Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
WATERBURY PUBLIC SCHOOLS
Moving Forward for Student Success
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
1
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Background
The Waterbury Public Schools Curriculum Framework for Mathematics builds on the Common Core State Standards for Mathematics. The standards in this framework are the culmination of an extended, broadbased effort to fulfill the charge issued by the states to create the next generation of pre-kindergarten–12 standards in order to help ensure that all students are college and career ready in mathematics no later than the
end of high school.
The Council of Chief State School Officers (CCSSO) and the National Governors Association Center for Best Practice (NGA) began a multi-state standards development initiative in 2009, the two efforts merged. The
standards in this document draw on the most important international models as well as research and input from numerous sources, including state departments of education, scholars, assessment developers,
professional organizations, educators from pre-kindergarten through college, and parents, students, and other members of the public. In their design and content, refined through successive drafts and numerous
rounds of feedback, the Standards represent a synthesis of the best elements of standards-related work to date and an important advance over that previous work. As specified by CCSSO and NGA, the Standards are
(1) research and evidence based, (2) aligned with college and work expectations, (3) rigorous, and (4) internationally benchmarked. A particular standard was included in the document only when the best available
evidence indicated that its mastery was essential for college and career readiness in a twenty-first-century, globally competitive society. The standards are intended to be a living work: as new and better evidence
emerges, the standards will be revised accordingly.
Waterbury Public Schools Mathematics Department Statement of Philosophy
Waterbury Public Schools provides a rich and rigorous mathematics curriculum that prepares students for rewarding postsecondary experiences. . All courses are carefully aligned to the Common Core State
Standards in Mathematics. A rich and rigorous mathematics education is about becoming an effective problem solver. This entails evaluating given information, accessing prior knowledge and intertwining these to
move toward a potential solution. Attaining such abilities requires students to become driven, independent, competent and confident in their math abilities. Based on this; the philosophy underscoring the units is that of
teaching mathematics for understanding, this philosophy will have tangible benefits for both students and teachers. For students, mathematics should cease to be seen as a set of disjointed facts and rules. Rather, students
should come to view mathematics as an interesting, powerful tool that enables them to better understand their world. All students should be able to reason mathematically; thus, activities will have multiple levels so
that the able student can go into more depth while a student having trouble can still make sense out of the activity. For teachers, the reward of seeing students excited by mathematical inquiry, a redefined role as
guide and facilitator of inquiry, and collaboration with other teachers should result in innovative approaches to instruction, increased enthusiasm for teaching, and a more positive image with students and society.
Students exiting the Waterbury Public Schools Mathematics program will understand and be able to solve non-routine problems in nearly any mathematical situation they might encounter in their daily lives. In
addition, they will have gained powerful heuristics, vis-à-vis the interconnectedness of mathematical ideas, that they can apply to most new problems typically requiring multiple modes of representation, abstraction,
and communication. This knowledge base will serve as a springboard for students to continue in any endeavor they choose, whether it be further mathematical study in high school and college, technical training in
some vocation, or the mere appreciation of mathematical patterns they encounter in their future lives. Furthermore, instruction and assignments are designed to aid students in improving their testing skills. An
additional goal of the Waterbury Public Schools Department is that all students are prepared for the numerous standardized tests that they will encounter as they progress through high school and beyond. .
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
2
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
To be sure the goals of the Philosophy are met. The Mathematics Curriculum will be guided by the following ideas (adapted from the State of Massachusetts Mathematics Framework, 2011):
Mathematical ideas should be explored in ways that stimulate curiosity, create enjoyment of mathematics, and develop depth of understanding.
Students need to understand mathematics deeply and use it effectively. The standards of mathematical practice describe ways in which students increasingly engage with the subject matter as they grow in
mathematical maturity and expertise through the elementary, middle, and high school years. To achieve mathematical understanding, students should have a balance of mathematical procedures and conceptual
understanding. Students should be actively engaged in doing meaningful mathematics, discussing mathematical ideas, and applying mathematics in interesting, thought-provoking situations. Tasks should be designed
to challenge students in multiple ways. Short- and long-term investigations that connect procedures and skills with conceptual understanding are integral components of an effective mathematics program. Activities
should build upon curiosity and prior knowledge, and enable students to solve progressively deeper, broader, and more sophisticated problems. Mathematical tasks reflecting sound and significant mathematics should
generate active classroom talk, promote the development of conjectures, and lead to an understanding of the necessity for mathematical reasoning.
An effective mathematics program is based on a carefully designed set of content standards that are clear and specific, focused, and articulated over time as a coherent sequence.
The sequence of topics and performances should be based on what is known about how students’ mathematical knowledge, skill, and understanding develop over time. Students should be asked to apply their learning
and to show their mathematical thinking and understanding by engaging in the first Mathematical Practice, Making sense of problems and persevere in solving them. This requires teachers who have a deep knowledge of
mathematics as a discipline. Mathematical problem solving is the hallmark of an effective mathematics program. Skill in mathematical problem solving requires practice with a variety of mathematical problems as well
as a firm grasp of mathematical techniques and their underlying principles. Armed with this deeper knowledge, the student can then use mathematics in a flexible way to attack various problems and devise different
ways of solving any particular problem. Mathematical problem solving calls for reflective thinking, persistence, learning from the ideas of others, and going back over one's own work with a critical eye. Students
should construct viable arguments and critique the reasoning of others, they analyze situations and justify their conclusions and are able to communicate them to others and respond to the arguments of others. (See
Mathematical Practice 3, Construct viable arguments and critique reasoning of others.) Students at all grades can listen or read the arguments of others and decide whether they make sense, and ask questions to clarify or
improve the arguments.
Technology is an essential tool that should be used strategically in mathematics education.
Technology enhances the mathematics curriculum in many ways. Tools such as measuring instruments, manipulatives (such as base ten blocks and fraction pieces), scientific and graphing calculators, and computers
with appropriate software, if properly used, contribute to a rich learning environment for developing and applying mathematical concepts. However, appropriate use of calculators is essential; calculators should not
be used as a replacement for basic understanding and skills. Elementary students should learn how to perform the basic arithmetic operations independent of the use of a calculator. Although the use of a graphing
calculator can help middle and secondary students to visualize properties of functions and their graphs, graphing calculators should be used to enhance their understanding and skills rather than replace them. Teachers
and students should consider the available tools when presenting or solving a problem. Student should be familiar with tools appropriate for their grade level to be able to make sound decisions about which of these
tools would be helpful. (See Mathematical Practice 5, Use appropriate tools strategically.)
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
3
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
All students should have a high quality mathematics program that prepares them for college and a career.
All Waterbury students should have high quality mathematics programs that meet the goals and expectations of these standards and address students’ individual interests and talents. The standards provide clear
signposts along the way to the goal of college and career readiness for all students. The standards provide for a broad range of students, from those requiring tutorial support to those with talent in mathematics. To
promote achievement of these standards, teachers should encourage classroom talk, reflection, use of multiple problem solving strategies, and a positive disposition toward mathematics. They should have high
expectations for all students. At every level of the education system, teachers should act on the belief that every child should learn challenging mathematics. Teachers and guidance personnel should advise students and
parents about why it is important to take advanced courses in mathematics and how this will prepare students for success in college and the workplace. All students must have the opportunity to learn and meet the
same high standards.
An effective mathematics program builds upon and develops students’ literacy skills and knowledge.
Supporting the development of students’ literacy skills will allow them to deepen their understanding of mathematics concepts and help them determine the meaning of symbols, key terms, and mathematics phrases
as well as develop reasoning skills that apply across the disciplines. Mathematics classrooms should make use of a variety of text materials and formats, including textbooks, math journals, contextual math problems,
and data presented in a variety of media. Mathematics classrooms should incorporate a variety of written assignments ranging from math journals to formal written proofs. In speaking and listening, teachers should
provide students with opportunities for mathematical discourse, to use precise language to convey ideas, to communicate a solution, and support an argument.
Assessment of student learning in mathematics should take many forms to inform instruction and learning.
