Pennsauken Public Schools
Pennsauken School District
Curriculum Guide
Grade 5 Mathematics
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Pennsauken Public Schools
Content Area: Mathematics
Course Title: Grade 5 Math
Grade Level: 5
Unit 1: Topics 1-4
Topic 1: Understand Place Value
Topic 2: Add and Subtract Decimals to Hundredths
Topic 3: Fluently Multiply Multi-Digit Whole Numbers
Topic 4: Use Models and Strategies to Multiply Decimals
Unit 2: Topics 5-8
42 days
50 days
Topic 5: Use Models/Strategies to Divide Whole Numbers
Topic 6: Use Models and Strategies to Divide Decimals
Topic 7: Use Equiv Fractions to Add/Subtract Fractions
Topic 8: Apply Understanding of Multiplication to
Multiply Fractions
Unit 3: Topics 9-12
34 days
Topic 9: Apply Understanding of Div to Divide Fractions
Topic 10: Understand Volume Concepts
Topic 11: Convert Measurements
Topic 12: Represent and Interpret Data
Unit 4: Topics 13-16
Topic 13: Write and Interpret Numerical Expressions
Topic 14: Graph Points on the Coordinate Plane
Topic 15: Algebra: Analyze Patterns and Relationships
Topic 16: Geometric Measurement: Classify TwoDimensional Figures
Date Created:
July 2015
Board Approved on:
24 days
August 2015
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Pennsauken Public Schools
Fifth Grade Mathematics Pacing Guide for 2016-2017
Topic
Number
I-Ready
1
2
3
4
1-4
5
6
7
8
1-8
9
10
11
Title
Instructional
Period
Number of
Days
Readiness Testing
Sept 6-7, 2016
2
Understand Place Value
Sep 8-20, 2016
9
Benchmark - Topic 1 Assessment
Sep 21, 2016
1
Add and Subtract Decimals to Hundredths
Sep 22 - Oct 5, 2016
9
Benchmark - Topic 2 Assessment
Oct 6, 2016
1
Fluently Multiply Multi-Digit Whole Numbers
Oct 7-20, 2016
9
Benchmark - Topic 3 Assessment
Oct 21, 2016
1
Use Models and Strategies to Multiply Decimals
Oct 24 - Nov 9, 2016
12
Online Benchmark Assessment
Nov 14-15, 2016
2
Use Models and Strategies to Divide Whole Numbers
Nov 16 - Dec 1,
2016
10
Benchmark - Topic 5 Assessment
Dec 2, 2016
1
Use Models and Strategies to Divide Decimals
Dec 5-20, 2017
12
Benchmark - Topic 6 Assessment
Dec 21-22, 2017
2
Use Equivalent Fractions to Add and Subtract
Fractions
Jan 2- 24, 2017
15
Benchmark - Topic 7 Assessment
Jan 25, 2017
1
Apply Understanding of Multiplication to Multiply
Fractions
Jan 26-Feb 10, 2017
12
Online Benchmark Assessment
Feb 13-14, 2017
2
Apply Understanding of Division to Divide Fractions
Feb 15- Mar 6, 2017
12
Benchmark - Topic 9 Assessment
March 7, 2017
1
Understand Volume Concepts
Mar 8-20, 2017
9
Benchmark - Topic 10 Assessment
March 21, 2017
1
Convert Measurements
Mar 22- Apr 5, 2017
11
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Pennsauken Public Schools
Benchmark - Topic 11 Assessment
April 6, 2017
1
PARCC Adjustment
April 7-13, 2017
5
12
Represent and Interpret Data
Apr 19-26, 2017
6
13
Write and Interpret Numerical Expressions
Apr 27- May 5, 2017
7
Benchmark - Topic 12&13 Assessment
May 8, 2017
1
14
Graph Points on the Coordinate Plane
May 9-16, 2017
6
15
Algebra: Analyze Patterns and Relationships
May 17-24, 2017
6
Benchmark - Topic 14&15 Assessment
May 25, 2017
1
Geometric Measurement: Classify Two-Dimensional
Figures
May 30- June 6,
2017
6
Online Benchmark Assessment
June 7-8, 2017
2
16
1-16
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Pennsauken Public Schools
Pennsauken Public Schools
Grade Cluster:
5th
Course Description
This course is a required 5th grade mathematics course for all students. The students will be instructed for 84
minutes daily throughout the year.
Content Area:
Mathematics
In Grade 5, instructional time focuses on three critical areas: (1) developing fluency with addition and subtraction
of fractions, and developing understanding of the multiplication of fractions and of division of fractions in limited
cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2) extending
division to 2-digit divisors, integrating decimal fractions into the place value system and developing understanding
of operations with decimals to hundredths, and developing fluency with whole number and decimal operations;
and (3) developing understanding of volume.
