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```							                                                               Grade 2 Overview
Operations and Algebraic Thinking (OA)                                          Mathematical Practices (MP)
 Represent and solve problems involving addition and                        1. Make sense of problems and persevere in solving them.
subtraction. (1*)                                                        2. Reason abstractly and quantitatively.
 Add and subtract within 20. (2)                                            3. Construct viable arguments and critique the reasoning of others.
 Work with equal groups of objects to gain foundations for                  4. Model with mathematics.
multiplication. (3, 4)                                                   5. Use appropriate tools strategically.
6. Attend to precision.
Number and Operations in Base Ten (NBT)                                         7. Look for and make use of structure.
 Understand place value. (1, 2, 3, 4)                                       8. Look for and express regularity in repeated reasoning.
 Use place value understanding and properties of operations to
add and subtract. (5, 6, 7, 8, 9)

Measurement and Data (MD)
 Measure and estimate lengths in standard units. (1, 2, 3, 4)
 Relate addition and subtraction to length. (5, 6)
 Work with time and money. (7, 8)
 Represent and interpret data. (9, 10)

Geometry (G)
 Reason with shapes and their attributes. (1, 2, 3)
*Numbers following cluster heading indicate standards included in the cluster.

Tucson Unified School District                                                                                                       Grade 2
Mathematics Curriculum                                                                                              Board Approved 03/27/2012
1
In Grade 2, instructional time should focus on four critical areas: (1) extending understanding of base-ten notation; (2) building fluency with
addition and subtraction; (3) using standard units of measure; and (4) describing and analyzing shapes.

(1) 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) 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 generalizable
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) 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 an iteration of units. They recognize that the smaller the unit, the more iterations they need to cover a
given length.

(4) 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 area, volume, congruence, similarity, and symmetry in later grades.

Tucson Unified School District                                                                                                          Grade 2
Mathematics Curriculum                                                                                                 Board Approved 03/27/2012
2
Standards for Mathematical Practice
Standards                                                    Explanations and Examples
Students are expected to:    Mathematical Practices are
level document in the 2nd
column to reflect the need to
connect the mathematical
practices to mathematical
content in instruction.
2.MP.1. Make sense of                                        In second grade, students realize that doing mathematics involves solving problems and
problems and persevere in                                    discussing how they solved them. Students explain to themselves the meaning of a problem and
solving them.                                                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.
2.MP.2. Reason abstractly                                    Younger students recognize that a number represents a specific quantity. They connect the
and quantitatively.                                          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.
2.MP.3. Construct viable                                     Second graders may construct arguments using concrete referents, such as objects, pictures,
arguments and critique the                                   drawings, and actions. They practice their mathematical communication skills as they participate
reasoning of others.                                         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.
2.MP.4. Model with                                           In early grades, students experiment with representing problem situations in multiple ways
mathematics.                                                 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.
2.MP.5. Use appropriate                                      In second grade, students consider the available tools (including estimation) when solving a
tools strategically.                                         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.
2.MP.6. Attend to                                            As children begin to develop their mathematical communication skills, they try to use clear and
precision.                                                   precise language in their discussions with others and when they explain their own reasoning.
2.MP.7. Look for and make                                    Second graders look for patterns. For instance, they adopt mental math strategies based on
use of structure.                                            patterns (making ten, fact families, doubles).

Tucson Unified School District                                                                                                       Grade 2
Mathematics Curriculum                                                                                              Board Approved 03/27/2012
3
Standards for Mathematical Practice
Standards                                                   Explanations and Examples
Students are expected to:   Mathematical Practices are
level document in the 2nd
column to reflect the need to
connect the mathematical
practices to mathematical
content in instruction.
2.MP.8. Look for and                                        Students notice repetitive actions in counting and computation, etc. When children have multiple
express regularity in                                       opportunities to add and subtract, they look for shortcuts, such as rounding up and then
repeated reasoning.                                         adjusting the answer to compensate for the rounding. Students continually check their work by
asking themselves, “Does this make sense?”

Tucson Unified School District                                                                                                     Grade 2
Mathematics Curriculum                                                                                            Board Approved 03/27/2012
4
Operations and Algebraic Thinking (OA) (3 Clusters)
2.OA Represent and solve problems involving addition and subtraction (Cluster 1- Standard 1)
Essential Concepts                                       Essential Questions
 Addition and subtraction situations can be: add-to, take-from, put-              How are addition and subtraction related?
together/take apart, and compare (see Table 1).                                  What kinds of problems can be modeled and solved using addition
 Some addition and subtraction problems may require two-steps to                   and/or subtraction?
solve.                                                                           When does the order of the numbers matter when you solve
 The unknown can be represented algebraically with a symbol (a box, a              contextual problems? Why?
blank, or a question mark, NOT a letter at this grade level) and                 How might different strategies be helpful when solving a problem?
pictorially to solve all types of addition and subtraction situations.           Will the end result be more or less than the amount you started with?
 The position of the unknown can change creating easier and more                  How does your model represent your mathematical thinking?
difficult problem types.                                                         How does your equation represent your mathematical thinking?
 Students’ modeling of story problems helps them figure out what
operation is involved in a problem, regardless of the size of the
numbers.
 Estimating is an important tool to determine the reasonableness of an
2.OA.1
Standard 2.OA.1                  Mathematical        Examples & Explanations
Use addition and subtraction     Practices           Word problems that are connected to students’ lives can be used to develop fluency with addition
within 100 to solve one- and     2.MP.1. Make        and subtraction. Table 1 describes the four different addition and subtraction situations and their
two-step word problems           sense of problems   relationship to the position of the unknown.
involving situations of adding   and persevere in
to, taking from, putting         solving them.       Examples:
together, taking apart, and                              Take From example: David had 63 stickers. He gave 37 to Susan. How many stickers does
comparing, with unknowns in      2.MP.2. Reason            David have now? 63 – 37 =
all positions, e.g., by using    abstractly and          Add To example: David had \$37. His grandpa gave him some money for his birthday. Now
drawings and equations with      quantitatively.           he has \$63. How much money did David’s grandpa give him? \$37 +          = \$63
a symbol for the unknown                                 Compare example: David has 63 stickers. Susan has 37 stickers. How many more stickers
number to represent the          2.MP.3. Construct         does David have than Susan? 63 – 37 =
problem. (See Table 1.)          viable arguments              o Even though the modeling of the two problems above is different, the equation, 63
and critique the                  - 37 = ?, can represent both situations (How many more do I need to make 63?)
Connections: 2.NBT.5; 2.RI.3;    reasoning of            Take From (Start Unknown) David had some stickers. He gave 37 to Susan. Now he has
2.RI.4; 2.SL.2; ET02-S2C1-       others.                   26 stickers. How many stickers did David have before?      - 37 = 26
01a
2.MP.4. Model       It is important to attend to the difficulty level of the problem situations in relation to the position of
with mathematics.   the unknown.
Continued on next page
Tucson Unified School District                                                                                                             Grade 2
Mathematics Curriculum                                                                                                    Board Approved 03/27/2012
5
2.MP.5. Use                Result Unknown, Total Unknown, and Both Addends Unknown problems are the least
appropriate tools           complex for students.
strategically.             The next level of difficulty includes Change Unknown, Addend Unknown, and Difference
Unknown
2.MP.8. Look for           The most difficult are Start Unknown and versions of Bigger and Smaller Unknown
and express                 (compare problems).
regularity in
repeated            Second graders should work on ALL problem types regardless of the level of difficulty. Mastery is
reasoning.          expected in second grade. 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.

Tucson Unified School District                                                                                                  Grade 2
Mathematics Curriculum                                                                                         Board Approved 03/27/2012
6
2.OA Add and subtract within 20 (Cluster 2- Standard 2)
Essential Concepts                                                           Essential Questions
 Flexibility of using multiple strategies helps students make sense of          What strategies can be helpful when solving a problem?
number relationships (see examples and explanations for all strategies).       How could you use mental math to estimate the sum or difference?
 Decomposing and recomposing numbers to solve addition and                      How might you use mental strategies to solve any given problem?
subtraction problems helps students make sense of number                       How can you use a known fact to help you with an unknown fact?
relationships.
 Fluency in addition and subtraction within 20 (using various strategies)
is critical to understanding addition and subtraction of larger numbers.
2.OA.2
Standard 2.OA.2                  Mathematical        Examples & Explanations
Fluently add and subtract        Practices           This standard is strongly connected to all the standards in this domain. It focuses on students being
within 20 using mental           2.MP.2. Reason      able to fluently add and subtract numbers to 20. Adding and subtracting fluently refers to
strategies. By end of Grade 2,   abstractly and      knowledge of procedures, knowledge of when and how to use them appropriately, and skill in
know from memory all sums        quantitatively.     performing them flexibly, accurately, and efficiently.
of two one-digit numbers.
(See standard 1.OA.6 for a       2.MP.7. Look for    Mental strategies help students make sense of number relationships as they are adding and
list of mental strategies.)      and make use of     subtracting within 20. The ability to calculate mentally with efficiency is very important for all
structure.          students. Mental strategies may include the following:
Connections: 2.NBT.5;                                     Counting on
2.NBT.9; ET02-S2C1-01            2.MP.8. Look for         Making tens (9 + 7 = 10 + 6)
and express              Decomposing a number leading to a ten ( 14 – 6 = 14 – 4 – 2 = 10 – 2 = 8)
regularity in            Fact families (8 + 5 = 13 is the same as 13 - 8 = 5)
repeated                 Doubles
reasoning.               Doubles plus one (7 + 8 = 7 + 7 + 1)
The use of objects, diagrams, or interactive whiteboards, and various strategies will help students
develop fluency.

