Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Grade: 3
Module: 2
Title: It’s Time to Round It All Up!
Date: 2013-2014
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity,
K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin, www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the
local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Grade Level: 3
Module Title: It’s Time to Round It All Up!
Conceptual Lens: Approximation
Operations
Place Value
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Rounding
Estimation
Reasonable Answers
Addition/Subtraction Strategies
Multiplication Strategy
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Module Title:
Addition
Subtraction
Multiplication
Division
Properties
Inverse Operations
Order of Operations
Word Problems
Variables (Unknowns in All
Positions)
Equations
Symbols
Mental Math
It’s Time to Round It All Up!
Models
Measurement
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Concrete
Pictorial representations
Abstract
Time
Elapsed time
Time intervals
Increments
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity,
K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin, www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the
local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Module Title: It’s Time to Round It All Up!
Conceptual Lens: Approximation
Module Overview:
In this module students will have the opportunity to investigate place value as it pertains to addition and
subtraction of numbers within 1000. A strong understanding of place value is essential for the development
of number sense. Students will apply their knowledge of place value to round numbers and determine
reasonableness of an answer. Students will be able to solve real-life situations involving two-step equations
and using all operations. Students will explore time to the nearest minute using concrete models and pictorial
representations. Students will then apply their knowledge of word problems in situations involving elapsed
time.
Technology Integration:
Teachers should be proficient utilizing interactive whiteboard technology and internet resources such as
Think Central and other websites that provide interactive math tools. Also, teachers should demonstrate
knowledge of administering online testing, interpreting data, and selecting computer based activities for
students.
Standards addressed in this module:
3.OA.7
3.OA.8
3.NBT.1
3.NBT.2
3.NBT.3
3.MD.1
3.MD.3
Standards for Mathematical Practice addressed in this module:
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.
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity,
K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin, www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the
local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Generalizations
Guiding Questions
(F = factual; C = conceptual; P = philosophical)
1. Place value concepts and properties of operations can
be utilized to perform calculations efficiently and
accurately.
a. What is a place value strategy that is useful in problem solving? (F)
b. How is knowledge of the properties of operations useful in problem
solving? (F)
c. How is place value important in addition and subtraction of multi-digit
numbers? (C)
d. Why does the standard algorithm work? (C)
e. How is place value related to multiples of ten? (C)
f. What happens to a number when it is multiplied by ten? (F)
g. What patterns do I notice when I am multiplying by ten? (F)
2. Inverse operations can be used to solve for unknown
numbers and to verify solutions to problems.
a. How does the relationship between addition and subtraction help us
problem solve? (F)
b. How can you solve 32 ÷ ? = 4 using multiplication?
How can you solve 135 - ? = 87 using addition?
c. How does the relationship between multiplication and division help us
problem solve? (F)
d. How can I verify the results of an addition (or subtraction) problem?
e. How can I verify the results of a multiplication (or division) problem?
f. How can we determine a missing number in an equation by using what
we know about inverse operations?
a. When and why might we use a variable? (F)
b. Why are letters used to represent unknown quantities? (C)
c. What is the difference between an expression and an equation? (F)
d. Given this problem, where would the variable go in your equation? (C)
a. What does it mean to tell time to the nearest minute? (C)
b. How many minutes are in an hour? Seconds in a minute? (F)
c. What strategies can I use to help me tell and write time to the nearest
minute and measure time intervals in minutes? (F)
d. How can hours be decomposed to help measure time and solve word
problems involving elapsed time? (F)
e. What connections can I make between a clock and a number line? (F)
f. How can I use what I know about number lines to help me figure out how
much time has passed between two events? (F)
g. When do you regroup in problems involving time? (F)
h. What part does elapsed time play in our daily life? (C)
i. How can we determine the amount of time that passes between two
events? (F)
j. Why do we measure time? (C)
a. What is mental computation? (F)
b. What does it mean to round? (F)
c. What strategies do we use to round to the nearest ____? (F)
d. What type of rounding is most precise? (F)
e. What strategies do we use to check or evaluate our mental calculations?
