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Instructional Focus Document
Mathematical Models with Applications
TITLE : Unit 07: Savings, Investments, and Insurance SUGGESTED DURATION : 15 days

Unit Overview

This unit bundles student expectations that address savings, investments, and insurance options. Concepts are incorporated into both mathematical and real-world problem situations. According to the Texas Education Agency, mathematical process standards including application, 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 4, students compared the advantages and disadvantages of various savings options. In Grade 5, students learned multiplication of decimals. In Grade 7, students calculated and compared simple interest and compound interest earnings. In Grade 8, students used the compound interest formula with only annual compounding. In Algebra I, students were introduced to the concept of a function in terms of a linear relationship and studied the exponential parent function f(x) = abx.

During this unit, students explore and compare options for life insurance, considering permanent and term policies, amount of coverage, premiums, and needs of different individuals based on income and family situation. Students explore and compare options for medical insurance considering coverage options, deductibles, premiums, and an individual's health needs, situation, and income. Students explore and compare options for homeowner's and renter's insurance, considering coverage, deductibles, premiums, and the different needs of individuals based on income and living situation. Students explore and compare options for automobile insurance, considering coverage options for state requirements for liability coverage, collision and comprehensive coverage, medical coverage, rental coverage, and premiums based on the value of the automobile being insured and the profile of the driver(s). Students define investment options, including the analysis of stocks, bonds, annuities, certificates of deposit, and retirement plans. Students explore and compare different investment options and the advantages and disadvantages, considering individual needs and time, earnings, fees, and accessibility of funds. Students explore savings options and compare simple and compound interest using multiple representations. Students demonstrate financial literacy and reasoning by presenting their preferences of insurance options, investments, and savings, supporting their preferences with tables, function models, and other influential factors.

After this unit, in MMA Unit 08, students will extend personal financial literacy to include the analysis of loan amortizations, including financed purchases, home loans, and automobile loans.

This unit is supporting the development of the Texas College and Career Readiness Standards (TxCCRS): I. Numeric Reasoning B1; II. Algebraic Reasoning B1; VII. Functions A2; VIII. Problem Solving and Reasoning; IX. Communication and Representation; X. Connections. 

According to the Connections Standard for Grades 9-12 from the National Council of Teachers of Mathematics (NCTM), “Instructional programs from pre-kindergarten through grade 12 should enable students to:

  • recognize and use connections among mathematical ideas;
  • understand how mathematical ideas interconnect and build on one another to produce a coherent whole;
  • recognize and apply mathematics in contexts outside of mathematics.

When students can see the connections across different mathematical content areas, they develop a view of mathematics as an integrated whole. As they build on their previous mathematical understandings while learning new concepts, students become increasingly aware of the connections among various mathematical topics. As students' knowledge of mathematics, their ability to use a wide range of mathematical representations, and their access to sophisticated technology and software increase, the connections they make with other academic disciplines, especially the sciences and social sciences, give them greater mathematical power” (NCTM, 2000, p. 354).

National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics: Connections standard for grades 9-12. Reston, VA: National Council of Teachers of Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009). Texas college and career readiness standards. Retrieved from http://www.thecb.state.tx.us/collegereadiness/crs.pdf

OVERARCHING UNDERSTANDINGS and QUESTIONS

Function models for problem situations can be determined by collecting and analyzing data using a variety of representations and applied to make predictions and critical judgments in terms of the problem situation.

  • Why is it important to determine and apply function models for problem situations?
  • What representations can be used to analyze collected data and how are the representations interrelated?
  • Why is it important to analyze various representations of data when determining appropriate function models for problem situations?
  • How do the key attributes and characteristics of the function differ from the key attributes and characteristics of the function model for the problem situation?
  • How does technology aid in the analysis and application of modeling and solving problem situations?

 Knowledgeable consumers and investors develop an economic way of thinking and problem solving.

  • How does financial literacy affect financial responsibility and long term goals?
  • How does being financially literate protect an individual’s financial stability?
Performance Assessment(s) Overarching Concepts
Unit Concepts
Unit Understandings
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.

Algebraic Reasoning

  • Rates

 

Personal Financial Literacy

  • Insurance

 

Associated Mathematical Processes

  • Application
  • Tools and Techniques
  • Problem Solving Model
  • Communication
  • Representations
  • Relationships 
  • Justification

Financial literacy requires consumers to become knowledgeable regarding available insurance options, and financial reasoning requires consumers to analyze and compare insurance plans in terms of personal needs, costs, and risk factors. 