Tucson Unified School District                                                                                                        Grade 2
Mathematics Curriculum                                                                                               Board Approved 03/27/2012
7
2.OA Work with equal groups of objects to gain foundations for multiplication (Cluster 3- Standards 3 and 4)
Essential Concepts                                         Essential Questions
 Adding multiple groups of equal size is the foundation for multiplication.      What arrays can you build from 24?
 Sets of objects can be arranged in a rectangular array.                         What equation(s) expresses the array?
 Even numbers can be divided into two equal sets, arranged into pairs or         How can you use a model to decide if a number is even or odd?
counted by twos; odd numbers cannot.
2.OA.3
Standard 2.OA.3                  Mathematical         Examples & Explanations
Determine whether a group of     Practices            Students explore odd and even numbers in a variety of ways including the following: students may
objects (up to 20) has an odd    2.MP.2. Reason       investigate if a number is odd or even by determining if the number of objects can be divided into
or even number of members,       abstractly and       two equal sets, arranged into pairs or counted by twos. After the above experiences, students may
e.g., by pairing objects or      quantitatively.      derive that they only need to look at the digit in the ones place to determine if a number is odd or
counting them by 2s; write an                         even since any number of tens will always split into two even groups.
equation to express an even      2.MP.3. Construct    Continued on next page
number as a sum of two           viable arguments
equal addends.                   and critique the     Example:
reasoning of
Connections: 2.OA.4; 2.RI.3;     others.              Students need opportunities writing equations representing sums of two equal addends, such as: 2
2.RI.4;                                               + 2 = 4, 3 + 3 = 6, 5 + 5 = 10, 6 + 6 = 12, or 8 + 8 =16. This understanding will lay the foundation
ET02-S1C1-01; ET02-S2C1-        2.MP.7. Look for      for multiplication and is closely connected to 2.OA.4.
01                              and make use of
structure.            The use of objects and/or interactive whiteboards will help students develop and demonstrate
various strategies to determine even and odd numbers.
2.MP.8. Look for
and express
regularity in
repeated
reasoning.

Tucson Unified School District                                                                                                         Grade 2
Mathematics Curriculum                                                                                                Board Approved 03/27/2012
8
2.OA Work with equal groups of objects to gain foundations for multiplication (Cluster 3- Standards 3 and 4)
2.OA.4
Standard 2.OA.4                Mathematical Examples & Explanations
Use addition to find the total Practices    Students may arrange any set of objects into a rectangular array. Objects can be cubes, buttons,
number of objects arranged in    2.MP.2. Reason      counters, etc. Objects do not have to be square to make an array. Geoboards can also be used to
rectangular arrays with up to    abstractly and      demonstrate rectangular arrays. Students then write equations that represent the total as the sum
5 rows and up to 5 columns;      quantitatively.     of equal addends as shown below.
write an equation to express
the total as a sum of equal      2.MP.3, Construct
and critique the
Connections: 2.OA.3, 2.RI.3;     reasoning of                4 + 4 + 4 = 12                 5 + 5 + 5 + 5 = 20
ET02-S1C2-01;                    others.
ET02-S1C2-02; ET02-S2C1-                             Interactive whiteboards and document cameras may be used to help students visualize and create
01                               2.MP.7. Look for    arrays.
and make use of
structure.

2.MP.8. Look for
and express
regularity in
repeated
reasoning

Additional Domain Information – Operations and Algebraic Thinking (OA)
Key Vocabulary
   Addend                             Decomposing                         Fact families                        Odd
   Area model                         Difference                          Factor                               Product
   Array                              Doubles                             Minuend                              Strategy
   Composing                          Even                                Multiplication                       Sum

Example Resources

       Books
    Teaching Student-Centered Mathematics – Grades K-3 Van de Walle 2006.
    Elementary and Middle School Mathematics – Teaching Developmentally Van de Walle 2008.
    Developing Essential Understanding of Number and Numeration – Pre-K- Grade 2 NCTM. 2010.
    Focus in Grade 2 – Teaching with Curriculum Focal Points. NCTM. 2011.

Tucson Unified School District                                                                                                      Grade 2
Mathematics Curriculum                                                                                             Board Approved 03/27/2012
9
   Technology
 Five Frames and Ten Frames:
http://www.ablongman.com/vandewalleseries/Vol_1_BLM_PDFs/BLM1-2.pdf
 Grid Paper:
http://www.ablongman.com/vandewalleseries/Vol_1_BLM_PDFs/BLM30-36.pdf
 NCTM – Interactive Five Frame Activity
http://illuminations.nctm.org/ActivityDetail.aspx?ID=74
 NCTM – Interactive Ten Frame Activity
http://illuminations.nctm.org/ActivityDetail.aspx?ID=75
 NCTM – Interactive Addition/Subtraction Practice
http://illuminations.nctm.org/ActivityDetail.aspx?ID=198
 NCTM – Primary Krypto – using operations to reach a target number (extension activity for students proficient at the cluster)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=173

   Exemplary Lessons
 Illustrative Mathematics Project - http://illustrativemathematics.org/standards/k8
 ORC # 4243 From the National Council of Teachers of Mathematics: Get the Picture—Get the Story
In this lesson, students act as reporters at the Super Bowl. Students study four pictures of things that they would typically find at a
football game then create problem situations that correspond to their interpretation of each of the pictures.
http://illuminations.nctm.org/LessonDetail.aspx?ID=U85
 ORC # 4308 From the National Council of Teachers of Mathematics: Looking back and moving forward
In the game Race to Zero at the bottom of the page, students take turns rolling a number cube and subtracting the number they
rolled each time from 20. The first person to reach 0 wins the round.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L43
 ORC # 4314 From the National Council of Teachers of Mathematics: Finding fact families
In this lesson, the relationship of subtraction to addition is introduced with a book and with dominoes.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L57

Assessments
All assessments used must align with our TUSD Curriculum and hold everyone involved accountable for the important mathematical concepts of this
domain. That is, all assessments for this domain must focus on assessing the degree to which second grade learners can, within the parameters
specified in the 4 standards included in this domain,
 represent and solve problems involving addition and subtraction,

   add and subtract within 20, and

   work with equal groups of objects to gain foundations for multiplication.

Both formative and summative assessments are vital components of effective mathematics curricula. Formative assessments, (e.g., pre-assessments,
observation checklists, discussions of strategies students use to solve problems, etc.) assist in instructional planning and implementation; summative
Tucson Unified School District                                                                                                          Grade 2
Mathematics Curriculum                                                                                                 Board Approved 03/27/2012
10
assessments (e.g., unit assessments, quarterly benchmarks, etc.) inform learner growth related to important mathematics concepts. All district-adopted
resources contain multiple assessment tools and include online resources that can be used for the purposes delineated above.

Arizona, as a state, is a governing member of the Partnership for Assessment of Readiness for College and Career (PARCC) Consortium
(http://www.parcconline.org/), one of two consortia funded by the US Dept. of Education to provide “next generation K-12 ELA and Mathematics
assessments” and tools for classroom use to assist teachers in assessing learners in formative ways. Teachers and administrators will be
informed of PARCC updates received by mathematics specialists via the Curriculum Connection and Elementary Edition.

Common Student Misconceptions

Students don’t understand story problems.
Maintain student focus on the meaning of the actions and number relationships, and encourage them to model the problem as needed. Students often
depend on key words, a strategy that often is not effective. For example, they might assume that the word left always means that subtraction must be
used. Providing problems in which key words are used to represent different operations is essential. For example, the use of the word left in this problem
does not indicate subtraction: Suzy took the 8 stickers she no longer wanted and gave them to Anna. Now Suzy has 11 stickers left. How many stickers
did Suzy have to begin with? Students need to make sense of relationships in word problems.

Students believe that subtraction is commutative.
After students have discovered and applied the commutative property for addition, ask them to investigate whether this property works for subtraction.
Have students share and discuss their reasoning and guide them to conclude that the commutative property does not apply to subtraction.

Students misunderstand the meaning of the equal sign.
The equal sign means “is the same quantity as” but most primary students believe the equal sign tells you that the “answer is coming up” to the right of
the equal sign. Students need to see equations written multiple ways. It is important to model equations in various ways, i.e., 18 = 10 + 8, or 9 + 1 = 2 +
8.

Students may over-generalize the idea that sums for addition problems must be greater than their addends.
Adding 0 to any number results in a sum that is equal to that number. Provide word problems involving 0 and have students model them using drawings
with an empty space for 0.

Students practice strategies for computation (such as making tens or using doubles) but revert to counting when given problems to solve.
Ask students to name a strategy that would work for a given problem. Have them explain why they chose that strategy, and then show how to use it.
Discuss how different strategies can be more or less efficient in a given situation. Monitor and track student independent use of strategies for
computation.

Tucson Unified School District                                                                                                           Grade 2
Mathematics Curriculum                                                                                                  Board Approved 03/27/2012
11
Number and Operations in Base Ten (NBT) (2 Clusters)
2.NBT Understand place value (Cluster 1- Standards 1, 2, 3, and 4)
Essential Concepts                                           Essential Questions
 Three-digit numbers decompose into units of hundreds, tens and ones.             What number is in the tens place? What is its value?
 The position of digits in numbers determines their value.                        How does a digit’s position affect its value?
 The base-ten number system is based on the idea that a unit of higher            How might you represent the number with a model?
value is created by grouping ten of the previous value units. This               How might you use place value to compare two or more quantities?
process can be repeated to obtain larger and larger units of higher              In what other way might you decompose 125 using hundreds, tens,
value.                                                                            and/or ones?
 Numbers can be represented with models using place value.
o Sets of ten, and ten sets of ten, can be perceived as single entities.
These sets can be counted and used as a means for describing
and comparing quantities.
o Numbers can be grouped into units in different ways. For example,
298 can be 29 tens and 8 ones.
 Place value can be used to compare two or more quantities.
2.NBT.1
Standard 2.NBT.1                     Mathematical       Examples & Explanations
Understand that the three            Practices          Understanding that 10 ones make one ten and that 10 tens make one hundred is fundamental to
digits of a three-digit number       2.MP.2. Reason     students’ mathematical development.
represent amounts of                 abstractly and          Students need multiple opportunities counting and “bundling” groups of tens in first grade.
hundreds, tens, and ones;            quantitatively.           In second grade, students build on their understanding by making bundles of 100s with or
e.g., 706 equals 7 hundreds,                                    without leftovers using base ten blocks, cubes in towers of 10, ten frames, etc. This
0 tens, and 6 ones.                  2.MP.7. Look for           emphasis on bundling hundreds will support students’ discovery of place value patterns.
Understand the following as          and make use of
special cases:                       structure.         As students are representing the various amounts, it is important that emphasis is placed on the
a. 100 can be thought of as                            language associated with the quantity.
a bundle of ten tens—          2.MP.8. Look for        For example, 243 can be expressed in multiple ways such as 2 groups of hundred, 4
called a “hundred.”            and express               groups of ten and 3 ones, as well as 24 tens and 3 ones. When students read numbers,
b. The numbers 100, 200,            regularity in             they should read in standard form as well as using place value concepts. For example, 243
300, 400, 500, 600, 700,       repeated                  should be read as “two hundred forty-three” as well as two hundreds, 4 tens, 3 ones.
800, 900 refer to one,         reasoning.
two, three, four, five, six,                      A document camera or interactive whiteboard can also be used to demonstrate “bundling” of
seven, eight, or nine                             objects. This gives students the opportunity to communicate their thinking.
hundreds (and 0 tens
and 0 ones).
Connections: 2.NBT.5;
2.RI.3; 2.RI.4; 2.SL.3; ET02-

Tucson Unified School District                                                                                                         Grade 2
Mathematics Curriculum                                                                                                Board Approved 03/27/2012
12
S1C2-01; ET02-S1C2-01
2.NBT Understand place value (Cluster 1- Standards 1, 2, 3, and 4)
2.NBT.2
Standard 2.NBT.2              Mathematical Examples & Explanations
Count within 1000; skip-count Practices    Students need many opportunities counting, up to 1000, from different starting points. They should
by 5s, 10s, and 100s.         2.MP.2. Reason      also have many experiences skip counting by 5s, 10s, and 100s to develop the concept of place
abstractly and      value.
Connections: 2.NBT.8; ET02-   quantitatively.
S1C3-01                                           Examples:
2.MP.7. Look for        The use of the 100s chart may be helpful for students to identify the counting patterns.
and make use of         The use of money (nickels, dimes, dollars) or base ten blocks may be helpful visual cues.
structure.              The use of an interactive whiteboard may also be used to develop counting skills.