(F)
f. What are some situations where we want an exact answer? (C)
g. What are some situations when an estimate is acceptable? (C)
h. How do we use rounding in everyday life? (F)
i. How does rounding a number make mental computation easier? (C)
j. How does estimation and mental math help us problem solve? (C)
k. How can I learn to calculate quickly in my head? (F)
3. Unknown numbers in an equation and word
problems can be represented by a variable.
4. Solving elapsed time problems involves composing
and decomposing units of hours, minutes, and seconds.
5. Rounded numbers result in solutions that are
approximate, not exact.
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity,
K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin, www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the
local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Generalizations
Guiding Questions
(F = factual; C = conceptual; P = philosophical)
6. Estimation determines the reasonableness of an
answer.
7. Effective mathematicians utilize appropriate tools
and strategies to solve problems and justify solutions.
a. What does it mean for an answer to be reasonable? (F)
b. What types of estimation can we use (besides rounding)? (F)
c. How can you use compatible numbers to estimate? (F)
d. Which type of estimation would be most precise (in a given situation)?
(F)
e. Why is it important to assess the reasonableness of an answer? (C)
f. How does estimation help you determine if an exact answer is
reasonable? (C)
g. How can we select among the most useful mental math strategies for the
task we are trying to solve? (C)
h. What is an effective way to estimate numbers? (C)
a. How can you prove that your solution was correct? (C)
b. What strategies do you use to add and subtract multi-digit numbers?
(C)
c. What are some methods for solving multiplication problems? (C)
d. What are some methods for solving division problems? (C)
e. How can you use the situation in a word problem to determine the best
operation to use? (C)
f. How can you use the information in a word problem to determine how
many steps you will need to solve it? (C)
g. How can you determine what is unknown in a multistep word
problem? (C)
h. How can you represent this word problem with an equation?(C)
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity,
K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin, www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the
local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Critical Content
Key Skills
What Students Will Know
What Students Will Be Able to Do
Place Value:
 Round to nearest 10 or 100
 Use estimation and to determine reasonable answers
 Use strategies based on place value to add and subtract
 Use strategies based on place value to multiply by
multiples of 10
Operations:
 Use all four operations to solve one and two-step word
problems
 Use properties and inverse operations to check solutions
to word problems
 Use appropriate symbols to model situations with an
equation
 Represent the unknown in an equation with a variable
 Use mental math to assess reasonableness of an answer
3.NBT.1.
Use place value understanding to round whole numbers to
the nearest 10 or 100.
3.NBT.2.
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. *
*
A range of algorithms may be used.
3.NBT.3.
Multiply one-digit whole numbers by multiples of 10 in the
range 10–90 (e.g., 9  80, 5  60) using strategies based on
place value and properties of operations. *
* A range of algorithms may be used.
Models:
 Use models to solve situations involving all four
operations
3.OA.7.
Fluently multiply and divide within 100, using strategies
such as the relationship between multiplication and division
(e.g., knowing that 8 × 5 = 40, one knows that 40 ÷ 5 = 8) or
properties of operations. By the end of grade 3, know from
memory all products of two one-digit numbers.
Measurement:
 Tell time to the nearest minute
 Measure time intervals and elapsed time
 Use time various increments to calculate elapsed time
 Use time intervals, addition, and subtraction to solve
word problems
3.OA.8
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
3
This standard is limited to problems posed with whole numbers and having
whole-number answers; students should know how to perform operations in the
conventional order when there are no parentheses to specify a particular order
(Order of Operations).
3.MD.1.
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.
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity,
K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin, www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the
local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Suggested
Timeline
Learning Experiences
Spiral
throughout
the year
Multiplication and division are the focus for Grade 3 all
year long. Fluency and use of strategies must be focused on
in every module.
Days 1-7
Round numbers to the closest 10 or 100. (G: 1, 5, 6, 7)
Have students use vertical and horizontal number lines to
round 2- and 3-digit numbers to the
nearest ten and
hundred.
