
Legend:  Knowledge and Skills Statements (TEKS) identified by TEA are in italicized, bolded, black text.
 Student Expectations (TEKS) identified by TEA are in bolded, black text.
 Portions of the Student Expectations (TEKS) that are not included in this unit but are taught in previous or future units are indicated by a
strikethrough.

Legend:  Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
 Unitspecific clarifications are in italicized, blue text.
 Information from Texas Education Agency (TEA), Texas College and Career Readiness Standards (TxCCRS), Texas Response to Curriculum Focal Points (TxRCFP) is labeled.
 A Partial Specificity label indicates that a portion of the specificity not aligned to this unit has been removed.

1.1 
Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:


1.1A 
Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply
MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:
 Mathematical problem situations within and between disciplines
 Everyday life
 Society
 Workplace
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing an understanding of place value
 Solving problems involving addition and subtraction
 Analyzing attributes of twodimensional shapes and threedimensional solids
 Developing the understanding of length
 TxCCRS:

1.1B 
Use a problemsolving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problemsolving process and the reasonableness of the solution.

Use
A PROBLEMSOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEMSOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:
 Problemsolving model
 Analyze given information
 Formulate a plan or strategy
 Determine a solution
 Justify the solution
 Evaluate the problemsolving process and the reasonableness of the solution
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing an understanding of place value
 Solving problems involving addition and subtraction
 Analyzing attributes of twodimensional shapes and threedimensional solids
 Developing the understanding of length
 TxCCRS:
 VIII. Problem Solving and Reasoning

1.1C 
Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select
TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH AND NUMBER SENSE AS APPROPRIATE, TO SOLVE PROBLEMS
Including, but not limited to:
 Appropriate selection of tool(s) and techniques to apply in order to solve problems
 Tools
 Real objects
 Manipulatives
 Paper and pencil
 Technology
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing an understanding of place value
 Solving problems involving addition and subtraction
 Analyzing attributes of twodimensional shapes and threedimensional solids
 Developing the understanding of length
 TxCCRS:
 VIII. Problem Solving and Reasoning

1.1D 
Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate
MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Language
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing an understanding of place value
 Solving problems involving addition and subtraction
 Analyzing attributes of twodimensional shapes and threedimensional solids
 Developing the understanding of length
 TxCCRS:
 IX. Communication and Representation

1.1E 
Create and use representations to organize, record, and communicate mathematical ideas.

Create, Use
REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Representations of mathematical ideas
 Organize
 Record
 Communicate
 Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
 Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing an understanding of place value
 Solving problems involving addition and subtraction
 Analyzing attributes of twodimensional shapes and threedimensional solids
 Developing the understanding of length
 TxCCRS:
 IX. Communication and Representation

1.1F 
Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze
MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:
 Mathematical relationships
 Connect and communicate mathematical ideas
 Conjectures and generalizations from sets of examples and nonexamples, patterns, etc.
 Current knowledge to new learning
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing an understanding of place value
 Solving problems involving addition and subtraction
 Analyzing attributes of twodimensional shapes and threedimensional solids
 Developing the understanding of length
 TxCCRS:

1.1G 
Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify
MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:
 Mathematical ideas and arguments
 Validation of conclusions
 Displays to make work visible to others
 Diagrams, visual aids, written work, etc.
 Explanations and justifications
 Precise mathematical language in written or oral communication
Note(s):
 The mathematical process standards may be applied to all content standards as appropriate.
 TxRCFP:
 Developing an understanding of place value
 Solving problems involving addition and subtraction
 Analyzing attributes of twodimensional shapes and threedimensional solids
 Developing the understanding of length
 TxCCRS:
 IX. Communication and Representation

1.2 
Number and operations. The student applies mathematical process standards to represent and compare whole numbers, the relative position and magnitude of whole numbers, and relationships within the numeration system related to place value. The student is expected to:


1.2B 
Use concrete and pictorial models to compose and decompose numbers up to 120 in more than one way as so many hundreds, so many tens, and so many ones.