A comprehensive assessment program is an integral component of an instructional program. It provides students with frequent feedback on their performance, teachers with diagnostic tools for gauging students’
depth of understanding of mathematical concepts and skills, parents with information about their children’s performance in the context of program goals, and administrators with a means for measuring student
achievement. Assessments take a variety of forms, require varying amounts of time, and address different aspects of student learning. Having students “think aloud” or talk through their solutions to problems permits
identification of gaps in knowledge and errors in reasoning. By observing students as they work, teachers can gain insight into students’ abilities to apply appropriate mathematical concepts and skills, make
conjectures, and draw conclusions. Homework, mathematics journals, portfolios, oral performances, and group projects offer additional means for capturing students’ thinking, knowledge of mathematics, facility
with the language of mathematics, and ability to communicate what they know to others. Tests and quizzes assess knowledge of mathematical facts, operations, concepts, and skills and their efficient application to
problem solving. They can also pinpoint areas in need of more practice or teaching. Taken together, the results of these different forms of assessment provide rich profiles of students’ achievements in mathematics
and serve as the basis for identifying curricula and instructional approaches to best develop their talents. Assessment should also be a major component of the learning process. As students help identify goals for lessons
or investigations, they gain greater awareness of what they need to learn and how they will demonstrate that learning. Engaging students in this kind of goal-setting can help them reflect on their own work,
understand the standards to which they are held accountable, and take ownership of their learning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
4
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Grade 2 Overview
Operations and Algebraic Thinking (OA)
 Represent and solve problems involving addition and subtraction
 Add and subtract within 20.
 Work with equal groups of objects to gain foundations for multiplication.
Mathematical Practices (MP)
1.
2.
3.
4.
5.
6.
7.
8.
Number and Operations in Base Ten (NBT)
 Understand place value.
 Use place value understanding and properties of operations to add and
subtract.
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.
Measurement and Data (MD)
 Measure and estimate lengths in standard units.
 Relate addition and subtraction to length.
 Work with time and money.
 Represent and interpret data.
Geometry (G)
 Reason with shapes and their attributes.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
5
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
In Grade 2, instructional time should focus on four critical areas:
1. Extending understanding of base-ten notation
Students extend their understanding of the base-ten system. This includes ideas of counting in fives, tens, and multiples of hundreds, tens, and ones, as well as number relationships involving these units, including comparing. Students
understand multi-digit numbers (up to 1000) written in base-ten notation, recognizing that the digits in each place represent amounts of thousands, hundreds, tens, or ones (e.g., 853 is 8 hundreds + 5 tens + 3 ones).
2. Building fluency with addition and subtraction
Students use their understanding of addition to develop fluency with addition and subtraction within 100. They solve problems within 1000 by applying their understanding of models for addition and subtraction, and they develop,
discuss, and use efficient, accurate, and generalized methods to compute sums and differences of whole numbers in base-ten notation, using their understanding of place value and the properties of operations. They select and accurately
apply methods that are appropriate for the context and the numbers involved to mentally calculate sums and differences for numbers with only tens or only hundreds.
3. Using standard units of measure
Students recognize the need for standard units of measure (centimeter and inch) and they use rulers and other measurement tools with the understanding that linear measure involves iteration of units. They recognize that the smaller the
unit, the more iteration they need to cover a given length.
4. Describing and analyzing shapes
Students describe and analyze shapes by examining their sides and angles. Students investigate, describe, and reason about decomposing and combining shapes to make other shapes. Through building, drawing, and analyzing two- and
three-dimensional shapes, students develop a foundation for understanding attributes of two- and three-dimensional shapes, students develop a foundation for understanding area, volume, congruence, similarity, and symmetry in later
grades.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
6
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Standards for Mathematical Practice
Mathematical Practice Standards
Mathematically proficient students should
be able to:
2.MP.1. Make sense of problems and
persevere in solving them.
2.MP.2. Reason abstractly and
quantitatively.
2.MP.3. Construct viable arguments and
critique the reasoning of others.
2.MP.4. Model with mathematics.
2.MP.5. Use appropriate tools
strategically.
2.MP.6. Attend to precision.
2.MP.7. Look for and make use of
structure.
2.MP.8. Look for and express regularity in
repeated reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Explanations and Examples
In second grade, students realize that doing mathematics involves solving problems and discussing how they solved them. Students explain to themselves the
meaning of a problem and look for ways to solve it. They may use concrete objects or pictures to help them conceptualize and solve problems. They may check
their thinking by asking themselves, “Does this make sense?” They make conjectures about the solution and plan out a problem-solving approach.
Younger students recognize that a number represents a specific quantity. They connect the quantity to written symbols. Quantitative reasoning entails creating a
representation of a problem while attending to the meanings of the quantities. Second graders begin to know and use different properties of operations and relate
addition and subtraction to length.
Second graders may construct arguments using concrete referents, such as objects, pictures, drawings, and actions. They practice their mathematical
communication skills as they participate in mathematical discussions involving questions like “How did you get that?”, “Explain your thinking,” and “Why is that
true?” They not only explain their own thinking, but listen to others’ explanations. They decide if the explanations make sense and ask appropriate questions.
In early grades, students experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures,
using objects, acting out, making a chart or list, creating equations, etc. Students need opportunities to connect the different representations and explain the
connections. They should be able to use all of these representations as needed.
In second grade, students consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be better
suited. For instance, second graders may decide to solve a problem by drawing a picture rather than writing an equation.
As children begin to develop their mathematical communication skills, they try to use clear and precise language in their discussions with others and when they
explain their own reasoning.
Second graders look for patterns. For instance, they adopt mental math strategies based on patterns (making ten, fact families, doubles).
Students notice repetitive actions in counting and computation, etc. When children have multiple opportunities to add and subtract, they look for shortcuts, such
as rounding up and then adjusting the answer to compensate for the rounding. Students continually check their work by asking themselves, “Does this make
sense?”
Grade 2
7
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Operations and Algebraic Thinking
 Represent and solve problems involving addition and subtraction
Standards
Students will be able to:
Mathematical
Practices
2.OA.1. Use addition and
subtraction within 100 to
solve one- and two-step
word problems involving
situations of adding to,
taking from, putting
together, taking apart, and
comparing, with unknowns
in all positions, e.g., by
using drawings and
equations with a symbol for
the unknown number to
represent the problem.
1. Make sense of
problems and
persevere in
solving them.
CMT CONNECTIONS:
5,6,7,9
2. Reason
abstractly and
quantitatively.
3. Construct
viable arguments
and critique the
reasoning of
others.
4. Model with
mathematics.
5. Use
appropriate tools
strategically.
8. Look for and
express
regularity in
repeated
reasoning.
Explanations and Examples of Standard
Word problems that are connected to students’ lives can be used to develop fluency with
addition and subtraction. Table 1 describes the four different addition and subtraction
situations and their relationship to the position of the unknown.
Examples:
• Take-from example: David had 63 stickers. He gave 37 to Susan. How many
stickers does David have now? 63 – 37 =
• Add to example: David had $37. His grandpa gave him some money for his
birthday. Now he has $63. How much money did David’s grandpa give him? $37 +
= $63
• Compare example: David has 63 stickers. Susan has 37 stickers. How many more
stickers does David have than Susan? 63 – 37 = o Even though the modeling of the
two problems above is different, the equation, 63 - 37 = ?, can represent both
situations (How many more do I need to make 63?)
• Take-from (Start Unknown) David had some stickers. He gave 37 to Susan. Now
he has 26 stickers. How many stickers did David have before? - 37 = 26
It is important to attend to the difficulty level of the problem situations in relation to the
position of the unknown.
• Result Unknown problems are the least complex for students followed by Total
Unknown and Difference Unknown.
• The next level of difficulty includes Change Unknown, Addend Unknown,
followed by Bigger Unknown.
• The most difficult are Start Unknown, Both Addends Unknown, and Smaller
Unknown.
Second grade students should work on ALL problem types regardless of the level of difficulty.
Students can use interactive whiteboard or document camera to demonstrate and justify their
thinking.
This standard focuses on developing an algebraic representation of a word problem through
addition and subtraction --the intent is not to introduce traditional algorithms or rules.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Unit 1
Unit 3
Unit 9
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 1:
Lessons 9-10;
13-15; 20
T.E. Unit 3:
Overview 195K-O
Lessons 1-3; 5-7;
10-13
T.E. Unit 9:
Lessons 3-5
Minimum Required
Strategies
Count on Strategies for:
Addition:
 Count on from the
greater number
 Count on to find
the total
 Count on to find a
partner
Subtraction:
 Count on using
fingers to find the
partner
 Make a ten
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 10.02;11.10;
11.19; 11.20; 11.22
Mega Math:
Numberopolis:
Cross Town Number Line
Levels: B, F
Carnival Stories
Levels: O, Q
Shapes Ahoy:
Sea Cave Sorting Level: H
Country Countdown:
Block Busters Level: R
Destination:
Course II: Modules 1 & 2:
Unit 1:
 Sums Less than
100
 Differences within
100
 Comparing and
Ordering
 Expanded form
and equivalent
representations of
a number
Grade 2
8
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Operations and Algebraic Thinking
 Add and subtract within 20
Standards
Students will be able to:
Mathematical
Practices
2.OA.2. Fluently add and
1. Make sense of
subtract within 20 using mental problems and
strategies.
persevere in
solving them.