Students will determine the place value to which they are
rounding.
Step 1: Identify the two benchmark numbers on either side of
the target number.
Step 2: Find the halfway point between the target numbers.
Step 3: Place the target number on the number line.
Step 4: Choose the benchmark number that is closer to the target
number. What do you do if the number is at the halfway point?
*All learning experiences allow for student discourse.
Assessments
**Performance Task
(End of Module)
CFA’s
Differentiation
(For Support and
Extension)_
Resources
Math Expressions
Refer to Differentiated
Instruction pages in T.E.
or on ThinkCentral.
Grade 3 Unpacked Standards
Math Expressions
Units 5
Intervention: Online
Soar to Success
Hands-On Standards Common
Core Gr.3, ETA hand2mind ©
2012
Extension: Online
Destination Math
eduplace.com
Teacher Observations
Math Expressions
Formative Assessments
Ongoing Assessments
 Quick Quizzes
 Unit Tests
Learnzillion Videos
www.thinkcentral.com


iTools Primary
Mega Math
Module Two Lessons (see
attatched):
Happy to Eat Healthy
Shake Rattle and Roll
The Great Round Up
Engage NY Module 2
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity, K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin,
www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Learning Experiences
Assessments
Suggested
Timeline
Days 8-19
Model place value strategies and properties to add and
subtract whole numbers. (Sums and differences to the
thousands place.) Start with concrete models (base 10
blocks) then move on to pictorial (open number lines, place
value drawings, etc.) Finish with the abstract (standard
algorithm). (G: 1, 2, 7)
Use inverse operations to verify solutions.
Have students build a number using base 10 blocks and then
regroup the blocks to come up with a sum or difference.
**Performance Task
(End of Module)
CFA’s
Differentiation
(For Support and
Extension)
Resources
Math Expressions
Refer to Differentiated
Instruction pages in T.E.
or on ThinkCentral.
Grade 3 Unpacked Standards
Math Expressions
Unit 1
Intervention: Online
Soar to Success
Hands-On Standards Common
Core Gr.3, ETA hand2mind ©
2012
Extension: Online
Destination Math
Learnzillion videos
Teacher Observations
Math Expressions
Formative Assessments
Ongoing Assessments
 Quick Quizzes
 Unit Tests
eduplace.com
Have students model addition and subtraction (with and
without regrouping) by making drawings.
Decompose 2- and 3-digit numbers to add and subtract with
and without regrouping.
Have students use an open number line strategy to model
jumps of hundreds, tens, and ones to solve addition and
subtraction problems.
Make connections between models, drawings, and the steps
involved with the standard algorithm.
www.thinkcentral.com


iTools Primary
Mega Math
Module Two Lessons (see
attatched):
Perfect 500!
Field Day Fun
Engage NY Module 2
Student
**All learning experiences allow for student discourse.
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity, K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin,
www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Learning Experiences
Assessments
Suggested
Timeline
Days 20-24
Model multiplying one-digit whole numbers by a multiple
of ten using concrete objects (i.e. base-ten blocks). Then
move to pictorial representations (arrays, drawings, etc.).
Lastly, move on to writing equations. (G: 1, 7)
**Performance Task
(End of Module)
CFA’s
Differentiation
(For Support and
Extension)
Resources
Math Expressions
Refer to Differentiated
Instruction pages in T.E.
or on ThinkCentral.
Grade 3 Unpacked Standards
Math Expressions
Unit 7
Intervention: Online
Soar to Success
Hands-On Standards Common
Core Gr.3, ETA hand2mind ©
2012
Extension: Online
Destination Math
eduplace.com
Teacher Observations
Have students build multiple of ten arrays with concrete
objects.
Have students represent one-digit multiplication with multiples
of ten on a number line.
Math Expressions
Formative Assessments
Ongoing Assessments
 Quick Quizzes
 Unit Tests
Have students explain patterns they discover when multiplying
multiples of ten.