  • What is the purpose of insurance and what can be covered by insurance?
  • What are types of life insurance?
  • What factors should be considered when purchasing life insurance?
  • What are types of homeowner’s and property insurance?
  • What factors should be considered when purchasing homeowner’s insurance?
  • What are types of health insurance?
  • What factors should be considered when purchasing health insurance?
  • What are types of automobile insurance?
  • What factors should be considered when purchasing automobile insurance?
  • What are risk factors that affect insurance rates?
  • How does being financially literate in terms of insurance protect an individual’s financial stability?

 

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.

Algebraic Reasoning

  • Equations
  • Rates

 

Functions

  • Non-Linear Functions

 

Personal Financial Literacy

  • Interest
  • Investments/Savings

 

Associated Mathematical Processes

  • Application
  • Tools and Techniques
  • Problem Solving Model
  • Communication
  • Representations
  • Relationships 
  • Justification

In order to make financially responsible decisions and set long term goals, it is critical to analyze and compare investment and savings options.

  • What are types of investment and savings options?
  • Why is it important to develop a retirement plan using a variety of investment options?
  • What information is important to analyze and compare investment and savings options?
  • What are the advantages and disadvantages of investment and savings options?
  • How does being financially literate in terms of investments and savings protect an individual’s financial stability?

 

Algebraic models can be used to represent, calculate, and compare investment and savings options.

  • What algebraic models can be used to represent investment and savings options?
  • How are linear functions used to represent and calculate investment and savings options?
  • How are exponential functions used to represent and calculate investment and savings options?
  • How can graphs of representative functions aid in analyzing and comparing investment and savings options?
  • How can tables of representative functions aid in analyzing and comparing investment and savings options?
  • How does the algebraic function model aid in analyzing and comparing investment and savings options?
  • How does technology aid in calculating and analyzing investment and savings options?
  • How does the analysis of algebraic models influence decisions regarding investments and savings?
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.

Algebraic Reasoning

  • Equations
  • Patterns/Rules
  • Rates

 

Functions

  • Linear Functions
  • Non-Linear Functions

 

Personal Financial Literacy

  • Interest
  • Investments/Savings

 

Associated Mathematical Processes

  • Application
  • Tools and Techniques
  • Problem Solving Model
  • Communication
  • Representations
  • Relationships 
  • Justification

In order to make financially responsible decisions and set long term goals, it is critical to analyze and compare investment and savings options.

  • What are types of investment and savings options?
  • What information is important to analyze and compare investment and savings options?
  • What are the advantages and disadvantages of investment and savings options?
  • How does being financially literate in terms of investments and savings protect an individual’s financial stability?

 

Algebraic models can be used to represent, calculate, and compare investment and savings options.

  • What algebraic models can be used to represent investment and savings options?
  • How are linear functions used to represent and calculate investment and savings options?
  • How are exponential functions used to represent and calculate investment and savings options?
  • How can graphs of representative functions aid in analyzing and comparing investment and savings options?
  • How can tables of representative functions aid in analyzing and comparing investment and savings options?
  • How does the algebraic function model aid in analyzing and comparing investment and savings options?
  • How does technology aid in calculating and analyzing investment and savings options?
  • How does the analysis of algebraic models influence decisions regarding investments and savings?

MISCONCEPTIONS / UNDERDEVELOPED CONCEPTS

Misconceptions:

  • Some students may not distinguish between linear and exponential relationships and which type of function applies in a situation.
  • Some students may think that compounding of interest can only occur annually instead of applying multiple compounding periods within a year (e.g., $3,000 compounded quarterly at an interest rate of 4.5%   A = 3000, where n = 4 represents the number of times interest is compounded annually).