By end of Grade 2, know from
2. Reason
memory all sums of two oneabstractly and
digit numbers.
quantitatively.
CMT CONNECTIONS: 6
3. Construct viable
arguments and
critique the
reasoning of
others.
7. Look for and
make use of
structure.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Explanations and Examples of Standard
This standard is strongly connected to all the standards in this domain. It focuses
on students being able to fluently add and subtract numbers to 20. Adding and
subtracting fluently refers to knowledge of procedures, knowledge of when and
how to use them appropriately, and skill in performing them flexibly,
accurately, and efficiently.
Mental strategies help students make sense of number relationships as they are
adding and subtracting within 20. The ability to calculate mentally with
efficiency is very important for all students. Mental strategies may include the
following:
• Counting on
• Making tens (9 + 7 = 10 + 6)
• Decomposing a number leading to a ten
( 14 – 6 = 14 – 4 – 2 = 10 – 2 = 8)
• Fact families (8 + 5 = 13 is the same as 13 - 8 = 5)
• Doubles
• Doubles plus one (7 + 8 = 7 + 7 + 1)
However, the use of objects, diagrams, or interactive whiteboards, and various
strategies will help students develop fluency.
CT
Units of
Study
Unit 1
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 1:
Lessons 19-22
T.E. Unit 5:
Lesson 13
T.E. Unit 9:
Lessons 4-5; 8
T.E. Unit 11:
Lessons 14;19
Minimum Required
Strategies
Supporting
Technology Activities
Strategies :
 Partner Houses and
Math Mountains to show
break-aparts
 Show all totals
 Unknown partner
 Math Mountains
 Expanded method
 Ungroup first
method
 Quick draws
 Proof drawings
 Make a new ten
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 7.07; 10.13;
10.18; 10.19; 10.27; 11.19;
11.20; 11.27; 50.04; 50.05
Mega Math:
Numberopolis:
Carnival Stories, Levels H,M
Cross Town Number Line,
Level B
Country Countdown:
Counting Critters, Level R
Block Busters, Levels N,
R,W,X
White Water Graphing,
Levels D, E,F
Shapes Ahoy: Sea Cave
Sorting, Level H
Destination:
Course II: Modules 1,2;4:
Unit 1:
 Differences within
100
 Sums less than 100
 Number patterns
and properties
 Counting by
grouping
 Comparing and
ordering
Grade 2
9
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Operations and Algebraic Thinking
 Work with equal groups of objects to gain foundations for multiplication
Standards
Students will be able to:
2.OA.3. Determine whether a
group of objects (up to 20) has
an odd or even number of
members, e.g., by pairing
objects or counting them by
2s; write an equation to
express an even number as a
sum of two equal addends.
CMT CONNECTIONS: 1, 2,
6
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.
7. Look for and
make use of
structure.
Explanations and Examples of Standard
Students explore odd and even numbers in a variety of ways including the
following: students may investigate if a number is odd or even by determining if
the number of objects can be divided into two equal sets, arranged into pairs or
counted by twos. After the above experiences, students may derive that they
only need to look at the digit in the ones place to determine if a number is odd
or even since any number of tens will always split into two even groups
Example: Students need opportunities writing equations representing sums of
two equal addends, such as: 2 + 2 = 4, 3 + 3 = 6, 5 + 5 = 10, 6 + 6 = 12, or
8 + 8 =16.
This understanding will lay the foundation for multiplication and is closely
connected to 2.OA.4.
CT
Units of
Study
Unit 10
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 3:
Lesson 11
T.E. Unit 5
Lesson 7
Minimum Required
Strategies
Strategies for
Addition/Subtraction:
 Doubles plus1
 Doubles minus 1
 Make a ten
 Make pairs
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 10.15; 25.14;
Mega Math:
Numberopolis:
Cross Town Number Line,
Level L
Destination:
Course II: Modules 1:Unit 1:
 Counting by
Grouping
The use of objects and/or interactive whiteboards will help students develop
and demonstrate various strategies to determine even and odd numbers.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
10
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Operations and Algebraic Thinking
 Work with equal groups of objects to gain foundations for multiplication
Standards
Students will be able to:
2.OA.4. Use addition to find
the total number of objects
arranged in rectangular arrays
with up to 5 rows and up to 5
columns; write an equation to
express the total as a sum of
equal addends.
CMT CONNECTIONS: 5, 6,
22
Mathematical
Practices
1. Make sense of
problems and
persevere in
solving them.
Explanations and Examples of Standard
Students may arrange any set of objects into a rectangular array. Objects can be
cubes, buttons, counters, etc. Objects do not have to be square to make an
array. Geoboards can also be used to demonstrate rectangular arrays. Students
then write equations that represent the total as the sum of equal addends as
shown below.
2. Reason
abstractly and
quantitatively.
3, Construct viable
arguments and
critique the
reasoning of
others.
7. Look for and
make use of
structure.
4 + 4 + 4 = 12
5 + 5 + 5 + 5 = 20
CT
Units of
Study
Unit 10
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 13
Overview: 953J
Lesson 4
Minimum Required
Strategies
Strategies for Multiplication:
 Use fingers to show
each multiplier of
an equal group
 Use arrays to show
multiplication
 5’s count-bys
 Draw equal groups
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 12.20
Mega Math:
Numberopolis:
Cross Town Number Line,
Level Q
Destination:
Course II: Modules 2:Unit 2:
 Repeated Addition
and Arrays
Interactive whiteboards and document cameras may be used to help students
visualize and create arrays.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
11
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Understand place value.
Standards
Students will be able to:
2.NBT.1. Understand that the
three digits of a three-digit
number represent amounts of
hundreds, tens, and ones;
e.g., 706 equals 7 hundreds, 0
tens, and 6 ones. Understand
the following as special cases:
a. 100 can be thought of
as a bundle of ten
tens—called a
“hundred.”
b. The numbers 100,
200, 300, 400, 500,
600, 700, 800, 900
refer to one, two,
three, four, five, six,
seven, eight, or nine
hundreds (and 0 tens
and 0 ones).
CMT CONNECTIONS: 1, 2
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.
7. Look for and
make use of
structure.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Explanations and Examples of Standard
Understanding that 10 ones make one ten and that 10 tens make one hundred is
fundamental to students’ mathematical development. Students need multiple
opportunities counting and “bundling” groups of tens in first grade. In second
grade, students build on their understanding by making bundles of 100s with or
without leftovers using base ten blocks, cubes in towers of 10, ten frames, etc.
This emphasis on bundling hundreds will support students’ discovery of place
value patterns.
As students are representing the various amounts, it is important that emphasis
is placed on the language associated with the quantity. For example, 243 can be
expressed in multiple ways such as 2 groups of hundred, 4 groups of ten and 3
ones, as well as 24 tens and 3 ones. When students read numbers, they should
read in standard form as well as using place value concepts. For example, 243
should be read as “two hundred forty-three” as well as two hundreds, 4 tens, 3
ones.
A document camera or interactive whiteboard can also be used to demonstrate
“bundling” of objects. This gives students the opportunity to communicate their
thinking.
CT
Units of
Study
Unit 2
Unit 3
Unit 4
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
NBT.1.a. & 1.b.
T.E. Unit 5
Overview: 309L
Lessons 1-3
NBT.1.a. & 1.b.
T.E. Unit 11
Overview: 755L
Lesson 1
Minimum Required
Strategies
Strategies:
 Place Value
drawings (white
boards; freehand)
 Quick draws (tens
and circles)
 Quick draws
(hundreds)
 expanded for
 secret code cards
 Groups of ten
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 1.12;
2.13;26.15;
Mega Math:
Numberopolis:
Lulu’s Lunch Counter,
Level L
Country Countdown:
Block Busters, Level S
Counting Critters, Level E
Destination:
Course II: Modules 1:Unit 1:
 Place Value: Tens
and Ones
 Place Value:
Hundreds, Tens,
and Ones
Grade 2
12
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Understand place value.
Standards
Students will be able to:
2.NBT.2. Count within 1000;
skip-count by 5s, 10s, and
100s.
CMT CONNECTIONS: 1, 2,
5, 22
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.
7. Look for and
make use of
structure.
