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Instructional Focus Document
Grade 4 Mathematics
TITLE : Unit 02: Addition and Subtraction of Whole Numbers and Decimals SUGGESTED DURATION : 7 days

Unit Overview

Introduction
This unit bundles student expectations that address using various methods to estimate solutions to addition and subtraction problems, the standard algorithm for adding and subtracting whole numbers and decimal numbers, calculating profit, and describing the purposes of financial institutions. 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 Grade 3, students learned strategies for rounding to the nearest 10 or 100, and practiced the analysis of numbers within problems to determine a need for either rounding or using compatible numbers to justify the reasonableness of solutions. They progressed in addition and subtraction skills through solving one- and two-step problem situations that promoted the use of place value, properties of operations, and the examination of different ways to represent their solution process. Students also described the relationship between the availability or scarcity of resources and how that impacts cost, and explained that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest.

During this Unit
Students extend their understanding of rounding to numbers in the hundred thousands using their choice of strategies (e.g., number lines or numerical methods based on place value). Mathematical and real-world problem situations are analyzed for vocabulary that indicates estimation and for whether compatible numbers exist that could be used to find a reasonable estimate. Students develop the ability to recognize vocabulary descriptors that describe the effects of the adjustment on the estimation compared to the actual solution (e.g., about, close, little more/little less, around, approximately, estimated, etc.). Grade 4 students make connections between place value and the standard algorithms for adding and subtracting whole numbers to adding and subtracting decimals, including tenths and hundredths. They relate addition and subtraction of decimals to the hundredths place using concrete objects and pictorial models (e.g., tenths and hundredths grids, number lines, base-10 blocks, etc.) to the standard algorithm for adding and subtracting decimals. Skill with the standard algorithm for the addition and subtraction of decimals is applied as students determine profit from single or multiple sources for incomes and/or expenses. Also included in the unit is the expectation that students describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending money.

After this Unit
In Unit 05, students will revisit addition and subtraction as they apply their estimation, addition, and subtraction skills to one- and two-step problems. In Grade 5, students will extend their application of strategies for rounding numbers to rounding decimals to the tenths or hundredths place. They will also estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division.

Additional Notes
In Grade 4, adding and subtracting whole numbers and decimals to the hundredths place using the standard algorithm is identified as STAAR Readiness Standard 4.4A, and rounding numbers or using compatible numbers to estimate solutions to problems are identified as STAAR Supporting Standards 4.2D and 4.4G. Standard 4.2D is contained under the Grade 4 STAAR Reporting Category 1: Numerical Representations and Relationships, while standards 4.4A and 4.4G are included under the Grade 4 STAAR Reporting Category 2: Computations and Algebraic Relationships. Both standards 4.2D and 4.4A are further subsumed under the Grade 4 Texas Response to Curriculum Focal Points (TxRCFP): Understanding decimals and addition and subtraction of decimals. Standards 4.4A and 4.4G are also incorporated under the Grade 4 Focal Point: Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems (TxRCFP). Calculating profit in given situations and describing the basic purpose of financial institutions, are identified as STAAR Supporting Standards 4.10B and 4.10E. These standards are subsumed within the Grade 4 STAAR Reporting Category 4: Data Analysis and Personal Financial Literacy and are included in the Grade 4 Focal Point: Financial Literacy (TxRCFP). This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning A2, B1; II. Algebraic Reasoning D1 D2; V. Statistical Reasoning A1, C2; VII. Problem Solving and Reasoning A1, A2, A3, A4, A5, B1, 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 the National Council of Teachers of Mathematics (2010), “decimals are the most common form in which we encounter rational numbers. Decimals are essential to metric measurement and are extremely useful in science and technology” (p. 36). Van de Walle and Lovin assert that “the base-ten place-value system extends infinitely in two directions: to tiny values as well as to large values. Between any two place values, the ten-to-one ratio remains the same.” They further state that “addition and subtraction with decimals are based on the fundamental concept of adding and subtracting the numbers in like position values – a simple extension from whole numbers” (p. 181). As published by the National Research Council (2001), “when students fail to grasp the concepts that underlie procedures or cannot connect the concepts to the procedures, they frequently generate flawed procedures that result in systematic patterns of errors” (p. 196). Introducing students to the real-life concepts of earning and saving is supported by the National Institute of Food and Agriculture on their Financial Security (2014) which states, “An early, clear understanding of the basic principles of budgeting and saving will usually result in increased household wealth later in life. Financial education can help people learn the lifelong skills of creating and sticking with a spending and savings plan and making strategic investment decisions.”