Use
CONCRETE AND PICTORIAL MODELS OF NUMBERS UP TO 120
Including, but not limited to:
 Whole numbers (0 – 120)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Numeral – a symbol used to name a number
 Digit – any numeral from 0 – 9
 Place value – the value of a digit as determined by its location in a number such as ones, tens, hundreds, etc.
 Hundreds place
 Tens place
 Ones place
 Base10 place value system
 A number system using ten digits 0 – 9
 Relationships between places are based on multiples of 10.
 The magnitude (relative size) of one hundred
 Concrete models
 Proportional models – a visual representation that demonstrates the relative size of each place value using models with proportional dimensions, meaning the model of each place value is exactly 10 times larger than the place value model to the right (e.g., the base10 long is exactly 10 times as big as the unit showing that one 10 is equal to ten ones)
 Linking cubes (proportional representation of the magnitude of a number with 1to10 relationship)
 Bundled sticks (proportional representation of the magnitude of a number with 1to10 relationship)
 Base10 blocks (proportional representation of the magnitude of a number with 1to10 relationship)
 Nonproportional models – a visual representation that does not maintain the proportional relationship of size, meaning the size of each place value model is not 10 times larger than the place value model to the right (e.g., the value of each place value disk is indicated by the numerical label and color but does not change in size)
 Place value disks (nonproportional representation with a 1to10 relationship)
 Pictorial models
 Base10 block representations
 Place value disk representations
 Open number line – an empty number line where tick marks are added to represent landmarks of numbers, often indicated with arcs above the number line (referred to as jumps) demonstrating approximate proportional distances
To Compose, To Decompose
NUMBERS UP TO 120 IN MORE THAN ONE WAY AS SO MANY HUNDREDS, SO MANY TENS, AND SO MANY ONES
Including, but not limited to:
 Whole numbers (0 – 120)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Compose numbers – to combine parts or smaller values to form a number
 Decompose numbers – to break a number into parts or smaller values
 Compose a number in more than one way.
 As so many hundreds, so many tens, and so many ones
 Decompose a number in more than one way.
 As so many hundreds, so many tens, and so many ones
Note(s):
 Grade Level(s):
 Kindergarten composed and decomposed numbers up to 10 with objects and pictures.
 Grade 2 will use concrete and pictorial models to compose and decompose numbers up to 1,200 in more than one way as a sum of so many thousands, hundreds, tens, and ones.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation

1.2C 
Use objects, pictures, and expanded and standard forms to represent numbers up to 120.

Use
OBJECTS, PICTURES, AND EXPANDED AND STANDARD FORMS TO REPRESENT NUMBERS UP TO 120
Including, but not limited to:
 Whole numbers (0 – 120)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Place value – the value of a digit as determined by its location in a number such as ones, tens, hundreds, etc.
 Objects
 Proportional models – a visual representation that demonstrates the relative size of each place value using models with proportional dimensions, meaning the model of each place value is exactly 10 times larger than the place value model to the right (e.g., the base10 long is exactly 10 times as big as the unit showing that one 10 is equal to ten ones)
 Linking cubes (proportional representation of the magnitude of a number with 1to10 relationship)
 Bundled sticks (proportional representation of the magnitude of a number with 1to10 relationship)
 Base10 blocks (proportional representation of the magnitude of a number with 1to10 relationship)
 Beaded number line (proportional representation of the magnitude of a number with 1to10 relationship)
 Nonproportional models – a visual representation that does not maintain the proportional relationship of size, meaning the size of each place value model is not 10 times larger than the place value model to the right (e.g., the value of each place value disk is indicated by the numerical label and color but does not change in size)
 Place value disks (nonproportional representation with a 1to10 relationship)
 Pictures
 Base10 block representations
 Place value disk representations
 Open number line – an empty number line where tick marks are added to represent landmarks of numbers, often indicated with arcs above the number line (referred to as jumps) demonstrating approximate proportional distances
 Place value stacking cards
 Expanded form – the representation of a number as a sum of place values (e.g., 119 as 100 + 10 + 9)
 Zero may or may not be written as an addend to represent the digit 0 in a number (e.g., 107 as 100 + 0 + 7 or 100 + 7).
 Expanded form is written following the order of place value.
 The sum of place values written in random order is an expression but not expanded form.
 Standard form – the representation of a number using digits (e.g., 118)
 Period – a threedigit grouping of whole numbers where each grouping is composed of a ones place, a tens place, and a hundreds place, and each grouping is separated by a comma
 Units period is composed of the ones place, tens place, and hundreds place.
 The word “unit” after the numerical value of the units period is not stated when read.
 The word “hundred” in each period is stated when read.
 The words “ten” and “one” in each period are not stated when read.
 The tens place digit and ones place digit in each period are stated as a twodigit number when read.
 Zeros are used as place holders between digits as needed to maintain the value of each digit (e.g., 107).
 Leading zeros in a whole number are not commonly used in standard form, but are not incorrect and do not change the value of the number (e.g., 037 equals 37).
 Multiple representations
 Number presented in concrete or pictorial form represented in expanded form
 Number presented in concrete or pictorial form represented in standard form
 Number presented in standard form represented in expanded form
 Number presented in expanded form represented in standard form
Note(s):
 Grade Level(s):
 Grade 1 introduces representing numbers in expanded and standard forms.
 Grade 2 will introduce representing numbers up to 1,200 in word form.
 Grade 2 will use standard, word, and expanded forms to represent numbers up to 1,200.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation

1.2D 
Generate a number that is greater than or less than a given whole number up to 120.

Generate
A NUMBER THAT IS GREATER THAN OR LESS THAN A GIVEN WHOLE NUMBER UP TO 120
Including, but not limited to:
 Whole numbers (0 – 120)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Comparative language
 Greater than, more than
 Less than, fewer than
 Place value relationships
 1 more or 1 less
 Increasing the digit in the ones place by 1 will generate a number that is 1 more than the original number.
 Decreasing the digit in the ones place by 1 will generate a number that is 1 less than the original number.
 10 more or 10 less
 Increasing the digit in the tens place by 10 will generate a number that is 10 more than the original number.
 Decreasing the digit in the tens place by 10 will generate a number that is 10 less than the original number.
 Numerical relationships
 Counting order
 Skip counting
 Doubles
 Concrete and pictorial models
 Hundreds chart
 Moving one place to the right will generate a number that is 1 more than the original number.
 Moving one place to the left will generate a number that is 1 less than the original number.
 Moving one row down will generate a number that is 10 more than the original number.
 Moving one row up will generate a number that is 10 less than the original number.
 Base10 blocks
 Adding unit cubes will increase a number by increments of 1.
 Removing unit cubes will decrease a number by increments of 1.
 Adding longs will increase a number by increments of 10.
 Removing longs will decrease a number by increments of 10.
 Number line
 Numbers increase from left to right.
 Numbers decrease from right to left.
 Calendar
 Moving one place to the right will generate a number that is 1 more than the original number.
 Moving one place to the left will generate a number that is 1 less than the original number.
 Moving one row down will generate a number that is 7 more than the original number.
 Moving one row up will generate a number that is 7 less than the original number.
Note(s):
 Grade Level(s):
 Kindergarten generated a number that is one more than or one less than another number up to 20.
 Grade 2 will generate a number that is greater than or less than a given whole number up to 1,200.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation

1.2E 
Use place value to compare whole numbers up to 120 using comparative language.