Explanations and Examples of Standard
Students need many opportunities counting, up to 1000, from different starting
points. They should also have many experiences skip counting by 5s, 10s, and
100s to develop the concept of place value.
Examples:



The use of the 100s chart may be helpful for students to identify the
counting patterns.
The use of money (nickels, dimes, dollars) or base ten blocks may be
helpful visual cues.
The use of an interactive whiteboard may also be used to develop
counting skills.
The ultimate goal for second graders is to be able to count in multiple ways with
no visual support.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Unit 2
Unit 8
Unit 10
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 5
Lesson 17
T.E. Unit 11
Lessons 1;3;7
T.E. Unit 13
Overview 953J
Lessons 4-5
Extension
Lesson 2
pgs. 1075-1078
Minimum Required
Strategies
Supporting
Technology Activities
Strategies:
 Math Mountains
 Forward/backward
sequences
 Place value draws
 Count bys: ones,
tens
 Partners of one
hundred
 Use fingers to show
each multiplier of
an equal group
 Use arrays to show
multiplication
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 2.13;2.15;3.10;
12.20;26.06;
Mega Math:
Country Countdown:
Block Busters, Level N
Counting Critters, Level W
Numberopolis:
Cross Town Number Line,
Levels O,P,Q
Lulu’s Lunch counter,
Levels K, L
Destination:
Course II: Modules 1,2,3:
Units 1;2:
 Sums less than 100
 Place Value:
Hundreds, tens
and ones
 Comparing and
ordering
 Money
 Repeated additions
and arrays
 Skip-Counting
to show
Multiplication
Grade 2
13
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
14
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Understand place value.
Standards
Students will be able to:
Mathematical
Practices
2.NBT.3. Read and write
numbers to 1000 using baseten numerals, number names,
and expanded form.
1. Make sense of
problems and
persevere in
solving them.
CMT CONNECTIONS: 1, 2,
22
2. Reason
abstractly and
quantitatively.
3. Construct viable
arguments and
critique the
reasoning of
others.
Explanations and Examples of Standard
Students need many opportunities reading and writing numerals in multiple
ways.
Base-ten numerals
Number names
Expanded form
637
(standard form)
six hundred thirty seven
(written form)
600 + 30 + 7
(expanded notation)
When students say the expanded form, it may sound like this: “6 hundreds plus
3 tens plus 7 ones” OR 600 plus 30 plus 7.”
7. Look for and
make use of
structure.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Unit 2
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 5
Lessons 1-3
Examples:



CT
Units of
Study
T.E. U nit 11
Lessons 1-3
Minimum Required
Strategies
Supporting
Technology Activities
Strategies:
 Place Value
drawings (quick
hundreds, tens,
ones)
 Expanded form
 Secret Code Cards
 Label quantities of
10
 Visualize 100
 Discuss numbers
greater than 100
 Count by Ones,
Tens
 Word names for
greater numbers
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 1.12; 2.13; 2.15;
26.15;
Mega Math:
Country Countdown:
Blocks Busters, Level S
Counting Critters, Level E
Numberopolis:
Lulu’s Lunch Counter, Level
L
Cross Town Number Line,
Level P
Destination:
Course II: Modules 1:
Units 1:
 Place Value: Tens
and Ones
 Place Value:
Hundreds, Tens,
and Ones
 Expanded form
and equivalent
representations of
a number
 Comparing and
Ordering
Grade 2
15
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Understand place value.
Standards
Students will be able to:
2.NBT.4. Compare two
three-digit numbers based on
meanings of the hundreds,
tens, and ones digits, using
>, =, and < symbols to
record the results of
comparisons.
CMT CONNECTIONS: 1, 2,
4
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.
Explanations and Examples of Standard
Students may use models, number lines, base ten blocks, interactive
whiteboards, document cameras, written words, and/or spoken words that
represent two three-digit numbers. To compare, students apply their
understanding of place value. They first attend to the numeral in the hundreds
place, then the numeral in tens place, then, if necessary, to the numeral in the
ones place.
Comparative language includes but is not limited to: more than, less than,
greater than, most, greatest, least, same as, equal to and not equal to. Students
use the appropriate symbols to record the comparisons.
CT
Units of
Study
Unit 2
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 11
Lesson 9
Minimum Required
Strategies
Strategies:
 Proof drawings
 Methods for adding
3-digit numbers:
 Show all totals
 New groups below
 New groups above
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 10.29
Mega Math:
Numberopolis:
Cross Town Number Line,
Level R
Destination:
Course II: Modules 4:
Unit 1:
 Number Patterns
and Properties
6. Attend to
precision.
7. Look for and
make use of
structure.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
16
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Use place value understanding and properties of operations to add and subtract.
Standards
Students will be able to:
2.NBT.5. Fluently add and
subtract within 100 using
strategies based on place value,
properties of operations,
and/or the relationship
between addition and
subtraction.
CMT CONNECTIONS: 1, 2,
6, 7
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.
7. Look for and
make use of
structure.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples of Standard
Adding and subtracting fluently refers to knowledge of procedures, knowledge
of when and how to use them appropriately, and skill in performing them
flexibly, accurately, and efficiently. Students should have experiences solving
problems written both horizontally and vertically. They need to communicate
their thinking and be able to justify their strategies both verbally and with paper
and pencil.
Addition strategies based on place value for 48 + 37 may include:
 Adding by place value: 40 + 30 = 70 and 8 + 7 = 15 and 70 + 15 =
85.
 Incremental adding (breaking one number into tens and ones); 48 + 10
= 58, 58 + 10 = 68, 68 + 10 = 78, 78 + 7 = 85
 Compensation (making a friendly number): 48 + 2 = 50, 37 – 2 =
35, 50 + 35 = 85
Subtraction strategies based on place value for 81 - 37 may include:
 Adding up (from smaller number to larger number): 37 + 3 = 40, 40
+ 40 = 80, 80 + 1 = 81, and 3 + 40 + 1 = 44.
 Incremental subtracting: 81 -10 = 71, 71 – 10 = 61, 61 – 10 = 51, 51
– 7 = 44
 Subtracting by place value: 81 – 30 = 51, 51 – 7 = 44
Properties that students should know and use are:
 Commutative property of addition (Example: 3 + 5 = 5 + 3)
 Associative property of addition (Example: (2 + 7) + 3 = 2 + (7+3) )
 Identity property of 0 (Example: 8 + 0 = 8)
Continued on next page….
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Unit 3
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 1
Lessons:3;6;15;2
2
T.E. Unit 4
Lesson 3
T.E. Unit 5
Lessons 4-5;9;11
T.E. Unit 9
Lessons 3-5;12
Minimum Required
Strategies
Strategies:
 Representations:
math drawings
 Exploring BreakAparts
 Switch partners
 Math mountains:
up to teen totals
 Make a ten
 Make a ten with a
friend to find an
unknown partner
 Add three
numbers: totals less
than/greater than
10
 Place value
drawings (white
boards, freehand)
 Expanded form
 Secret Code Cards
 The new ten
 New groups below
method: add the
Ones; add the Tens
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 1.09;10.04;
10.05; 10.13;10.19;10.20;
10.21; 10.23;10.24;
11.19;11.20; 11.22;35.22;
Mega Math:
Numberopolis:
Cross Town Number Line,
Levels D,P
Carnival Stories,
Levels N,P,Q
Country Countdown:
Counting Critters,
Levels G, R
Bock Busters, Levels M, R
Shapes Ahoy: Ship Shapes,
Levels H, K
Destination:
Course II: Modules 1,2;3:
Unit 1:
 Sums Less than
100
 Area
 Counting by
Grouping
 Estimating and
Finding Sums less
than 1,000
Grade 2
17
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
18
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Use place value understanding and properties of operations to add and subtract.
Standards
Students will be able to:
Mathematical
Practices
Explanations and Examples of Standard
Students in second grade need to communicate their understanding of why some
properties work for some operations and not for others.
 Commutative Property: In first grade, students investigated
whether the commutative property works with subtraction. The intent
was for students to recognize that taking 5 from 8 is not the same as
taking 8 from 5. Students should also understand that they will be
working with numbers in later grades that will allow them to subtract
larger numbers from smaller numbers. This exploration of the
commutative property continues in second grade.
 Associative Property: Recognizing that the associative property
does not work for subtraction is difficult for students to consider at this
grade level as it is challenging to determine all the possibilities.

Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Resources/
Lessons
Supporting
CT Standard(s)
Minimum Required
Strategies
Supporting
Technology Activities



Comparing and
Ordering
Differences with
100
Expanded Form
and Equivalent
representations of
a Number
Associative Property: Recognizing that the associative property does
not work for subtraction is difficult for students to consider at this
grade level as it is challenging to determine all the possibilities.
Grade 2
19
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Use place value understanding and properties of operations to add and subtract.
Standards
Students will be able to:
Mathematical
Practices
2.NBT.6. Add up to four twodigit numbers using strategies
based on place value and
properties of operations.
1. Make sense of
problems and
persevere in
solving them.
CMT CONNECTIONS: 1,5,
6,7,9
2. Reason
abstractly and
quantitatively.
Explanations and Examples of Standard
Students demonstrate addition strategies with up to four two-digit numbers
either with or without regrouping. Problems may be written in a story problem
format to help develop a stronger understanding of larger numbers and their
values. Interactive whiteboards and document cameras may also be used to
model and justify student thinking.
Unit 3
Math
Expressions
T.E. Unit 1
Lessons 3;6; 22
T.E. Unit 5
Lessons 14; 17
3. Construct viable
arguments and
critique the
reasoning of
others.
7. Look for and
make use of
structure.
Minimum Required
Strategies
Strategies:
 Representations
 Break-Aparts
 Using Partner
Houses and Math
Mountains to show
Break-Aparts
 Switch the Partners
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 10.04;10.05;
10.19; 26.06; 44.29
Mega Math:
Numberopolis:
Cross Town Number Line,
Level D
Country Countdown:
Counting Critters, Levels G,
R
Block Busters, Level N
Shapes Ahoy:
Made to Measure, Level H
Destination:
Course II: Modules1;2;3
Unit 1:
 Sums Less than
100
 Counting by
Grouping
 Area
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Resources/
Lessons
Supporting
CT
Standard(s)
Grade 2
20
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Use place value understanding and properties of operations to add and subtract.
Standards
Students will be able to:
2.NBT.7. Add and subtract
within 1000, 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.
Understand that in adding or
subtracting three-digit
numbers, one adds or subtracts
hundreds and hundreds, tens
and tens, ones and ones; and
sometimes it is necessary to
compose or decompose tens or
hundreds.
CMT CONNECTIONS: 1, 2,
6, 7
Mathematical
Practices
1. Make sense of
problems and
persevere in
solving them.
2. Reason
abstractly and
quantitatively.
Explanations and Examples of Standard
There is a strong connection between this standard and place value
understanding with addition and subtraction of smaller numbers. Students may
use concrete models or drawings to support their addition or subtraction of
larger numbers. Strategies are similar to those stated in 2.NBT.5, as students
extend their learning to include greater place values moving from tens to
hundreds to thousands. Interactive whiteboards and document cameras may also
be used to model and justify student thinking.
3. Construct viable
arguments and
critique the
reasoning of
others.
4. Model with
mathematics.
Unit 4
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 9
Lessons 7; 11;13
T.E. Unit 11
Lessons 8-10;
12-19
Minimum Required
Strategies
Supporting
Technology Activities
Strategies:
 Expanded method
 Ungroup First
Method
 Expanded Method:
Ungrouping left to
right/Ungrouping
right to left
 Secret Code Cards
 Adding up Method
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:3.16; 10.18;
10.24; 10.27; 10.29; 10.30;
11.23;27.11
Mega Math:
Country Countdown:
Block Buster, Levels L,U,W
Numberopolis:
Carnival Stories, Levels R
Lulu’s Lunch counter, Level
O
Cross Town Number Line,
Level R
Destination:
Course II: Modules 2;3;4
Unit 1:
 Estimating and
finding Differences
within 1,000
 Differences within
100 Story
Problems with
Addition and
Subtraction
 Money
 Number Patterns
and Properties
5. Use appropriate
tools strategically.
7. Look for and
make use of
structure.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Grade 2
21
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
22
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Use place value understanding and properties of operations to add and subtract.
Standards
Students will be able to:
2.NBT.8. Mentally add 10 or
100 to a given number 100–
900, and mentally subtract 10
or 100 from a given number
100–900.
CMT CONNECTIONS:
1,2,4, 6, 7, 22
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.
7. Look for and
make use of
structure.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Explanations and Examples of Standard
Students need many opportunities to practice mental math by adding and
subtracting multiples of 10 and 100 up to 900 using different starting points.
They can practice this by counting and thinking aloud, finding missing numbers
in a sequence, and finding missing numbers on a number line or hundreds
chart. Explorations should include looking for relevant patterns.
counting on; 300, 400, 500, etc.
counting back; 550, 450, 350, etc.
T.E. Unit 1
Lessons 14; 18
Extension
Lesson 2
pgs. 1074-1075
Examples:



Unit 4
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 9
Lesson 13
Mental math strategies may include:


CT
Units of
Study
100 more than 653 is _____ (753)
10 less than 87 is ______ (77)
“Start at 248. Count up by 10s until I tell you to stop.”
An interactive whiteboard or document camera may be used to help students
develop these mental math skills.
Minimum Required
Strategies
Strategies:
 Relate Math
Mountains to
equations and story
problems
 Finding totals and
partners
 Not equal to sign
 Equation chains
 Vertical/horizontal
forms
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 10.08;10.13;
10.24;12.13
Mega Math:
Country Countdown:
Blocks Busters, Levels C,L
Numberopolis:
Carnival Stories, Level N
Cross Town Number Line,
Level O
Destination:
Course II: Modules 2
Unit 1:
 Sums Less than
100
 Differences within
100
 Estimating and
Finding differences
within 1,000
 Skip-Counting
to Show
Multiplication
Grade 2
23
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Numbers and Operations in Base Ten
 Use place value understanding and properties of operations to add and subtract.
Standards
Students will be able to:
2.NBT.9. Explain why
addition and subtraction
strategies work, using place
value and the properties of
operations. (Explanations may
be supported by drawings or
objects.)
CMT CONNECTIONS:
1,2,6,7,9
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.
7. Look for and
make use of
structure.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Explanations and Examples of Standard
Students need multiple opportunities explaining their addition and subtraction
thinking. Operations embedded within a meaningful context promote
development of reasoning and justification.
Example:
Mason read 473 pages in June. He read 227 pages in July. How many pages did
Mason read altogether?
 Karla’s explanation: 473 + 227 = _____. I added the ones together
(3 + 7) and got 10. Then I added the tens together (70 + 20) and got
90. I knew that 400 + 200 was 600. So I added 10 + 90 for 100 and
added 100 + 600 and found out that Mason had read 700 pages
altogether.
 Debbie’s explanation: 473 + 227 = ______. I started by adding 200
to 473 and got 673. Then I added 20 to 673 and I got 693 and finally I
added 7 to 693 and I knew that Mason had read 700 pages altogether.
 Becky’s explanation: I used base ten blocks on a base ten mat to help
me solve this problem. I added 3 ones (units) plus 7 ones and got 10
ones which made one ten. I moved the 1 ten to the tens place. I then
added 7 tens rods plus 2 tens rods plus 1 tens rod and got 10 tens or
100. I moved the 1 hundred to the hundreds place. Then I added 4
hundreds plus 2 hundreds plus 1 hundred and got 7 hundreds or 700.
So Mason read 700 books.
Students should be able to connect different representations and explain the
connections. Representations can include numbers, words (including
mathematical language), pictures, number lines, and/or physical objects.
Students should be able to use any/all of these representations as needed.
An interactive whiteboard or document camera can be used to help students
develop and explain their thinking.
CT
Units of
Study
Unit 1
Unit 3
Unit 4
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 5
Lessons 9-11
T.E. Unit 9
Lessons 5- 6;
8;13;15
T.E. Unit 11
Lessons 10;14
Minimum Required
Strategies
Supporting
Technology Activities
Strategies:
 Make a new ten,
hundred
 Show all totals
method with proof
drawings: add the
tens; add the ones;
find the tens total;
find the ones total
 Totals less/greater
than 100
 Expanded method
 Ungroup first
method
 Good thinkers and
Justifications
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:10.09;10.18
10.21; 10.24; 11.19; 11.22;
11.24;11.27
Mega Math:
Numberopolis:
Carnival Stories, Levels P,R
Country Countdown:
Block Busters, Levels
L,M,R,Q, X
Destination:
Course II: Modules 2;4
Unit 1:
 Estimating and
Finding Sums less
than 1,000
 Number Patterns
and Properties
 Sums Less than
100
 Expanded form
and Equivalent
Representations of
a Number
Grade 2
24
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Measure and estimate lengths in standard units.