 

National Council of Teachers of Mathematics. (2010). Developing essential understanding of rational numbers grades 3 – 5. Reston, VA: National Council of Teachers of Mathematics, Inc.
National Research Council. (2001). Adding it up: Helping children learn mathematics. Kilpatrick, J., Swafford, J., and Findell, B. (Eds.) Mathematics Learning Study Committee, Center for Education Division of Behavioral and Social Sciences and Education. Washington, DC: National Academy Press.
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
United States Department of Agriculture. Financial Security. National Institute of Food and Agriculture, 24 Feb. 2014. Web. 09 Apr. 2014. Retrieved from http://www.csrees.usda.gov/ProgViewOverview.cfm?prnum=20083
Van de Walle, J., & Lovin, L. (2006). Teaching student-centered mathematics grades 3 – 5. Boston, MA: Pearson Education, Inc.


  • Understanding and generalizing operational relationships leads to more sophisticated representations and solution strategies in order to investigate or solve problem situations in everyday life.
    • What relationships exist within and between mathematical operations?
    • How does generalizing operational relationships lead to developing more flexible, efficient representations and/or solution strategies?
    • Why is understanding the problem solving process an essential part of learning and working mathematically?
  • Financial and economic knowledge leads to informed and rational decisions allowing for effective management of financial resources when planning for a lifetime of financial security.
    • Why is financial stability important in everyday life?
    • What economic and financial knowledge is critical for planning for a lifetime of financial security?
    • How can mapping one’s financial future lead to significant short and long-term benefits?
    • How can current financial and economic factors in everyday life impact daily decisions and future opportunities?
Unit Understandings
and Questions
Overarching Concepts
and Unit Concepts
Performance Assessment(s)
  • Estimation strategies can be used to mentally approximate solutions and determine reasonableness of solutions (addition and subtraction of whole numbers and decimals).
    • What strategies can be used to estimate solutions to problems?
    • What are the similarities and differences between …
      • rounding numbers and using compatible numbers to estimate a solution?
      • rounding whole numbers and rounding decimals?
    • When might an estimated answer be preferable to an exact answer?
    • How can an estimation aid in determining the reasonableness of an actual solution?
    • When might one estimation strategy be more beneficial than another?
  • Recognizing and understanding operational relationships in a variety of problem situations leads to efficient, accurate, and flexible representations and solution strategies (addition and subtraction of whole numbers and decimals).
    • How does the context of a problem situation affect the representation, operation(s), and/or solution strategy that could be used to solve the problem?
    • What patterns and relationships can be found within and between the words, pictorial models, and equations used to represent a problem situation?
    • How does understanding …
      • relationships within and between operations
      • properties of operations
      • place value
      • income, expenses, costs, and profit
      … aid in determining an efficient strategy or representation to investigate problem situations?
    • What strategies can be used to determine …
      • the sum
      • the difference
      • any unknown
      … in an addition or subtraction situation involving whole numbers and decimals?
    • Why is it important to understand when and how to use standard algorithms?
    • When adding or subtracting decimal numbers, why is it important to align the place values?
    • What relationships exist between …
      • addition and subtraction?
      • operations with whole numbers and operations with decimals?
      • operations and calculating profit?
    • When using addition to solve a problem situation, why can the order of the addends be changed?
    • When using subtraction to solve a problem situation, why can the order of the minuend and subtrahend not be changed?
  • Operational understandings lead to generalizations that aid in determining the reasonableness of solutions (addition and subtraction of whole numbers and decimals).
    • When adding two non-zero whole numbers and/or positive decimals, why is the sum always greater than each of the addends?
    • When subtracting two non-zero whole numbers and/or positive decimals with the minuend greater than the subtrahend, why is the difference always less than the minuend?
  • Understanding profit and the purpose of financial institutions aids in making informed financial management decisions, which promotes a more secured financial future.
    • How is profit calculated?
    • How is profit affected by …
      • expenses (costs)?
      • income (revenue)?
    • How does understanding profit affect decisions about selling and buying?
    • What are some …
      • types of financial institutions?
      • functions of financial institutions?
    • Whom do financial institutions serve?
    • How is money that is deposited used by banks?
    • How do financial institutions have a positive impact on the growth of your money?
  • Number and Operations
    • Estimation
      • Rounding
      • Compatible numbers
    • Number
      • Counting (natural) numbers
      • Whole numbers
      • Decimals
    • Operations
      • Addition
      • Subtraction
    • Properties of Operations
    • Relationships and Generalizations
      • Operational
      • Equivalence
    • Solution Strategies and Algorithms
  • Personal Financial Literacy
    • Borrowing and Lending
    • Financial Institutions
    • Profit
  • 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.