Unit Vocabulary

  • Annuities – contracts sold, usually by insurance companies, for which the buyer pays regular premiums for a specified time, and then receives a stated amount of money per month or year for life, usually beginning with the time of retirement
  • APY (Annual Percentage Yield) – the effective annual rate of return taking into account the effect of compounding interest
  • Available balance – the amount available in an account for a person, business, or organization to spend. Some types of savings accounts have limitations on time and amount of withdrawals allowed without penalty.
  • Bank service fees – bank charges for different services for different types of accounts
  • Bonds – investments made as a loan to a government entity, company, non-profit organization, for a stated amount of time and on which the investor (bond buyer) receives interest. Interest is usually paid periodically over the pre-determined time.
  • Certificates of deposit (CD) – a specified amount deposited with a bank for a predetermined amount of time, from a few months to several years, that earns interest at a set rate. At the end of the specified time, on the maturity date, the deposited amount accrues the interest for the entire time.  
  • Compound interest – interest that is computed on the latest balance, including any previously earned interest that has been added to the original principal
  • Employer pension programs – a retirement plan through which an employer puts a portion of an employee's earnings into an account set aside and invested to grow for the employee's retirement. These funds are usually tax exempt at the time of deposit.  
  • Insurance coverage – the total or maximum amount by the insurance company a consumer will be paid in the event of a loss
  • Insurance policy – a contract between an insurance company and customer that states the terms of the coverage, the limitations, and the premiums
  • Insurance rates – premiums for different aspects of insurance that vary with amount of coverage, deductibles, and various risk factors
  • Money market account – a savings account that pays interest based on current interest rates. Money market accounts pay higher interest rates than other savings options and usually require a higher minimum balance.
  • Premiums – the amount of money paid by the customer to the insurance company for specified coverage as stated in the policy
  • Savings 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. The owner of the account can make deposits and withdrawals at any time without penalty.
  • Simple interest – interest paid on the original principal in an account, disregarding any previously earned interest
  • Stocks – shares or pieces of a corporation's assets and earnings

 

Related Vocabulary

  • Automobile insurance
  • Collision coverage
  • Comprehensive coverage
  • Constant rate of change
  • Deductible
  • Exponential function
  • Health insurance
  • Homeowner’s insurance
  • Individual Retirement Account (IRA)
  • Interest
  • Interest rate
  • Investment
  • Liability coverage
  • Life insurance
  • Linear function
  • Risk factor
  • Risk multiplier
  • Roth IRA
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 Creator 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 (select CCRS from Standard Set dropdown menu)

Texas Instruments – Graphing Calculator Tutorials

Texas Education Agency – STAAR Mathematics Resources

Texas Education Agency – Revised Mathematics TEKS: Vertical Alignment Charts

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

Texas Education Agency – Mathematics Curriculum

Texas Education Agency – Mathematics TEKS: Supporting Information

Texas Education Agency – Interactive Mathematics Glossary

TEKS# SE# TEKS Unit Level Specificity
 
  • Bold black text in italics: Knowledge and Skills Statement (TEKS)
  • Bold black text: Student Expectation (TEKS)
  • Strike-through: Indicates portions of the Student Expectation that are not included in this unit but are taught in previous or future unit(s)
  • Blue text: Supporting information / Clarifications from TCMPC (Specificity)
  • Blue text in italics: Unit-specific clarification
  • Black text: Texas Education Agency (TEA); Texas College and Career Readiness Standards (TxCCRS)
M.1 Mathematical process standards. The student uses mathematical processes to acquire and demonstrate mathematical understanding. The student is expected to:
M.1A Apply mathematics to problems arising in everyday life, society, and the workplace.

Apply

MATHEMATICS TO PROBLEMS ARISING IN EVERYDAY LIFE, SOCIETY, AND THE WORKPLACE
Including, but not limited to:

  • Mathematical problem situations within and between disciplines
    • Everyday life
    • Society
    • Workplace

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • X. Connections
M.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.

Use

A PROBLEM-SOLVING MODEL THAT INCORPORATES ANALYZING GIVEN INFORMATION, FORMULATING A PLAN OR STRATEGY, DETERMINING A SOLUTION, JUSTIFYING THE SOLUTION, AND EVALUATING THE PROBLEM-SOLVING PROCESS AND THE REASONABLENESS OF THE SOLUTION
Including, but not limited to:

  • Problem-solving model
    • Analyze given information
    • Formulate a plan or strategy
    • Determine a solution
    • Justify the solution
    • Evaluate the problem-solving process and the reasonableness of the solution

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
M.1C Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.

Select

TOOLS, INCLUDING REAL OBJECTS, MANIPULATIVES, PAPER AND PENCIL, AND TECHNOLOGY AS APPROPRIATE, AND TECHNIQUES, INCLUDING MENTAL MATH, 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.
  • TxCCRS:
    • VIII. Problem Solving and Reasoning
M.1D Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.

Communicate

MATHEMATICAL IDEAS, REASONING, AND THEIR IMPLICATIONS USING MULTIPLE REPRESENTATIONS, INCLUDING SYMBOLS, DIAGRAMS, GRAPHS, AND LANGUAGE AS APPROPRIATE
Including, but not limited to:

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

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • IX. Communication and Representation
M.1E Create and use representations to organize, record, and communicate mathematical ideas.