Overarching Understanding(s) for the Course
Operations and Algebraic Thinking
● Write and interpret numerical expressions.
● Analyze patterns and relationships.
Number and Operations in Base Ten
● Understand the place value system.
● Perform operations with multi-digit whole numbers and with decimals to hundredths.
Number and Operations- Fractions
● Use equivalent fractions as a strategy to add and subtract fractions.
● Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
Measurement and Data
● Convert like measurement units within a given measurement system.
● Represent and interpret data
● Geometric measurement: understand concepts of volume and relate volume to multiplication and to
addition.
Geometry
● Graph points on the coordinate plane to solve real-world and mathematical problems.
● Classify two-dimensional figures into categories based on their properties.
21st Century Theme(s), Interdisciplinary Opportunities
21st Century Themes
● Global Awareness
○ Using 21st century skills to understand and address global issues. (Topics 1, 3, 4, 12)
● 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. (Topics 1, 2, 3, 4, 12, 16)
○ Demonstrate knowledge and understanding of society’s impact on the natural world (e.g.,
population growth, population development, resource consumption rate, etc.). (Topics 1, 3, 4, 12)
○ Investigate and analyze environmental issues, and make accurate conclusions about effective
solutions. (Topic 1, 12)
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Pennsauken Public Schools
Learning and Innovation Skills
● Creativity and Innovations
○ Think Creatively, Work Creatively with Others and Implement Innovations (throughout)
● Critical Thinking and Problem Solving
○ Reason Effectively, Use Systems Thinking, Make Judgements and Decisions, Solve Problems
(throughout)
● Communication and Collaboration
○ Communicate Clearly, Collaborate with Others (throughout)
Life and Career Skills
● Flexibility and Adaptability
○ Adapt to change, be flexible (throughout)
● Initiative and Self-Direction
○ Manage goals and time, work independently, be self-directed learners (throughout)
● Social and Cross Cultural Skills
○ Interact effectively with others, work effectively in diverse teams (throughout)
● Productivity and Accountability
○ Manage projects, produce results (throughout)
● Leadership and Responsibility
○ Guide and lead others, be responsible to others (throughout)
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)
● Use and Manage Information
Media Literacy
● Analyze Media
● Create Media Products
ICT (Information, Communications and Technology) Literacy
● Apply technology effectively (Center games, Math Tools, Student e-book)
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Pennsauken Public Schools
Desired Results
Topics 1- 4
Topic 1: Understand Place Value
Topic 2: Add and Subtract Decimals to Hundredths
Topic 3: Fluently Multiply Multi-Digit Whole Numbers
Topic 4: Use Models and Strategies to Multiply Decimals
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 and Operations in Base Ten
● Understand the place value systems
○ 5.NBT.A1. Recognize that in a multi-digit number, a digit in one place represents 10 times as much
as it represents in the place to its right and 1/10 of what it represents in the place to its right and
1/10 of what it represents in the place to its left.
○ 5.NBT.A2. Explain patterns in the number of zeros of the product when multiplying a number by
powers of 10, and explain patterns in the placement of the decimal point when a decimal is
multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
○ 5.NBT.A3 Read, write, and compare decimals to thousandths.
■ Read and write decimals to thousandths using base-ten numerals, number names, and
expanded form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1/10)+9 x (1/100) + 2
(1/1000).
■ Compare two decimals to thousandths based on meanings of the digits in each place, using
>, =, and < symbols to record the results of comparisons.
○ 5.NBT.A4 Use place value understanding to round decimals to any place.
● Perform operations with multi-digit whole numbers and with decimals to hundredths.
○ 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
○ 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or
drawings and strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written method and explain the reasoning
used.
Essential Question(s)
Topic 1: How are whole numbers and decimals written, compared, and ordered?
Topic 2: How can sums and differences of decimals be estimated? What are the standard procedures for adding
and subtracting decimals? How can sums and differences be found mentally?
Topic 3: What are the standard procedures for estimating and finding products of multi-digit numbers?
Topic 4: What are the standard procedures for estimating and finding products involving decimals?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Unit:
1
Unit
Name:
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Pennsauken Public Schools
Topic 1: Understand Place Value
The students will:
● Use exponents to write powers of 10 and calculate products. (1.1)
● Read and write whole numbers using standard form, expanded form, and number names. (1.2)
● Represent decimals to thousandths as fractions and fractions with denominators of 1,000 as decimals. (1.3)
● Read and write decimals through thousandths in different ways. (1.4)
● Use place value to compare decimals through thousandths. (1.5)
● Round decimals to different places. (1.6)
● Use the structure of the decimal place-value system to solve problems involving patterns (1.7)
Topic 2: Add and Subtract Decimals to Hundredths
The students will:
● Use properties of addition and strategies to solve problems mentally. (2.1)
● Use rounding or compatible numbers to estimate sums and differences. (2.2)
● Model sums and differences of decimals. (2.3)
● Add decimals to the hundredths using the standard algorithm. (2.4)
● Subtract decimals to the hundredths using the standard algorithm. (2.5)
● Add and subtract decimals. (2.6)
● Use prior math knowledge and equations or bar diagrams to solve problems. (2.7)
Topic 3: Fluently Multiply Multi-Digit Whole Numbers
The students will:
● Use place-value understandings and patterns to mentally multiply whole numbers and powers of 10. (3.1)
● Use rounding and compatible numbers to estimate products. (3.2)
● Multiply 3-digit by 2-digit numbers by combining equal groups and adding partial products. (3.3)
● Use knowledge about place value and multiplying with 2-digit and 3-digit numbers to multiply with zeros.
(3.4)
● Use properties and the standard algorithm for multiplication to find the product of multi-digit numbers.
(3.5)
● Use models and strategies to solve word problems. (3.6)
● Critique the reasoning of others by asking questions, looking for flaws, and using prior knowledge of
estimating products. (3.7)
Topic 4: Use Models and Strategies to Multiply Decimals
The students will:
● Use knowledge about place value and patterns to find the product of a decimal number and a power of 10.
(4.1)
● Use rounding and compatible numbers to estimate the product of a decimal and a whole number. (4.2)
● Use models to represent multiplying a decimal and a whole number. (4.3)
● Use place-value understanding and the standard multiplication algorithm to multiply a decimal by a whole
number. (4.4)
● Use grids to model decimals and find the product of a decimal and a decimal. (4.5)
● Multiply decimals using partial products and models. (4.6)
● Use properties to multiply decimals. (4.7)
● Use number sense and reasoning to place the decimal point in a product. (4.8)
● Multiply decimals using the standard algorithm for multiplication and multiplication strategies. (4.9)
● Use previously learned concepts and skills to represent and solve problems. (4.10)
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Pennsauken Public Schools
Assessment Evidence
Performance Task(s)
Performance Assessment Topic 1 pages 53-54 in Volume 1 Student Book
Performance Assessment Topic 2 pages 107-108 in Volume 1 Student Book
Performance Assessment Topic 3 pages 161-162 in Volume 1 Student Book
Performance Assessment Topic 4 pages 235-236 in Volume 1 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● (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 1 Assessment pages 51-52 in Volume 1 Student Book
● (S) Topic 2 Assessment pages 105-106 in Volume 1 Student Book
● (S) Topic 3 Assessment pages 159-160 in Volume 1 Student Book
● (S) Topic 4 Assessment pages 231-234 in Volume 1 Student Book
● (S) After Topics 1-4 Cumulative/Benchmark Topic via Scantron
● (PBL) Topic 1: Topic Opener-Math & Science Project: Pollinating Insects, Lessons 1.1 and 1.5
● (PBL) Topic 2: Topic Opener-Math & Science Project: Producers and Consumers, Lessons 2.3 and 2.5
● (PBL) Topic 3: Topic Opener-Math & Science Project: Water Usage, Lessons 3.1 and 3.7
● (PBL) Topic 4: Topic Opener-Math & Science Project: Solar Energy, Lessons 4.1 and 4.4
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
enVisions 2.0 Common Core 2016 will be used as the basic resource.
Topic 1: Understand Place Value
Topic 2: Add and Subtract Decimals to Hundredths
Topic 3: Fluently Multiply Multi-Digit Whole Numbers
Topic 4: Use Models and Strategies to Multiply Decimals
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
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Pennsauken Public Schools
● 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: Use Models and Strategies to Divide Whole Numbers
Topic 6: Use Models and Strategies to Divide Decimals
Topic 7: Use Equivalent Fractions to Add and Subtract Fractions
Topic 8: Apply Understanding of Multiplication to Multiply Fractions
New Jersey Core Curriculum State Standards:
Mathematical Practices
● Make sense of problems and persevere in solving them.
● Reason abstractly and quantitatively.
● Construct viable arguments and critique the reasoning of others.
● Model with mathematics.
● Use appropriate tools strategically.
● Attend to precision.
● Look for and make use of structure.
● Look for and express regularity in repeated reasoning.
Number and Operations in Base Ten
● Understand the place value systems
○ 5.NBT.A2. Explain patterns in the number of zeros of the product when multiplying a number
by powers of 10, and explain patterns in the placement of the decimal point when a decimal is
multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
● Perform operations with multi-digit whole numbers and with decimals to hundredths text-indent:-.25in;
○ 5.NBT.B6 Find whole-number quotients of whole numbers with up to four-digit dividends and
two-digit divisors, using strategies based on place value, the properties of operations, and/or the
relationship between multiplication and division, illustrate and explain the calculation by using
equations, rectangular arrays, and/or area models.