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Some students may think that rounding is the only way to make an estimate rather than understanding that there are multiple ways to determine an estimate.
  • Some students may think that rounding and estimating are the same skill rather than rounding as one way to make the numbers friendly in order to compute and determine a reasonable estimate.
  • Some students may think that decimal numbers should be lined up vertically according to the maximum number of digits in order to use the standard algorithm rather than realizing that they must be lined up according to place values.

Underdeveloped Concepts:

  • Some students may think the word “more” means to add rather than a term that could lead to addition or subtraction.
  • Some students may think the words “take away” means to subtract rather than a term that could lead to multiple structures of subtraction.
  • Some students may not transfer the understanding that 10 in any place value position (place) makes one (group) in the next place value position or vice versa when adding or subtracting whole numbers to adding or subtracting decimals.
  • Some students may have a procedural understanding of the standard algorithms for addition and/or subtraction while lacking conceptual understanding of the operations.
  • Some students who work through the standard algorithm procedures may think about numbers as digits and ignore place value, leading to an unreasonable amount, rather than think about place value to help determine a reasonable amount.

Unit Vocabulary

  • Compatible numbers – numbers that are slightly adjusted to create groups of numbers that are easy to compute mentally
  • Counting (natural) numbers – the set of positive numbers that begins at one and increases by increments of one each time {1, 2, 3, ..., n}
  • Decimal number – a number in the base-10 place value system used to represent a quantity that may include part of a whole and is recorded with a decimal point separating the whole from the part
  • Estimation – reasoning to determine an approximate value
  • Expense – payment for goods and services
  • Financial institution – an establishment that focuses on dealing with financial transactions such as investments, loans, and deposits
  • Income – money earned or received
  • Profit – money that is made in a business after all the costs and expenses are paid
  • Rounding – a type of estimation with specific rules for determining the closest value
  • Trailing zeros – a sequence of zeros in the decimal part of a number that follow the last non-zero digit, and whether recorded or deleted, does not change the value of the number
  • Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}

Related Vocabulary:

  • About
  • Account
  • Approximately
  • Around
  • Borrower
  • Close
  • Consecutive
  • Deposit
  • Depositor
  • Difference
  • Estimate
  • Financial
  • Halfway
  • Hundredth
  • Lend
  • Little less
  • Little more
  • Magnitude
  • Multiple
  • Number line
  • Open number line
  • Standard algorithm
  • Sum
  • Tenth
  • Transaction
Unit Assessment Items System Resources Other Resources

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Unit Assessment Items that have been published by your district may be accessed through Search All Components in the District Resources tab. Assessment items may also be found using the Assessment Center if your district has granted access to that tool.

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 4 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.
  • Student Expectations (TEKS) are labeled Readiness as identified by TEA of the assessed curriculum.
  • Student Expectations (TEKS) are labeled Supporting as identified by TEA of the assessed curriculum.
  • Student Expectations (TEKS) are labeled Process standards as identified by TEA of the assessed curriculum.
  • 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
4.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
4.1A Apply mathematics to problems arising in everyday life, society, and the workplace.
Process Standard

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 fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • X. Connections
4.1B 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.
Process Standard

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 fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
4.1C 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.
Process Standard

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

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
      • Estimation
      • Number sense

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
4.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
Process Standard

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 fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.1E Create and use representations to organize, record, and communicate mathematical ideas.
Process Standard

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 fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.1F Analyze mathematical relationships to connect and communicate mathematical ideas.
Process Standard

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 fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • X. Connections
4.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
Process Standard

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 fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Measuring angles
    • Understanding decimals and addition and subtraction of decimals
    • Building foundations for addition and subtraction of fractions
  • TxCCRS:
    • IX. Communication and Representation
4.2 Number and operations. The student applies mathematical process standards to represent, compare, and order whole numbers and decimals and understand relationships related to place value. The student is expected to:
4.2D Round whole numbers to a given place value through the hundred thousands place.
Supporting Standard

Round

WHOLE NUMBERS TO A GIVEN PLACE VALUE THROUGH THE HUNDRED THOUSANDS PLACE

Including, but not limited to:

  • Whole numbers (0 – 1,000,000,000)
    • 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}
  • Rounding – a type of estimation with specific rules for determining the closest value
  • Nearest 10; 100; 1,000; 10,000; or 100,000
  • Number lines
    • Proportionally scaled number lines (pre-determined intervals)
    • Open number lines (no marked intervals)
    • Relative magnitude of a number describes the size of a number and its relationship to another number.
    • Rounding to the nearest 10 on a number line
      • Determine the two consecutive multiples of 10 that the number being rounded falls between.
        • Begin with the value of the original tens place within the number and then identify the next highest value in the tens place.
      • Determine the halfway point between the consecutive multiples of 10.
      • Locate the position of the number being rounded on the number line.
      • Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 10 on the number line.
        • If the number being rounded is before the halfway point on the number line, round to the value of the original tens place.
        • If the number being rounded is past the halfway point on the number line, round to the value of the next highest tens place.
        • If the number being rounded is on the halfway point on the number line, round to the value of the next highest tens place.
    • Rounding to the nearest 100 on a number line
      • Determine the two consecutive multiples of 100 that the number being rounded falls between.
        • Begin with the value of the original hundreds place within the number and then identify the next highest value in the hundreds place.
      • Determine the halfway point between the consecutive multiples of 100.
      • Locate the position of the number being rounded on the number line.
      • Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 100 on the number line.
        • If the number being rounded is before the halfway point on the number line, round to the value of the original hundreds place.
        • If the number being rounded is past the halfway point on the number line, round to the value of the next highest hundreds place.
        • If the number being rounded is on the halfway point on the number line, round to the value of the next highest hundreds place.
    • Rounding to the nearest 1,000 on a number line
      • Determine the two consecutive multiples of 1,000 that the number being rounded falls between.
        • Begin with the value of the original thousands place within the number and then identify the next highest value in the thousands place.
      • Determine the halfway point between the consecutive multiples of 1,000.
      • Locate the position of the number being rounded on the number line.
      • Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 1,000 on the number line.
        • If the number being rounded is before the halfway point on the number line, round to the value of the original thousands place.
        • If the number being rounded is past the halfway point on the number line, round to the value of the next highest thousands place.
        • If the number being rounded is on the halfway point on the number line, round to the value of the next highest thousands place.
    • Rounding to the nearest 10,000 on a number line
      • Determine the two consecutive multiples of 10,000 that the number being rounded falls between.
        • Begin with the value of the original ten thousands place within the number and then identify the next highest value in the ten thousands place.
      • Determine the halfway point between the consecutive multiples of 10,000.
      • Locate the position of the number being rounded on the number line.
      • Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 10,000 on the number line.
        • If the number being rounded is before the halfway point on the number line, round to the value of the original ten thousands place.
        • If the number being rounded is past the halfway point on the number line, round to the value of the next highest ten thousands place.
        • If the number being rounded is on the halfway point on the number line, round to the value of the next highest ten thousands place.
    • Rounding to the nearest 100,000 on a number line
      • Determine the two consecutive multiples of 100,000 that the number being rounded falls between.
        • Begin with the value of the original hundred thousands place within the number and then identify the next highest value in the hundred thousands place.
      • Determine the halfway point between the consecutive multiples of 100,000.
      • Locate the position of the number being rounded on the number line.
      • Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 100,000 on the number line.
        • If the number being rounded is before the halfway point on the number line, round to the value of the original hundred thousands place.
        • If the number being rounded is past the halfway point on the number line, round to the value of the next highest hundred thousands place.
        • If the number being rounded is on the halfway point on the number line, round to the value of the next highest hundred thousands place.
    • Round a given number to the closest multiple of 10; 100; 1,000; 10,000; or 100,000 on a number line.
    • Round a given number to the higher multiple of 10; 100; 1,000; 10,000; or 100,000 if it falls exactly halfway between the multiples on a number line.
  • Rounding numerically based on place value
    • Find the place to which you are rounding.
      Look at the digit of the next lowest place value, the digit to the right of which you are rounding.
      If the digit in that place is less than 5, then the digit in the rounding place remains the same.
      If the digit in that place is greater than or equal to 5, then the digit in the rounding place increases by 1.
      The digit(s) to the right of the place of which you are rounding is replaced with “0”.

Note(s):

  • Grade Level(s):
    • Grade 3 introduced rounding to the nearest 10 or 100 or using compatible numbers to estimate solutions to addition and subtraction problems.
    • Grade 5 will round decimals to the tenths or hundredths.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Understanding decimals and addition and subtraction of decimals
  • TxCCRS:
    • I. Numeric Reasoning
    • IX. Communication and Representation
4.4 Number and operations. The student applies mathematical process standards to develop and use strategies and methods for whole number computations and decimal sums and differences in order to solve problems with efficiency and accuracy. The student is expected to:
4.4A Add and subtract whole numbers and decimals to the hundredths place using the standard algorithm.
Readiness Standard

Add, Subtract

WHOLE NUMBERS AND DECIMALS TO THE HUNDREDTHS PLACE USING THE STANDARD ALGORITHM

Including, but not limited to:

  • Whole numbers
    • 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}
  • Addition and subtraction of whole numbers
    • Connection between place value and the standard algorithm
    • Standard algorithm
  • Decimals (less than or greater than one to the tenths and hundredths)
    • Decimal number – a number in the base-10 place value system used to represent a quantity that may include part of a whole and is recorded with a decimal point separating the whole from the part
  • Addition and subtraction of decimals
    • Relate addition and subtraction of decimals to the hundredths place using concrete objects and pictorial models to the standard algorithm for adding and subtracting decimals.
    • Trailing zeros – a sequence of zeros in the decimal part of a number that follow the last non-zero digit, and whether recorded or deleted, does not change the value of the number
    • Standard algorithm 

Note(s):

  • Grade Level(s):
    • Grade 3 solved with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
    • Grade 4 extends adding and subtracting of whole numbers from 1,000 to 1,000,000 and introduces adding and subtracting decimals, including tenths and hundredths.
    • Grade 5 will estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
    • Understanding decimals and addition and subtraction of decimals
  • TxCCRS:
    • I. Numeric Reasoning
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
4.4G Round to the nearest 10, 100, or 1,000 or use compatible numbers to estimate solutions involving whole numbers.
Supporting Standard

Round

TO THE NEAREST 10, 100, OR 1,000 TO ESTIMATE SOLUTIONS INVOLVING WHOLE NUMBERS

Including, but not limited to:

  • Whole numbers
    • 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}
  • Addition
    • Sums of whole numbers
  • Subtraction
    • Differences of whole numbers
  • Recognition of operations in mathematical and real-world problem situations
    • Multi-step problems
  • Estimation – reasoning to determine an approximate value
    • Rounding – a type of estimation with specific rules for determining the closest value
      • To the nearest 10; 100; or 1,000
  • Number lines
    • Proportionally scaled number lines (pre-determined intervals)
    • Open number line (no marked intervals)
    • Relative magnitude of a number describes the size of a number and its relationship to another number.
    • Rounding to the nearest 10 on a number line
      • Determine the two consecutive multiples of 10 that the number being rounded falls between.
        • Begin with the value of the original tens place within the number and then identify the next highest value in the tens place.
      • Determine the halfway point between the consecutive multiples of 10.
      • Locate the position of the number being rounded on the number line.
      • Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 10 on the number line.
        • If the number being rounded is before the halfway point on the number line, round to the value of the original tens place.
        • If the number being rounded is past the halfway point on the number line, round to the value of the next highest tens place.
        • If the number being rounded is on the halfway point on the number line, round to the value of the next highest tens place.
    • Rounding to the nearest 100 on a number line
      • Determine the two consecutive multiples of 100 that the number being rounded falls between.
        • Begin with the value of the original hundreds place within the number and then identify the next highest value in the hundreds place.
      • Determine the halfway point between the consecutive multiples of 100.
      • Locate the position of the number being rounded on the number line.
      • Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 100 on the number line.
        • If the number being rounded is before the halfway point on the number line, round to the value of the original hundreds place.
        • If the number being rounded is past the halfway point on the number line, round to the value of the next highest hundreds place.
        • If the number being rounded is on the halfway point on the number line, round to the value of the next highest hundreds place.
    • Rounding to the nearest 1,000 on a number line
      • Determine the two consecutive multiples of 1,000 that the number being rounded falls between.
        • Begin with the value of the original thousands place within the number and then identify the next highest value in the thousands place.
      • Determine the halfway point between the consecutive multiples of 1,000.
      • Locate the position of the number being rounded on the number line.
      • Determine if the number being rounded is before, past, or on the halfway point between the consecutive multiples of 1,000 on the number line.
        • If the number being rounded is before the halfway point on the number line, round to the value of the original thousands place.
        • If the number being rounded is past the halfway point on the number line, round to the value of the next highest thousands place.
        • If the number being rounded is on the halfway point on the number line, round to the value of the next highest thousands place.
    • Round a given number to the closest multiple of 10; 100; or 1,000 on a number line.
    • Round a given number to the higher multiple of 10; 100; or 1,000 if it falls exactly halfway between the multiples on a number line.
    • Round numbers to a common place then compute.
      • If not designated, find the greatest common place value of all numbers in the problem to determine the place value to which you are rounding (e.g., round to the nearest 10 if only two-digit numbers are being considered in the problem; round to the nearest 100 if only three-digit numbers are being considered in the problem; round to the nearest 1,000 if only four-digit numbers are being considered; round to the nearest 10 if both two-digit and three-digit numbers are being considered in the problem; round to the nearest 100 if both three-digit and four-digit numbers are being considered; etc.).
      • Vocabulary indicating estimation in mathematical and real-world problem situations (e.g., about, approximately, estimate, etc.)
      • Vocabulary descriptors of the effects of the adjustment on the estimation compared to the actual solution (e.g., about, close, little more/little less, around, approximately, estimated, etc.)
        • Variation of the estimate from the actual solution is dependent upon the magnitude of the adjustment(s) of the actual numbers.
  • Rounding numerically based on place value
    • Find the place to which you are rounding.
      Look at the digit of the next lowest place value, the digit to the right of which you are rounding.
      If the digit in that place is less than 5, then the digit in the rounding place remains the same.
      If the digit in that place is greater than or equal to 5, then the digit in the rounding place increases by 1.
      The digit(s) to the right of the place of which you are rounding is replaced with “0”.
    • Round numbers to a common place then compute.
      • If not designated, find the greatest common place value of all numbers in the problem to determine the place value to which you are rounding (e.g., round to the nearest 10 if only two-digit numbers are being considered in the problem; round to the nearest 100 if only three-digit numbers are being considered in the problem; round to the nearest 1,000 if only four-digit numbers are being considered; round to the nearest 10 if both two-digit and three-digit numbers are being considered in the problem; round to the nearest 100 if both three-digit and four-digit numbers are being considered; etc.).
      • Vocabulary indicating estimation in mathematical and real-world problem situations (e.g., about, approximately, estimate, etc.)
      • Vocabulary descriptors of the effects of the adjustment on the estimation compared to the actual solution (e.g., about, close, little more/little less, around, approximately, estimated, etc.)Variation of the estimate from the actual solution is dependent upon the magnitude of the adjustment(s) of the actual numbers.
        • Variation of the estimate from the actual solution is dependent upon the magnitude of the adjustment(s) of the actual numbers.