2.MP.8. Look for    The ultimate goal for second graders is to be able to count in multiple ways with no visual support.
and express
regularity in
repeated
reasoning.
2.NBT.3
Standard 2.NBT.3              Mathematical        Examples & Explanations
Read and write numbers to     Practices           Students need many opportunities reading and writing numerals in multiple ways.
1000 using base-ten           2.MP.2. Reason
numerals, number names,       abstractly and      Examples:
and expanded form.            quantitatively.         Base-ten numerals           637                         (standard form)
 Number names                six hundred thirty seven    (written form)
Connections: 2.SL.2; 2.RI.3   2.MP.7. Look for        Expanded form               600 + 30 + 7                (expanded notation)
and make use of
structure.          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.”
2.MP.8. Look for
and express
regularity in
repeated
reasoning.
2.NBT.4
Standard 2.NBT.4              Mathematical        Examples & Explanations
Compare two three-digit       Practices           Students may use models, number lines, base ten blocks, interactive whiteboards, document
numbers based on meanings     2.MP.2. Reason      cameras, written words, and/or spoken words that represent two three-digit numbers.
of the hundreds, tens, and    abstractly and
Tucson Unified School District                                                                                                     Grade 2
Mathematics Curriculum                                                                                            Board Approved 03/27/2012
13
ones digits, using >, =, and <   quantitatively.     Continued on next page
symbols to record the results                        To compare, students apply their understanding of place value. They first attend to the numeral in
of comparisons.                  2.MP.6. Attend to   the hundreds place, then the numeral in tens place, then, if necessary, to the numeral in the ones
precision.          place.
Connections: 2.NBT.03;
2.RI.3; ET02-S1C2-02             2.MP.7. Look for    Comparative language includes but is not limited to: more than, less than, greater than, most,
and make use of     greatest, least, same as, equal to and not equal to. Students use the appropriate symbols to record
structure.          the comparisons.

2.MP.8. Look for
and express
regularity in
repeated
reasoning.

2.NBT Use place value understanding and properties of operations to add and subtract (Cluster 2- Standards 5, 6, 7, 8,
and 9)
Essential Concepts                                        Essential Questions
    Composing and decomposing numbers by place value allows for                 How can I compose or decompose this number using place value to
    Sometimes it is necessary to compose a unit of the next higher value        Which mathematical property(ies) helped you solve this problem?
    Flexible methods for computation require a strong understanding of          How are the commutative and associative properties of addition
the operations of addition and subtraction and their properties.             similar to and different from each other?
   What strategy could you use to solve 48 + 27? What other strategy
could you use?
   How might you use place value to explain why addition and
subtraction strategies work?
   What is ten more/less than 35? What is ten more/less than 67? What
stayed the same? What changed? Why? Will this always happen?

2.NBT.5
Standard 2.NBT.5                 Mathematical        Examples & Explanations
Fluently add and subtract        Practices           Adding and subtracting fluently refers to knowledge of procedures, knowledge of when and how to
within 100 using strategies      2.MP.2. Reason      use them appropriately, and skill in performing them flexibly, accurately, and efficiently. Students
based on place value,            abstractly and      should have experiences solving problems written both horizontally and vertically. They need to
properties of operations,        quantitatively.     communicate their thinking and be able to justify their strategies both verbally and with paper and
and/or the relationship                              pencil.
between addition and             2.MP.7. Look for    Continued on next page
Tucson Unified School District                                                                                                        Grade 2
Mathematics Curriculum                                                                                               Board Approved 03/27/2012
14
subtraction.                and make use of
structure.         Addition strategies based on place value for 48 + 37 may include:
Connections: 2.OA.2;                               Adding by place value: 40 + 30 = 70 and 8 + 7 = 15 and 70 + 15 = 85.
2.NBT.1; 2.NBT.3; 2.RI.3;   2.MP.8. Look for       Incremental adding (breaking one number into tens and ones); 48 + 10 = 58, 58 + 10 = 68,
2.W.2; 2.SL.3               and express                68 + 10 = 78, 78 + 7 = 85
regularity in          Compensation (making a friendly number): 48 + 2 = 50, 37 – 2 = 35, 50 + 35 = 85
repeated
reasoning.         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)

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.

Tucson Unified School District                                                                                                     Grade 2
Mathematics Curriculum                                                                                            Board Approved 03/27/2012
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2.NBT Use place value understanding and properties of operations to add and subtract (Cluster 2- Standards 5, 6, 7, 8,
and 9)
2.NBT.6
Standard 2.NBT.6         Mathematical  Examples & Explanations
Add up to four two-digit Practices     Students demonstrate addition strategies with up to four two-digit numbers either with or without
numbers using strategies        2.MP.2. Reason      regrouping.
based on place value and        abstractly and
properties of operations.       quantitatively.     Problems may be written in a story problem format to help develop a stronger understanding of
larger numbers and their values.
Connections: 2.NBT.5; 2.RI.3;   2.MP.7. Look for
2.W.2; 2.SL.2; ET02-S2C1-01     and make use of     Interactive whiteboards and document cameras may also be used to model and justify student
structure.          thinking.

2.MP.8. Look for
and express
regularity in
repeated
reasoning.
2.NBT.7
Standard 2.NBT.7                Mathematical        Examples & Explanations
Add and subtract within 1000,   Practices           There is a strong connection between this standard and place value understanding with addition
using concrete models or        2.MP.2. Reason      and subtraction of smaller numbers. Students may use concrete models or drawings to support
drawings and strategies         abstractly and      their addition or subtraction of larger numbers.
based on place value,           quantitatively.
properties of operations,                           Strategies are similar to those stated in 2.NBT.5, as students extend their learning to include
and/or the relationship         2.MP.4. Model       greater place values moving from tens to hundreds to thousands.
subtraction; relate the                             Interactive whiteboards and document cameras may also be used to model and justify student
strategy to a written method.   2.MP.5. Use         thinking.
Understand that in adding or    appropriate tools
subtracting three-digit         strategically.
subtracts hundreds and          2.MP.7. Look for
hundreds, tens and tens,        and make use of
ones and ones; and              structure.
sometimes it is necessary to
compose or decompose tens       2.MP.8. Look for
or hundreds.                    and express
Connections: 2.NBT.5;           regularity in       Continued on next page
Tucson Unified School District                                                                                                        Grade 2
Mathematics Curriculum                                                                                               Board Approved 03/27/2012
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2.NBT.6; 2.RI.3; 2.SL.3;         repeated
2.W.2; ET02-S1C2-01; ET02-       reasoning.
S2C1-01
2.NBT.8
Standard 2.NBT.8                 Mathematical        Examples & Explanations
Mentally add 10 or 100 to a      Practices           Students need many opportunities to practice mental math by adding and subtracting multiples of
given number 100–900, and        2.MP.2. Reason      10 and 100 up to 900 using different starting points. They can practice this by counting and
mentally subtract 10 or 100      abstractly and      thinking aloud, finding missing numbers in a sequence, and finding missing numbers on a number
from a given number 100–         quantitatively.     line or hundreds chart. Explorations should include looking for relevant patterns.
900.
2.MP.7. Look for    Mental math strategies may include:
Connections: 2.RI.3; 2.SL.1;     and make use of         counting on; 300, 400, 500, etc.
2.SL.2; 2.SL.3; ET02-S2C1-       structure.              counting back; 550, 450, 350, etc.
01
2.MP.8. Look for    Examples:
and express             100 more than 653 is _____ (753)
regularity in           10 less than 87 is ______ (77)
repeated                “Start at 248. Count up by 10s until I tell you to stop.”
reasoning.
An interactive whiteboard or document camera may be used to help students develop these mental
math skills.
2.NBT.9
Standard 2.NBT.9                 Mathematical        Examples & Explanations
Explain why addition and         Practices           Students need multiple opportunities explaining their addition and subtraction thinking. Operations
subtraction strategies work,     2.MP.2. Reason      embedded within a meaningful context promote development of reasoning and justification.
using place value and the        abstractly and
properties of operations.        quantitatively.     Example:
(Explanations may be                                 Mason read 473 pages in June. He read 227 pages in July. How many pages did Mason read
supported by drawings or         2.MP.3. Construct   altogether?
objects.)                        viable arguments
and critique the           Karla’s explanation: 473 + 227 = _____. I added the ones together (3 + 7) and got 10.
Connections: 2.NBT.1; 2.RI.3;    reasoning of                Then I added the tens together (70 + 20) and got 90. I knew that 400 + 200 was 600. So I
2.RI.4; 2.W.2; 2.SL.2; 2.SL.3;   others.                     added 10 + 90 for 100 and added 100 + 600 and found out that Mason had read 700
ET02-S2C1-01                                                 pages altogether.
2.MP.4. Model              Debbie’s explanation: 473 + 227 = ______. I started by adding 200 to 473 and got 673.
with mathematics.           Then I added 20 to 673 and I got 693 and finally I added 7 to 693 and I knew that Mason
appropriate tools
strategically.      Continued on next page

Tucson Unified School District                                                                                                         Grade 2
Mathematics Curriculum                                                                                                Board Approved 03/27/2012
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   Becky’s explanation: I used base-ten blocks on a base ten mat to help me solve this
2.MP.7. Look for                problem. I added 3 ones (units) plus 7 ones and got 10 ones which made one ten. I moved
and make use of                 the 1 ten to the tens place. I then added 7 tens rods plus 2 tens rods plus 1 tens rod and
structure.                      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.
2.MP.8. Look for
and express         Students should be able to connect different representations and explain the connections.
regularity in       Representations can include numbers, words (including mathematical language), pictures, number
repeated            lines, and/or physical objects. Students should be able to use any/all of these representations as
reasoning.          needed.