○ 5.NBT.B7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or
drawings and strategies based on place value, properties of operations, and/or the relationship
between addition and subtraction; relate the strategy to a written method and explain the
reasoning used.
Number and Operations - Fractions
● Use equivalent fractions as a strategy to add and subtract fractions.
○ 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by
replacing given fractions with equivalent fractions in such a way as to produce an equivalent
sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 =
23/12 (in general, a/b + c/d = (ad + bc/bd).
○ 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the
same whole, including cases of unlike denominators, e.g., by using visual fraction models or
equations to represent the problem. Use benchmark fractions and number sense of fractions to
estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect
result 2/5 + 1/ 2 = 3/7, by observing that 3/7 < 1/2.
● Apply and extend previous understandings of multiplications and division to multiply and divide
fraction
○ 5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or
whole number by a fraction.
■ Interpret the product (a/b) x q as a parts of a partition of q into b equal parts;
equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a
Unit:
2
Unit
Name:
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Pennsauken Public Schools
visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation.
Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
■ Find the area of a rectangle with fractional side lengths by tiling it with unit squares of
the appropriate unit fraction side lengths, and show that the area is the same as would be
found by multiplying the side lengths. Multiply fractional side lengths to find areas of
rectangles, and represent fraction products as rectangular areas.
○ 5.NF.5 Interpret multiplication as scaling (resizing), by:
■ Comparing the size of a product to the size of one factor on the basis of the size of the
other factor, without performing the indicated multiplication.
■ Explaining why multiplying a given number by a fraction greater than 1 results in a
product greater than the given number (recognizing multiplication by whole numbers
greater than 1 as a familiar case); explaining why multiplying a given number by a
fraction less than 1 results in a product smaller than the given number; and relating the
principle of fraction equivalence a/b = (nxa)/(nxb) to the effect of multiplying a/b by 1.
○ 5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g.,
by using visual fraction models or equations to represent the problem.
Essential Question(s)
Topic 5: What is the standard procedure for division and why does it work?
Topic 6: What are the standard procedures for estimating and finding quotients involving decimals?
Topic 7: How can sums and differences of fractions and mixed numbers be estimated? What are standard
procedures for adding and subtracting fractions and mixed numbers?
Topic 8: What does it mean to multiply whole numbers and fractions? How can multiplication with whole
numbers and fractions be shown using models and symbols?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 5: Use Models and Strategies to Divide Whole Numbers
The students will:
● Use place-value patterns and mental math to find quotients. (5.1)
● Use compatible numbers and place-value patterns to estimate quotients. (5.2)
● Use models to find quotients. (5.3)
● Solve division problems using partial quotients. (5.4)
● Find the quotient when the divisor is a multiple of 10. (5.5)
● Decide where to place the first digit of the quotient when dividing whole numbers. (5.6)
● Use estimation to decide whether a quotient is reasonable when dividing by 2-digit divisors. (5.7)
● Make sense of problems and keep work. (5.8)
Topic 6: Use Models and Strategies to Divide Decimals
The students will:
● Use mental math and place-value patterns to divide a decimal by a power of 10. (6.1)
● Use reason and strategies such as rounding and compatible numbers to estimate quotients in problems
with decimals. (6.2)
● Use models to help find quotients in problems involving decimals. (6.3)
● Use the standard algorithm for division to divide decimals by a whole number. (6.4)
● Use models to visualize the relationship between division and multiplication to divide decimals by a 2digit whole number. (6.5)
● Use number sense and reasoning to place the decimal point in the quotient when dividing two decimals.