Use

COMPATIBLE NUMBERS TO ESTIMATE SOLUTIONS INVOLVING WHOLE NUMBERS

Including, but not limited to:      

  • Whole numbers
    • 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}
  • Addition
    • Sums of whole numbers
  • Subtraction
    • Differences of whole numbers
  • Recognition of operations in mathematical and real-world problem situations
    • Multi-step problems
  • Estimation – reasoning to determine an approximate value
    • Compatible numbers – numbers that are slightly adjusted to create groups of numbers that are easy to compute mentally
  • Determine compatible numbers then compute.
    • Vocabulary indicating estimation in mathematical and real-world problem situations (e.g., about, approximately, estimate, etc.)
    • Vocabulary descriptors of the effects of the adjustment on the estimation compared to the actual solution (e.g., about, close, little more/little less, around, approximately, estimated, etc.)
      • Variation of the estimate from the actual solution is dependent upon the magnitude of the adjustment(s) of the actual numbers.

Note(s):

  • Grade Level(s):
    • Grade 3 rounded to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems.
    • Grade 5 will round decimals to tenths or hundredths.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems
  • TxCCRS:
    • I. Numeric Reasoning
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
4.10 Personal financial literacy. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security. The student is expected to:
4.10B Calculate profit in a given situation.
Supporting Standard

Calculate

PROFIT IN A GIVEN SITUATION

Including, but not limited to:

  • Whole numbers
  • Decimals (less than or greater than one to the tenths and hundredths)
  • Addition
    • Sums of whole numbers
    • Sums of decimals up to the hundredths
  • Subtraction
    • Differences of whole numbers
    • Differences of decimals with values limited to the hundredths
  • Income – money earned or received
    • Income in a business also called revenue
  • Expense – payment for goods and services
    • Expenses in a business also called costs
  • Profit – money that is made in a business after all the costs and expenses are paid
    • Profit is calculated by subtracting expenses (costs) from income (revenue).
      • Income – expenses = profit
      • Revenue – costs = profit
  • Determining profit from a single source for income and/or expenses
  • Determining profit from multiple sources for incomes and/or expenses
  • Relationship between income, expenses, and profit
    • When income is greater than expenses there is a profit.
    • When income is less than expenses, there is no profit or the costs exceed the income.