An interactive whiteboard or document camera can be used to help students develop and explain
their thinking.

Additional Domain Information – Number and Operations in Base Ten (NBT)

Key Vocabulary
    Addend                        Decompose                      Landmark                       Skip Counting              Three-digit number
    Addition                      Difference                      (benchmark)                    Subtraction                Two-digit number
    Associative property          Digit                           numbers                        Sum                        Whole
    Base-Ten blocks               Grouping                       Minuend                        Ten Frames
    Commutative                    (regrouping)                   Models                         Tens
property                      Hundreds                       Ones                           Thousands
    Compose                       Identity property              Part
    Place Value

Example Resources
       Books
    Teaching Student-Centered Mathematics – Grades K-3 Van de Walle 2006.
    Elementary and Middle School Mathematics – Teaching Developmentally Van de Walle 2008.
    Developing Essential Understanding of Number and Numeration – Pre-K- Grade 2 NCTM. 2010.
    Focus in Grade 2 – Teaching with Curriculum Focal Points. NCTM. 2011.

       Technology
 National Library of Virtual Manipulatives
http://nlvm.usu.edu
 Base Ten Blocks – Place Value Mat
http://nlvm.usu.edu/en/nav/frames_asid_152_g_1_t_1.html?from=category_g_1_t_1.html

Tucson Unified School District                                                                                                              Grade 2
Mathematics Curriculum                                                                                                     Board Approved 03/27/2012
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   Practice with Skip Counting on Hundreds Chart
http://nlvm.usu.edu/en/nav/frames_asid_337_g_1_t_1.html?from=category_g_1_t_1.html
   Illuminations – NCTM
http://illuminations.nctm.org
   Electronic Abacus
http://illuminations.nctm.org/ActivityDetail.aspx?ID=8

   Exemplary Lessons
 Illustrative Mathematics Project
http://illustrativemathematics.org/standards/k8
 Number Cents – Using coins to practice number sense -
http://illuminations.nctm.org/LessonDetail.aspx?id=U67
 Tallies, Ten Frames and Baseball Games
http://illuminations.nctm.org/LessonDetail.aspx?id=L876
http://www.uen.org/Lessonplan/preview.cgi?LPid=21446

Assessments
All assessments used must align with our TUSD Curriculum and hold everyone involved accountable for the important mathematical concepts of this
domain. That is, all assessments for this domain must focus on assessing the degree to which second grade learners can, within the parameters
specified in the 9 standards included in this domain,
 demonstrate understanding of place value and

   use place value understanding and properties of operations to add and subtract.

Both formative and summative assessments are vital components of effective mathematics curricula. Formative assessments, (e.g., pre-assessments,
observation checklists, discussions of strategies students use to solve problems, etc.) assist in instructional planning and implementation; summative
assessments (e.g., unit assessments, quarterly benchmarks, etc.) inform learner growth related to important mathematics concepts. All district-adopted
resources contain multiple assessment tools and include online resources that can be used for the purposes delineated above.

Arizona, as a state, is a governing member of the Partnership for Assessment of Readiness for College and Career (PARCC) Consortium
(http://www.parcconline.org/), one of two consortia funded by the US Dept. of Education to provide “next generation K-12 ELA and Mathematics
assessments” and tools for classroom use to assist teachers in assessing learners in formative ways. Teachers and administrators will be
informed of PARCC updates received by mathematics specialists via the Curriculum Connection and Elementary Edition.

Common Student Misconceptions
Students do not understand the place value structure of our number system.
It is not uncommon to have students understand 125 as a 1, a 2 and a 5. Many students do not interpret multi-digit numbers in a multiplicative fashion.

Tucson Unified School District                                                                                                        Grade 2
Mathematics Curriculum                                                                                               Board Approved 03/27/2012
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While 358 does mean 3 x 100, 5 x 10 and 8 x 1, some students consider the number 358 as 300 ones plus 50 ones plus 8 ones. Students benefit from
bundling and unbundling objects, and using base-ten blocks to model numbers. This helps students construct the idea that 358 can be 8 singles, 5
bundles of 10 singles (or tens), and 3 bundles of 10 tens (or hundreds). It is important that students connect a group of 10 ones with the word ten and a
group of 10 tens with the word hundred.

Students may think that numbers can be grouped in only one way.
Some students may not move beyond thinking of 358 as 3 hundreds, 5 tens and 8 ones. Have students use base-ten blocks and place value mats to
model the number in as many ways as they can (358 ones; 35 tens and 8 ones; 2 hundreds; 15 tens and 8 ones; 1 hundred, 23 tens and 28 ones; etc.).
This concept will help students understand regrouping when adding and subtracting.

Students don’t consider place value when adding or subtracting multi-digit numbers.
When adding or subtracting two-digit numbers, some students incorrectly apply the traditional algorithm. Encourage the use of alternative approaches
and tools that develop place value understandings, such as adding by place value using base-ten blocks, or adding up on a number line to subtract.

Measurement and Data (MD) (4 Clusters)
2.MD Measure and estimate lengths in standard units (Cluster 1- Standards 1, 2, 3, and 4)
Essential Concepts                                         Essential Questions
 Standard units of measurement are necessary to measure an object                Why does “what” we measure influence “how” we measure?
accurately.                                                                     What tool would you use to measure the classroom? Why?
 Rulers and other measurement tools can be used for quantifying                  How did you measure that?
measurement.                                                                    Estimate the length of your foot. Now choose a tool to measure it.
 Linear measurement involves units of equal size repeated over and                What tool will you choose? How close was your estimate?
over. The smaller the unit, the more of it you will need to measure the         How does the size of the unit of measure impact the number of units
length of an object.                                                             needed to measure an object or shape?
 The better we understand the size of a unit, the better we can estimate
a length.
 The length of an object or shape can be measured using standard or
non-standard units of measure.
2.MD.1
Standard 2.MD.1                 Mathematical          Examples & Explanations
Measure the length of an        Practices                    Students in second grade will build upon what they learned in first grade from measuring
object by selecting and using   2.MP.5. Use                   length with non-standard units to the new skill of measuring length in metric and U.S.
appropriate tools such as       appropriate tools             Customary with standard units of measure.
rulers, yardsticks, meter       strategically.               They should have many experiences measuring the length of objects with rulers,
sticks, and measuring tapes.                                  yardsticks, meter sticks, and tape measures.
2.MP.6. Attend to            They will need to be taught how to actually use a ruler appropriately to measure the length
Connections: 2.SL.3; SC02-      precision.
S1C2-03                                               Continued on next page
2.MP.7. Look for
Tucson Unified School District                                                                                                         Grade 2
Mathematics Curriculum                                                                                                Board Approved 03/27/2012
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and make use of             of an object especially as to where to begin the measuring. Do you start at the end of the
structure                   ruler or at the zero?
2.MD Measure and estimate lengths in standard units (Cluster 1- Standards 1, 2, 3, and 4)
2.MD.2
Standard 2.MD.2          Mathematical   Examples & Explanations
Measure the length of an Practices          Students need multiple opportunities to measure using different units of measure. They
object twice, using length       2.MP.2. Reason              should not be limited to measuring within the same standard unit.
units of different lengths for   abstractly and             Students should have access to tools, both U.S. Customary and metric.
the two measurements;            quantitatively.            The more students work with a specific unit of measure, the better they become at
describe how the two                                         choosing the appropriate tool when measuring.
measurements relate to the       2.MP.3. Construct          Students measure the length of the same object using different tools (ruler with inches,
size of the unit chosen.         viable arguments            ruler with centimeters, a yardstick, or meter stick). This will help students learn which tool is
and critique the            more appropriate for measuring a given object.
Connections: 2.MD.1;             reasoning of               They describe the relationship between the size of the measurement unit and the number
2.MD.3; 2.MD.4; 2.RI.3;          others.                     of units needed to measure something. For instance, a student might say, “The longer the
2.RI.4; 2.W.2; 2.SL.3;                                       unit, the fewer I need.” Multiple opportunities to explore provide the foundation for relating
SC02-S1C2-03;                    2.MP.5. Use                 metric units to customary units, as well as relating within customary (inches to feet to unit,
ET02-S2C1-02                     appropriate tools           the fewer I need. Multiple opportunities to explore provide the foundation for relating metric
strategically.              units to customary units, as well as relating within customary (inches to feet to yards) and
within metric (centimeters to meters).
2.MP.6. Attend to
precision.