Learnzillion Videos
Have students explain the relationship to basic multiplication
facts.
www.thinkcentral.com
 iTools Primary
 Mega Math
Module Two Lessons (see
attatched):
Multiples of Ten
How Many Tens
Engage NY Module 3
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity, K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin,
www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Suggested
Timeline
Days 25-34
Learning Experiences
Assessments
Model the process of solving two-step word problems
involving all four operations including variables to
represent unknowns in all positions. (G: 1, 2, 3, 5, 6, 7)
**Performance Task
(End of Module)
CFA’s
Introduce and explain George Polya’s Problem-Solving
Method:
Teacher Observations
1. Understand the problem.
2. Devise a plan.
3. Carry out the plan.
4. Look back and evaluate the answer.
Have students to use inverse relationships to verify solutions to
problems.
Have students represent the problem situation with counters,
blocks, or drawings. Students should analyze the structure of
the problem and make sense of it. They should think through
the problem and the meaning of the answer before attempting to
solve it.
Have students represent an unknown number with a symbol in
all positions, and use all four operations.
*Students should know how to perform operations in the
conventional order with and without the use of parentheses
to specify a particular order (Order of Operations)
Math Expressions
Formative Assessments
Ongoing Assessments
 Quick Quizzes
 Unit Tests
Differentiation
(For Support and
Extension)_
Math Expressions
Refer to Differentiated
Instruction pages in
T.E. or on
ThinkCentral.
Intervention: Online
Soar to Success
Resources
Grade 3 Unpacked Standards
Math Expressions
Units 3 and 9
Hands-On Standards Common
Core Gr.3, ETA hand2mind ©
2012
eduplace.com
Extension: Online
Destination Math
Learnzillion Videos
www.thinkcentral.com


iTools Primary
Mega Math
Module Two Lessons (see
attatched):
Hooked on Solutions
Engage NY Module 2
Have students estimate solutions to problems to determine if an
answer is reasonable.
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity, K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin,
www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Suggested
Timeline
35-42
Learning Experiences
Assessments
Model telling time to the nearest minute and measuring
time intervals in minutes (elapsed time), using concrete
objects (clocks), moving to pictorial representations
(drawing, and number lines), and lastly the abstract.
(G: 4, 1, 7)
**Performance Task
(End of Module)
CFA’s
Have students model reading and making given times on an
analog or digital clock.
Math Expressions
Formative Assessments
Ongoing Assessments
 Quick Quizzes
 Unit Tests
Have students draw analog and write digital times to the nearest
minute.
Have students use number lines with increments indicated to
measure intervals and solve elapsed time situations.
Have students use an open number line to measure time
intervals and solve elapsed time situations (word problems).
Teacher Observations
Differentiation
(For Support and
Extension)_
Math Expressions
Refer to Differentiated
Instruction pages in
T.E. or on
ThinkCentral.
Intervention: Online
Soar to Success
Resources
Grade 3 Unpacked Standards
Math Expressions
Unit 10
Hands-On Standards Common
Core Gr.3, ETA hand2mind ©
2012
eduplace.com
Extension: Online
Destination Math
Learnzillion Videos
www.thinkcentral.com
 iTools Primary
 Mega Math
Module One Lessons (see
attatched):
Let’s Talk About Time
Time to Get Clean
Daily Schedule
Engage NY Module 3
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity, K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin,
www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the local school site or nonprofit organization that has purchased this book.
Waterbury Public Schools
Mathematics Concept-Based Curriculum
Grade 3 - Module 2
2013-2014
Source: Adapted from Erickson, 2008.
Retrieved from the companion website for Designing a Concept-Based Curriculum for English Language Arts: Meeting the Common Core With Intellectual Integrity,
K–12 by Lois A. Lanning. Thousand Oaks, CA: Corwin, www.corwin.com. Copyright © 2013 by Corwin. All rights reserved. Reproduction authorized only for the
local school site or nonprofit organization that has purchased this book.