Note(s):

  • Grade Level(s):
    • Grade 3 described the relationship between the availability or scarcity of resources and how that impacts cost.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Financial Literacy
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
4.10E Describe the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending.
Supporting Standard

Describe

THE BASIC PURPOSE OF FINANCIAL INSTITUTIONS, INCLUDING KEEPING MONEY SAFE, BORROWING MONEY, AND LENDING

Including, but not limited to:

  • Financial institution – an establishment that focuses on dealing with financial transactions such as investments, loans, and deposits
  • Purposes of financial institutions
    • Take in funds (deposits), pool that money, and lend that money to those who need funds.
    • Keep deposits safe and regulate accounts and transactions according to federal and/or state laws.
    • Provide a place where individuals, businesses, and governments can deposit and borrow money.
    • Serve as agents for depositors (who lend money to the bank) and borrowers (to whom the bank lends money).
      • Depositors and borrowers can be individuals and households, financial and nonfinancial firms, or national and local governments.
    • Keep individual funds available on demand (e.g., checking accounts) or with some restrictions (e.g., savings or investments).
    • Process payments to and from account holders and other financial institutions.

Note(s):

  • Grade Level(s):
    • Grade 3 explained that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest.
    • Grade 5 will identify the advantages and disadvantages of different methods of payment, including check, credit card, debit card, and electronic payments.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Financial Literacy
  • TxCCRS:
    • IX. Communication and Representation
    • X. Connections
The English Language Proficiency Standards (ELPS), as required by 19 Texas Administrative Code, Chapter 74, Subchapter A, §74.4, outline English language proficiency level descriptors and student expectations for English language learners (ELLs). School districts are required to implement ELPS as an integral part of each subject in the required curriculum.

School districts shall provide instruction in the knowledge and skills of the foundation and enrichment curriculum in a manner that is linguistically accommodated commensurate with the student’s levels of English language proficiency to ensure that the student learns the knowledge and skills in the required curriculum.


School districts shall provide content-based instruction including the cross-curricular second language acquisition essential knowledge and skills in subsection (c) of the ELPS in a manner that is linguistically accommodated to help the student acquire English language proficiency.

http://ritter.tea.state.tx.us/rules/tac/chapter074/ch074a.html#74.4 


Choose appropriate ELPS to support instruction.

ELPS# Subsection C: Cross-curricular second language acquisition essential knowledge and skills.
Click here to collapse or expand this section.
ELPS.c.1 The ELL uses language learning strategies to develop an awareness of his or her own learning processes in all content areas. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.1A use prior knowledge and experiences to understand meanings in English
ELPS.c.1B monitor oral and written language production and employ self-corrective techniques or other resources
ELPS.c.1C use strategic learning techniques such as concept mapping, drawing, memorizing, comparing, contrasting, and reviewing to acquire basic and grade-level vocabulary
ELPS.c.1D speak using learning strategies such as requesting assistance, employing non-verbal cues, and using synonyms and circumlocution (conveying ideas by defining or describing when exact English words are not known)
ELPS.c.1E internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment
ELPS.c.1F use accessible language and learn new and essential language in the process
ELPS.c.1G demonstrate an increasing ability to distinguish between formal and informal English and an increasing knowledge of when to use each one commensurate with grade-level learning expectations
ELPS.c.1H develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations.
ELPS.c.2 The ELL listens to a variety of speakers including teachers, peers, and electronic media to gain an increasing level of comprehension of newly acquired language in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in listening. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.2A distinguish sounds and intonation patterns of English with increasing ease
ELPS.c.2B recognize elements of the English sound system in newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters
ELPS.c.2C learn new language structures, expressions, and basic and academic vocabulary heard during classroom instruction and interactions
ELPS.c.2D monitor understanding of spoken language during classroom instruction and interactions and seek clarification as needed
ELPS.c.2E use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex and elaborated spoken language
ELPS.c.2F listen to and derive meaning from a variety of media such as audio tape, video, DVD, and CD ROM to build and reinforce concept and language attainment
ELPS.c.2G understand the general meaning, main points, and important details of spoken language ranging from situations in which topics, language, and contexts are familiar to unfamiliar
ELPS.c.2H understand implicit ideas and information in increasingly complex spoken language commensurate with grade-level learning expectations
ELPS.c.2I demonstrate listening comprehension of increasingly complex spoken English by following directions, retelling or summarizing spoken messages, responding to questions and requests, collaborating with peers, and taking notes commensurate with content and grade-level needs.
ELPS.c.3 The ELL speaks in a variety of modes for a variety of purposes with an awareness of different language registers (formal/informal) using vocabulary with increasing fluency and accuracy in language arts and all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in speaking. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. The student is expected to:
ELPS.c.3A practice producing sounds of newly acquired vocabulary such as long and short vowels, silent letters, and consonant clusters to pronounce English words in a manner that is increasingly comprehensible
ELPS.c.3B expand and internalize initial English vocabulary by learning and using high-frequency English words necessary for identifying and describing people, places, and objects, by retelling simple stories and basic information represented or supported by pictures, and by learning and using routine language needed for classroom communication
ELPS.c.3C speak using a variety of grammatical structures, sentence lengths, sentence types, and connecting words with increasing accuracy and ease as more English is acquired
ELPS.c.3D speak using grade-level content area vocabulary in context to internalize new English words and build academic language proficiency
ELPS.c.3E share information in cooperative learning interactions
ELPS.c.3F ask and give information ranging from using a very limited bank of high-frequency, high-need, concrete vocabulary, including key words and expressions needed for basic communication in academic and social contexts, to using abstract and content-based vocabulary during extended speaking assignments
ELPS.c.3G express opinions, ideas, and feelings ranging from communicating single words and short phrases to participating in extended discussions on a variety of social and grade-appropriate academic topics
ELPS.c.3H narrate, describe, and explain with increasing specificity and detail as more English is acquired
ELPS.c.3I adapt spoken language appropriately for formal and informal purposes
ELPS.c.3J respond orally to information presented in a wide variety of print, electronic, audio, and visual media to build and reinforce concept and language attainment.
ELPS.c.4 The ELL reads a variety of texts for a variety of purposes with an increasing level of comprehension in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in reading. In order for the ELL to meet grade-level learning expectations across the foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations apply to text read aloud for students not yet at the stage of decoding written text. The student is expected to:
ELPS.c.4A learn relationships between sounds and letters of the English language and decode (sound out) words using a combination of skills such as recognizing sound-letter relationships and identifying cognates, affixes, roots, and base words
ELPS.c.4B recognize directionality of English reading such as left to right and top to bottom
ELPS.c.4C develop basic sight vocabulary, derive meaning of environmental print, and comprehend English vocabulary and language structures used routinely in written classroom materials
ELPS.c.4D use prereading supports such as graphic organizers, illustrations, and pretaught topic-related vocabulary and other prereading activities to enhance comprehension of written text
ELPS.c.4E read linguistically accommodated content area material with a decreasing need for linguistic accommodations as more English is learned
ELPS.c.4F use visual and contextual support and support from peers and teachers to read grade-appropriate content area text, enhance and confirm understanding, and develop vocabulary, grasp of language structures, and background knowledge needed to comprehend increasingly challenging language
ELPS.c.4G demonstrate comprehension of increasingly complex English by participating in shared reading, retelling or summarizing material, responding to questions, and taking notes commensurate with content area and grade level needs
ELPS.c.4H read silently with increasing ease and comprehension for longer periods
ELPS.c.4I demonstrate English comprehension and expand reading skills by employing basic reading skills such as demonstrating understanding of supporting ideas and details in text and graphic sources, summarizing text, and distinguishing main ideas from details commensurate with content area needs
ELPS.c.4J demonstrate English comprehension and expand reading skills by employing inferential skills such as predicting, making connections between ideas, drawing inferences and conclusions from text and graphic sources, and finding supporting text evidence commensurate with content area needs
ELPS.c.4K demonstrate English comprehension and expand reading skills by employing analytical skills such as evaluating written information and performing critical analyses commensurate with content area and grade-level needs.
ELPS.c.5 The ELL writes in a variety of forms with increasing accuracy to effectively address a specific purpose and audience in all content areas. ELLs may be at the beginning, intermediate, advanced, or advanced high stage of English language acquisition in writing. In order for the ELL to meet grade-level learning expectations across foundation and enrichment curriculum, all instruction delivered in English must be linguistically accommodated (communicated, sequenced, and scaffolded) commensurate with the student's level of English language proficiency. For Kindergarten and Grade 1, certain of these student expectations do not apply until the student has reached the stage of generating original written text using a standard writing system. The student is expected to:
ELPS.c.5A learn relationships between sounds and letters of the English language to represent sounds when writing in English
ELPS.c.5B write using newly acquired basic vocabulary and content-based grade-level vocabulary
ELPS.c.5C spell familiar English words with increasing accuracy, and employ English spelling patterns and rules with increasing accuracy as more English is acquired
ELPS.c.5D edit writing for standard grammar and usage, including subject-verb agreement, pronoun agreement, and appropriate verb tenses commensurate with grade-level expectations as more English is acquired
ELPS.c.5E employ increasingly complex grammatical structures in content area writing commensurate with grade-level expectations, such as:
ELPS.c.5F write using a variety of grade-appropriate sentence lengths, patterns, and connecting words to combine phrases, clauses, and sentences in increasingly accurate ways as more English is acquired
ELPS.c.5G narrate, describe, and explain with increasing specificity and detail to fulfill content area writing needs as more English is acquired.
Last Updated 08/01/2018
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