Unit #: 2
Subject(s): Math
Grade(s): 4th
Designer(s): Amity Allman, Amy DeFord, Christin Nelson, Jan Ragan
PREAMBLE
In this unit, students will multiply and divide multiples of ten; read, write and compare base ten numerals in expanded form; round multi-digit whole numbers
between 1,000 and 1,000,000; fluently add and subtract multi-digit whole numbers; and solve multi-step word problems with remainders. It is important to use area
models, partial product methods, computation strategies and algorithms. Equally important, students must be able to explain why the procedures work using place
value and the distributive property. The representations required to support the work of operations and algebraic thinking across grade levels involve model drawings,
numeric expressions, arrays, tables, letter notation, ordered pairs, concrete materials and manipulatives. The four areas across grade levels that support development
of these representations are:
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Properties and Structures: properties, including but not limited to, part whole relationships
Interpreting Reasonableness: using mental computations and estimations to promote reflection
Generating and Analyzing Patterns: using input-output relations or number sequence using rules
Syntax of Expressions: involving boxes or placeholders, parentheses, brackets, and braces in expressions
Foote, M. Q., Earnest, D., & Mukhopadhyay, S. (2014). Implementing the common core state standards through mathematical problem solving:
Grades 3-5. Reston, VA: National Council of Teachers of Mathematics.
Lannin, J. K., Ellis, A. B., & Elliott, R. (2011). Developing essential understanding of mathematical reasoning for teaching mathematics in
prekindergarten-grade 8. Reston, VA: National Council of Teachers of Mathematics.
Schwartz, S. L. (2013). Implementing the common core state standards through mathematical problem solving Kindergarten-grade 2. Reston, VA:
The National Council of Teachers of Mathematics.
STAGE 1 – DESIRED RESULTS
Unit Title: Understanding Place Value
Transfer Goal: Students will be able to independently use their learning to solve mathematical operations.
Essential Questions:
Enduring Understandings:
Students will understand that…
 The place of a digit within a number determines its value.
 Rounding and estimating are used to solve math problems and check for
reasonableness of answers.
 Problems can be solved in many ways with many different strategies.
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Students will know:
Students will be able to:
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Whole numbers can be used in calculations using the four operations.
Standard algorithms for addition and subtraction and how they connect
to other strategies.
The following multiplication strategies (rectangular arrays, area models,
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How does understanding the base ten system make sense of problem solving?
How can representing numbers in a variety of ways help solve problems?
What is the benefit of using estimation versus finding an exact answer?
Apply an appropriate problem solving strategy to a multi-step situation.
Use a method consistently and recognize a variety of methods (arrays, models,
equations) to multiply and divide.
Use a method consistently (arrays, models, equations) to explain calculations.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 8/10/16
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Unit #: 2
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Subject(s): Math
Grade(s): 4th
Designer(s): Amity Allman, Amy DeFord, Christin Nelson, Jan Ragan
and/or equations) and how they build the foundation for the standard
algorithm.
The position of a digit affects its value.
Place value is related to multiplication and division by multiples of 10.
When the digit moves to the left, it is multiplied by 10. When it moves
to the right, it is divided by 10 or multiplied by 1/10.
The various ways to write and compare numbers.
Place value is used to understand rounding.
Estimation can be used to check for reasonableness of an answer.
Multiple strategies for problem solving (model drawing, tables, number
lines, etc.).
How to use appropriate mathematical language in discussions: place
value, greater than, less than, equal to, ‹, ›, =, comparisons/compare,
round add, addend, sum, subtract, difference, equation, strategies,
(properties)-rules about how numbers work, rectangular arrays,
area model, multiply, divide, factor, product, quotient,
reasonableness, remainder.
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Write statements and equations for all four operations
Interpret the remainder in division problems.
Identify the place and value of each digit in a number.
Explain that in a multi-digit whole number, a digit in one place represents ten
times what it represents in the place to its right.
Use expanded, word, and standard forms to make problem solving easier.
Use their knowledge of place value to compare two multi-digit numbers using
correct symbols.
Fluently add and subtract multi-digit whole numbers using the standard algorithm.
Use their knowledge of place value to round/estimate numbers to any place while
checking for reasonableness.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 8/10/16
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Unit #: 2
Subject(s): Math
Grade(s): 4th
Designer(s): Amity Allman, Amy DeFord, Christin Nelson, Jan Ragan
STAGE 1– STANDARDS
Cluster
4.OA
4.OA
4.NBT
4.NBT
MP1
MP2
MP3
MP4
MP5
MP6
MP7
MP8
Standards
Solve multistep word problems posed with whole numbers and having
whole-number answers using the four operations, including problems in
which remainders must be interpreted. Represent these problems using
Use the four operations with whole numbers to solve problems.
4.OA.3
equations with a letter standing for the unknown quantity. Assess the
reasonableness of answers using mental computation and estimation
strategies including rounding.
