 Hello, Guest!
 TITLE : Unit 09: Number Relationships up to 120 and Coins SUGGESTED DURATION : 10 days

#### Unit Overview

Introduction
This unit bundles student expectations that address identifying U.S. coins by value, recording the value of coins using a cent symbol, determining the value of a collection of coins using skip counting, determining numbers that are 10 more or 10 less than a given number, and reciting numbers. According to the Texas Education Agency, mathematical process standards including application, a problem-solving model, tools and techniques, communication, representations, relationships, and justifications should be integrated (when applicable) with content knowledge and skills so that students are prepared to use mathematics in everyday life, society, and the workplace.

Prior to this Unit
In Unit 07, students discovered numerical patterns in the place value system for numbers up to 99. Students recited numbers up to 99 forward and backward by ones and tens; skip counted by 2s, 5s, and 10s; and determined a number that is 10 more or 10 less than a given number up to 99. In Kindergarten, students used attributes to identify U.S. coins by name. Students have had no prior experience identifying coins by value or counting coins according to the Kindergarten standards.

During this Unit
Students continue to explore place value and numerical relationships in numbers up to 120. Students further develop the understanding of cardinal numbers, meaning numbers that name the quantity of objects in a set, and hierarchical inclusion, meaning each prior number in the counting sequence is included in the set as the set increases. Students recite numbers up to 120 forward and backward by ones and tens; skip count by 2s, 5s, and 10s; and use place value patterns to determine a number that is 10 more or 10 less than a given number. Students use attributes to identify pennies, nickels, dimes, and quarters by value and record the value using the cent symbol. Students explore the relationships that exist between the values of different coins and use these relationships to exchange coins or sets of coins for other equivalent denominations. Students apply skip counting by 2s, 5s, and 10s and compound counting to determine the value of a collection of pennies, nickels, and dimes up to 120 cents, where the collection of coins may include only like coins or a mixed collection.

Other considerations: Reference the Mathematics COVID-19 Gap Implementation Tool Grade 1

After this Unit
In Grade 2, students will extend using counting strategies to determine the value of a collection of coins up to one dollar that includes pennies, nickels, dimes, and/or quarters. Students will record the value of the collection of coins using either cent symbol notation or the dollar sign and decimal symbol notation. Also in Grade 2, students extend the use of place value patterns to include determining a number that is 10 or 100 more or less than a given number up to 1,200.

In Grade 1, identifying U.S. coins by value, recording the value of coins using a cent symbol, determining the value of a collection of coins, and reciting numbers are all identified within the Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of place value. Determining numbers that are 10 more or 10 less than a given number and skip counting are also identified within Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Developing an understanding of place value in addition to the Grade 1 Texas Response to Curriculum Focal Points (TxRCFP): Solving problems involving addition and subtraction. This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning A1, A2, B1; II. Algebraic Reasoning D1, D2; V. Statistical Reasoning A1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, C1, D1, D2; VIII. Communication and Representation A1, A2, A3, B1, B2, C1, C2, C3; IX. Connections A1, A2, B1, B2, B3.

Research
According to Van De Walle (2006), a prerequisite for a true understanding of coin values is an “understanding of 5, 10, and 25. More than that, students need to be able to think of these quantities without seeing countable objects. Nowhere else do we say this is five, while pointing to a single item” (p. 150). Students will need to experience number relationships with the use of manipulative materials. The authors of So You Have to Teach Math (2000) claim, “At every level from kindergarten on up, manipulative materials can help by providing students opportunities to get their hands – and also their minds – around abstract math ideas” (p. 52).

Silbey, R. & Burns, M. (2000). So you have to teach math? Sausalito, CA: Math Solutions Publications.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/index.cfm?objectid=E21AB9B0-2633-11E8-BC500050560100A9
Texas Education Agency. (2013). Texas response to curriculum focal points for kindergarten through grade 8 mathematics. Retrieved from https://www.texasgateway.org/resource/txrcfp-texas-response-curriculum-focal-points-k-8-mathematics-revised-2013
Van de Walle, J., & Lovin, L. (2006). Teaching student-centered mathematics grades k – 3. Boston, MA: Pearson Education, Inc.

 Numeracy requires the ability to work flexibly with quantities in order to recognize, reason, and solve situations of varying contexts in everyday life, society, and the work place. How is numeracy like literacy? What are some examples of numeracy in everyday life, society, and the work place? How does context influence understanding of a quantity? Why is the ability to work flexibly with quantities essential to developing the foundations of numeracy? Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Recognizing the distinct attributes, values, and relationships between the values of U.S. coins leads to efficient and accurate determination of the value of a collection of money (value of a collection of pennies, nickels, and dimes up to 120¢).
• Why is it important to be able to identify US coins?
• What are the distinct attributes of the …
• penny?
• nickel?
• dime?
• quarter?
• What is the value of the …
• penny?
• nickel?
• dime?
• quarter?
• How can the value of a coin be represented using words, numbers, and/or symbols?
• What relationships exist between the values of coins?
• What numerical patterns and counting strategies could be used to efficiently determine the value of a collection of coins?
• How is skip counting related to determining the value of a collection of coins?
• How can different collections of coins equal the same amount?
• Recognizing and understanding numerical patterns and relationships leads to efficient, accurate, and flexible representations (skip counting by twos, fives, and tens up to 120; 10 more or 10 less up to 120).
• What patterns can be found when skip counting by …
• twos?
• fives?
• tens?
• How are patterns in place value relationships used to determine a number that is …
• 10 more
• 10 less
… than a given number?
• Number
• Money
• Coin identification
• Value of a coin
• Value of a collection
• Algebraic Reasoning
• Equivalence
• Patterns and Relationships
• Skip counting
• Multiples
• Associated Mathematical Processes
• Application
• Problem Solving Model
• Tools and Techniques
• Communication
• Representations
• Relationships
• Justification
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

 Quantitative relationships model problem situations efficiently and can be used to make generalizations, predictions, and critical judgements in everyday life. What patterns exist within different types of quantitative relationships and where are they found in everyday life? Why is the ability to model quantitative relationships in a variety of ways essential to solving problems in everyday life?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
• Recognition of patterns in the number word sequence, which are repeated with every grouping of ten, leads to efficient and accurate reciting of numbers (reciting numbers forward and backward between 1 and 120).
• What patterns can be found between each grouping of ten when reciting numbers in sequence …
• forward by ones?
• forward by tens?
• backward by ones?
• backward by tens?
• Algebraic Reasoning
• Patterns and Relationships
• Reciting numbers
• Associated Mathematical Processes
• Problem Solving Model
• Relationships
 Assessment information provided within the TEKS Resource System are examples that may, or may not, be used by your child’s teacher. In accordance with section 26.006 (2) of the Texas Education Code, "A parent is entitled to review each test administered to the parent’s child after the test is administered." For more information regarding assessments administered to your child, please visit with your child’s teacher.

#### MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

• Some students may think when increasing or decreasing a number by a multiple of 10, the tens place is increasing or decreasing by 1 rather than understanding that a change of 1 in the tens place means a change by 1 group of 10.
• Some students may think the pattern used to recite numbers backward is different than the pattern used to recite numbers forward rather than applying the same place value relationships to reciting forward or backward (e.g., if, when reciting numbers forward, the digit in the ones place increases by one, then when reciting numbers backward, the digit in the ones place will decrease by one, etc.).
• Some students may think skip counting numbers in sequence is a memorization task rather than understanding that each number represents a group of objects and that each group of objects in the skip counting sequence represents a quantity of one group more than the previous number.
• Some students may think the relative size of coins is related to their value rather than recognizing that the size of a coin has no impact on its value (e.g., students may think a nickel or penny have a greater value than a dime because the dime is smaller in size).
• Some students may think each coin has only one set of images on the head side and tail side rather than realizing there are multiple views for each coin, such as commemorative views (e.g., state quarters, buffalo nickels, etc.).
• Some students may think a given value can only be represented by one collection of coins rather than recognizing how different collections of coins can equal the same total value.
• Some students may think a collection of coins must be counted in the order the coins are presented rather than realizing like coins can be grouped in order to allow for more efficient counting strategies such as skip counting.

Underdeveloped Concepts:

• Some students may be confused about the counting sequence for the numbers 11 – 15 and recite these numbers as “one-teen, two-teen, three-teen, four-teen, five-teen” rather than “eleven, twelve, thirteen, fourteen, fifteen.”
• Although some students may be able to correctly recite numbers forward from 0 – 99, they may have difficulty beginning with a number other than 0.
• Some students may have difficulty remembering which multiple of 10 follows a number with a 9 in the ones place (e.g., 40 comes after 39, 30 comes after 29, 20 comes after 19, etc.).

#### Unit Vocabulary

• Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {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.
• Recite – to verbalize from memory
• Skip counting – counting numbers in sequence forward or backward by a whole number other than 1
• Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}

Related Vocabulary:

 Cent symbol (¢) Decrease Dime Equal to, same as Exchange Greater than, more than Heads Hundreds place Increase Less than, fewer than Nickel Ones place Penny Quarter Sequence Tails Tens place
System Resources Other Resources

System Resources may be accessed through Search All Components in the District Resources Tab.

Texas Higher Education Coordinating Board – Texas College and Career Readiness Standards

Texas Education Agency – Texas Response to Curriculum Focal Points for K-8 Mathematics Revised 2013

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency Texas Gateway – Revised Mathematics TEKS: Vertical Alignment Charts

Texas Education Agency Texas Gateway – Mathematics TEKS: Supporting Information

Texas Education Agency Texas Gateway – Interactive Mathematics Glossary

Texas Education Agency Texas Gateway – Resources Aligned to Grade 1 Mathematics TEKS

TAUGHT DIRECTLY TEKS

TEKS intended to be explicitly taught in this unit.

TEKS/SE 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 strike-through.

Specificity Legend:

• Supporting information / clarifications (specificity) written by TEKS Resource System are in blue text.
• Unit-specific 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.
TEKS# SE# TEKS SPECIFICITY
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 two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.1. Interpret results of the mathematical problem in terms of the original real-world situation.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
• IX.B.2. Understand and use appropriate mathematical models in the natural, physical, and social sciences.
• IX.B.3. Know and understand the use of mathematics in a variety of careers and professions.
1.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION

Including, but not limited to:

• Problem-solving model
• Analyze given information
• Formulate a plan or strategy
• Determine a solution
• Justify the solution
• Evaluate the problem-solving 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 two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.A. Statistical Reasoning – Design a study
• V.A.1. Formulate a statistical question, plan an investigation, and collect data.
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VII.A.2. Formulate a plan or strategy.
• VII.A.3. Determine a solution.
• VII.A.4. Justify the solution.
• VII.A.5. Evaluate the problem-solving process.
• VII.D. Problem Solving and Reasoning – Real-world problem solving
• VII.D.2. Evaluate the problem-solving process.
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
• Techniques
• Mental math
• Number sense

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 two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• I.B. Numeric Reasoning – Number sense and number concepts
• I.B.1. Use estimation to check for errors and reasonableness of solutions.
• V.C. Statistical Reasoning – Analyze, interpret, and draw conclusions from data
• V.C.2. Analyze relationships between paired data using spreadsheets, graphing calculators, or statistical software.
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 two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• II.D. Algebraic Reasoning – Representing relationships
• II.D.1. Interpret multiple representations of equations, inequalities, and relationships.
• II.D.2. Convert among multiple representations of equations, inequalities, and relationships.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
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 two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
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 non-examples, 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 two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.1. Analyze given information.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.1. Use mathematical symbols, terminology, and notation to represent given and unknown information in a problem.
• VIII.A.2. Use mathematical language to represent and communicate the mathematical concepts in a problem.
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.1. Communicate mathematical ideas, reasoning, and their implications using symbols, diagrams, models, graphs, and words.
• VIII.C.2. Create and use representations to organize, record, and communicate mathematical ideas.
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
• IX.A. Connections – Connections among the strands of mathematics
• IX.A.1. Connect and use multiple key concepts of mathematics in situations and problems.
• IX.A.2. Connect mathematics to the study of other disciplines.
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 two-dimensional shapes and three-dimensional solids
• Developing the understanding of length
• TxCCRS:
• VII.A. Problem Solving and Reasoning – Mathematical problem solving
• VII.A.4. Justify the solution.
• VII.B. Problem Solving and Reasoning – Proportional reasoning
• VII.B.1. Use proportional reasoning to solve problems that require fractions, ratios, percentages, decimals, and proportions in a variety of contexts using multiple representations.
• VII.C. Problem Solving and Reasoning – Logical reasoning
• VII.C.1. Develop and evaluate convincing arguments.
• VIII.A. Communication and Representation – Language, terms, and symbols of mathematics
• VIII.A.3. Use mathematical language for reasoning, problem solving, making connections, and generalizing.
• VIII.B. Communication and Representation – Interpretation of mathematical work
• VIII.B.1. Model and interpret mathematical ideas and concepts using multiple representations.
• VIII.B.2. Summarize and interpret mathematical information provided orally, visually, or in written form within the given context.
• VIII.C. Communication and Representation – Presentation and representation of mathematical work
• VIII.C.3. Explain, display, or justify mathematical ideas and arguments using precise mathematical language in written or oral communications.
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
• Non-proportional 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
• Tails: back of coin
• Presidents
• Penny: Abraham Lincoln
• Nickel: Thomas Jefferson
• Dime: Franklin Delano Roosevelt
• Quarter: George Washington
• 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
• Non-proportional relationship between size and value of coin

Note(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.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
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 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.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
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, real-life 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 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 half-dollars.
• Various mathematical process standards will be applied to this student expectation as appropriate.
• TxRCFP:
• Developing an understanding of place value
• TxCCRS:
• I.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
• IX.B. Connections – Connections of mathematics to nature, real-world situations, and everyday life
• IX.B.1. Use multiple representations to demonstrate links between mathematical and real-world situations.
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):

• 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.A. Numeric Reasoning – Number representations and operations
• I.A.1. Compare relative magnitudes of rational and irrational numbers, and understand that numbers can be represented in different ways.
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, real-life objects, etc.

Note(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, equal-sized 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.A. Numeric Reasoning – Number representations and operations
• I.A.2. Perform computations with rational and irrational numbers.
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.
• Base-10 blocks
• Adding longs will increase a number by increments of 10.
• Removing longs will decrease a number by increments of 10.

Note(s): 