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Instructional Focus Document
Grade 4 Mathematics
TITLE : Unit 13: Essential Understandings of All Operations SUGGESTED DURATION : 10 days

Unit Overview

Introduction
This unit bundles student expectations that address solving one-, two-, or multistep problems using all four operations including problems involving time and money as well as aspects of financial literacy such as expenses, financial institutions, and various savings options. 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 Units 02 – 05, students solved problems that required adding and subtracting whole numbers and decimals as well as solving one- and two-step problems involving multiplication and division. Students investigated the basic purpose of financial institutions, distinguished between fixed and variable expenses, and calculated profit.

During this Unit
Students revisit and solidify essential understandings of all operations to solve one-, two-, or multistep problems. Students apply concepts of addition and subtraction of whole numbers and decimals to solve problems, including situations involving calculating profit. Students apply concepts of multiplication and division of whole numbers to solve problems, including division situations that require interpreting remainders. Students also demonstrate solving problems involving intervals of time and money. Financial understandings are discussed and examined by comparing advantages and disadvantages of saving operations; distinguishing between fixed and variable expenses; describing how to allocate a weekly allowance among spending, saving, including for college, and sharing; and describing the basic purpose of financial institutions, including keeping money safe, borrowing money, and lending.

After this Unit
In Grade 5, students will multiply with fluency a three-digit number by a two-digit number. This includes multiplying decimals with products limited to the hundredths. Students will be expected to solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor. This includes dividing a decimal by a whole number divisor with quotients to the hundredths. Students will be expected to add and subtract positive rational numbers, which includes whole numbers, decimals through the thousandths, and fractions with unequal denominators. In Grade 6, students will be expected to multiply and divide positive rational numbers fluently.

Additional Notes
In Grade 4, adding and subtracting whole numbers and decimals to the hundredths place using the standard algorithm as well as solving with fluency one- and two-step problems involving multiplication and division including interpreting remainders are identified as STAAR Readiness Standards 4.4A and 4.4H. These standards are included in STAAR Reporting Category 2: Computations and Algebraic Relationships. Solving problems that deal with intervals of time as well as money, using addition, subtraction, multiplication, or division as appropriate is addressed in STAAR Readiness Standard 4.8C. This standard is included in the Grade 4 STAAR Reporting Category 3: Geometry and Measurement. These three standards are further incorporated under the Grade 4 Texas Response to Curriculum Focal Points (TxRCFP): Developing fluency with efficient use of the four arithmetic operations on whole numbers and using this knowledge to solve problems. STAAR Readiness Standard 4.4A is also incorporated under the Grade 4 Focal Point: Understanding decimals and addition and subtraction of decimals (TxRCFP).

Distinguishing between fixed and variable expenses, calculating profit in given situations, and describing the basic purpose of financial institutions are addressed by STAAR Supporting Standards 4.10A, 4.10B, and 4.10E. These standards are included in STAAR Reporting Category 4: Data Analysis and Personal Financial Literacy. Comparing the advantages and disadvantages of various savings options, and describing how to allocate a weekly allowance among spending, saving, and sharing, are identified as standards 4.10C and 4.10D, which are neither supporting nor readiness standards, but are foundational to the conceptual understanding of financial literacy. These five standards are subsumed under 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; III. Geometric and Spatial Reasoning D3; 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 Mathematics Advisory Panel (2008), “to prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem-solving skills” (p. 19). 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 Mathematics Advisory Panel. (2008). Foundations for success: The final report of the national mathematics advisory panel. Washington, DC: U.S. Department of Education.
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


  • 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)
  • 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; multiplication and division of whole numbers).
    • 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 strategies can be used to determine …
      • the sum
      • the difference
      • any unknown
      … in an addition or subtraction situation involving …
      • whole numbers and decimals?
      • fractions with like denominators?
    • What strategies can be used to determine …
      • the product
      • an unknown factor
      … in a multiplication situation?
    • What strategies can be used to determine …
      • the quotient
      • an unknown
      … in a division situation?
    • What strategies can be used to solve problems involving …
      • intervals of time?
      • money?
    • 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?
    • Why is it important to be able to perform operations with whole numbers fluently?
    • What relationships exist between …
      • addition and subtraction?
      • addition and multiplication?
      • multiplication and division?
      • subtraction and division?
      • quotients and remainders?
      • operations with whole numbers and operations with decimals?
      • addition and subtraction of decimals and addition and subtraction of money?
    • 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?
    • When using multiplication to solve a problem situation, why can the order of the factors be changed?
    • When using division to solve a problem situation, why can the order of the dividend and divisor not be changed?
  • Operational understandings lead to generalizations that aid in determining the reasonableness of solutions (addition and subtraction of whole numbers and decimals; multiplication and division of whole numbers)
    • 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?
    • When multiplying two counting numbers greater than one, why is the product always greater than each of the factors?
    • When dividing two counting numbers greater than one with the dividend greater than the divisor, why is the quotient always …
      • less than the dividend?
      • greater than one?
  • Understanding expenses, profit, spending and saving options, and the purpose of financial institutions aids in making informed financial management decisions, which promotes a more secured financial future.
    • What are some examples of …
      • fixed expenses?
      • variable expenses?
    • How can an expense be fixed for one person but variable for another person?
    • 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 advantages and disadvantages of various savings options?
    • Why is it important to compare the advantages and disadvantages of various savings options?
    • What decisions and choices should be considered when deciding how to allocate a weekly allowance among spending; saving, including for college; and sharing?
    • 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
    • Number
      • Counting (natural) numbers
      • Whole numbers
      • Fractions
      • Decimals
    • Operations
      • Addition
      • Subtraction
      • Multiplication
      • Division
    • Relationships and Generalizations
      • Operational
      • Equivalence
    • Solution Strategies and Algorithms
  • Measurement
    • Measureable Attributes
      • Time
      • Money
  • Personal Financial Literacy
    • Borrowing and Lending
    • Charitable Giving
    • Expenses
      • Fixed and variable
    • Financial Institutions
    • Money
      • Allowance
    • Profit
    • Savings Plans
    • Saving
    • Spending
  • 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

Underdeveloped Concepts:

  • 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.
  • Although some students may recognize the relationship between multiplication and division when using basic facts, they do not apply this knowledge beyond the basic facts.
  • Some students may be able to perform a symbolic procedure for multiplication or division with limited understanding of the multiplication or division concepts involved.
  • Some students may misunderstand the distinction between fixed and variable expenses.

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}
  • 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
  • Dividend – the number that is being divided
  • Divisor – the number the dividend is being divided by
  • Expense – payment for goods and services
  • Factor – a number multiplied by another number to find a product
  • Financial institution – an establishment that focuses on dealing with financial transactions such as investments, loans, and deposits
  • Fixed expenses – expenses that are consistent from month to month
  • Fluency – efficient application of procedures with accuracy
  • Income – money earned or received
  • Interest – money received for saving money in a bank account; money paid for borrowing money or making purchases on credit
  • Interest bearing account – a bank or credit union account in which the money deposited earns interest so there will be more money in the future than originally deposited
  • Interest rate – price paid for using someone else’s money; the price paid to you for someone else to use your money
  • Investing – purchasing something of value (e.g., stocks, bonds, real estate, etc.) with the goal of earning money over time if the value increases
  • Product – the total when two or more factors are multiplied
  • Profit – money that is made in a business after all the costs and expenses are paid
  • Quotient – the size or measure of each group or the number of groups when the dividend is divided by the divisor
  • Savings – money set aside for future use
  • 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
  • Variable expenses – expenses that vary in cost from month to month
  • Whole numbers – the set of counting (natural) numbers and zero {0, 1, 2, 3, ..., n}

Related Vocabulary:

  • Analog clock
  • Borrower
  • Day
  • Deposit
  • Depositor
  • Difference
  • Digital clock
  • Dollar
  • Duration
  • Elapsed time
  • End time
  • Hour
  • Hundredth
  • Interval
  • Minute
  • Money
  • Month
  • Number line
  • Place value
  • Remainder
  • Saving
  • Second
  • Sharing
  • Spending
  • Standard algorithm
  • Start time
  • Stop watch
  • Sum
  • Tenth
  • Transaction
  • Week
  • Year
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, AND LANGUAGE AS APPROPRIATE

Including, but not limited to:

  • Mathematical ideas, reasoning, and their implications
    • Multiple representations, as appropriate
      • Symbols
      • Diagrams
      • Language

 

Note(s):

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxRCFP:
    • Developing 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
4.4 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
4.4H Solve with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.
Readiness Standard

Solve

WITH FLUENCY ONE- AND TWO-STEP PROBLEMS INVOLVING MULTIPLICATION AND DIVISION, INCLUDING INTERPRETING REMAINDERS

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}
  • Fluency – efficient application of procedures with accuracy
    • Standard algorithms for the four operations
    • Automatic recall of basic facts
  • Multiplication
    • Product – the total when two or more factors are multiplied
    • Factor – a number multiplied by another number to find a product
    • Products of two-digit factors by two-digit factors and up to four-digit factors by one-digit factors
  • Division
    • Quotient – the size or measure of each group or the number of groups when the dividend is divided by the divisor
    • Dividend – the number that is being divided
    • Divisor – the number the dividend is being divided by
    • Quotients up to four-digit dividends by one-digit divisors
      • Quotients may include remainders
        • Remainder dependent upon the mathematical or real-world situation
          • Various ways to record remainder
            • Ignore the remainder
            • Add one to the quotient
            • Remainder is the answer
            • Remainder recorded as a fraction
  • One- and two-step problem situations
    • One-step problems
      • Recognition of multiplication and division in mathematical and real-world problem situations
    • Two-step problems
      • Two-step problems must have one-step in the problem that involves multiplication and/or divison; however, the other step in the problem can involve addition and/or subtraction.
        • Recognition of multiplication and division in mathematical and real-world problem situations
  • Equation(s) to reflect solution process

Note(s):

  • Grade Level(s):
    • Grade 4 introduces solving with fluency one- and two-step problems involving multiplication and division, including interpreting remainders.
    • Grade 5 will multiply with fluency a three-digit number by a two-digit number using the standard algorithm.
    • Grade 5 will solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm.
    • 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
4.8 Geometry and measurement. The student applies mathematical process standards to select appropriate customary and metric units, strategies, and tools to solve problems involving measurement. The student is expected to:
4.8C

Solve problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.


Readiness Standard

Solve

PROBLEMS THAT DEAL WITH INTERVALS OF TIME AND MONEY USING ADDITION, SUBTRACTION, MULTIPLICATION, OR DIVISION AS APPROPRIATE

Including, but not limited to:

  • Whole numbers (0 – 1,000,000,000)
    • Products of two-digit factors by two-digit factors and up to four-digit factors by one-digit factors
    • Quotients up to four-digit dividends by one-digit divisors
  • Decimals (greater than one and less than one)
    • Addition and subtraction of money amounts up to hundredths
    • Conversions limited to multiples of halves (e.g., 0.5, 1.5, 4.5, etc.)
      • Determined using reasoning that half of any value is that value divided by 2
  • Fractions (proper, improper, and mixed numbers)
    • Addition and subtraction of fractions with like denominators
    • Conversions limited to multiples of halves (e.g.,  etc.)
      • Determined using reasoning that half of any value is that value divided by 2
  • Problem situations that deal with intervals of time (clocks: hours, minutes, seconds)
    • Addition and subtraction of time intervals in minutes
      • Such as a 1 hour and 45-minute event minus a 20-minute event equals 1 hour 25 minutes
    • Time intervals given
    • Pictorial models and tools
      • Measurement conversion tables
      • Analog clock with gears, digital clock, stop watch, number line, etc.
    • Time conversions
      • 1 hour = 60 minutes; 1 minute = 60 seconds
      • Fractional values of time limited to multiples of halves
    • Elapsed time
      • Finding the end time
      • Finding the start time
      • Finding the duration
  • Problem situations that deal with intervals of time (calendar: years, months, weeks, days)
    • Time conversions
      • 1 year = 12 months; 1 year = 52 weeks; 1 week = 7 days; 1 day = 24 hours
      • Fractional values of time limited to multiples of halves
  • Problem situations that deal with money
    • Addition and subtraction may include whole number or decimal amounts
    • Multiplication and division limited to amounts expressed as cents or dollars with no decimal values
    • Comparison of money amounts
    • Making change
    • Range of dollar amounts

Note(s):

  • Grade Level(s):
    • Grade 3 determined solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes.
    • Grade 4 introduces solving problems that deal with measurements of length, intervals of time, liquid volumes, mass, and money using addition, subtraction, multiplication, or division as appropriate.
    • Grade 5 will solve problems by calculating conversions within a measurement system, customary or metric.
    • 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
    • X. Connections
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:
4.10A Distinguish between fixed and variable expenses.
Supporting Standard

Distinguish

BETWEEN FIXED AND VARIABLE EXPENSES

Including, but not limited to:

  • Expense – payment for goods and services
    • Fixed expenses – expenses that are consistent from month to month
      • Allows for greater planning in spending
      • Often associated with necessary spending
      • Often reflects needs
      • Sometimes reflects wants
    • Variable expenses – expenses that vary in cost from month to month
      • Allows for greater personal control in spending
      • Often associated with discretionary spending
      • Often reflects wants
      • Sometimes reflects needs
  • Relationship between fixed and variable expenses
    • Some expenses do not change from month to month and some expenses do change each month
    • Some expenses that may be fixed for you may be variable for others depending on the situation

Note(s):

  • Grade Level(s):
    • Grade 3 explained the connection between human capital/labor and income.
    • Grade 5 will define income tax, payroll tax, sales tax, and property tax.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Financial Literacy
  • TxCCRS:
    • IX. Communication and Representation
    • X. Connections
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
  • Multiplication
    • Products of whole numbers up to two-digit factors by two-digit factors and up to four-digit factors by one-digit factors
  • Division
    • Quotients of whole numbers up to four-digit dividends by one-digit divisors
  • 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
4.10C Compare the advantages and disadvantages of various savings options.

Compare

THE ADVANTAGES AND DISADVANTAGES OF VARIOUS SAVINGS OPTIONS

Including, but not limited to:

  • Savings – money set aside for future use
  • Interest – money received for saving money in a bank account; money paid for borrowing money or making purchases on credit
    • Interest earned from saving
      • Used to encourage people to put money in a bank or credit union or to invest money
      • Factors that affect the interest earned in a savings account
        • Amount of money deposited in the account
        • Interest rate
        • Length of time the money is in the account
  • Interest rate – price paid for using someone else’s money; the price paid to you for someone else to use your money
  • Savings options (choices)
    • Piggy bank
      • Advantages of saving using a piggy bank
        • Money is easy to access
      • Disadvantages of piggy bank
        • Does not earn interest
        • Low risk of theft or loss
    • Interest bearing account – a bank or credit union account in which the money deposited earns interest so there will be more money in the future than originally deposited
      • Saving accounts
        • Advantages of savings accounts
          • Money is easy to access and withdrawal usually does not incur a penalty
          • No risk
          • Earns interest
        • Disadvantages of savings accounts
          • Interest rate is usually low
      • Certificates of deposit (CDs) and bonds are common types of investment accounts
        • Advantages of CDs and bonds
          • Low to almost no risk
          • Interest rate is usually slightly higher than a savings account
          • Earns interest
        • Disadvantages of CDs and bonds
          • Access to money without penalty occurs on maturity date
          • Withdrawal prior to maturity date usually incurs a penalty
    • Investing – purchasing something of value (e.g., stocks, bonds, real estate, etc.) with the goal of earning money over time if the value increases
      • Advantages of investing
        • Potential for profit is higher than an interest bearing account
      • Disadvantages of investing
        • Money is sometimes hard to access and/or a penalty is charged for withdrawal
        • Low to high risk depending on the type of investment
        • Potential loss due to economic situations

Note(s):

  • Grade Level(s):
    • Grade 3 listed reasons to save and explained the benefit of a savings plan, including for college.
    • Grade 7 will calculate and compare simple interest and compound interest earning.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Financial Literacy
  • TxCCRS:
    • IX. Communication and Representation
    • X. Connections
4.10D Describe how to allocate a weekly allowance among spending; saving, including for college; and sharing.

Describe

HOW TO ALLOCATE A WEEKLY ALLOWANCE AMONG SPENDING; SAVING, INCLUDING FOR COLLEGE; AND SHARING

Including, but not limited to:

  • Process to allocate (assign or distribute) weekly allowance
    • Set a goal every week for both spending and saving.
      • Calculate fixed and variable expenses for each week.
      • Calculate the desired amount for savings each week.
      • The remaining money, after expenses and savings, is allocated for personal spending and/or sharing.
  • Reasons to allocate (assign or distribute) weekly allowance
    • Pre-determined spending amounts
    • Ability to earn interest on savings
      • Saving to pay for college
      • Saving to purchase future wants and needs
      • Saving to cover unexpected future expenses

Note(s):

  • Grade Level(s):
    • Grade 2 distinguished between a deposit and a withdrawal.
    • Grade 5 will develop a system for keeping and using financial records.
    • Grade 8 will estimate the cost of a two-year and four-year college education, including family contribution, and devise a periodic savings plan for accumulating the money needed to contribute to the total cost of attendance for at least the first year of college.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxRCFP:
    • Financial Literacy
  • TxCCRS:
    • 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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