2.MP.7. Look for
and make use of
structure.
2.MD.3
Standard 2.MD.3                  Mathematical        Examples & Explanations
Estimate lengths using units     Practices           Estimation helps develop familiarity with the specific unit of measure being used. To measure the
of inches, feet, centimeters,    2.MP.5. Use         length of a shoe, knowledge of an inch or a centimeter is important so that one can approximate
and meters.                      appropriate tools   the length in inches or centimeters. Students should begin practicing estimation with items which
strategically.      are familiar to them (length of desk, pencil, favorite book, etc.).
Connections: 2.MD.1; 2.W.2;
2.SL.3                           2.MP.6. Attend to   Some useful benchmarks for measurement are:
precision.              First joint to the tip of a thumb is about an inch
 If your arm is held out perpendicular to your body, the length from your nose to the tip of

Continued on next page

Tucson Unified School District                                                                                                          Grade 2
Mathematics Curriculum                                                                                                 Board Approved 03/27/2012
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2.MD.4
Standard 2.MD.4                   Mathematical        Examples & Explanations
Measure to determine how          Practices           Second graders should be familiar enough with inches, feet, yards, centimeters, and meters to be
much longer one object is         2.MP.5. Use         able to compare the differences in lengths of two objects. They can make direct comparisons by
than another, expressing the      appropriate tools   measuring the difference in length between two objects by laying them side by side and selecting
length difference in terms of a   strategically.      an appropriate standard length unit of measure.
standard length unit.
2.MP.6. Attend to   Students should use comparative phrases such as “It is longer by 2 inches” or “It is shorter by 5
Connections: 2.MD.1; 2.RI.3;      precision.          centimeters” to describe the difference between two objects. An interactive whiteboard or
2.RI.4; 2.W.2; 2.SL.3; ET02-                          document camera may be used to help students develop and demonstrate their thinking.
S2C1-01; SC02-S1C1-03

2.MD Relate addition and subtraction to length (Cluster 2- Standards 5 and 6)
Essential Concepts                                          Essential Questions
 Addition and subtraction are routinely applied in situations that require       How might you use addition or subtraction to solve a measurement
measurement.                                                                     problem?
 Variables or symbols can be used to express an unknown quantity in an           How might you use a letter in an equation to represent a missing part
equation.                                                                        or a missing whole?
 A number line measures distances from zero as a ruler does.                     How is a ruler like a number line?
 An unmarked number line (an open number line) can be used to add                How might a number line help you add and subtract?
and subtract. (Note: This standard supports NBT: Addition and
subtraction.)
2.MD.5
Standard 2.MD.5                   Mathematical        Examples & Explanations
Use addition and subtraction      Practices           Students need experience working with addition and subtraction to solve word problems which
within 100 to solve word          2.MP.1. Make        include measures of length. It is important that word problems stay within the same unit of
problems involving lengths        sense of problems   measure.
that are given in the same        and persevere in
units, e.g., by using drawings    solving them.       Counting on and/or counting back on a number line will help tie this concept to previous
(such as drawings of rulers)                          knowledge.
and equations with a symbol       2.MP.2. Reason
for the unknown number to         abstractly and      Continued on next page
Tucson Unified School District                                                                                                         Grade 2
Mathematics Curriculum                                                                                                Board Approved 03/27/2012
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represent the problem.        quantitatively.     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
Connections: 2.OA.1;          2.MP.4. Model       demonstrate their thinking.
2.NBT.5; 2.RI.3; 2.W.2;       with mathematics.
2.SL.2; 2.SL.3; ET02-S1C2-                        Equations include:
02                            2.MP.5. Use             20 + 35 = c
appropriate tools       c - 20 = 35
strategically.          c – 35 = 20
 20 + b = 55
2.MP.8. Look for        35 + a = 55
and express             55 = a + 35
regularity in           55 = 20 + b
repeated
reasoning.          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.
2.MD.6
Standard 2.MD.6               Mathematical        Examples & Explanations
Represent whole numbers as    Practices           Students represent their thinking when adding and subtracting within 100 by using a number line.
lengths from 0 on a number    2.MP.2. Reason      An interactive whiteboard or document camera can be used to help students demonstrate their
line diagram with equally     abstractly and      thinking.
spaced points corresponding   quantitatively.
to the numbers 0, 1, 2, …,                        Example: 10 – 6 = 4
and represent whole-number    2.MP.4. Model
sums and differences within   with mathematics.
100 on a number line
diagram.                      2.MP.5. Use
appropriate tools
Connections: 2.NBT.2;         strategically.
2.OA.1; 2.MD.5; 2.RI.3;
2.SL.3; ET02-S1C2-02

Tucson Unified School District                                                                                                    Grade 2
Mathematics Curriculum                                                                                           Board Approved 03/27/2012
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2.MD Work with time and money (Cluster 3- Standards 7 and 8)
Essential Concepts                                       Essential Questions
 Time can be measured in units of time.                                             How are analog and digital clocks similar to and different from each
 One day includes two cycles of 12 hours or one cycle of 24 hours; the               other?
12 hours from midnight to noon can be indicated by “a.m.”, while the 12            How might you prove that 15 minutes is the same time as one quarter
hours from noon to midnight can be indicated by “p.m.”.                             of an hour?
 Units of time include hours (60 minutes), half-hours (30 minutes),                 How might you prove that two dimes and one nickel is equal to one
minutes (60 seconds), and seconds.                                                  quarter?
 The symbols ¢ and \$ represent cents and dollars in United States                   How is the measurement of time and the measurement of money the
currency.                                                                           same or different?
 U.S. currency includes coins worth 1, 5, 10, 25, 50, and 100 cents and             What are different ways that you can make 72 cents? How do you
paper money worth 1, 2, 5, 10, 20, 50, and 100 dollars; amounts of                  know you have all the ways?
money can be configured in multiple ways.
2.MD.7
Standard 2.MD.7                     Mathematical        Examples & Explanations
Tell and write time from            Practices           In first grade, students learned to tell time to the nearest hour and half-hour. Students build on this
analog and digital clocks to        2.MP.5. Use         understanding in second grade by skip-counting by 5 to recognize 5-minute intervals on the clock.
the nearest five minutes,           appropriate tools
using a.m. and p.m.                 strategically.      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.
Connections: 2.NBT.2; 2.RI.3;       2.MP.6. Attend to
2.W.2; 2.SL.2; ET02-S1C2-           precision.          Common time phrases include the following: quarter till ___, quarter after ___, ten till ___, ten after
01; ET02-S1C2-02                                        ___, 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.
2.MD.8
Standard 2.MD.8                     Mathematical        Examples & Explanations
Solve word problems                 Practices           Since money is not specifically addressed in kindergarten, first grade, or third grade, students
involving dollar bills, quarters,   2.MP.1. Make        should have multiple opportunities to identify, count, recognize, and use coins and bills in and out
dimes, nickels, and pennies,        sense of problems   of context. They should also experience making equivalent amounts using both coins and bills.
using \$ and ¢ symbols               and persevere in    “Dollar bills” should include denominations up to one hundred (\$1.00, \$5.00, \$10.00, \$20.00,
appropriately. Example: If you      solving them.       \$100.00).
have 2 dimes and 3 pennies,
how many cents do you               2.MP.2. Reason
have?                               abstractly and
quantitatively.     Continued on next page

Tucson Unified School District                                                                                                             Grade 2
Mathematics Curriculum                                                                                                    Board Approved 03/27/2012
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Connections: 2.NBT.1;             2.MP.4. Model       Students should solve story problems connecting the different representations. These
2.NBT.5; 2.RI.3; 2.RI.4;          with mathematics.   representations may include objects, pictures, charts, tables, words, and/or numbers. Students
2.W.2; 2.SL.2; ET02-S1C2-                             should communicate their mathematical thinking and justify their answers. An interactive
01; ET02-S1C2-02                  2.MP.5. Use         whiteboard or document camera may be used to help students demonstrate and justify their
appropriate tools   thinking.
strategically.
Example:
2.MP.8. Look for    Sandra went to the store and received \$ 0.76 in change. What are three different sets of coins she
regularity in
repeated
reasoning.

2.MD Represent and interpret data (Cluster 4- Standards 9 and 10)
 Categorical data can be represented in many ways, including picture Essential Questions
graphs and bar graphs.                                                          Why would you display data in different ways?
 Measurement data can be represented on line plots.                              How might you represent your data in a way that makes sense?
 The foundation of a line plot is a number line; an ‘X’ corresponds to the       What put together problem might you create from your data?
value of the nearest whole unit on the line for every piece of data.            What take apart problem might you create from your data?
 Labeling graphs or line plots helps to interpret the representation.            What compare problem might you create from your data?
 Data can be analyzed to compare and contrast information.
2.MD.9
Standard 2.MD.9                   Mathematical        Examples & Explanations
Generate measurement data         Practices           This standard emphasizes representing data using a line plot. Students will use the measurement
by measuring lengths of           2.MP.4. Model       skills learned in earlier standards to measure objects. Line plots are first introduced in this grade
several objects to the nearest    with mathematics.   level. A line plot can be thought of as plotting data on a number line. An interactive whiteboard may
whole unit, or by making                              be used to create and/or model line plots.
repeated measurements of          2.MP.5. Use
the same object. Show the         appropriate tools
measurements by making a          strategically.
line plot, where the horizontal   2.MP.6. Attend to
scale is marked off in whole-     precision.
number units.
Connections: 2.RI.3; 2.RI.4;      2.MP.8. Look for
2.W.2; SC02-S1C2-04;              and express
SC02-S1C3-01;                     regularity in
ET02-S2C1-01                      repeated
reasoning.

Tucson Unified School District                                                                                                         Grade 2
Mathematics Curriculum                                                                                                Board Approved 03/27/2012
25
2.MD Represent and interpret data (Cluster 4- Standards 9 and 10)
2.MD.10
Standard 2.MD.10           Mathematical Examples & Explanations
Draw a picture graph and a Practices    Students should draw both picture and bar graphs representing data that can be sorted up to four
bar graph (with single-unit      2.MP.1. Make        categories using single unit scales (e.g., scales should count by ones). The data should be used to
scale) to represent a data set   sense of problems   solve put together, take-apart, and compare problems as listed in Table 1.
with up to four categories.      and persevere in
Solve simple put-together,       solving them.       In second grade, picture graphs (pictographs) include symbols that represent single units.
take-apart, and compare                              Pictographs should include a title, categories, category label, key, and data.
problems using information       2.MP.2. Reason
presented in a bar graph.        abstractly and
(See Table 1.)                   quantitatively.

Connections: 2.RI.3; 2.RI.4;     2.MP.4. Model
2.W.2; 2.SL.2; 2.SL.3; SC02-     with mathematics.
S1C2-04; SC02-S1C3-01;
SC02-S1C3-03; ET02-S2C1-
01
Second graders should draw both horizontal and vertical bar graphs. Bar graphs include a title,
scale, scale label, categories, category label, and data.

Tucson Unified School District                                                                                                       Grade 2
Mathematics Curriculum                                                                                              Board Approved 03/27/2012
26
Additional Domain Information – Measurement and Data (MD)
Key Vocabulary
    Bar graph                          Data                   Graph                        Linear                       Pictograph
    Categories                         Dime                   Hour                         Measure,                     Quarter
    Centimeter, meter                  Dollar                 Inch, Feet, yard              measurement                  Represent
    Clock (analog and digital)         Equation               Length                       Minute                       Ruler
    Coin                               Estimate               Line plot                    Nickel                       Variable/symbol
   Penny                        Width
Example Resources

       Books
    Teaching Student-Centered Mathematics – Grades K-3 Van de Walle 2006.
    Elementary and Middle School Mathematics – Teaching Developmentally Van de Walle 2008.
    Developing Essential Understanding of Number and Numeration – Pre-K- Grade 2 NCTM. 2010.
    Focus in Grade 2 – Teaching with Curriculum Focal Points. NCTM. 2011.