Generate a number or shape pattern that follows a given rule. Identify
apparent features of the pattern that were not explicit in the rule itself. For
example, given the rule “Add 3” and the starting number 1, generate terms
Generate and analyze patterns.
4.OA.5
in the resulting sequence and observe that the terms appear to alternate
between odd and even numbers. Explain informally why the numbers will
continue to alternate in this way.
Recognize that in a multi-digit whole number, a digit in one place
represents ten times what it represents in the place to its right. For
4.NBT.1
example, recognize that 700 / 70 = 10 by applying concepts of place value
and division.
Generalize place value understanding for multi-digit whole
Read and write multi-digit whole numbers using base-ten numerals,
numbers.
number names, and expanded form. Compare two multi-digit numbers
4.NBT.2
based on meanings of the digits in each place, using >, =, and < symbols
to record the results of comparisons.
Use place value understanding to round multi-digit whole numbers to any
4.NBT.3
place.
Fluently add and subtract multi-digit whole numbers using the standard
Use place value understanding and properties of operations to
4.NBT.4
perform multi-digit arithmetic.
algorithm.
Standards for 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.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 8/10/16
3
Unit #: 2
Subject(s): Math
Performance Tasks:
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Grade(s): 4th
Designer(s): Amity Allman, Amy DeFord, Christin Nelson, Jan Ragan
STAGE 2 – ASSESSMENT EVIDENCE
Other Evidence:
Construction Task: Reality Checking
Formative Assessment Rubric
Formative Assessment Task 4.NBT.3
Problem Solving Rubric 3-5
Problem Solving Rubric 9
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Click here to access the performance task(s) described above.
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Numeral, Word and Expanded Form (4.NBT.2)
Unit 2 Summative
Georgia State Performance Tasks
Georgia Task NFL Salaries
NCDPI Games
o Appalachian Steps
o Becca’s Battle
o Climbing Chimney
o Corn Shucks
o Digit Skis
o Valuable Digits
NCDPI Math Wiki Formative Assessment Tasks
o Adding Zeros
o Arranging Tables
o Arranging the Students
o Coin Collection
o Enlarging the Yard
o How Many Teams?
o Making Gift Bags
o Open Number Lines
o Packaging Soup Cans
o Table Dilemma
o Value of the Bills
o Remainders
o Rounding Numbers and Products
o School Shopping 4.OA.3, 4.NBT.2
School Shopping 4.OA.3 and 4.NBT.2
School Box Top Contest 4.OA.5
Click here to access the other evidences described above.
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 8/10/16
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Unit #: 2
Subject(s): Math
Grade(s): 4th
Designer(s): Amity Allman, Amy DeFord, Christin Nelson, Jan Ragan
STAGE 3 – RESOURCES FOR THE LEARNING PLAN
District Resources:
Supplemental Resources:
When designing the learning plan, these resources are intended to be a primary
These are considered additional resources that are recommended by the
resource used by all teachers.
Curriculum Writing Teams. Those resources with an asterisk* may be purchased
by each individual school.
 Unpacking Document: 4.NBT.1-2
 Engage NY Instructional Resources
 Unpacking Document: 4.OA.3-5
o Unit 1, Modules 1-7
 NCDPI: Lessons for Learning
o Read and Write Multi-Digit Numbers
o Building 10,000
o Read, Write and Expand with Explanations
o Multi-step Multiplication
o Rounding and Solving Multi-Step Problems
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Georgia
State Standards Math Grade 4 Unit 1
Click here to access the resources above.
 Illustrative Mathematics
o Ordering 4-digit Numbers
 Unit 5: Investigations and Common Core State Standards Book
o Thousands and Millions of Fourth Graders
o Investigation #1 Lessons 1.1- 1.5, 1.5A
o What’s My Number?
o Investigation #3 Lessons 3.1-3.2, 3.6A
o Investigation #4 Lesson 4.3 Assessment
Click here to access the resources above.
o Assessment: Numbers to 1,000
o Session 4.3 Assessment: Numbers to 10,000
 NCDPI Fourth Grade Math Wikispaces
 Greg Tang Math Place Value
 K-5 Math Resources Website
 OrgLib- Math Assessments and Activities for 4.NBT.1, 4.NBT.2, 4.NBT.3
Considerations for Differentiating Instruction (AIG, EL, EC, etc.):
These resources are intended to be used when differentiating instruction to meet the varied needs of students in your classroom.
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Achieve the Core Coherence map shows progressions of skills and can be used for EC and AIG
Investigations - Differentiation and Intervention Guide
Investigations - See Differentiation section of each lesson for ESL, EC, and AIG
AIG lessons from NCDPI
4.NBT.1 Place Value Pirates
Adapted from Understanding by Design, Unit Design Planning Template (Wiggins/McTighe 2005)
Last revision 8/10/16
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