(6.6)
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Pennsauken Public Schools
● Use the standard algorithm and place-value patterns to divide a decimal by another decimal. (6.7)
● Use the standard algorithm to divide decimals, annexing zeros as needed. (6.8)
● Use reasoning to solve problems by making sense of quantities and relationships in the situation. (6.9)
Topic 7: Use Equivalent Fractions to Add and Subtract Fractions
The students will:
● Estimate sums and differences of fractions by using the nearest half or whole number (7.1)
● Find common denominators for fractions with unlike denominators. (7.2)
● Add fractions with unlike denominators using equivalent fractions with a common denominator. (7.3)
● Subtract fractions with unlike denominators. (7.4)
● Write equivalent fractions to add and subtract fractions with unlike denominators. (7.5)
● Estimate sums and differences of fractions and mixed numbers. (7.6)
● Add mixed numbers using models. (7.7)
● Add mixed numbers using equivalent fractions and a common denominator. (7.8)
● Use models to subtract mixed numbers. (7.9)
● Subtract mixed numbers using equivalent fractions and a common denominator. (7.10)
● Add and subtract mixed numbers using equivalent fractions and a common denominator. (7.11)
● Represent a problem situation with a mathematical model. (7.12)
Topic 8: Apply Understanding of Multiplication to Multiply Fractions
The students will:
● Multiply a whole number by a fraction. (8.1)
● Multiply a fraction by a whole number. (8.2)
● Multiply fractions and whole numbers. (8.3)
● Use models to multiply two fractions. (8.4)
● Multiply two fractions. (8.5)
● Find the area of a rectangle using fractions and diagrams. (8.6)
● Use models, equations, and previously learned strategies to multiply mixed numbers. (8.7)
● Compare the size of the product to the size of one factor without multiplying to consider multiplication
as scaling. (8.8)
● Use previously learned knowledge to make sense of problems and persevere in solving them. (8.9)
Assessment Evidence
Performance Task(s)
Performance Assessment Topic 5 pages 297-298 in Volume 1 Student Book
Performance Assessment Topic 6 pages 365-366 in Volume 1 Student Book
Performance Assessment Topic 7 pages 453-454 in Volume 1 Student Book
Performance Assessment Topic 8 pages 521-522 in Volume 2 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● (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 5 Assessment pages 293-296 in Volume 1 Student Book
● (S) Topic 6 Assessment pages 361-364 in Volume 1 Student Book
● (S) Topic 7 Assessment pages 449-452 in Volume 1 Student Book
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Pennsauken Public Schools
● (S) Topic 8 Assessment pages 517-520 in Volume 2 Student Book
● (S) After Topics 5-8 Cumulative/Benchmark Topic via Scantron
● (PBL) Topic 5: Topic Opener-Math & Science Project: Average Temperature, Lesson 5.6 and Lesson
5.8
● (PBL) Topic 6: Topic Opener-Math & Science Project: States of Water, Lesson 6.4 and Lesson 6.8
● (PBL) Topic 7: Topic Opener-Math & Science Project: Fossils Tell Story, Lesson 7.9 and Lesson 7.12
● (PBL) Topic 8: Topic Opener-Math & Science: Kitchen Chemistry, Lesson 8.3 and Lesson 8.9
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Envisions Common Core 2016 will be used as the basic resource.
Topic 5: Use Models and Strategies to Divide Whole Numbers
Topic 6: Use Models and Strategies to Divide Decimals
Topic 7: Use Equivalent Fractions to Add and Subtract Fractions
Topic 8: Apply Understanding of Multiplication to Multiply Fractions
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
● 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
Topic 9-12
Topic 9: Apply Understanding of Division to Divide Fractions
Topic 10: Understand Volume Concepts
Topic 11: Convert Measurements
Topic 12: Represent and Interpret Data
New Jersey Core Curriculum State Standards:
Mathematical Practices
● Make sense of problems and persevere in solving them.
● Reason abstractly and quantitatively.
● Construct viable arguments and critique the reasoning of others.
● Model with mathematics.
● Use appropriate tools strategically.
● Attend to precision.
● Look for and make use of structure.
● Look for and express regularity in repeated reasoning.
Unit:
3
Unit
Name:
Number and Operations in Base Ten
● Understand the place value systems
○ 5.NBT.A2. Explain patterns in the number of zeros of the product when multiplying a number
by powers of 10, and explain patterns in the placement of the decimal point when a decimal is
multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
● Perform operations with multi-digit whole numbers and with decimals to hundredths
○ 5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.
○ 5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and
two-digit divisors, using strategies based on place value, the properties of operations, and/or the
relationship between multiplication and division, illustrate and explain the calculation by using
equations, rectangular arrays, and/or area models
Number and Operations-Fractions
● Use equivalent fractions as a strategy to add and subtract fractions
○ 5.NF.A2 Solve word problems involving addition and subtraction of fractions referring to the
same whole, including cases of unlike denominators, e.g., by using visual fraction models or
equations to represent the problem. Use benchmark fractions and number sense of fractions to
estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect
result 2/5 + 1/ 2 = 3/7, by observing that 3/7 < 1/2.
● Apply and extend previous understandings of multiplications and division to multiply and divide
fractions
○ 5.NF.B3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b).
Solve word problems involving division of whole numbers leading to answers in the form of
fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the
problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by
4 equals 3, and that when 3 whiles are shared equally among 4 people each person has a share of
size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds
of rice should each person get? Between what two whole numbers does your answer lie?
○ 5.NF.B6 Solve real world problems involving multiplication of fractions and mixed numbers,
e.g., by using visual fraction models or equations to represent the problem.
○ 5.NF.B7 Apply and extend previous understandings of division to divide unit fractions by whole
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numbers and whole numbers by unit fractions.
■ Interpret division of a unit fraction by a non-zero whole number, 1 Students able to
multiply fractions in general can develop strategies to divide fractions in general, by
reasoning about the relationship between multiplication and division. But division of a
fraction by a fraction is not a requirement at this grade. For example, create a story
context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the
relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because
(1/12) × 4 = 1/3.
■ b Interpret division of a whole number by a unit fraction, and compute such quotients.
For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show
the quotient. Use the relationship between multiplication and division to explain that 4 ÷
(1/5) = 20 because 20 × (1/5) = 4.
■ c. Solve real world problems involving division of unit fractions by non-zero whole
numbers and division of whole numbers by unit fractions, e.g., by using visual fraction
models and equations to represent the problem. For example, how much chocolate will
each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup
servings are in 2 cups of raisins?
Measurement and Data
● Convert like measurement units within a given measurement system
○ 5.MD.A1 Convert among different-sized standard measurement units within a given
measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep, real world problems
● Represent and interpret data to 0.05 m), and use these conversions in solving multi-step, real world
problems
○ 5.MD.B2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4 ,
1/8). Use operations on fractions for this grade to solve problems involving information
presented in line plots. For example, given different measurements of liquid in identical beakers,
find the amount of liquid each beaker would contain if the total amount in all the beakers were
redistributed equally.
● Geometric measurement: understood concepts of angle and measure angles
○ 5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume
measurement.
■ A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of
volume, and can be used to measure volume.
■ A solid figure which can be packed without gaps or overlaps using n unit cubes is said to
have a volume of n cubic units.
○ 5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and
improvised units.
○ 5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and
mathematical problems involving volume.
■ Find the volume of a right rectangular prism with whole-number side lengths by packing
it with unit cubes, and show that the volume is the same as would be found by
multiplying the edge lengths, equivalently by multiplying the height by the areas of the
base. Represent threefold whole-number products as volumes, e.g., to represent the
associative property of multiplication.
■ Apply the formulas V= l x w x h and V= b x h for rectangular prisms to find volumes of
right rectangular prisms with whole number edge lengths in the context of solving real
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world and mathematical problems.
■ Recognize volume as additive. Find volumes of solid figures composted of two nonoverlapping right rectangular prisms by adding the volumes of the non-overlapping parts,
applying this technique to solve real world problems.
Essential Question(s)
Topic 9: How are fractions related to division? How can you divide with whole numbers and unit fractions?
Topic 10: What is the meaning of volume of a solid? How can the volume of a rectangular prism be found?
Topic 11: What are customary measurement units and how are they related? What are metric measurement
units and how are they related?
Topic 12: How can line plots be used to represent data and answer questions?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 9: Apply Understanding of Division to Divide Fractions
The students will:
● Understand how fractions are related to division. (9.1)
● Implement division of fractions to show quotients as fractions and mixed numbers. (9.2)
● Use multiplication to divide a whole number by a unit fraction. (9.3)
● Use models such as pictorial models or a number line to show dividing a whole number by a unit
fraction. (9.4)
● Use models to divide unit fractions by non-zero whole numbers. (9.5)
● Use models to divide whole numbers and unit fractions. Check your answer using multiplication. (9.6)
● Solve multi-step problems involving division with unit fractions. (9.7)
● Notice repetition in calculations and generalize about how to divide whole numbers and unit fractions.
(9.8)
Topic 10: Understand Volume Concepts
The students will:
● Find the volume of solid figures. (10.1)
● Find the volume of rectangular prisms using a formula. (10.2)
● Find the volume of prisms in different ways. (10.3)
● Find the volume of a solid figure that is the combination of two or more rectangular prisms. (10.4)
● Use models, prior knowledge of volumes, and previously learned strategies to solve word problems
involving volume. (10.5)
● Use previously learned knowledge about volumes to choose the appropriate tools to solve volume
problems. (10.6)
Topic 11: Convert Measurements
The students will:
● Convert customary units of length. (11.1)
● Convert customary units of capacity. (11.2)
● Convert customary units of weight. (11.3)
● Convert metric units of length. (11.4)
● Convert metric units of capacity. (11.5)
● Convert metric units of mass. (11.6)
● Solve real-world problems with measurement conversions. (11.7)
● Be precise when solving measurement problems. (11.8)
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Topic 12: Represent and Interpret Data
The student will:
● Read and analyze line plots. (12.1)
● Organize and display data in a line plot. (12.2)
● Solve problems using data in a line plot. (12.3)
● Critique the reasoning of others using understanding of line plots and fractions. (12.4)
Assessment Evidence
Performance Task(s)
Performance Assessment Topic 9 pages 581-582 in Volume 2 Student Book
Performance Assessment Topic 10 pages 629-630 in Volume 2 Student Book
Performance Assessment Topic 11 pages 693-694 in Volume 2 Student Book
Performance Assessment Topic 12 pages 729-730 in Volume 2 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● (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 9 Assessment pages 579-580 in Volume 2 Student Book
● (S) Topic 10 Assessment pages 627-628 in Volume 2 Student Book
● (S) Topic 11 Assessment pages 691-692 in Volume 2 Student Book
● (S) Topic 12 Assessment pages 727-728 in Volume 2 Student Book
● (S) After Topics 9-12 Cumulative/Benchmark Topic via Scantron
● (PBL) Topic 9: Topic Opener-Math & Science Project: Thermal Energy, Lesson 9.3 and Lesson 9.5
● (PBL) Topic 10: Topic Opener-Math & Science Project: Everyday Energy, Lesson 10.2 and Lesson
10.5
● (PBL) Topic 11: Topic Opener-Math & Science Project: Grand Canyon, Lesson 11.1 and Lesson 11.8
● (PBL) Topic 12: Topic Opener-Math & Science Project: Wildfires, Lesson 12.1 and Lesson 12.4
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Envisions Common Core 2016 will be used as the basic resource.
Topic 9: Apply Understanding of Division to Divide Fractions
Topic 10: Understand Volume Concepts
Topic 11: Convert Measurements
Topic 12: Represent and Interpret Data
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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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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Desired Results
Unit:
4
Unit
Name:
Topic 13-16
Topic 13: Write and Interpret Numerical Expressions
Topic 14: Graph Points on the Coordinate Plane
Topic 15: Algebra: Analyze Patterns and Relationships
Topic 16: Geometric Measurement: Classify Two-Dimensional Figures
New Jersey Core Curriculum State Standards:
Mathematical Practices
● Make sense of problems and persevere in solving them.
● Reason abstractly and quantitatively.
● Construct viable arguments and critique the reasoning of others.
● Model with mathematics.
● Use appropriate tools strategically.
● Attend to precision.
● Look for and make use of structure.
● Look for and express regularity in repeated reasoning.
Operations in Algebraic Thinking
● Write and interpret numerical expressions
○ 5.OA.A1. Use parentheses, brackets, or braces in numerical expressions, and evaluate
expressions with these symbols.
○ 5.OA.A2. Write simple expressions that record calculations with numbers, and interpret
numerical expressions without evaluating them. For example, express the calculation “add 8 and
7, then multiply by 2” as 2 x (8+7). Recognize that 3 x (18932 +921) is three times as large as
18932 +921, without having to calculate the indicated sum of product
● Analyze patterns and relationships
○ 5.OA.B3. Generate two numerical patterns using two given rules. Identify apparent relationships
between corresponding terms. Form ordered pairs consisting of corresponding terms from the
two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule
“Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0,
generate terns in the resulting sequences, and observe that the terns in one sequence are twice
the corresponding terms in the other sequence. Explain informally why this is so
Geometry
● Graph points on the coordinate plane to solve real-world and mathematical problems by graphing points
in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of
the situation.
○ 5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system,
with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a
given point in the plane located by using an ordered pair of numbers, called its coordinates .
Understand that the first number indicates how far to travel from the origin in the direction of
one axis, and the second number indicates how far to travel in the direction of the second axis,
with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis
and x-coordinate, y-axis and y-coordinate).
○ 5.G.A2 Represent real world and mathematical problems by graphing points in the first
quadrant of the coordinate plane, and interpret coordinate values of points in the content of the
situation
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Pennsauken Public Schools
● Classify two-dimensional figures into categories based on their properties
○ 5.G.B3 Understand that attributes belonging to a category of two dimensional figures also
belong to all subcategories of that category. For example, all rectangles have four right angels
and squares are rectangles, so all squares have four right angles.
○ 5.G.B4 Classify two-dimensional figures ion a hierarchy based on properties
Essential Question(s)
Topic 13: How is the value of a numerical expression found?
Topic 14: How are points plotted? How are relationships shown on a graph?
Topic 15: How can number patterns be analyzed and graphed? How can number patterns and graphs be used to
solve problems?
Topic 16: How can triangles and quadrilaterals be described, classified, and named?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 13: Write and Interpret Numerical Expressions
The students will:
● Use the order of operations to evaluate expressions. (13.1)
● Evaluate expressions with parentheses, brackets, and braces. (13.2)
● Write simple expressions that show calculations with numbers. (13.3)
● Interpret numerical expressions without evaluating them. (13.4)
● Use reasoning to solve problems by making sense of quantities and relationships in the situation. (13.5)
Topic 14: Graph Points on the Coordinate Plane
The students will:
● Locate points on a coordinate grid. (14.1)
● Graph points on a coordinate grid. (14.2)
● Solve real-world problems by graphing points. (14.3)
● Use reasoning to solve problems by making sense of quantities and relationships in the situation. (14.4)
Topic 15: Algebra: Analyze Patterns and Relationships
The students will:
● Analyze numerical patterns. (15.1)
● Use tables to identify relationships between patterns. (15.2)
● Analyze patterns and graph ordered pairs generated from number sequences. (15.3)
● Make sense of problems and persevere in solving them. (15.4)
Topic 16: Geometric Measurement: Classify Two-Dimensional Figures
The students will:
● Classify triangles by their angles and sides. (16.1)
● Classify quadrilaterals by their properties. (16.2)
● Classify quadrilaterals using a hierarchy. (16.3)
● Construct arguments about geometric figures. (16.4)
Assessment Evidence
Performance Task(s)
Performance Assessment Topic 13 pages 771-772 in Volume 2 Student Book
Performance Assessment Topic 14 pages 807-808 in Volume 2 Student Book
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Pennsauken Public Schools
Performance Assessment Topic 15 pages 843-844 in Volume 2 Student Book
Performance Assessment Topic 16 pages 881-882 in Volume 2 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
●
●
●
●
●
●
●
●
●
●
●
(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 13 Assessment pages 769-770 in Volume 2 Student Book
(S) Topic 14 Assessment pages 805-806 in Volume 2 Student Book
(S) Topic 15 Assessment pages 841-842 in Volume 2 Student Book
(S) Topic 16 Assessment pages 879-880in Volume 2 Student Book
(S) After Topics 13-15 Cumulative/Benchmark Topic via Scantron
(PBL) Topic 13: Lesson Topic-Math & Science Project: Food Chains and Food Webs, Lesson 13.1 and
Lesson 13.4
● (PBL) Topic 14: Lesson Topic-Math & Science Project: Earth’s Rotation, Lesson 14.1 and Lesson 14.4
● (PBL) Topic 15: Lesson Topic-Math & Science Project: Analyze Patterns, Lesson 15.1 and Lesson 15.4
● (PBL) Topic 16: Lesson Topic-Math & Science Project:Ecosystems, Lesson 16.2 and Lesson 16.4
Learning Plan
Differentiation of Activities, Assessments, and Multiple Resources,
for high achieving, grade level, struggling students, and special needs/ELL
Envisions Common Core 2016 will be used as the basic resource.
Topic 13: Write and Interpret Numerical Expressions
Topic 14: Graph Points on the Coordinate Plane
Topic 15: Algebra: Analyze Patterns and Relationships
Topic 16: Geometric Measurement: Classify Two-Dimensional Figures
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
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Pennsauken Public Schools
● 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
Board Approved Course Textbook: Envisions 2.0 Common Core, Pearson copyright 2016
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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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Fifth Grade Mathematics Pacing Guide for 2015 –2016
Topic
Number
Title
Instructional
Period
Number of
Days
1
Understand Place Value
9/3/15 - 9/18/15
10
2
Add and Subtract Decimals to Hundredths
9/21/15 - 10/2/15
9
3
Fluently Multiply Multi-Digit Whole Numbers
10/6/15 - 10/16/15
9
4
Use Models and Strategies to Multiply Decimals
10/19/15 - 11/10/15
14
Remediation /Enrichment/ Review - Benchmark Assessment
11/12/15 - 11/18/15
5
5
Use Models and Strategies to Divide Whole Numbers
11/19/15 - 12/4/15
10
6
Use Models and Strategies to Divide Decimals
12/7/15 - 12/23/15
13
7
Use Equivalent Fractions to Add and Subtract Fractions
1/4/16 - 1/27/16
16
8
Apply Understanding of Multiplication to Multiply Fractions
1/28/16 - 2/11/16
11
Remediation /Enrichment/ Review - Benchmark Assessment
2/16/16 - 2/19/16
4
9
Apply Understanding of Division to Divide Fractions
2/22/16 - 3/4/16
10
10
Understand Volume Concepts
3/7/16 - 3/16/16
8
11
Convert Measurements
3/17/16 - 4/1/16
9
12
Represent and Interpret Data
4/4/16 - 4/8/16
5
Remediation /Enrichment/ Review - Benchmark Assessment
4/11/16 - 4/15/16
5
13
Write and Interpret Numerical Expressions
4/18/16 - 4/26/16
7
14
Graph Points on the Coordinate Plane
4/27/16 - 5/3/16
5
15
Algebra: Analyze Patterns and Relationships
5/4/16 - 5/10/16
5
16
Geometric Measurement: Classify Two-Dimensional Figures
5/11/16 - 5/17/16
5
Remediation /Enrichment/ Review - Benchmark Assessment
5/18/16 - 5/24/16
5
5/25/16 - 6/13/16
12
1-4
5-8
9-12
13-16
Step Up
to 6th
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