       Technology
 Coin Box – Illuminations – N CTM – This activity helps students practice counting, grouping, and changing out various coins.
http://illuminations.nctm.org/ActivityDetail.aspx?ID=217
 National Library of Virtual Manipulatives, Utah State University: Bar Chart - This manipulative can be used to make a bar chart with 1 to
20 for the vertical axis and 1 to 12 bars on the horizontal axis. The colors for the bars are predetermined however users can type in
their own title for the graph and labels for the bars.
http://nlvm.usu.edu/en/nav/frames_asid_190_g_1_t_1.html?from=category_g_1_t_1.html

       Exemplary Lessons
 Illustrative Mathematics Project
http://illustrativemathematics.org/standards/k8
 ORC # 3991 From the National Council of Teachers of Mathematics: Hopping Backward to Solve Problems
In this lesson, students determine differences using the number line to compare lengths.
http://illuminations.nctm.org/LessonDetail.aspx?id=L871
 ORC # 3979 From the National Council of Teachers of Mathematics: Where Will I Land?
In this lesson, the students find differences using the number line, a continuous model for subtraction.
http://illuminations.nctm.org/LessonDetail.aspx?ID=L118
 From the National Library of Virtual Manipulatives, Utah State University: Time – Match Clocks
Students manipulate a digital clock to show the time given on an analog clock. They can also manipulate the hands on a face clock
to show the time given on a digital clock. Times are given to the nearest five minutes.
http://nlvm.usu.edu/en/nav/frames_asid_317_g_1_t_4.html?from=category_g_1_t_4.html

Tucson Unified School District                                                                                                         Grade 2
Mathematics Curriculum                                                                                                Board Approved 03/27/2012
27
Assessments
All assessments used must align with our TUSD Curriculum and hold everyone involved accountable for the important mathematical concepts of this
domain. That is, all assessments for this domain must focus on assessing the degree to which second grade learners can, within the parameters
specified in the 10 standards included in this domain,
 measure and estimate lengths in standard units,

   relate addition and subtraction to length, and

   represent and interpret data.

Both formative and summative assessments are vital components of effective mathematics curricula. Formative assessments, (e.g., pre-assessments,
observation checklists, discussions of strategies students use to solve problems, etc.) assist in instructional planning and implementation; summative
assessments (e.g., unit assessments, quarterly benchmarks, etc.) inform learner growth related to important mathematics concepts. All district-adopted
resources contain multiple assessment tools and include online resources that can be used for the purposes delineated above.

Arizona, as a state, is a governing member of the Partnership for Assessment of Readiness for College and Career (PARCC) Consortium
(http://www.parcconline.org/), one of two consortia funded by the US Dept. of Education to provide “next generation K-12 ELA and Mathematics
assessments” and tools for classroom use to assist teachers in assessing learners in formative ways. Teachers and administrators will be
informed of PARCC updates received by mathematics specialists via the Curriculum Connection and Elementary Edition.

Common Student Misconceptions:
Students misunderstand how to read the markings on a ruler.
They believe that number markings on a ruler are counting the marks instead of the units or spaces between the marks. Have students use informal or
standard length units to make their own rulers by marking each whole unit with a number in the middle of the mark. They will see that the ruler is a
representation of a row of units and focus on the spaces.

Students believe that measuring lengths with a ruler always starts on the left edge.
Provide situations where the ruler does not start at zero. For example, a ruler is broken and the first inch number that can be seen is 2. If a pencil is
measured and it is 9 inches on this ruler, the students must subtract 2 inches from the 9 inches to adjust for where the measurement started.

Students misunderstand how to read the hour and minute hands.
For the time of 3:45, they say the time is 9:15. Also, some students name the numeral closest to the hands, regardless of whether this is appropriate. For
instance, for the time of 3:45 they say the time is 3:09 or 9:03. Assess students’ understanding of the roles of the minute and hour hands and the
relationship between them. Provide opportunities for students to experience and measure times to the nearest five minutes and the nearest hour. Have
them focus on the movement and features of the hands.

Students misunderstand the value of coins when they count them.
They might count them as individual objects. Also some students think that the value of a coin is directly related to its size, so the bigger the coin, the
more it is worth. Place pictures of a nickel on the top of five-frames that are filled with pictures of pennies. In like manner, attach pictures of dimes and
Tucson Unified School District                                                                                                              Grade 2
Mathematics Curriculum                                                                                                     Board Approved 03/27/2012
28
pennies to ten-frames and pictures of quarters to 5 x 5 grids filled with pennies. Have students use these materials to determine the value of a set of
coins in cents.

Students misunderstand that the attributes of the same kind of object can vary.
This will cause equal values in an object graph to appear unequal. For example, use equal size objects when making an object graph.

Geometry (G) (1Cluster)
2.G Reason with shapes and their attributes (Cluster 1- Standards 1, 2, and 3)
Essential Concepts                                          Essential Questions
 Shapes can be classified by their attributes.                                    How might you describe the attributes of this shape?
 Shapes can be composed and decomposed to make different shapes.                  How might you make a different shape by combining smaller shapes?
 Shapes can be used to represent fractions by partitioning them into              How might you partition this rectangle into four equal shares (pieces)?
equal shares (pieces).                                                           In what other ways might you partition the rectangle into four shares?
 Rectangles can be partitioned into rows and columns of equal sized
pieces (Note: This is a foundation for multiplication and area)
 Equal shares can be different shapes within the same whole.
2.G.1
Standard 2.G.1                     Mathematical        Examples & Explanations
Recognize and draw shapes          Practices               Students identify, describe, and draw triangles, quadrilaterals, pentagons, and hexagons.
having specified attributes,       2.MP.4. Model           Pentagons, triangles, and hexagons should appear as both regular (equal sides and equal
such as a given number of          with mathematics.        angles) and irregular.
angles or a given number of                                Students recognize all four sided shapes as quadrilaterals.
equal faces. Identify triangles,   2.MP.7. Look for        Students use the vocabulary word “angle” in place of “corner” but they do not need to name
quadrilaterals, pentagons,         and make use of          angle types.
hexagons, and cubes. (Sizes        structure.              Interactive whiteboards and document cameras may be used to help identify shapes and their
are compared directly or                                    attributes.
visually, not compared by                                  Shapes should be presented in a variety of orientations and configurations.
measuring.)

Connections: 2.RI.3; 2.RI.4;
2.W.2; 2.SL.2; 2.SL.3; SC02-
S5C1-01; ET02-S2C1-01

Tucson Unified School District                                                                                                          Grade 2
Mathematics Curriculum                                                                                                 Board Approved 03/27/2012
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2.G.2
Standard 2.G.2                     Mathematical        Examples & Explanations
Partition a rectangle into rows    Practices           This standard is a precursor to learning about the area of a rectangle and using arrays for
and columns of same-size           2.MP.2. Reason      multiplication. An interactive whiteboard or manipulatives such as square tiles, cubes, or other
squares and count to find the      abstractly and      square shaped objects can be used to help students partition rectangles.
total number of them.              quantitatively.

Connections: 2.OA.4; 2.SL.2;       2.MP.6. Attend to   Rows are horizontal and columns are vertical.
2.RI.3;                            precision.
ET02-S1C2-02
2.MP.8. Look for
and express
regularity in
repeated
reasoning.
2.G.3
Standard 2.G.3                     Mathematical        Examples & Explanations
Partition circles and              Practices           This standard introduces fractions in an area model. Students need experiences with different
rectangles into two, three, or     2.MP.2. Reason      sizes, circles, and rectangles. For example, students should recognize that when they cut a circle
four equal shares, describe        abstractly and      into three equal pieces, each piece will equal one third of its original whole. In this case, students
the shares using the words         quantitatively.     should describe the whole as three thirds. If a circle is cut into four equal pieces, each piece will
halves, thirds, half of, a third                       equal one fourth of its original whole and the whole is described as four fourths.
of, etc., and describe the         2.MP.3. Construct
whole as two halves, three         viable arguments
thirds, four fourths.              and critique the
Recognize that equal shares        reasoning of
of identical wholes need not       others.
have the same shape.

Connections: 2.RI.3; 2.RI.4;       2.MP.6. Attend to
2.W.2; 2.SL.2; 2.SL.3; ET02-       precision.
S1C2-02
2.MP.8. Look for
and express
regularity in
repeated
reasoning.

Continued on next page

Tucson Unified School District                                                                                                            Grade 2
Mathematics Curriculum                                                                                                   Board Approved 03/27/2012
30
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.

Additional Domain Information – Geometry (G)
Key Vocabulary
    Angle (instead of corner)        Fourths                One-fourth                   Rhombus                       Trapezoid
    Attribute                        Fraction               One-half                     Rows                          Triangle
    Circle                           Halves                 One-third                    Shape                         Vertex (vertices)
    Columns (2-dimensional)          Hexagon                Pentagon                     Side                          Vertical
    Edges                            Horizontal             Quadrilateral                Square
    Faces (3-dimensional)            Line                   Rectangle                    Thirds
Example Resources

       Books
    Teaching Student-Centered Mathematics – Grades K-3 Van de Walle 2006.
    Elementary and Middle School Mathematics – Teaching Developmentally Van de Walle 2008.
    Developing Essential Understanding of Number and Numeration – Pre-K- Grade 2 NCTM. 2010.
    Focus in Grade 2 – Teaching with Curriculum Focal Points. NCTM. 2011.

