment 8 pages 419-420 in Volume 1 Student Book
(S) After a group of Topics Cumulative/Benchmark Assessment via Scantron.
(PBL) Topic 5: Lesson Opener, Lessons 5-3 and 5-6
(PBL) Topic 6: Lesson Opener, Lessons 6-4 and 6-6
(PBL) Topic 7: Lesson Opener, Lessons 7-2 and 7-7
(PBL) Topic 8: Lesson Opener, Lessons 8-1 and 8-4
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
Prevent Misconceptions: During the Learning Bridge
Error Intervention (If...Then…): During Guided Practice
Reteaching Set: Before Independent Practice
Learning Aids Online: In Practice Buddy during lesson practice
Higher Order Thinking problems: In lesson practice
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Pennsauken Public Schools
Strategic Intervention: At the End of a Lesson
Intervention Activity: Teacher time with struggling students
Reteach to Build Understanding: Guided reteaching
Center Game: In the On-Level and Advanced Activity Centers
Math and Science Activity: In the On-Level and Advanced Activity Center
Problem-Solving Reading Activity: In the On-Level and Advanced Activity Center
Digital Math Tools Activity: In the Technology Center
Online Math Games: In the Technology Center
Leveled Homework and Practice: Within differentiated assignments
Learning Aids Online: In Practice Buddy during homework and practice
Intensive Intervention As needed ANYTIME
Intervention Lesson: Two pages of guided instruction and practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
Visual Learning Animation Plus: For use anytime to refresh understanding
Online Math Games: For use anytime for more reinforcement
Learning Aids Online: In Practice Buddy for use anytime
Fluency sub skills practice: For use anytime
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Pennsauken Public Schools
Desired Results
Topics 9-12
Topic 9: Ratio Concepts and Reasoning
Topic 10: Ratio Concepts: Rates
Topic 11: Ratio Concepts: Percents
Topic 12: Divide Fractions by Fractions
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 and Proportional Relationship
● Understand ratio concepts and use ratio reasoning to solve problems.
○ 6.RP.A1 Understand the concept of a ratio and use ratio language to describe a ratio relationship
between two quantities.
Unit:
3
Unit
Name:
○ 6.RP.A2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠
0, and use rate language in the context of a ratio relationship.
○ 6.RP.A3.Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by
reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or
equations.
■ Make tables of equivalent ratios relating quantities with whole number measurements,
find missing values in tables, and plot the pairs of values on the coordinate plane. Use
tables to compare ratios
■ Solve unit rate problems including those involving unit pricing and constant speed.
■ Find a percent of a quantity as a rate per 100.
■ Use ratio reasoning to convert measurement units; manipulate and transform units
appropriately when multiplying or dividing quantities.
Number System
● Apply and extend previous understandings of arithmetic to algebraic expressions.
○ 6.NS.1. Interpret and compute quotients of fractions, and solve word problems involving
division of fractions by fractions, e.g., by using visual fraction models and equations to represent
the problem.
Expressions and Equations
● Apply and extend previous understandings of arithmetic to algebraic expressions.
○ 6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers.
■ Evaluate expressions at specific values of their variables. Include expressions that arise
from formulas used in real-world problems. Perform arithmetic operations, including
those involving whole-number exponents, in the conventional order when there are no
parentheses to specify a particular order (Order of Operations).
● Reason about and solve one-variable equations and inequalities.
○ 6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the
form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
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Pennsauken Public Schools
Essential Question(s)
● Topic 9: What is a ratio? how can you use ratios to describe quantities?
● Topic 10: What are ratios and rates and how are they used in solving problems? How can customary
and metric measurements be converted to other units?
● Topic 11: What is the meaning of percent? how can percent be estimated and found?
● Topic 12: What are standard procedures for estimating and finding quotients of fractions and mixed
numbers?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 9-Ratios Concepts and Reasoning
● Use ratios and ratio language to describe the relationships between two quantities. (Lesson 9-1)
● Use diagrams and other models to represent and solve ratio problems. (Lesson 9-2)
● Find equivalent ratios. (Lesson 9-3)
● Compare ratios to solve problems. (Lesson 9-4)
● Use tables and graphs to display equivalent ratios and solve problems.(Lesson 9-5)
● Use previously learned concepts and skills to make sense of ratio problems and persevere in solving
them.(Lesson 9-6)
Topic 10-Ratios Concepts: Rates
● Use rates to solve problems. (Lesson 10-1)
● Solve problems involving unit rates. (Lesson 10-2)
● Use unit rated to make comparisons. (Lesson 10-3)
● Use unit prices to compare costs. (Lesson 10-4)
● Use unit rates to solve problems involving constant speed. (Lesson 10-5)
● Use ratio reasoning and conversion factors to convert customary units of measure. (Lesson 10-6)
● Use ratio reasoning and conversion factors to convert metric units of measure. (Lesson 10-7)
● Use ratio reasoning and conversion factors to convert between customary and metric units of measure.
(Lesson 10-8)
● Be precise when solving problems involving rates. (Lesson 10-9)
Topic 11-Ratio Concepts: Percent
● Represent and find the percent of a whole (Lesson 11-1)
● Write equivalent values as fractions,decimals or percents. (Lesson 11-2)
● Write percents that are greater than 100 or less than 1. (Lesson 11-3)
● Estimate the percent of a number. (Lesson 11-4)
● Find the percent of a number. (Lesson 11-5)
● Find the whole amount when given a part and the percent. (Lesson 11-6)
● Use repeated reasoning when solving percent problems. (Lesson 11-7)
Topic 12-Divide Fractions by Fractions
● Use models to divide with fractions. (Lesson 12-1)
● Divide whole numbers by fractions. (Lesson 12-2)
● Use model to divide fractions by fractions. (Lesson 12-3)
● Divide fractions by fractions. (Lesson 12-4)
● Estimate quotients of mixed numbers. (Lesson 12-5)
● Find the quotient of mixed numbers. (Lesson 12-6)
● Evaluate algebraic expressions with fractions. (Lesson 12-7)
● Solve one-step equations that contain fractions and mixed numbers. (Lesson 12-8)
● Be precise when solving problems involving division with fractions. (Lesson 12-9)
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Assessment Evidence
Performance Task(s)
● Topic 9 Performance Assessment p.469-470 in Volume 2 Student Book
● Topic 10 Performance Assessment p.535-536 in Volume 2 Student Book
● Topic 11 Performance Assessment p. 589-590in Volume 2 Student Book
● Topic 12 Performance Assessment p. 653-654 in Volume 2 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
Envisions Common Core 2016 will be used as the basic resource.
●
●
●
●
●
●
●
●
●
●
●
●
●
●
(F) Questions in the Visual Learning Animation Plus
(F) Questions to use with the Visual Learning Bridge
(F) Do You Understand? Convince Me!
(F)Guided Practice
(F) Quick Checks
(S) Topic Assessment 9 pages 467-468 in Volume 2 Student Book
(S) Topic Assessment 10 pages 533-534 in Volume 2 Student Book
(S) Topic Assessment 11 pages 587-588 in Volume 2 Student Book
(S) Topic Assessment 12 pages 651-652 in Volume 2 Student Book
(S) After a group of Topics Cumulative/Benchmark Assessment via Scantron.
(PBL) Topic 9: Lesson Opener, Lessons 9-2 and 9-7
(PBL) Topic 10: Lesson Opener, Lessons 10-1 and 10-9
(PBL) Topic 11: Lesson Opener, Lessons 11-4 and 11-7
(PBL) Topic 12: Lesson Opener, Lessons 12-7 and 12-9
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
Prevent Misconceptions: During the Learning Bridge
Error Intervention (If...Then…): During Guided Practice
Reteaching Set: Before Independent Practice
Learning Aids Online: In Practice Buddy during lesson practice
Higher Order Thinking problems: In lesson practice
Strategic Intervention: At the End of a Lesson
Intervention Activity: Teacher time with struggling students
Reteach to Build Understanding: Guided reteaching
Center Game: In the On-Level and Advanced Activity Centers
Math and Science Activity: In the On-Level and Advanced Activity Center
Problem-Solving Reading Activity: In the On-Level and Advanced Activity Center
Digital Math Tools Activity: In the Technology Center
Online Math Games: In the Technology Center
Leveled Homework and Practice: Within differentiated assignments
Learning Aids Online: In Practice Buddy during homework and practice
Intensive Intervention As needed ANYTIME
Intervention Lesson: Two pages of guided instruction and practice
Intervention Lesson Teacher Support: A plan for a short, teacher-guided lesson
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Pennsauken Public Schools
Visual Learning Animation Plus: For use anytime to refresh understanding
Online Math Games: For use anytime for more reinforcement
Learning Aids Online: In Practice Buddy for use anytime
Fluency sub skills practice: For use anytime
Board Approved Course Textbook:
Envisions Common Core, Pearson copyright 2016
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Pennsauken Public Schools
K-6 MATH SAMPLE LESSON FORMAT
LESSON SECTIONS
OPENING
Daily Common Core Review
Today’s Challenge
DEVELOP PROBLEM BASED
LEARNING
Solve and Share
TEACHER LED INSTRUCTION
Visual Learning Animation
Do You Understanding? (show me convince
me)
Guided Practice
Independent Practice
ASSESS AND DIFFERENTIATE
Quick check
Intervention Activity
Reteach to Build Understanding
On-level and Advanced Centers
CLOSURE
Exit Slip/Final check for understanding
Leveled homework/practice
Another look homework video
WHOLE GROUP /SMALL
GROUP/INDIVIDUAL
TIME
5-8 minutes
individual
individual
15-20 minutes
small group
20-25 minutes
whole group
individual
whole group
individual
25-30 minutes
individual(teacher anecdotal notes from
independent practice
small group(based on data)
small group(based on data)
small group(based on data)
individual or whole group
individual-based on assessment data
5 minutes
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