Standards
Students are expected to:
2.MD.1. Measure the length of
an object by selecting and using
appropriate tools such as
rulers, yardsticks, meter sticks,
and measuring tapes.
CMT CONNECTIONS: 15,
16
Mathematical
Practices
1. Make sense of
problems and
persevere in
solving them.
3. Construct viable
arguments and
critique the
reasoning of
others.
Explanations and Examples of Standard
Students in second grade will build upon what they learned in first grade from
measuring length with non-standard units to the new skill of measuring length
in metric and U.S. Customary with standard units of measure. They should
have many experiences measuring the length of objects with rulers, yardsticks,
meter sticks, and tape measures. They will need to be taught how to actually
use a ruler appropriately to measure the length of an object especially as to
where to begin the measuring. Do you start at the end of the ruler or at the
zero?
5. Use appropriate
tools strategically.
CT
Units of
Study
Unit 7
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 14
Lessons 2-3
Minimum Required
Strategies
Strategies:
 Make an inch ruler;
yard stick
 Measure to the
nearest inch
 Estimate and
measure
 Use appropriate
measurement tools
Supporting
Technology Activities
www.thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:38.15;40.06
Mega Math:
Shapes Ahoy:
Made to Measure, Level F
Country Countdown:
Harrison’s Comparisons,
Level E
Destination:
Course II: Modules 3
Unit 1:
 Area
6. Attend to
precision.
7. Look for and
make use of
structure.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
25
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Measure and estimate lengths in standard units.
Standards
Students will be able to:
2.MD.2. Measure the length of
an object twice, using length
units of different lengths for
the two measurements;
describe how the two
measurements relate to the size
of the unit chosen.
CMT CONNECTIONS: 6,
15, 16
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.
5. Use appropriate
tools strategically.
Explanations and Examples of Standard
Students need multiple opportunities to measure using different units of
measure. They should not be limited to measuring within the same standard
unit. Students should have access to tools, both U.S.Customary and metric. The
more students work with a specific unit of measure, the better they become at
choosing the appropriate tool when measuring.
Students measure the length of the same object using different tools (ruler with
inches, ruler with centimeters, a yardstick, or meter stick). This will help
students learn which tool is more appropriate for measuring a given object.
They describe the relationship between the size of the measurement unit and
the number of units needed to measure something. For instance, a student
might say, “The longer the unit, the fewer I need.” Multiple opportunities to
explore provide the foundation for relating metric units to customary units, as
well as relating within customary (inches to feet to yards) and within metric
(centimeters to meters).
CT
Units of
Study
Unit 7
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 14
Lessons 1-2
Minimum Required
Strategies
Strategies:
 Explore nonstandards units of
length
 Count the total
number of units
 Compare nonstandards units of
length to standard
units of length
 Estimate and
measure
 Use appropriate
measurement tools
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:38.15;39.08;
Mega Math:
Shapes Ahoy:
Made to Measure,
Levels D, F
Destination:
Course II: Modules 3
Unit 1:
 Area
6. Attend to
precision.
7. Look for and
make use of
structure.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
26
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Measure and estimate lengths in standard units.
Standards
Students will be able to:
2.MD.3. Estimate lengths
using units of inches, feet,
centimeters, and meters.
CMT CONNECTIONS: 6,
15, 16
Mathematical
Practices
1. Make sense of
problems and
persevere in
solving them.
3. Construct viable
arguments and
critique the
reasoning of
others.
5. Use appropriate
tools strategically.
Explanations and Examples of Standard
Estimation helps develop familiarity with the specific unit of measure being
used. To measure the length of a shoe, knowledge of an inch or a centimeter is
important so that one can approximate the length in inches or centimeters.
Students should begin practicing estimation with items which are familiar to
them (length of desk, pencil, favorite book, etc.).
Some useful benchmarks for measurement are:
 First joint to the tip of a thumb is about an inch
 Length from your elbow to your wrist is about a foot
 If your arm is held out perpendicular to your body, the length from
your nose to the tip of your fingers is about a yard
6. Attend to
precision.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Unit 7
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 8
Lesson 2
T.E. Unit 12
Lessons 1-2
T.E. Unit 14
Lesson 2
Minimum Required
Strategies
Strategies:
 Finding midpoints
of a line segment
 Use doubles to
compute
numerically
 Marking and
counting lengths
 Estimating and
checking
 Folding
 Make and use
appropriate tools of
measurement
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:37.04; 38.09;
38.14; 38.15
Mega Math:
Shapes Ahoy:
Shapes, Level J
Made to Measure, Level F,I
Destination:
Course II: Module 3:
Unit 1:
 Area
Grade 2
27
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Measure and estimate lengths in standard units.
Standards
Students will be able to:
2.MD.4. Measure to
determine how much longer
one object is than another,
expressing the length
difference in terms of a
standard length unit.
CTM CONNECTIONS: 15,
16
Mathematical
Practices
1. Make sense of
problems and
persevere in
solving them.
3. Construct viable
arguments and
critique the
reasoning of
others.
Explanations and Examples of Standard
Second graders should be familiar enough with inches, feet, yards, centimeters,
and meters to be able to compare the differences in lengths of two objects.
They can make direct comparisons by measuring the difference in length
between two objects by laying them side by side and selecting an appropriate
standard length unit of measure. Students should use comparative phrases such
as “It is longer by 2 inches” or “It is shorter by 5 centimeters” to describe the
difference between two objects. An interactive whiteboard or document
camera may be used to help students develop and demonstrate their thinking.
5. Use appropriate
tools strategically.
6. Attend to
precision.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Unit 7
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 12
Lesson 1
T.E. Unit 14
Lesson 2
Minimum Required
Strategies
Strategies:
 Make and use
appropriate
measurement tool
(inch ruler, yard
stick meter stick)
 Compare metric
system to monetary
systems
 Estimate and
measure
 Create questions
based on collected
data
 Select appropriate
unit of measure for
precise
measurement
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:38.09; 38.15
Mega Math:
Shapes Ahoy:
Made to Measure, Level F,I
Destination:
Course II: Modules 3
Unit 1:
 Area
Grade 2
28
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Relate addition and subtraction to length.
Standards
Students will be able to:
2.MD.5. Use addition and
subtraction within 100 to solve
word problems involving
lengths that are given in the
same units, e.g., by using
drawings (such as drawings of
rulers) and equations with a
symbol for the unknown
number to represent the
problem.
CMT CONNECTIONS:
6,7,9,15, 16, 23
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.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Explanations and Examples of Standard
Students need experience working with addition and subtraction to solve word
problems which include measures of length. It is important that word problems
stay within the same unit of measure. Counting on and/or counting back on a
number line will help tie this concept to previous knowledge. Some
representations students can use include drawings, rulers, pictures, and/or
physical objects. An interactive whiteboard or document camera may be used to
help students develop and demonstrate their thinking.
Equations include:
 20 + 35 = c
 c - 20 = 35
 c – 35 = 20
 20 + b = 55
 35 + a = 55
 55 = a + 35
 55 = 20 + b
CT
Units of
Study
Unit 3
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 1
Lesson 20
T.E. Unit 2
Lesson3
T.E. Unit 5
Lesson 14
T. E. Unit 9
Lesson 11
T. E. Unit 11
Lesson 19
Example:
 A word problem for 5 – n = 2 could be: Mary is making a dress. She has
5 yards of fabric. She uses some of the fabric and has 2 yards left. How
many yards did Mary use?
There is a strong connection between this standard and demonstrating fluency
of addition and subtraction facts. Addition facts through 10 + 10 and the related
subtraction facts should be included.
T.E. Unit 12
Lesson 1
T. E. Unit 14
Lesson 2
Minimum Required
Strategies
Supporting
Technology Activities
Strategies:
 Using Partner
Houses and Math
Mountains to show
Break-Aparts
 Unknown partners
 Unknown totals
 Label squares and
rectangles
 Count the lengths
 Find totals
 Make a new ten
 Proof drawings
 Good thinkers and
Justifications
 Rounding
 Ungroup first
method/expanded
for subtraction
 New groups
below/above
 Make and use
appropriate tools of
measurement
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 10.13; 10.27;
27.11; 38.09; 38.15;44.27;
44.29;
Mega Math:
Numberopolis:
Carnival Stories, Level M,R
Shapes Ahoy:
Made to Measure,
Level F, H,I
Country Countdown:
Block Busters, Level W
Destination:
Course II: Modules 2,3
Unit 1:
 Sums Less than
100
 Area
 Differences within
100
 Estimating and
Finding
Differences within
1,000
Grade 2
29
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Relate addition and subtraction to length.
Standards
Students will be able to:
2.MD.6. Represent whole
numbers as lengths from 0 on a
number line diagram with
equally spaced points
corresponding to the numbers
0, 1, 2, …, and represent
whole-number sums and
differences within 100 on a
number line diagram.
CMT CONNECTIONS: 4, 6,
7, 10
Mathematical
Practices
Explanations and Examples of Standard
1. Make sense of
problems and
persevere in
solving them.
Students represent their thinking when adding and subtracting within 100 by
using a number line. An interactive whiteboard or document camera can be
used to help students demonstrate their thinking.
2. Reason
abstractly and
quantitatively.
Example: 10 – 6 = 4
Unit 3
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 1
Lesson 17
T.E. Unit 5
Overview:
Pg. 309H
Lessons 5; 11
3. Construct viable
arguments and
critique the
reasoning of
others.
T.E. Unit 9
Lesson 6
Daily Routine pg.
xxv Vol. 1
4. Model with
mathematics.
5. Use appropriate
tools strategically.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Minimum Required
Strategies
Strategies:
 Counting on to
add/subtract: use
of number paths,
number lines,
 Make a new ten
 Secret Code Cards
 Quick draws of
tens/ones
 Unknown partners
for teen totals
 New groups
below/above
method: addition/
subtraction
 Estimating sums:
rounding
 Number Flashes
 Using the Math
Board
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:10.02; 10.21;
10.23;11.19
Mega Math:
Numberopolis:
Cross Town Number Line,
Level F, P
Carnival Stories, Level Q
Country Countdown:
Block Busters, Level M
Destination:
Course II: Modules 2
Unit 1:
 Sums Less than
100
 Counting by
Grouping
 Estimating and
Finding
Differences within
1,000
Grade 2
30
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Work with time and money.
Standards
Students will be able to:
Mathematical
Practices
2.MD.7. Tell and write time
from analog and digital clocks
to the nearest five minutes,
using a.m. and p.m.
1. Make sense of
problems and
persevere in
solving them.
CMT CONNECTIONS: 6, 14
3. Construct viable
arguments and
critique the
reasoning of
others.
5. Use appropriate
tools strategically.
Explanations and Examples of Standard
In first grade, students learned to tell time to the nearest hour and half-hour.
Students build on this understanding in second grade by skip-counting by 5 to
recognize 5-minute intervals on the clock. They need exposure to both digital
and analog clocks. It is important that they can recognize time in both formats
and communicate their understanding of time using both numbers and
language. Common time phrases include the following: quarter till ___,
quarter after ___, ten till ___, ten after ___, and half past ___.
Students should understand that there are 2 cycles of 12 hours in a day - a.m.
and p.m. Recording their daily actions in a journal would be helpful for making
real-world connections and understanding the difference between these two
cycles. An interactive whiteboard or document camera may be used to help
students demonstrate their thinking.
6. Attend to
precision.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Unit 8
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 6
Lessons 1-3
Daily Routine
Telling Time
Pg. xxv-xxvi Vol. 2
Minimum Required
Strategies
Strategies:
 Discuss
functions/features
of clocks:
analog/digital
 Make appropriate
tools: clocks
 Tell/write time to
the hour
 Math Boards
 Counting by 5s
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:48.08; 48.13
Mega Math:
Country Countdown: ClockaDoodle-Doo,
Level B,H, I
Destination:
Course II: Modules 3;
Unit 2:
 Time
Grade 2
31
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Work with time and money.
Standards
Students will be able to:
2.MD.8. Solve word problems
involving dollar bills, quarters,
dimes, nickels, and pennies,
using $ and ¢ symbols
appropriately.
Example: If you have 2 dimes and
3 pennies, how many cents do you
have?
CMT CONNECTIONS:1, 2
,9 ,11
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.
Explanations and Examples of Standard
Since money is not specifically addressed in kindergarten, first grade, or third
grade, students should have multiple opportunities to identify, count, recognize,
and use coins and bills in and out of context. They should also experience
making equivalent amounts using both coins and bills. “Dollar bills” should
include denominations up to one hundred ($1.00, $5.00, $10.00, $20.00,
$100.00).
Students should solve story problems connecting the different representations.
These representations may include objects, pictures, charts, tables, words,
and/or numbers. Students should communicate their mathematical thinking and
justify their answers. An interactive whiteboard or document camera may be
used to help students demonstrate and justify their thinking.
Example:
 Sandra went to the store and received $ 0.76 in change. What are three
different sets of coins she could have received?
5. Use appropriate
tools strategically.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Unit 5
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 5
Lessons 7; 20
T.E. Unit 9
Lessons 10; 15
T.E. Unit 11
Lessons 7-8;11;
16; 22
Minimum Required
Strategies
Supporting
Technology Activities
Strategies:
 Make pairs
 Sort odd/even
 Make/check
predictions
 Make/test/check
mathematical
statements
 Decimal notation
for money
 Unknown partners
 Add up from a
partner
 Partners of one
hundred
 Math mountains
 Secret code Cards
 Quick draws of
hundreds, tens,
ones
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:2.13;3.10; 3.15;
3.16; 3.17; 10.31; 11.222;
25.14; 27.21;
Mega Math:
Numberopolis:
Cross Town Number Line,
Level L
Lulu’s Lunch counter, Level
K,O,Q,S,T
Country Countdown:
Block Busters, Level M,R
Destination:
Course II: Modules 1,2,3
Unit 1,2:
 Counting by
Grouping
 Differences within
100
 Money
 Estimating and
Finding Sums less
than 1,000
Grade 2
32
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Represent and interpret data.
Standards
Students will be able to:
2.MD.9. Generate
measurement data by
measuring lengths of several
objects to the nearest whole
unit, or by making repeated
measurements of the same
object. Show the
measurements by making a line
plot, where the horizontal
scale is marked off in wholenumber units.
CMT CONNECTIONS:
4,15,19,20
Mathematical
Practices
1. Make sense of
problems and
persevere in
solving them.
3. Construct viable
arguments and
critique the
reasoning of
others.
Explanations and Examples of Standard
This standard emphasizes representing data using a line plot. Students will use
the measurement skills learned in earlier standards to measure objects. Line
plots are first introduced in this grade level. A line plot can be thought of as
plotting data on a number line. An interactive whiteboard may be used to create
and/or model line plots.
CT
Units of
Study
Unit 9
Resources/
Lessons
Supporting
CT Standard(s)
No Math
Expression
Resource Match
Linear Plot
PowerPoint
Lesson
Data, Frequency
Table and Line
Plot PowerPoint
Lesson
4. Model with
mathematics.
Minimum Required
Strategies
Strategies:
 Counting on to
add/subtract: use
of number paths,
number lines
 Use of number
lines to plot and
analyze data.
Supporting
Technology Activities
Thinkcentral.com
No Resource available
through ThinkCentral
Matching Data
Line Plots Lesson
5. Use appropriate
tools strategically.
6. Attend to
precision.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
33
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Measurement and Data (MD)
 Represent and interpret data.
Standards
Students will be able to:
2.MD.10. Draw a picture
graph and a bar graph (with
single-unit scale) to
represent a data set with up
to four categories. Solve
simple put-together, takeapart, and compare
problems using information
presented in a bar graph.
(See Table 1.)
CMT CONNECTIONS:
19, 20
Mathematical
Practices
1. Make sense of
problems and
persevere in
solving them.
2. Reason
abstractly and
quantitatively.
Explanations and Examples of Standard
Students should draw both picture and bar graphs representing data that can be
sorted up to four categories using single unit scales (e.g., scales should count by
ones). The data should be used to solve put together, take-apart, and compare
problems as listed in Table 1.
In second grade, picture graphs (pictographs) include symbols that represent single
units. Pictographs should include a title, categories, category label, key, and data.
3. Construct
viable arguments
and critique the
reasoning of
others.
4. Model with
mathematics.
Second graders should draw both horizontal and vertical bar graphs. Bar graphs
include a title, scale, scale label, categories, category label, and data.
CT
Units of
Study
Unit 9
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 7
Lessons 8-10;12
Minimum Required
Strategies
Strategies:
 Use of Math boards
 Convert Picture
Graph into a Bar
Graph
 Create a data table
 Good thinkers and
Justifications
 Generate and solve
problems based on
a given circle graph
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:50.05;51.06;
51.08; 51.17
Mega Math:
Country Countdown
White Water Graphing,
Level E,F,G
Destination:
Course II: Modules 1;
Unit 1:
 Comparing and
Ordering
5. Use appropriate
tools strategically.
6. Attend to
precision.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
34
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Geometry (G)
 Reason with shapes and their attributes.
Standards
Students will be able to:
Mathematical
Practices
2.G.1. Recognize and draw
shapes having specified
attributes, such as a given
number of angles or a given
number of equal faces.
Identify triangles,
quadrilaterals, pentagons,
hexagons, and cubes. (Sizes
are compared directly or
visually, not compared by
measuring.)
2.MP.4. Model
with mathematics.
2.MP.7. Look for
and make use of
structure.
Explanations and Examples of Standard
Students identify, describe, and draw triangles, quadrilaterals, pentagons, and
hexagons. Pentagons, triangles, and hexagons should appear as both regular (equal
sides and equal angles) and irregular. Students recognize all four sided shapes as
quadrilaterals. Students use the vocabulary word “angle” in place of “corner” but
they do not need to name angle types. Interactive whiteboards and document
cameras may be used to help identify shapes and their attributes. Shapes should be
presented in a variety of orientations and configurations.
CT
Units of
Study
Unit 6
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 2
Lessons 2;4
T.E. Unit 4
Lessons 1-3
T.E. Unit 5
Overview:
pg. 309H
Lessons 14; 1920
CMT CONNECTIONS:
17, 24
T.E. Unit 7
Lessons 5; 16
T.E. Unit 8
Overview:
pg.585D
Lessons 1-2
T.E. Unit 12
Lessons 5;6
T.E. Unit 13
Lesson 9
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Minimum Required
Strategies
Strategies:
 Label squares and
rectangles
 Count the lengths
 Use of Math Boards
 Estimation:
rounding lengths
 Use of appropriate
measurement tools
 Number paths
 Sorting/Identifying
 Quadrilaterals
 Math Mountains
 More than one ten
 Make/check
predictions
 Make/test/check
mathematical
statements
 Construct tables
for comparisons
 Find/connect
midpoints of line
segments
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
WarmUp:5.07;25.11;27.21;
35.07; 35.12; 35.22; 35.31;
36.19;36.21;37.04; 44.27;
44.29;50.04;57.02
Mega Math:
Shapes Ahoy:
Shapes Ahoy, Level E,G,H
Made to Measure, Level H
Ship Shapes,
Level G,I,J,K,Q
Undersea 3D, Level E,H
Country Countdown:
Block Busters, Level R
White Water Graphing,
Level E
Numberopolis:
Wash ‘n Spin, Level C
Destination:
Course II: Modules 2;3;4;
Unit 1:

Area/Volume

Number Patterns and
Properties

Differences within
100

Comparing and
Ordering

Fractional Parts
Grade 2
35
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Geometry (G)
 Reason with shapes and their attributes.
Standards
Students will be able to:
2.G.2. Partition a rectangle
into rows and columns of
same-size squares and count
to find the total number of
them.
CMT CONNECTIONS: 5,
6
Mathematical
Practices
2. Reason
abstractly and
quantitatively.
6. Attend to
precision.
Explanations and Examples of Standard
This standard is a precursor to learning about the area of a rectangle and using
arrays for multiplication. An interactive whiteboard or manipulatives such as
square tiles, cubes, or other square shaped objects can be used to help students’
partition rectangles.
Rows are horizontal and columns are vertical.
8. Look for and
express regularity
in repeated
reasoning.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
CT
Units of
Study
Unit 10
Resources/
Lessons
Supporting
CT Standard(s)
Math
Expressions
T.E. Unit 10
Lesson 5
Minimum Required
Strategies
Strategies:
 Find area by
covering and
counting of
nonstandard square
units
 Estimation
 Use of appropriate
measuring tools
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up: 37.20
Mega Math:
Shapes Ahoy:
Ship Shapes, Level X
Destination:
Course II: Modules 3
Unit 1:
 Area
Grade 2
36
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Geometry (G)
 Reason with shapes and their attributes.
Standards
Students will be able to:
2.G.3. Partition circles and
rectangles into two, three, or
four equal shares, describe the
shares using the words halves,
thirds, half of, a third of, etc.,
and describe the whole as two
halves, three thirds, four
fourths. Recognize that equal
shares of identical wholes need
not have the same shape.
CMT CONNECTIONS:
2,5,6, 8
Mathematical
Practices
2. Reason
abstractly and
quantitatively.
3. Construct viable
arguments and
critique the
reasoning of
others.
Explanations and Examples of Standard
This standard introduces fractions in an area model. Students need experiences
with different sizes, circles, and rectangles. For example, students should
recognize that when they cut a circle into three equal pieces, each piece will
equal one third of its original whole. In this case, students should describe the
whole as three thirds. If a circle is cut into four equal pieces, each piece will
equal one fourth of its original whole and the whole is described as four fourths.
CT
Units of
Study
Resources/
Lessons
Supporting
CT Standard(s)
Unit 6
Unit 8
Math
Expressions
T.E. Unit 13
Lesson 9
Fraction Lesson
13 Ways to Make
a Half Lesson
6. Attend to
precision.
8. Look for and
express regularity
in repeated
reasoning.
Students should see circles and rectangles partitioned in multiple ways so they
learn to recognize that equal shares can be different shapes within the same
whole. An interactive whiteboard may be used to show partitions of shapes.
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Minimum Required
Strategies
Strategies:
 Partition different
basic 2D shapes into
equal parts in as
many different
ways as possible.
 Emphasize the fact
that the partitions
look different but
they are equal.
 Utilize
manipulative and
hands on activities.
 Help students
prove that the equal
shares can have
different shapes.
Supporting
Technology Activities
Thinkcentral.com
Soar to Success:
RTI: Tiers 2 and 3
Warm Up:5.07
Mega Math:
Shapes Ahoy:
Ship Shapes, Level Q
Destination:
Course II: Modules 2
Unit 3:
 Fractional Parts
PBS Kids
http://pbskids.org/cyber
chase/games/fractions/in
dex.html
Grade 2
37
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Table 1. Common addition and subtraction situations.6
Add to
Take from
Put Together / Take
Apart2
Compare3
Result Unknown
Two bunnies sat on the grass. Three more bunnies
hopped there. How many bunnies are on the grass now?
2+3=?
Five apples were on the table. I ate two apples. How
many apples are on the table now?
5–2=?
Total Unknown
Three red apples and two green apples are on the table.
How many apples are on the table?
3+2=?
Change Unknown
Two bunnies were sitting on the grass. Some more bunnies
hopped there. Then there were five bunnies. How many bunnies
hopped over to the first two?
2+?=5
Five apples were on the table. I ate some apples. Then there were
three apples. How many apples did I eat?
5–?=3
Addend Unknown
Five apples are on the table. Three are red and the rest are green.
How many apples are green?
3 + ? = 5, 5 – 3 = ?
Difference Unknown
(“How many more?” version):
Lucy has two apples. Julie has five apples. How many
more apples does Julie have than Lucy?
Bigger Unknown
(Version with “more”):
Julie has three more apples than Lucy. Lucy has two apples. How
many apples does Julie have?
Start Unknown
Some bunnies were sitting on the grass. Three more bunnies hopped
there. Then there were five bunnies. How many bunnies were on the
grass before?
?+3=5
Some apples were on the table. I ate two apples. Then there were
three apples. How many apples were on the table before?
?–2=3
Both Addends Unknown1
Grandma has five flowers. How many can she put in her red vase and
how many in her blue vase?
5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 = 4 + 1
5 = 2 + 3, 5 = 3 + 2
Smaller Unknown
(Version with “more”):
Julie has three more apples than Lucy. Julie has five apples. How many
apples does Lucy have?
(“How many fewer?” version):
Lucy has two apples. Julie has five apples. How many
fewer apples does Lucy have than Julie?
2 + ? = 5, 5 – 2 = ?
(Version with “fewer”):
Lucy has 3 fewer apples than Julie. Lucy has two apples. How
many apples does Julie have?
2 + 3 = ?, 3 + 2 = ?
(Version with “fewer”):
Lucy has 3 fewer apples than Julie. Julie has five apples. How many
apples does Lucy have?
5 – 3 = ?, ? + 3 = 5
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
38
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
CMT Connections:
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
39
Waterbury Public Schools Mathematics Standards Articulated by Grade Level
Grade 2
Explanations and Examples adopted from
Arizona Department of Education: Standards and Assessment Division
Grade 2
40