       Technology
 Grid paper
http://www.ablongman.com/vandewalleseries/Vol_1_BLM_PDFs/BLM30-36.pdf
 ORC # 1481 From the Math Forum: Introduction to fractions for primary students
http://mathforum.org/varnelle/knum1.html
http://mathforum.org/varnelle/knum2.html
http://mathforum.org/varnelle/knum5.html
 Illuminations – NCTM
http://illuminations.nctm.org
 Pattern Tool – making tessellations with shapes
http://illuminations.nctm.org/ActivityDetail.aspx?ID=27

Tucson Unified School District                                                                                                       Grade 2
Mathematics Curriculum                                                                                              Board Approved 03/27/2012
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    Shape Cutter – explorations in transformation of shapes (Extension)
http://illuminations.nctm.org/ActivityDetail.aspx?ID=72
    Shapes Galore- exploration of shapes and attributes
http://www.uen.org/Lessonplan/preview.cgi?LPid=21489

   Exemplary Lessons
 Illustrative Mathematics Project
http://illustrativemathematics.org/standards/k8
 Investigating Triangles – NCTM Illuminations:
http://illuminations.nctm.org/LessonDetail.aspx?id=U52
 Squares are Special Rectangles – NCTM:
http://illuminations.nctm.org/LessonDetail.aspx?id=L871

Assessments:
All assessments used must align with our TUSD Curriculum and hold everyone involved accountable for the important mathematical concepts of this
domain. That is, all assessments for this domain must focus on assessing the degree to which second grade learners can, within the parameters
specified in the 3 standards included in this domain,
 reason with shapes and their attributes.

Both formative and summative assessments are vital components of effective mathematics curricula. Formative assessments, (e.g., pre-assessments,
observation checklists, discussions of strategies students use to solve problems, etc.) assist in instructional planning and implementation; summative
assessments (e.g., unit assessments, quarterly benchmarks, etc.) inform learner growth related to important mathematics concepts. All district-adopted
resources contain multiple assessment tools and include online resources that can be used for the purposes delineated above.

Arizona, as a state, is a governing member of the Partnership for Assessment of Readiness for College and Career (PARCC) Consortium
(http://www.parcconline.org/), one of two consortia funded by the US Dept. of Education to provide “next generation K-12 ELA and Mathematics
assessments” and tools for classroom use to assist teachers in assessing learners in formative ways. Teachers and administrators will be
informed of PARCC updates received by mathematics specialists via the Curriculum Connection and Elementary Edition.

Tucson Unified School District                                                                                                       Grade 2
Mathematics Curriculum                                                                                              Board Approved 03/27/2012
32
Common Student Misconceptions:

Students believe that when shapes are rearranged or reoriented, their areas are different.
Some students may think that the area of a shape is changed by its orientation. They may see a rectangle with the longer side as the base, but claim that
the same rectangle with the shorter side as the base is a different shape. This is why is it so important to have young students handle shapes and
physically feel that the shape does not change regardless of the orientation, as illustrated below. Students can also be encouraged to place the shapes
on top of each other, or cut apart the shapes and match the pieces.

Students believe that any segmented shape represents equal shares.
Students also may believe that a region model represents one out of two, three or four fractional parts without regard to the fact that the parts have to be
equal shares, e.g., a circle divided by two equally spaced horizontal lines represents three thirds.

Students may interpret fractions as part-to part relationships rather than part-to whole.
For example, a student might see this fraction illustration and say that it is one-third, because one part is shaded and three parts are not shaded.

Have the student say the fractional name with meaning, by saying “one of four” or “one out of four equal parts.”

Tucson Unified School District                                                                                                           Grade 2
Mathematics Curriculum                                                                                                  Board Approved 03/27/2012
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Table 1                              Result Unknown                             Change Unknown                            Start Unknown
Two bunnies sat on the grass. Three        Two bunnies were sitting on the        Some bunnies were sitting on the grass.
more bunnies hopped there. How many        grass. Some more bunnies hopped        Three more bunnies hopped there. Then
bunnies are on the grass now?              there. Then there were five bunnies.   there were five bunnies. How many
Add to           2+3=?                                      How                                    bunnies were on the grass before?
many bunnies hopped over to the        ?+3=5
first two?
2+?=5
Five apples were on the table. I ate two   Five apples were on the table. I ate   Some apples were on the table. I ate
apples. How many apples are on the         some apples. Then there were three     two apples. Then there were three
Take from          table now?                                 apples. How many apples did I eat?     apples. How many apples were on the
5–2=?                                      5–?=3                                  table before?
?–2=3
1
Three red apples and two green apples      Five apples are on the table. Three    Grandma has five flowers. How many
are on the table. How many apples are      are red and the rest are green. How    can she put in her red vase and how
Put Together / Take    on the table?                              many apples are green?                 many in her blue vase?
2
Apart            3+2=?                                      3 + ? = 5, 5 – 3 = ?                   5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 = 4 + 1
5 = 2 + 3, 5 = 3 + 2
Difference Unknown                          Bigger Unknown                           Smaller Unknown
(“How many more?” version):                (Version with “more”):                 (Version with “more”):
Lucy has two apples. Julie has five        Julie has three more apples than       Julie has three more apples than Lucy.
apples. How many more apples does          Lucy. Lucy has two apples. How         Julie has five apples. How many apples
Julie have than Lucy?                      many apples does Julie have?           does Lucy have?
3
Compare
(“How many fewer?” version):               (Version with “fewer”):                (Version with “fewer”):
Lucy has two apples. Julie has five        Lucy has 3 fewer apples than Julie.    Lucy has 3 fewer apples than Julie. Julie
apples. How many fewer apples does         Lucy has two apples. How many          has five apples. How many apples does
Lucy have than Julie?                      apples does Julie have?                Lucy have?
2 + ? = 5, 5 – 2 = ?                       2 + 3 = ?, 3 + 2 = ?                   5 – 3 = ?, ? + 3 = 5
6
Adapted from Box 2-4 of Mathematics Learning in Early Childhood, National Research Council (2009, pp. 32, 33).
These take apart situations can be used to show all the decompositions of a given number. The associated equations, which have the total on the left
of the equal sign, help children understand that the = sign does not always mean makes or results in but always does mean is the same number as.
2
Either addend can be unknown, so there are three variations of these problem situations. Both Addends Unknown is a productive extension of this
basic situation, especially for small numbers less than or equal to 10.
3
For the Bigger Unknown or Smaller Unknown situations, one version directs the correct operation (the version using more for the bigger unknown
and using less for the smaller unknown). The other versions are more difficult.

Tucson Unified School District                                                                                                        Grade 2
Mathematics Curriculum                                                                                               Board Approved 03/27/2012
34
PLANNING FOR CONTENT SHIFTS

2010 STANDARD                                       2008 PO                             PLAN
2.OA.1 Use addition and subtraction within     M02-S1C2-01 Contextual problems using
100 to solve one- and two-step word            multiple representations involving
problems involving situations of adding to,         addition and subtraction with one-
taking from, putting together, taking apart,            and/or two-digit numbers,
and comparing, with unknowns in all                 multiplication for 1s, 2s, 5s, and 10s,
positions, e.g., by using drawings and                  and
equations with a symbol for the unknown             adding and subtracting money to
number to represent the problem.                        \$1.00.
(See Glossary, Table 1.)
M02-S1C2-05 Create and solve word
problems based on addition and subtraction
of two-digit numbers.
M02-S2C3-02 Solve a variety of problems
based on the addition principle of counting.
M02-S3C3-03 Represent a word problem
requiring addition or subtraction through 100
using an equation. (Includes unknowns)
M02-S3C3-04 Identify the value of an
unknown number in an equation involving an
2.OA.2 Fluently add and subtract within 20     M02-S1C2-02 Demonstrate the ability to add
using mental strategies. By end of Grade 2,    and subtract whole numbers (to at least two
know from memory all sums of two one-          digits) and decimals (in the context of money)
digit numbers. (See standard 1.OA.6 for a            with up to three addends and to
list of mental strategies.)                             \$1.00.
M02-S1C2-03 Demonstrate fluency of

M02-S1C2-04 Apply and interpret the concept
of addition and subtraction as inverse
operations to solve problems. (Includes fact
families)

Tucson Unified School District                                                                                         Grade 2
Mathematics Curriculum                                                                                Board Approved 03/27/2012
35
2010 STANDARD                                      2008 PO                               PLAN
2OA.3 Determine whether a group of             S M02-S1C1-06 Sort whole numbers through
objects (up to 20) has an odd or even          1000 into odd and even, and justify the sort.
number of members, e.g., by pairing
objects or counting them by 2s; write an
equation to express an even number as a
2.OA.4 Use addition to find the total number   NEW
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
2.NBT.1 Understand that the three digits of    M02-S1C1-01 Express whole numbers 0 to
a three-digit number represent amounts of        1000, in groups of hundreds, tens and ones
hundreds, tens, and ones; e.g., 706 equals       using and connecting multiple
7 hundreds, 0 tens, and 6 ones.                  representations.
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).
2.NBT.2 Count within 1000; skip-count by       M01-S1C1-02 Count forward to 100 and
5s, 10s, and 100s.                             backward from 100 by 1s and 10s using
different starting points, and count forward to
100 by 2s and 5s. (Includes skip-counting by
5s and 10s, but only to 100; extends to
counting backward from 100 by 1s and 10s)
CM02-S1C1-02 Count forward to 1000 and
backward from 1000 by 1s, 10s, and 100s
using different starting points. (Extends to
counting backward; does not include skip-
counting by 5s)

Tucson Unified School District                                                                                          Grade 2
Mathematics Curriculum                                                                                 Board Approved 03/27/2012
36
2010 STANDARD                                       2008 PO                             PLAN
2.NBT.3 Read and write numbers to 1000       M02-S1C1-01 Express whole numbers 0 to
using base-ten numerals, number names,       1000, in groups of hundreds, tens and ones
and expanded form.                           using and connecting multiple
representations.
M02-S3C3-01 Record equivalent forms of
whole numbers to 1000 by constructing
models and using numbers.

2.NBT.4 Compare two three-digit numbers      M02-S1C1-04 Compare and order whole
based on meanings of the hundreds, tens,      numbers through 1000 by applying the
and ones digits, using >, =, and < symbols    concept of place value.
to record the results of comparisons.
2.NBT.5 Fluently add and subtract within     M02-S1C2-02 Demonstrate the ability to add
100 using strategies based on place value,   and subtract whole numbers (to at least two
properties of operations, and/or the         digits) and decimals (in the context of money)
subtraction.                                       to \$1.00.
M02-S1C2-04 Apply and interpret the concept
of addition and subtraction as inverse
operations to solve problems.
M02-S1C2-08 Apply properties to solve
 identity property of

2.NBT.6 Add up to four two-digit numbers     M02-S1C2-02 Demonstrate the ability to add
using strategies based on place value and    and subtract whole numbers (to at least two
properties of                                digits) and decimals (in the context of money)
 with up to three addends and
 to \$1.00.
numbers to four digits.
Tucson Unified School District                                                                                       Grade 2
Mathematics Curriculum                                                                              Board Approved 03/27/2012
37
2010 STANDARD                                        2008 PO                              PLAN
using concrete models or drawings and            subtraction of numbers that total less than
strategies based on place value, properties      100 by using various representations that
of operations, and/or the relationship           connect to place value concepts.
between addition and subtraction; relate the
strategy to a written method. Understand         M02-S1C2-02 Demonstrate the ability to add
that in adding or subtracting three-digit        and subtract whole numbers (to at least two
numbers, one adds or subtracts hundreds          digits) and decimals (in the context of money)
and hundreds, tens and tens, ones and                  with up to three addends and
ones; and sometimes it is necessary to                 to \$1.00.
compose or decompose tens or hundreds..          M03-S1C2-01 Add and subtract whole
numbers to four digits.
2.NBT.8 Mentally add 10 or 100 to a given        M02-S1C1-03 Identify numbers which are 100
number 100–900, and mentally subtract 10          more or less than a given number to 900.
or 100 from a given number 100–900.
2.NBT.9 Explain why addition and                 M02-S1C2-04 Apply and interpret the concept
subtraction strategies work, using place         of addition and subtraction as inverse
value and the properties of operations.          operations to solve problems.
(Explanations may be supported by                M02-S1C2-08 Apply properties to solve
 identity property of

2.MD.1 Measure the length of an object by        M02-S4C4-02 Apply measurement skills to 1.
selecting and using appropriate tools such        measure the attributes of an object (length,
as rulers, yardsticks, meter sticks, and          capacity, weight).
measuring tapes.
2.MD.2 Measure the length of an object           NEW
twice, using length units of different lengths
for the two measurements; describe how
the two measurements relate to the size of
the unit chosen.

Tucson Unified School District                                                                                           Grade 2
Mathematics Curriculum                                                                                  Board Approved 03/27/2012
38
2010 STANDARD                                     2008 PO                                PLAN
2.MD.3 Estimate lengths using units of        M02-S4C4-02 Apply measurement skills to 2.
inches, feet, centimeters, and meters.         measure the attributes of an object (length,
Measure to determine how much longer           capacity, weight).
one object is than another, expressing the
length difference in terms of a standard
length unit.
2.MD.4 Use addition and subtraction within    NEW                                           3.
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.
2.MD.5 Represent whole numbers as             M02-S3C3-03 Represent a word problem          4.
lengths from 0 on a number line diagram       requiring addition or subtraction through 100
with equally spaced points corresponding to   using an equation.
the numbers 0, 1, 2, …, and represent         M02-S3C3-04 Identify the value of an
whole-number sums and differences within      unknown number in an equation involving an
100 on a number line diagram.                 addition or subtraction fact.
2.MD.6 Tell and write time from analog and    NEW                                           5.
digital clocks to the nearest five minutes,
using a.m. and p.m.
2.MD.7 Solve word problems involving          M02-S4C4-01 Tell time to the nearest minute6.
dollar bills, quarters, dimes, nickels, and    using analog and digital clocks.
pennies, using \$ and ¢ symbols
appropriately. Example: If you have 2 dimes
and 3 pennies, how many cents do you
have?

2.MD.8 Solve word problems involving          M02-S1C1-05 Count money to \$1.00.             7.

Tucson Unified School District                                                                                          Grade 2
Mathematics Curriculum                                                                                 Board Approved 03/27/2012
39
2010 STANDARD                                        2008 PO                              PLAN
dollar bills, quarters, dimes, nickels, and     M02-S1C2-01 Solve contextual problems
pennies, using \$ and ¢ symbols                  using multiple representations involving
appropriately. Example: If you have 2 dimes           addition and subtraction with one-
and 3 pennies, how many cents do you                     and/or two-digit numbers,
have?                                                 multiplication for 1s, 2s, 5s, and 10s,
and
 adding and subtracting money to
\$1.00.
M02-S1C2-02 Demonstrate the ability to add
and subtract whole numbers (to at least two
digits) and decimals (in the context of money)
 with up to three addends and
 to \$1.00.
M03-S1C1-03 Count and represent money
using coins and bills to \$100.00.
2.MD.9 Generate measurement data by             M01-S4C4-02 Measure and compare the           8.
measuring lengths of several objects to the       length of objects using the benchmark of
nearest whole unit, or by making repeated         one inch.
measurements of the same object. Show
the measurements by making a line plot,
where the horizontal scale is marked off in
whole-number units.
2.MD.10 Draw a picture graph and a bar          M02-S2C1-01 Collect, record, organize, and 9.
graph (with single-unit scale) to represent a   display data using pictographs, frequency
data set with up to four categories. Solve      tables, or single bar graphs.(Extends to using
simple put-together, take-apart, and            multiple-units scale)
compare problems using information
presented in a bar graph. (See Glossary,        M02-S2C1-02 Formulate and answer
Table 1.)                                        questions by interpreting displays of data,
including pictographs, frequency tables, or
single bar graphs.
2.G.1 Recognize and draw shapes having          M01-S4C1-01 Identify and draw 2-             10.
specified attributes, such as a given            dimensional geometric figures based on
number of angles or a given number of            given attributes regardless of size or
equal faces Identify triangles,                  orientation. (Includes drawing shapes)

Tucson Unified School District                                                                                            Grade 2
Mathematics Curriculum                                                                                   Board Approved 03/27/2012
40
2010 STANDARD                                      2008 PO                               PLAN
quadrilaterals, pentagons, hexagons, and      M02-S4C1-01 Describe and compare the
cubes. (Sizes of lengths and angles are       attributes of polygons up to six sides using the
compared directly or visually, not compared   terms side, vertex, point, and length.
by measuring.)
2.G.2 Partition a rectangle into rows and     NEW                                           11.
columns of same-size squares and count to
find the total number of them.

12. 2.G.3 Partition circles and rectangles into   M03-S1C1-05 Express benchmark fractions 13.
two, three, or four equal shares, describe     as fair sharing, parts of a whole, or parts of
the shares using the words halves, thirds,     a set.
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.
2.MP.1 Make sense of problems and             M01-S5C2-01 Identify the question(s) asked 14.
persevere in solving them.                      and any other questions that need to be
answered in order to find a solution.
M01-S5C2-02 Identify the given information
that can be used to find a solution.
M02-S5C2-03 Select from a variety of
problem-solving strategies and use one or
more strategies to arrive at a solution.
M02-S5C2-04 Represent a problem situation
using any combination of words, numbers,
pictures, physical objects, or symbols.
M02-S5C2-05 Explain and clarify
mathematical thinking.
M02-S5C2-06 Determine whether a solution
is reasonable.
2.MP.2 Reason abstractly and                  M01-S5C2-05 Explain and clarify             15.
quantitatively.                                 mathematical thinking.
2.MP.3 Construct viable arguments and         M02-S5C2-05 Explain and clarify             16.
critique the reasoning of others.               mathematical thinking.
2.MP.4 Model with mathematics.                M02-S5C2-03 Select from a variety of        17.
problem-solving strategies and use one or
more strategies to arrive at a solution.
Tucson Unified School District                                                                                           Grade 2
Mathematics Curriculum                                                                                  Board Approved 03/27/2012
41
2010 STANDARD                                      2008 PO                                     PLAN
M02-S5C2-04 Represent a problem situation
using any combination of words, numbers,
pictures, physical objects, or symbols.
2.MP.5 Use appropriate tools strategically.   M02-S5C2-03 Select from a variety of       18.
problem-solving strategies and use one or
more strategies to arrive at a solution.

M02-S5C2-06 Determine whether a solution
is reasonable.
2.MP.6 Attend to precision.                   M02-S5C2-05 Explain and clarify          19.
mathematical thinking.
2.MP.7 Look for and make use of structure.    M02-S5C2-05 Explain and clarify          20.
mathematical thinking.
2.MP.8 Look for and express regularity in     M02-S5C2-06 Determine whether a solution 21.
repeated reasoning.                            is reasonable.
MOVEMENT
2008 PO                                          PLAN
REMOVED                       M02-S1C2-06 Demonstrate the concept of
multiplication for 1s, 2s, 5s, and 10s.
REMOVED                       M02-S1C2-07 Describe the effect of
operations (addition and subtraction) on the
size of whole numbers.
MOVED TO KINDERGARTEN                   M02-S2C3-01 List all possibilities in counting
situations.
REMOVED                       M02-S1C3-01 Use estimation to determine if
sums of two 2-digit numbers are more or less
than 20, more or less than 50, or more or less
than 100.
REMOVED                       M02-S2C4-01 Color simple pictures or maps
using the least number of colors and justify
the coloring.

Tucson Unified School District                                                                                               Grade 2
Mathematics Curriculum                                                                                      Board Approved 03/27/2012
42
REMOVED      M02-S2C4-02 Build vertex-edge graphs using
concrete materials and explore simple
properties of vertex-edge graphs
 number of vertices and edges,
 neighboring vertices, and
 paths in a graph.
REMOVED      M02-S2C4-03 Construct simple vertex-edge
graphs from simple pictures or maps.
REMOVED      M02-S3C1-01 Recognize, describe, extend,
create, and find missing terms in a numerical
or symbolic pattern.
REMOVED      M02-S3C1-02 Explain the rule for a given
numerical or symbolic pattern and verify that
the rule works.
REMOVED      M02-S3C2-01 Describe a rule that represents
a given relationship between two quantities
using words or pictures.
REMOVED      M02-S3C3-02 Compare expressions using
spoken words and the symbols =, ≠, <, and >.
REMOVED       M02-S4C2-01 Identify, with justification,
whether a 2-dimensional figure has lines of
symmetry.
REMOVED      M02-S4C4-03 Read temperatures on a
thermometer using Fahrenheit and Celsius.
REMOVED      M02-S4C4-04 Demonstrate unit conversions
 1 foot = 12 inches,
 1 quart = 4 cups,
 1 pound = 16 ounces,
 1 hour = 60 minutes,
 1 day = 24 hours,
 1 week = 7 days, and
 1 year = 12 months.

Tucson Unified School District                                                                    Grade 2
Mathematics Curriculum                                                           Board Approved 03/27/2012
43

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