Use
PLACE VALUE OF WHOLE NUMBERS UP TO 120
Including, but not limited to:
 Whole numbers (0 – 120)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Place value – the value of a digit as determined by its location in a number such as ones, tens, hundreds, etc.
 Hundreds place
 Tens place
 Ones place
To Compare
WHOLE NUMBERS UP TO 120 USING COMPARATIVE LANGUAGE
Including, but not limited to:
 Whole numbers (0 – 120)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Comparative language
 Inequality language
 Greater than, more than
 Less than, fewer than
 Equality language
 Compare numbers – to consider the value of two numbers to determine which number is greater or less or if the numbers are equal in value
 Concrete models
 Compare the amount modeled in the highest place value position first.
 Proportional models – a visual representation that demonstrates the relative size of each place value using models with proportional dimensions, meaning the model of each place value is exactly 10 times larger than the place value model to the right (e.g., the base10 long is exactly 10 times as big as the unit showing that one 10 is equal to ten ones)
 Bundled sticks (proportional representation of the magnitude of a number with 1to10 relationship)
 Base10 blocks (proportional representation of the magnitude of a number with 1to10 relationship)
 Nonproportional models – a visual representation that does not maintain the proportional relationship of size, meaning the size of each place value model is not 10 times larger than the place value model to the right (e.g., the value of each place value disk is indicated by the numerical label and color but does not change in size)
 Place value disks (nonproportional representation with a 1to10 relationship)
 Pictorial models
 Compare the amount represented in the highest place value position first.
 Base10 block representations
 Place value disk representations
 Numerical
 Compare two numbers using place value charts.
 Compare digits in the same place value position beginning with the greatest place value.
 If these digits are the same, continue to the next smallest place until the digits are different.
 Numbers that have common digits but are not equal in value (different place values)
 Numbers that have a different number of digits
 Compare more than two numbers using place value to determine which number is the greatest.
 Compare digits in the greatest place value position to determine the number with the greatest value.
 If these digits are the same, continue to the next smallest place until the digits are different.
 Compare more than two numbers using place value to determine which number is the least.
 Compare digits in the greatest place value position to determine the number with the least value.
 If these digits are the same, continue to the next smallest place until the digits are different.
Note(s):
 Grade Level(s):
 Kindergarten used comparative language to describe two numbers up to 20 presented as written numerals.
 Grade 2 will use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and the symbols >, <, or =.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation

1.2F 
Order whole numbers up to 120 using place value and open number lines.

Order
WHOLE NUMBERS UP TO 120 USING PLACE VALUE AND OPEN NUMBER LINES
Including, but not limited to:
 Whole numbers (0 – 120)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Order numbers – to arrange a set of numbers based on their numerical value
 A set of numbers can be compared in pairs in the process of ordering numbers.
 Order a set of numbers using place value.
 Quantifying descriptors (e.g., between two given numbers, greatest/least, ascending/descending, tallest/shortest, warmest/coldest, fastest/slowest, longest/shortest, heaviest/lightest, closest/farthest, oldest/youngest, etc.)
 Order a set of numbers using open number lines.
 Characteristics of an open number line
 An open number line begins as a line with no intervals (or tick marks) and no positions/numbers labeled.
 Numbers/positions are placed on the empty number line only as they are needed.
 When reasoning on an open number line, the position of zero is often not placed.
 When working with larger numbers, an open number line without the constraint of distance from zero allows the ability to “zoomin” on the relevant section of the number line.
 The placement of the first two numbers on an open number line determines the scale of the number line.
 Once the scale of the number line has been established by the placement of the first two numbers, intervals between additional numbers placed are approximately proportional.
 The differences between numbers are approximated by the distance between the positions on the number line.
 Open number lines extend infinitely in both directions (arrows indicate the number line continues infinitely).
 Numbers increase from left to right on a horizontal number line and from bottom to top on a vertical number line.
 Points to the left of a specified point on a horizontal number line are less than points to the right.
 Points to the right of a specified point on a horizontal number line are greater than points to the left.
 Points below a specified point on a vertical number line are less than points above.
 Points above a specified point on a vertical number line are greater than points below.
 Landmark (or anchor) numbers may be placed on the open number line to help locate other numbers.
 Relative magnitude of a number describes the size of a number and its relationship to another number.
 Order a set of numbers on an open number line.
Note(s):
 Grade Level(s):
 Grade 1 introduces ordering whole numbers up to 120 using place value and open number lines.
 Grade 2 will locate the position of a given whole number on an open number line.
 Grade 2 will use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and the symbols >, <, or =.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation

1.2G 
Represent the comparison of two numbers to 100 using the symbols >, <, or =.

Represent
THE COMPARISON OF TWO NUMBERS TO 100 USING THE SYMBOLS >, <, OR =
Including, but not limited to:
 Whole numbers (0 – 100)
 Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
 Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}
 Compare numbers – to consider the value of two numbers to determine which number is greater or less or if the numbers are equal in value
 Comparative language and comparison symbols
 Inequality words and symbols
 Greater than (>)
 Less than (<)
 Equality words and symbol
Note(s):
 Grade Level(s):
 Grade 1 introduces the comparison symbols >, <, and =.
 Grade 2 will use place value to compare and order whole numbers up to 1,200 using comparative language, numbers, and the symbols >, <, or =.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation
