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, GRAPHS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:
 Mathematical ideas, reasoning, and their implications
 Multiple representations, as appropriate
 Symbols
 Diagrams
 Graphs
 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

1.4 
Number and operations. The student applies mathematical process standards to identify coins, their values, and the relationships among them in order to recognize the need for monetary transactions. The student is expected to:


1.4A 
Identify U.S. coins, including pennies, nickels, dimes, and quarters, by value and describe the relationships among them.

Identify
U.S. COINS, INCLUDING PENNIES, NICKELS, DIMES, AND QUARTERS, BY VALUE
Including, but not limited to:
 U.S. coins by value
 Penny: 1 cent
 Nickel: 5 cents
 Dime: 10 cents
 Quarter: 25 cents
 Nonproportional relationship between size and value of coin
 Attributes of pennies, nickels, dimes, and quarters
 Color
 Copper: penny
 Silver: nickel, dime, and quarter
 Size
 Relative sizes
 Largest to smallest: quarter, nickel, penny, dime
 Smallest to largest: dime, penny, nickel, quarter
 Texture
 Smooth edges: penny, nickel
 Ridged edges: dime, quarter
 Informal references
 Heads: front of coin
 Tails: back of coin
 Traditional head designs
 Presidents
 Penny: Abraham Lincoln
 Nickel: Thomas Jefferson
 Dime: Franklin Delano Roosevelt
 Quarter: George Washington
 Traditional tail designs
 Symbols
 Penny: Lincoln Memorial or union shield
 Nickel: Monticello
 Dime: Torch (liberty), Olive branch (peace), Oak branch (strength and independence)
 Quarter: Presidential coat of arms (eagle with outstretched arms)
 Special designs
 State coins
 U.S. territories
 Commemorative issues
 Concrete and pictorial models
 Views of both sides of coins
Describe
THE RELATIONSHIPS AMONG U.S. COINS
Including, but not limited to:
 U.S. coins
 Penny
 Nickel
 Dime
 Quarter
 Relationships by value
 Penny to nickel, dime, quarter
 5 pennies = 1 nickel; 10 pennies = 1 dime; 25 pennies = 1 quarter
 1 penny < 1 nickel; 1 penny < 1 dime; 1 penny < 1 quarter
 Nickel to penny, dime, quarter
 1 nickel = 5 pennies; 2 nickels = 1 dime; 5 nickels = 1 quarter
 1 nickel > 1 penny; 1 nickel < 1 dime; 1 nickel < 1 quarter
 Dime to penny, nickel, quarter
 1 dime = 10 pennies; 1 dime = 2 nickels; 5 dimes = 2 quarters
 1 dime > 1 penny; 1 dime > 1 nickel; 1 dime < 1 quarter
 Quarter to penny, nickel, dime
 1 quarter = 25 pennies; 1 quarter = 5 nickels; 2 quarters = 5 dimes
 1 quarter > 1 penny; 1 quarter > 1 nickel; 1 quarter > 1 dime
 Exchange of coins to other denominations
 Based on relationships between values
 Relationships between attributes
 Historically significant people on heads of all coins
 Nonproportional relationship between size and value of coin
Note(s):
 Grade Level(s):
 Kindergarten identified U.S. coins by name, including pennies, nickels, dimes, and quarters.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 IX. Communication and Representation
 X. Connections

1.4B 
Write a number with the cent symbol to describe the value of a coin.

Write
A NUMBER WITH THE CENT SYMBOL TO DESCRIBE THE VALUE OF A COIN
Including, but not limited to:
 Cent symbol (¢)
 Cent symbol written to the right of the numerical value
 Cent label read and written after numerical value
 Value of a coin named with numbers and symbols
 Penny: 1¢
 Nickel: 5¢
 Dime: 10¢
 Quarter: 25¢
 Value of a coin named with numbers and words
 Penny: 1 cent
 Nickel: 5 cents
 Dime: 10 cents
 Quarter: 25 cents
Note(s):
 Grade Level(s):
 Grade 1 introduces the cent symbol to describe the value of a coin.
 Grade 2 will use the cent symbol, the dollar sign, and decimal point to name the value of a collection of coins.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 IX. Communication and Representation
 X. Connections

1.4C 
Use relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes.

Use
RELATIONSHIPS TO COUNT BY TWOS, FIVES, AND TENS
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}
 Skip counting – counting numbers in sequence forward or backward by a whole number other than 1
 Counting sequence can begin at any number.
 Relationships in skip counting by twos
 When counting by twos, one number is skipped.
 When beginning with 0, all numbers counted have a 0, 2, 4, 6, or 8 in the ones place.
 Relationships when skip counting by fives
 When counting by fives, 4 numbers are skipped.
 When beginning with 0, all numbers counted alternate 0 or 5 in the ones place.
 Relationships when skip counting by tens
 When counting by tens, 9 numbers are skipped.
 When beginning with 0, all numbers counted have a 0 in the ones place.
 When beginning with any number, the digit in the ones place remains the same and the digit in the tens place increases by 1.
 When beginning with 0, all numbers counted by ten are also included in the count by twos and the count by fives.
 Relationships represented using concrete or pictorial models
 Hundreds chart, color tiles, number line, beaded number line, reallife objects, etc.
To Determine
THE VALUE OF A COLLECTION OF PENNIES, NICKELS, AND/OR DIMES
Including, but not limited to:
 Coins
 Penny: 1¢
 Nickel: 5¢
 Dime: 10¢
 Concrete and pictorial models
 Traditional and newly released designs
 Views of both sides of coins
 Collection of like coins up to 120 cents
 Collection of mixed coins up to 120 cents
 Skip counting
 Coins in like groups (e.g., dimes, nickels, pennies)
 By twos to determine the value of a collection of pennies
 2¢, 4¢, 6¢, 8¢, …, 28¢, 30¢, 32¢, 34¢, etc.
 By fives to determine the value of a collection of nickels
 5¢, 10¢, 15¢, 20¢, 25¢, 30¢, …, 95¢, 100¢, 105¢, 110¢, etc.
 By tens to determine the value of a collection of dimes
 10¢, 20¢, 30¢, 40¢, 50¢, …, 80¢, 90¢, 100¢, 110¢, 120¢
 Compound counting to determine the value of a collection of mixed coins
 Separate coins into like groups prior to counting (e.g., dimes, nickels, pennies).
 Begin by counting the largest denomination of coins and then count on each denomination of coins in order from largest to smallest.
 Count dimes by tens, count on nickels by fives, count on pennies by twos or ones
 Create a collection of coins for a given value.
 Comparison of the values of two collections of coins
 Number of coins may not be proportional to the value of the collection.
 Multiple combinations of the same value
 Minimal set
 Least number of coins to equal a given value
Note(s):
 Grade Level(s):
 Grade 1 introduces using relationships to count by twos, fives, and tens to determine the value of a collection of pennies, nickels, and/or dimes.
 Grade 2 will determine the value of a collection of coins up to one dollar, including quarters and halfdollars.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 TxCCRS:
 IX. Communication and Representation
 X. Connections

1.5 
Algebraic reasoning. The student applies mathematical process standards to identify and apply number patterns within properties of numbers and operations in order to describe relationships. The student is expected to:


1.5A 
Recite numbers forward and backward from any given number between 1 and 120.

Recite
NUMBERS FORWARD AND BACKWARD FROM ANY GIVEN NUMBER BETWEEN 1 AND 120
Including, but not limited to:
 Counting numbers (1 – 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}
 Number word sequence has a correct order.
 Recite – to verbalize from memory
 Development of automaticity
 Relationship to counting
 Cardinal number – a number that names the quantity of objects in a set
 Hierarchical inclusion – concept of nested numbers, meaning each prior number in the counting sequence is included in the set as the set increases (e.g., 58 is 57 increased by 1; 58 decreased by 1 is 57; etc.)
 Recite numbers forward from any given number between 1 and 120
 Orally by ones beginning with 1
 Orally by ones beginning with any given number
 Orally by tens beginning with 10
 Orally by tens beginning with any given number
 Recite numbers backward from any given number between 1 and 120
 Orally by ones beginning with 120
 Orally by ones beginning with any given number between 1 and 120
 Orally by tens beginning with 120
 Orally by tens beginning with any given number between 1 and 120
Note(s):
 Grade Level(s):
 Kindergarten recited numbers up to at least 100 by ones beginning with any given number and by tens beginning with any multiple of 10.
 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

1.5B 
Skip count by twos, fives, and tens to determine the total number of objects up to 120 in a set.

Skip Count
BY TWOS, FIVES, AND TENS TO DETERMINE THE TOTAL NUMBER OF OBJECTS UP TO 120 IN A SET
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}
 Skip counting – counting numbers in sequence forward or backward by a whole number other than 1
 Counting sequence can begin at any number.
 Determine the total number of objects in a set.
 Sets up to 120
 Skip counting by twos, fives, and tens
 More efficient than counting by ones
 Counting the same set of objects using different skip count increments results in the same total.
 Relationships in skip counting by twos
 When counting by twos, one number is skipped.
 When beginning with 0, all numbers counted have a 0, 2, 4, 6, or 8 in the ones place.
 Relationships when skip counting by fives
 When counting by fives, 4 numbers are skipped.
 When beginning with 0, all numbers counted alternate 0 or 5 in the ones place.
 Relationships when skip counting by tens
 When counting by tens, 9 numbers are skipped.
 When beginning with 0, all numbers counted have a 0 in the ones place.
 When beginning with any number, the digit in the ones place remains the same and the digit in the tens place increases by 1.
 When beginning with 0, all numbers counted by ten are also included in the count by twos and the count by fives.
 Relationships represented using concrete or pictorial models
 Hundreds chart, color tiles, number line, reallife objects, etc.
Note(s):
 Grade Level(s):
 Grade 1 introduces skip counting by twos, fives, and tens to determine the total number of objects up to 120 in a set.
 Grade 2 will determine whether a number up to 40 is even or odd using pairings of objects to represent the number.
 Grade 3 will represent multiplication facts by using a variety of approaches such as repeated addition, equalsized groups, arrays, area models, equal jumps on a number line, and skip counting.
 Various mathematical process standards will be applied to this student expectation as appropriate.
 TxRCFP:
 Developing an understanding of place value
 Solving problems involving addition and subtraction
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation

1.5C 
Use relationships to determine the number that is 10 more and 10 less than a given number up to 120.

Use
RELATIONSHIPS TO DETERMINE THE NUMBER THAT IS 10 MORE AND 10 LESS THAN A GIVEN NUMBER UP TO 120
Including, but not limited to:
 Whole numbers (1 – 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
 Comparative language
 Greater than, more than
 Less than, fewer than
 Relationships based on place value
 10 more or 10 less
 Adding 10 to a number increases the digit in the tens place by 1.
 Subtracting 10 from a number decreases the digit in the tens place by 1.
 Relationships based on patterns in concrete or pictorial models
 Hundreds chart
 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 longs will increase a number by increments of 10.
 Removing longs will decrease a number by increments of 10.
Note(s):
 Grade Level(s):
 Grade 1 introduces using relationships to determine the number that is 10 more and 10 less than a given number up to 120.
 Grade 2 will use an understanding of place value to determine the number that is 10 or 100 more or less than a given 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
 Solving problems involving addition and subtraction
 TxCCRS:
 I. Numeric Reasoning
 IX. Communication and Representation
