Download Grade 3 Math - 2016 - Pennsauken Public Schools

Pennsauken Public School
Pennsauken School District
Curriculum Guide
Grade 3 Mathematics
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Pennsauken Public School
Content Area: Mathematics
Course Title: Grade 3 Math
Grade Level: 3
Unit 1: Topics 1-4
Topic 1: Understand Mult and Division of Whole Numbers
Topic 2: Multiplication Facts: Use Patterns
Topic 3: Apply Properties: Mult Facts for 3, 4, 6, 7, 8
Topic 4: Use Multiplication to Divide: Division Facts
45 days
Unit 2: Topics 5-8
Topic 5 - Fluently Multiply and Divide Within 100.
Topic 6 - Connect Area to Multiplication and Addition
Topic 7 - Represent and Interpret Data
Topic 8 - Use Strategies and Properties to Add and Subtract
36 days
Unit 3: Topics 9-12
Topic 9 - Fluently Add and Subtract Within 1,000
Topic 10 - Multiply by Multiples of 10
Topic 11 - Use Oper w Whole Numbers to Solve Problems
Topic 12 - Understand Fractions as Numbers
30 days
Unit 4: Topics 13-16
Topic 13: Fraction Equivalence and Comparison
Topic 14: Solve Time, Capacity, and Mass Problems
Topic 15: Attributes of Two-Dimensional Shapes
Topic 16: Solve Perimeter Problems
36 days
Benchmark: Reteach and Enrichment
Date Created:
July 2015
Board Approved on:
5 days
August 2015
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Pennsauken Public School
Third Grade Mathematics Pacing Guide for 2016-2017
Topic
Number
I-Ready
Title
Instructional Period
Number of
Days
Readiness Testing
Sept 6-7, 2016
2
Understand Multiplication and Division of Whole
Numbers
Sep 8-21, 2016
10
Benchmark - Topic 1 Assessment
Sep 22, 2016
1
Multiplication Facts: Use Patterns
Sep 23 - Oct 6, 2016
9
Benchmark - Topic 2 Assessment
Oct 7, 2016
1
Apply Properties:
Multiplication Facts for 3, 4, 6, 7, 8
Oct 10-25, 2016
11
Benchmark - Topic 3 Assessment
Oct 26, 2016
1
Use Multiplication to Divide: Division Facts
Oct 27 - Nov 16,
2016
12
On-line Benchmark Assessment
Nov 17-18, 2016
2
Fluently Multiply and Divide Within 100
Nov 21 - Dec 7, 2016
11
Benchmark - Topic 5 Assessment
Dec 8, 2016
1
Connect Area to Multiplication and Addition
Dec 9-23, 2016
11
Benchmark - Topic 6 Assessment
Jan 2-3, 2017
2
Represent and Interpret Data
Jan 4-17, 2017
8
Benchmark - Topic 7 Assessment
Jan 18, 2017
1
Use Strategies and Properties to Add and Subtract
Jan 19 - Feb 2, 2017
11
On-line Benchmark Assessment
Feb 3-6, 2017
2
Fluently Add and Subtract Within 1,000
Feb 7-22, 2017
10
Benchmark - Topic 9 Assessment
Feb 23, 2017
1
10
Multiply by Multiples of 10
Feb 24 - Mar 3, 2017
6
11
Use Operations with Whole Numbers to Solve
Problems
Mar 6-13, 2017
6
Benchmark - Topics 10 - 11 Assessment
March 14, 2017
1
Understand Fractions as Numbers
Mar 15-29, 2017
11
1
2
3
4
1-4
5
6
7
8
1-8
9
12
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13
14
15
16
1-16
Benchmark - Topic 12 Assessment
Mar 30, 2017
1
PARCC Adjustment
Mar 31 - April 6,
2017
5
Fraction Equivalence and Comparison
Apr 7-26, 2017
11
Benchmark - Topic 13 Assessment
April 27, 2017
1
Solve Time, Capacity, and Mass Problems
Apr 28 - May 15,
2017
12
Benchmark - Topic 14 Assessment
May 16, 2017
1
Attributes of Two-Dimensional Shapes
May 17-24, 2017
6
Benchmark - Topic 15 Assessment
May 25, 2017
1
Solve Perimeter Problems
May 30 - June 9,
2017
9
On-line Benchmark Assessment
June 12-14
3
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Pennsauken Public Schools
Content Area: Mathematics
Grade Cluster:
3rd
Course Description
This course is a required 3rd grade mathematics course for all students. The students will be instructed for 60
minutes daily throughout the year.
In Grade 3, instructional time should focus on four critical areas: (1) developing understanding of multiplication
and division and strategies for multiplication and division within 100; (2) developing understanding of fractions,
especially unit fractions (fractions with numerator 1); (3) developing understanding of the structure of rectangular
arrays and of area; and (4) describing and analyzing two-dimensional shapes.
Overarching Understanding(s) for the Course
Operations and Algebraic Thinking
●
●
●
●
Represent and solve problems involving multiplication and division.
Understand properties of multiplication and the relationship between multiplication and division.
Multiply and divide within 100.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
Number and Operations in Base Ten
● Use place value understanding and properties of operations to perform multi-digit arithmetic.
Number and Operations—Fractions
● Develop understanding of fractions as numbers.
Measurement and Data
● Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of
objects.
● Represent and interpret data.
● Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
● Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between
linear and area measures.
Geometry
● Reason with shapes and their attributes.
21st Century Theme(s), Interdisciplinary Opportunities
21st Century Themes
● Global Awareness
○ Using 21st century skills to understand and address global issues (Topic 5,7,8,9)
○ 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 (Topic 1,2 ,3 ,4, 5, 6, 7, 8, 9, 10, 11, 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 (Topic 1, 5, 6, 8, 9, 10, 12, 13, 16)
○ Investigate and analyze environmental issues, and make accurate conclusions about effective
solutions (Topic 9)
Learning and Innovation Skills
● Creativity and Innovations
○ Think Creatively, Work Creatively with Others and Implement Innovations (Topics 4, 12)
● Critical Thinking and Problem Solving
○ Reason Effectively, Use Systems Thinking, Make Judgements and Decisions, Solve Problems
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(Topics 2, 3,4 , 5, 6, 7, 9, 11, 15)
● Communication and Collaboration
○ Communicate Clearly, Collaborate with Others (Topics 2, 4, 5, 6, 7, 9, 11, 12, 13, 14, 15)
Life and Career Skills
● Initiative and Self-Direction
○ Manage goals and time, work independently, be self-directed learners
● Social and Cross Cultural Skills
○ Interact effectively with others, work effectively in diverse teams
● Productivity and Accountability
○ Manage projects, produce results
● Leadership and Responsibility
○ Guide and lead others, be responsible to others
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
ICT (Information, Communications and Technology) Literacy
● Apply technology effectively (Center games, Math Tools, Student e-book)
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Desired Results
Unit:
Unit Name: Topics 1- 4
1
Topic 1: Understand Multiplication and Division of Whole Numbers
Topic 2: Multiplication Facts: Use Patterns
Topic 3: Apply Properties: Multiplication Facts for 3, 4, 6, 7, 8
Topic 4: Use Multiplication to Divide: Division Facts
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.
Operations and Algebraic Thinking
● Represent and solve problems involving multiplication and division
○ 3.OA.A1. Interpret products of whole numbers, e.g. interpret 5 x 7 as the total number of objects in
5 groups of objects each. For example, describe a context in which a total number of objects can be
expressed as 5 x 7.
○ 3.OA.A2. Interpret whole-numbers quotients of whole numbers, e.g., interpret 58 ÷ 8 as the number
of objects in each share when 56 objects are partitioned equally into 8 shares, or as a number of
shares when 56 objects are partitioned into equal shares of 8 objects each. For example, describe a
context in which a number of shares or a number of groups can be expressed as 56 ÷ 8.
○ 3.OA.A3. Use multiplication and division within 100 to solve word problems in situation involving
equals groups, arrays, and measurement quantities. e.g., by using drawings and equations within a
symbols for the unknown number to represent the problem.
● Understand properties of multiplication and the relationship between multiplication and division
○ 3.OA.B5. Apply properties of operations as strategies to multiply and divide. Examples, If 6 x 4 =
24 is known, then 4 x 6 =24 is also known. (Commutative property of multiplication.) 3 x 5 x 2 can
be found by 3 x 5 = 15, then 15 x 2 = 30, or by 5 x 2 = 10, then 15 x 2 = 30, or by 5 x 2 =10, then 3
x 10 =30. (Associative property of multiplication.) Knowing that 8 x 5 = 40 and 8 x 2 = 16, one can
find 8 x7 as 8 x (5 +2) = (8x5) + (8x2) = 40 and 8 x 2 = 16, one can find 8 x 7 as 8 x (5 + 2) = (8 x
5) + (8 x 2) = 40 + 16 = 56. (Distributive property).
○ 3.OA.B6. Understand division as an unknown-factor problem. For example, fine 32 ÷ 8 by finding
the number that makes 32 when multiplied by 8.
● Solve problems involving the four operations, and identify and explain pattern in arithmetic
○ 3.OA.D8. Solve two-step word problems using the four operations. Represent these problems using
equations with a letter standing for the unknown quantity. Assess the reasonableness of answers
using mental computation and estimation strategies including rounding.
○ 3.OA.D9. Identify arithmetic pattern (including patterns in the addition table or multiplication
table), and explain them using properties of operations. For example, observe that 4 times a
number is always even, and explain why 4 times a number can be decomposed into two equal
addends
Essential Question(s)
Topic 1 - What are different meanings of multiplication and division?
Topic 2 - How can unknown multiplication fact be found using patterns and properties?
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Topic 3 - How can unknown multiplication facts be found using known facts?
Topic 4 - How can unknown division facts be found using known multiplication facts.
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 1 Understand Multiplication and Division of Whole Numbers
The students will:
● Use repeated addition to show the relationship between multiplication and addition. (1-1)
● Use number lines to join equal lines. (1-2)
● Use arrays as one way to think about and understand multiplication. (1-3)
● Understand and use the Commutative Property of Multiplication. (1-4)
● Use Sharing to separate equal groups and to think about division. (1-5)
● Use repeated subtraction to show the relationship between division and subtraction. (1-6)
● Think Strategically about available tools that can be used to solve problems. (1-7)
Topic 2 Multiplication Facts: Use Patterns
The students will:
● Gain fluency in multiplication when using 2 and 5 as factors. (2-1)
● Gain fluency in multiplication when using 9 as a factor. (2-2)
● Gain fluency in multiplication when multiplying by 0 or 1. (2-3)
● Gain fluency in multiplication when multiplying by 10. (2-4)
● Students will use number relationships and patterns to develop reasoning strategies to support their recall
of the basic multiplication facts. (2-5)
● Use previously learned concepts and skills to represent and solve problems. (2-6)
Topic 3 Apply Properties: Multiplication Facts for 3, 4, 6, 7, 8
The students will:
● Use the Distributive Property to solve problems involving multiplication within 100. (3-1)
● Use appropriate tools and the Distributive Property to break apart unknown facts with 3 as a factor. (3-2)
● Use the Distributive Property to break apart unknown facts with 4 as a factor. ( 3-3)
● Use the Distributive Property to break apart unknown facts with 6 or 7 as a factor. ( 3-4)
● Use the Distributive Property to break apart unknown facts with 8 as a factor. ( 3-5)
● Use strategies such as bar diagrams and arrays with known facts to solve multiplication problems.
Topic 4 Use Multiplication to Divide: Division Facts
The students will:
● Use multiplication facts to divide. (4-1)
● Use multiplication facts to find division facts. (4-2)
● Use multiplication facts to find the related division facts. (4-3)
● Use multiplication facts to find related division facts. (4-4)
● Use knowledge of even and odd numbers to identify multiplication patterns. (4-5)
● Use properties to understand division involving 0 and 1. (4-6)
● Use patterns and known facts to find unknown multiplication facts. Use multiplication facts to find related
division facts. (4-7)
● Use multiplication and division facts to find unknown values in equations. (4-8)
● Use previously learned concepts to find and answer hidden questions to solve problems. (4-9)
Assessment Evidence
Performance Task(s)
● Topic 1 Performance Assessment pages 55-56 in Volume 1 Student Book
● Topic 2 Performance Assessment pages 101-102 in Volume 1 Student Book
● Topic 3 Performance Assessment pages 163-164 in Volume 1 Student Book
● Topic 4 Performance Assessment pages 233-234 in Volume 1 Student Book
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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 Assessment 1 pages 53-54 in Volume 1 Student Book
(S) Topic Assessment 2 pages 101-102 in Volume 1 Student Book
(S) Topic Assessment 3 pages 161-162 in Volume 1 Student Book
(S) Topic Assessment 4 pages 229-232 in Volume 1 Student Book
(S) After a group of Topics Cumulative/Benchmark Assessment
(PBL) Topic 1: Topic Opener, Lessons 1.2 and 1.6
(PBL) Topic 2: Topic Opener, Lessons 2.2 and 2.6
(PBL) Topic 3: Topic Opener, Lessons 3.3 and 3.5
(PBL) Topic 4: Topic Opener, Lessons 4.5 and 4.8
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 Multiplication and Division of Whole Numbers
Topic 2: Multiplication Facts: Use Patterns
Topic 3: Apply Properties: Multiplication Facts for 3, 4, 6, 7, 8
Topic 4: Use Multiplication to Divide: Division Facts
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
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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:
2
Unit
Name:
Topics 5-8
Topic 5 - Fluently Multiply and Divide Within 100.
Topic 6 - Connect Area to Multiplication and Addition
Topic 7 - Represent and Interpret Data
Topic 8 - Use Strategies and Properties to Add and Subtract
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.
Operations and Algebraic Thinking
● Represent and solve problems involving multiplication and division
○ 3.OA.A3. Use multiplication and division within 100 to solve word problems in situation
involving equals groups, arrays, and measurement quantities. e.g., by using drawings and
equations within a symbols for the unknown number to represent the problem.
● Multiply and divide within 100
○ 3.OA.C7. Fluently multiply and divide within 100, using strategies such as the relationship
between multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or
properties of operations. By the end of Grade 3, know from memory all products of two onedigit numbers
● Solve problems involving the four operations, and identify and explain pattern in arithmetic
○ 3.OA.D8. Solve two-step word problems using the four operations. Represent these problems
using equations with a letter standing for the unknown quantity. Assess the reasonableness of
answers using mental computation and estimation strategies including rounding.
○ 3.OA.D9. Identify arithmetic pattern (including patterns in the addition table or multiplication
table), and explain them using properties of operations. For example, observe that 4 times a
number is always even, and explain why 4 times a number can be decomposed into two equal
addends.
Number and Operations in Base Ten
● Understand place value understanding and properties of operations to perform multi-digit arithmetic
○ 3.NBT.A1. Use place value understanding to round whole numbers to the nearest 10 or 100.
○ 3.NBT.A2. Fluently add and subtract within 1000 using strategies and algorithms based on place
value, properties of operations, and/or the relationship between addition and subtraction.
Measurement and Data
● Represent and interpret data st 10 or 100.
○ 3.MD.B3. Draw a scaled picture graph and a scaled bar to represent a data set with several
categories. Solve one-and two step “how many more” and “how many less” problems using
information presented in scaled bar graphs. For example, draw a bar graph in which each
square in the bard graph might represent 5 pets.
● Geometric measurement: understand concepts of area and relate area to multiplication and to addition
○ 3.MD.C5. Recognize area as an attribute of plan figures and understand concepts of area
measurement.
■ A square with side length 1 unit, called “a unit square,” is said to have “one square unit”
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of area, and can be used to measure area.
■ A plane figure which can be covered without gaps or overlaps by n unit squares is said to
have an area of n square units.
○ 3.MD.C6. Measure areas by counting unit squares (square cm, square m, square in, square ft,
and improvised units).
○ 3.MD.C7. Relate areas to the operations of multiplication and addition.
■ Find the area of a rectangle with whole-number side lengths by tiling it, and show that
the area is the same as would be found by multiplying the side lengths.
■ Multiply side lengths to find areas of rectangles with whole-number side lengths in the
context of solving real world and mathematical problems, and represent whole-number
products as rectangular areas in mathematical reasoning.
■ Use tiling to show in a concrete case that the area of a rectangle with whole-number side
lengths a and b + c is the sum of a x c. Use area models top represent the distributive
property in mathematical reasoning.
■ Recognize area as additive. Find areas of rectilinear figures by decomposing them into
non-overlapping rectangles and adding the areas of the non-overlapping parts, applying
this technique to solve real world problems.
Essential Question(s)
● What are strategies to solve multiplication and division facts?
● How can area be measured and found?
● How can data be represented, interpreted, and analyzed?
● How can sums and differences be estimated and found mentally?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 5: Fluently Multiply and Divide Within 100
The students will:
● Use the multiplication table and the Distributive Property to find patterns in factors and products. (5-1)
● Use a multiplication table to find the missing factor in a division problem. (5-2)
● Use number sense and reasoning while practicing multiplication and division basic facts. (5-3)
● Use strategies such as skip counting and properties of operations to multiply. (5-4)
● Solve multiplication and division problems that involve different strategies and representations. (5-5)
● Use multiplication to write and solve real-world problems involving equal groups. (5-6)
● Use division to write and solve real-world problems involving equal groups. (5-7)
● Use the structures of multiplication and division to compare expressions. (5-8)
Topic 6: Connect Area to Multiplication and Addition
The students will:
● Use unit squares to find the area of a shape. (6-1)
● Use unit squares to find the area of a figure. (6-2)
● Use standard units to measure the area of a shape. (6-3)
● Use unit squares and multiplication to find the areas of squares and rectangles. (6-4)
● Use areas of rectangles to model the Distributive Property of Multiplication. (6-5)
● Use areas of rectangles to find the area of irregular shapes. (6-6)
● Solve problems by breaking apart or changing the problem in simpler problems. (6-7)
Topic 7: Represent and Interpret Data
The students will:
● Use graphs to compare and interpret data.
● Use frequency tables and picture graphs to compare and interpret data.
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● Use scaled bar graphs to represent data sets.
● Use graphs to solve problems.
● Use words, symbols, and numbers to accurately and precisely solve math problems.
Topic 8: Use Strategies and Properties to Add and Subtract
The students will:
● Solve real world problems using properties of addition. (8-1)
● Identify patterns in the addition table and explain them using algebraic thinking. (8-2)
● Use place value and a number line to round numbers. (8-3)
● Use mental math to add. (8-4)
● Use mental math to subtract. (8-5)
● Use rounding or compatible numbers to estimate a sum. (8-6)
● Use rounding or compatible numbers to estimate a difference. (8-7)
● Solve one step and multi-step problems using strategies based on the relationship between addition and
subtraction. (8-8)
● Solve one step and multi-step problems by modeling with math. (8-9)
Assessment Evidence
Performance Task(s)
● Topic 5 Performance Assessment pages 295-296 in Volume 1 Student Book
● Topic 6 Performance Assessment pages 353 -354 in Volume 1 Student Book
● Topic 7 Performance Assessment pages 399- 400 in Volume 1 Student Book
● Topic 8 Performance Assessment pages 467-468 in Volume 2 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● (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 291-294 in Volume 1 Student Book
● (S) Topic Assessment 6 pages 349-352 in Volume 1 Student Book
● (S) Topic Assessment 7 pages 395-396 in Volume 1 Student Book
● (S) Topic Assessment 8 pages 465-466 in Volume 2 Student Book
● (S) After a group of Topics Cumulative/Benchmark Assessment
● (PBL) Topic 5: Topic Opener, Lessons 5-1 and 5-3
● (PBL) Topic 6: Topic Opener, Lessons 6-1 and 6-5
● (PBL) Topic 7: Topic Opener, Lessons 7-1 and 7-4
● (PBL) Topic 8: Topic Opener, Lessons and 8-3 and 8-8
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 - Fluently Multiply and Divide Within 100.
Topic 6 - Connect Area to Multiplication and Addition
Topic 7 - Represent and Interpret Data
Topic 8 - Use Strategies and Properties to Add and Subtract
Differentiation:
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Pennsauken Public School
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 School
Desired Results
Unit:
Unit
3
Topics 9-12
Name:
Topic 9 - Fluently Add and Subtract Within 1,000
Topic 10 - Multiply by Multiples of 10
Topic 11 - Use Operations with Whole Numbers to Solve Problems
Topic 12 - Understand Fractions as 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.
Operations and Algebraic Thinking
● Solve problems involving the four operations, and identify and explain pattern in arithmetic
○ 3.OA.D8. Solve two-step word problems using the four operations. Represent these problems
using equations with a letter standing for the unknown quantity. Assess the reasonableness of
answers using mental computation and estimation strategies including rounding.
Number and Operations in Base Ten
● Understand place value understanding and properties of operations to perform multi-digit arithmetic
○ 3.NBT.A2. Fluently add and subtract within 1000 using strategies and algorithms based on place
value, properties of operations, and/or the relationship between addition and subtraction.
○ 3. NBT.A3. Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (e.g., 9 x
80, 5 x 60) using strategies based on place value and properties of operations
Number and Operations - Fractions
● Develop understanding of fractions as numbers
○ 3.NF.A1.Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned
into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.
○ 3.NF.A2. Understanding a fraction as a number on the number line; represent fractions on a
number line diagram.
■ Represent a fraction as 1/b on a number line diagram by defining the interval from 0 to 1
as the while and partitioning into b equal parts. Recognize that each part has size 1/b and
that the endpoint of the part based at 0 locates the number 1/b on the number line.
■ Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0.
Recognize that the resulting interval has size a/b and that its endpoint locates the number
a/b on the number line.
○ 3.NF.A3. Explain equivalence of fractions in special cases, and compare fractions by reasoning
about their size.
■ Express whole numbers as fractions, and recognize fractions that are equivalent to while
numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and
1 at the same point of a number line diagram.
Geometry
● Reason with shapes and their attributes
○ 3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction
of whole. For example, partition a shape into 4 parts with equal area, and describe the area of
each part as ¼ of the area of the shape
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Pennsauken Public School
Essential Question(s)
Topic 9: What are standard procedures for adding and subtracting whole numbers?
Topic 10: What are ways to multiply by multiples of 10?
Topic 11: What are ways to solve two-step problems?
Topic 12: What are different interpretations of a fraction?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 9 - Fluently Add and Subtract Within 1,000
The students will:
● Add two 3-digit numbers by breaking apart problems into simpler problems. (9.1)
● Add 3- digit numbers using the standard algorithm. (9.2)
● Add 3-digit numbers using the standard algorithm. (9.3)
● Add three or more numbers using the standard algorithm. (9.4)
● Subtract multi-digit numbers using the expanded algorithm. (9.5)
● Subtract 3-digit numbers using the standard algorithm. (9.6)
● Subtract a 3-digit number from another 3-digit number with one or more zeros by using the standard
algorithm. (9.7)
● Use addition and subtraction to justify a conjecture. (9.8)
Topic 10 - Multiply by Multiples of 10
The students will:
● Use an open number line to find products when one factor is a multiple of 10. (10.1)
● Use properties of multiplication to find products when one factor is a multiple of 10. (10.2)
● Use different strategies to find products when one factor is a multiple of 10. (10.3)
● Use the structure of multiplication and place value to find products when one factor is a multiple of 10.
(10.4)
Topic 11 - Use Operations with Whole Numbers to Solve Problems
The students will:
● Draw diagrams and write equations to solve two-step problems involving addition and subtraction of
whole numbers. (11.1)
● Draw diagrams and write equations to solve two-step problems involving multiplication and division of
whole numbers. (11.2)
● Examine relationships between quantities in a two-step word problem by writing equations. Choose
and apply the operations needed to find the answer. (11.3)
● Critique the reasoning of others by asking questions, identifying mistakes, and providing suggestions
for improvement. (11.4)
Topic 12 - Understand Fractions as Numbers
The students will:
● Understand how to read an write unit fractions for equal-size parts of region. (12.1)
● Use a fraction to represent multiple copies of a unit fraction. (12.2)
● Determine and draw the whole (unit) given one part (unit fraction). (12.3)
● Represent fractions on a number line. (12.4)
● Represent fractions greater than 1 on a number line. (12.5)
● Measure length to the nearest fourth inch and show the data on a line plot. (12.6)
● Measure length to the nearest half inch and show the data on a line plot. (12.7)
● Determine when a problem has either extra or missing information. (12.8)
Assessment Evidence
Performance Task(s)
● Topic 9 Performance Assessment pages 531-532 in Volume 2 Student Book
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● Topic 10 Performance Assessment pages 569-570 in Volume 2 Student Book
● Topic 11 Performance Assessment pages 603-604 in Volume 2 Student Book
● Topic 12 Performance Assessment pages 665-666 in Volume 2 Student Book
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● (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 529-530 in Volume 2 Student Book
● (S) Topic Assessment 10 pages 567-568 in Volume 2 Student Book
● (S) Topic Assessment 11 pages 601-602 in Volume 2 Student Book
● (S) Topic Assessment 12 pages 663-664 in Volume 2 Student Book
● (S) After a group of Topics Cumulative/Benchmark Assessment
● (PBL) Topic 9: Topic Opener, Lessons 9.1 and Lesson 9.6
● (PBL) Topic10: Topic Opener, Lessons 10.1 and Lesson 10.3
● (PBL) Topic11: Topic Opener, Lessons 11.2 and Lesson 11.4
● (PBL) Topic12: Topic Opener, Lessons 12.3 and Lesson 12.6
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
 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:
Unit
4
Topics 13-16
Name:
Topic 13: Fraction Equivalence and Comparison
Topic 14: Solve Time, Capacity, and Mass Problems
Topic 15: Attributes of Two-Dimensional Shapes
Topic 16: Solve Perimeter Problems
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 - Fractions
● Develop understanding of fractions as numbers
○ 3.NF.A3. Explain equivalence of fractions in special cases, and compare fractions by reasoning
about their size.
■ Understand two fractions as equivalent (equal) if they are the same size, or the same
point on a number line.
■ Recognize and generate simple equivalent fractions, e.g., ½ = 2/4, 4/6, = 2/3). Explain
why the fractions are equivalent, e.g., by using a visual fraction model.
■ Express whole numbers as fractions, and recognize fractions that are equivalent to while
numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and
1 at the same point of a number line diagram.
■ Compare two fractions with the same numerator or the same denominator by reasoning
about their size. Recognize that comparisons are valid only when the two fractions refer
to the same whole. Record the results of comparisons with the symbols >, =, or <, and
justify the conclusions, e.g., by using a visual fraction model
Measurement and Data
● Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses
of objects
○ 3.MD.A1. Tell and write time to the nearest minute and measure time intervals in minutes. Solve
word problems involving addition and subtraction of time intervals in minutes, e.g., by
representing the problem on a number line diagram.
○ 3.MD.A2. Measure and estimate liquid volumes and masses of objects using standard units of
grams (g), kilograms (kg), and liters (l). Add, subtract, multiply, or divide to solve one-step
word problems involving masses or volumes that are given in the same units, e.g., by using
drawings (such as a beaker with a measurement scale) to represent the problem
● Geometric measurement: understand concepts of area and relate area to multiplication and to addition
○ 3.MD.C7. Relate areas to the operations of multiplication and addition.
■ Multiply side lengths to find areas of rectangles with whole-number side lengths in the
context of solving real world and mathematical problems, and represent whole-number
products as rectangular areas in mathematical reasoning
● Geometric measurement: recognize perimeter as an attribute of plan figures and distinguish between
linear and area measures
○ 3.MD.D8. Solve real world and mathematical problems involving perimeters of polygons,
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Pennsauken Public School
including finding the perimeter given the side lengths, finding an unknown side length, and
exhibiting rectangles with the same perimeter and different areas or with the same area and
different perimeters
Geometry
● Reason with shapes and their attributes
○ 3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and other) may
share attributes (e.g., having four sides) and that the shared attributes can define a larger
category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of
quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these
subcategories
Essential Question(s)
Topic 13: What are different ways to compare fractions?
Topic 14: How can time, capacity, and mass be measured and found?
Topic 15: How can two-dimensional shapes be described, analyzed, and classified?
Topic 16: How can perimeter be measured and found?
Instructional Outcomes (Student Learning Objectives - SLOs) - measurable
Topic 13: Fraction Equivalence and Comparison
The students will:
● Find equivalent fractions that name the same part of the whole. (13.1)
● Represent equivalent fractions on a number line. (13.2)
● Use models such as fraction strips to compare fractions that refer to the same whole and have the same
denominator. (13.3)
● Use models such as fraction strips to compare fractions that refer to the same whole and have the same
numerator. (13.4)
● Use benchmark numbers to compare fractions. (13.5)
● Use a number line to compare fractions. (13.6)
● Use fraction names to represent whole numbers. (13.7)
● Construct math arguments using fractions. (13.8)
Topic 14: Solve Time, Capacity, and Mass Problems
The students will:
● Show and tell time to the nearest minute using analog and digital clocks. (14.1)
● Tell and write time to the nearest minute and measure time intervals in minutes. (14.2)
● Solve work problems involving addition and subtraction to measure quantities of time. (14.3)
● Use standard units to estimate liquid volume. (14.4)
● Use standard units to estimate liquid volume. (14.5)
● Use standard units to estimate the masses of solid objects. (14.6)
● Use a pan balance with metric weights to measure the mass of objects in grams and kilograms. (14.7)
● Use pictures to help solve problems about mass and volume. (14.8)
● Make sense of quantities and relationships in problems. (14.9)
Topic 15: Attributes of Two-Dimensional Shapes
The students will:
● Identify quadrilaterals and use attributes to describe them. (15.1)
● Classify shapes according to their attributes. (15.2)
● Analyze and compare quadrilaterals and group them by their attributes. (15.3)
● Solve math problems precisely, efficiently, and accurately by using appropriate tools and mathematics
vocabulary. (15.4)
Topic 16: Solve Perimeter Problems
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The students will:
● Find the perimeter of different polygons. (16.1)
● Find the perimeter of different polygons with common shapes. (16.2)
● Use the given sides of a polygon and the known perimeter to find the unknown side length. (16.3)
● Understand the relationship of shapes with the same perimeter and different areas. (16.4)
● Understand the relationship of shapes with the same area and different perimeters. (16.5)
● Understand the relationship between numbers in order to simplify and solve problems involving
perimeter. (16.6)
Assessment Evidence
Performance Task(s)
● Topic 13 Performance Assessment pages 729-730 in Student Book Volume 2
● Topic 14 Performance Assessment pages 803-804 in Student Book Volume 2
● Topic 15 Performance Assessment pages 841-842 in Student Book Volume 2
● Topic 16 Performance Assessment pages 889-890 in Student Book Volume 2
Other Evidence (Formative, Summative, Benchmark Assessments, Project-Based Learning Experiences)
● (F) Questions to use with the Visual Learning Bridge
● (F) Do You Understand? Convince Me!
● (F) Guided Practice
● (F) Quick Checks
● (S) Topic Assessment 13 pages 727-728 in Student Book Volume 2
● (S) Topic Assessment 14 pages 799-802 in Student Book Volume 2
● (S) Topic Assessment 15 pages 839-840 in Student Book Volume 2
● (S) Topic Assessment 16 pages 887-888 in Student Book Volume 2
● (S) After a group of Topics Cumulative/Benchmark Assessment
● (PBL) Topic13: Topic Opener, Lesson 13.2 and Lesson 13.6
● (PBL) Topic14: Topic Opener, Lesson 14.6 and Lesson 14.9
● (PBL) Topic15: Topic Opener, Lesson 15.2 and Lesson 15.4
● (PBL) Topic16: Topic Opener, Lesson 16.1 and Lesson 16.5
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
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Pennsauken Public School
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
Board Approved Course Textbook (Title, Publisher, copyright)
Envisions 2.0 Common Core, Pearson copyright 2016
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Pennsauken Public School
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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Third Grade Mathematics Pacing Guide for 2015 –2016
Topic #
Title
Instructional
Period
Number of
Days
1
Understand Multiplication and Division of Whole Numbers
9/8/15 - 9/22/15
10
2
Multiplication Facts: Use Patterns
9/24/15 - 10/7/15
9
3
Apply Properties: Multiplication Facts for 3, 4, 6, 7, 8
10/8/15 - 10/23/15
12
4
Use Multiplication to Divide: Division Facts
10/26/15 - 11/18/15
14
Benchmark Assessment: Reteach and Enrichment based on
data analysis
11/19/15 - 11/25/15
5
5
Fluently Multiply and Divide Within 100
11/30/15 - 12/11/15
10
6
Connect Area to Multiplication and Addition
12/14/15 - 12/23/15
8
7
Represent and Interpret Data
1/4/16 - 1/13/16
7
8
Use Strategies and Properties to Add and Subtract
1/14/16- 1/29/16
11
Benchmark Assessment: Reteach and Enrichment based on
data analysis
2/1/16 - 2/5/16
5
9
Fluently Add and Subtract Within 1,000
2/8/16 - 2/22/16
9
10
Multiply by Multiples of 10
2/23/16 - 2/29/16
5
11
Use Operations with Whole Numbers to Solve Problems
3/1/16 - 3/8/16
6
12
Understand Fractions as Numbers
3/9/16 - 3/22/16
10
Benchmark Assessment: Reteach and Enrichment based on
data analysis
3/23/16 - 4/1/16
5
Fraction Equivalence and Comparison
4/4/16 - 4/15/16
10
PARCC April 11- April 22 (Pacing guide will be reevaluated and adjusted as needed)
2 weeks allotted
14
Solve Time, Capacity, and Mass Problems
4/25/16 - 5/10/16
12
15
Attributes of Two-Dimensional Shapes
5/11/16 - 5/18/16
6
16
Solve Perimeter Problems
5/19/16 - 5/31/16
8
Benchmark Assessment: Reteach and Enrichment based on
data analysis
6/1/16 - 6/7/16
5
Note: There are 10 lessons in Step Up to Grade 5 to help
6/8/16-6/16/16
4 full, 3 half
1-4
5-8
9-12
13
13-16
Step Up
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Pennsauken Public School
to 4th
prepare students for 5th grade. Time permitting, choose which
lessons you determine will be most beneficial to your students
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