Create, Use

REPRESENTATIONS TO ORGANIZE, RECORD, AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:

  • Representations of mathematical ideas
    • Organize
    • Record
    • Communicate
  • Evaluation of the effectiveness of representations to ensure clarity of mathematical ideas being communicated
  • Appropriate mathematical vocabulary and phrasing when communicating mathematical ideas

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • IX. Communication and Representation
M.1F Analyze mathematical relationships to connect and communicate mathematical ideas.

Analyze

MATHEMATICAL RELATIONSHIPS TO CONNECT AND COMMUNICATE MATHEMATICAL IDEAS
Including, but not limited to:

  • Mathematical relationships
    • Connect and communicate mathematical ideas
      • Conjectures and generalizations from sets of examples and non-examples, patterns, etc.
      • Current knowledge to new learning

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • X. Connections
M.1G Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.

Display, Explain, Justify

MATHEMATICAL IDEAS AND ARGUMENTS USING PRECISE MATHEMATICAL LANGUAGE IN WRITTEN OR ORAL COMMUNICATION
Including, but not limited to:

  • Mathematical ideas and arguments
    • Validation of conclusions
      • Displays to make work visible to others
        • Diagrams, visual aids, written work, etc.
      • Explanations and justifications
        • Precise mathematical language in written or oral communication

Note(s):    

  • The mathematical process standards may be applied to all content standards as appropriate.
  • TxCCRS:
    • IX. Communication and Representation
M.4 Mathematical modeling in personal finance. The student uses mathematical processes with algebraic formulas, numerical techniques, and graphs to solve problems related to financial planning. The student is expected to:
M.4A Analyze and compare coverage options and rates in insurance.

Analyze, Compare

COVERAGE OPTIONS IN INSURANCE

Including, but not limited to:

  • Insurance policy – a contract between an insurance company and customer that states the terms of the coverage, the limitations, and the premiums
  • Insurance coverage – the total or maximum amount by the insurance company a consumer will be paid in the event of a loss
  • Types of insurance
    • Auto insurance
      • Most common types of auto coverage
        • Liability (required by law) coverage pays for damage(s) to property and/or medical costs for persons injured by the insured in an accident or other occurrence.
        • Collision coverage pays for damage(s) to automobile caused by a collision.
        • Comprehensive coverage pays for damage(s) from an event other than a collision, including damage from weather events, theft, vandalism, etc.
        • Rental coverage pays for rental of a vehicle for use while insured's vehicle is being repaired under an insured incident.
    • Homeowner's and property insurance
      • Most common types of property coverage
        • Fire, storm, natural disaster (required by lenders) coverage pays the property owner for damages due to almost any natural phenomenon other than flood or rising water.
        • Flood (may be required by lenders especially if house is located in a flood plain) coverage is available to property owners whose property is located in a place vulnerable to flooding and/or rising water.
        • Burglary/Theft coverage pays for damage and loss due to theft from burglary on insured property, theft of personal belongings at places away from insured property, and personal robbery.
        • Liability coverage protects the homeowner by paying for damages to personal property or personal injury to guests while on insured property.
        • Renter's insurance coverage pays for damage to personal property such as furnishings and personal effects while living in a rented property.
    • Health insurance
      • Most common types of health coverage
        • Medical
          • Physician
          • Hospital
          • Laboratory and testing
        • Prescription drugs
        • Dental
        • Vision
    • Personal insurance
      • Most common types of personal insurance
        • Life insurance
          • Term life insurance offers coverage for a limited period of time that provides a death benefit for the family of the insured if that person dies during that time period. Term policies generally do not accumulate cash value.
          • Permanent (Whole) life insurance offers coverage that is usually lifetime and provides cash value in addition to death benefits to the family of the insured
        • Total and permanent disability insurance provides a one-time payment if the insured is injured or becomes sick and is no longer able to work permanently.
        • Critical illness insurance provides a one-time payment if the insured suffers a serious injury or illness as specified by the policy agreement.
        • Income protection insurance replaces a portion of the insured's income during periods of time of economic stress due to lack of income.

Analyze, Compare

RATES IN INSURANCE

Including, but not limited to:

  • Premiums – the amount of money paid by the customer to the insurance company for specified coverage as stated in the policy.
  • Insurance rates – premiums for different aspects of insurance that vary with amount of coverage, deductibles, and various risk factors.
    • Homeowner's and property insurance
      • Factors that increase homeowner’s and property insurance rates may include age of home, poor construction, high risk location, previous claims, risk factors on property such as pools, low credit score, etc.
      • Factors that lower homeowner’s and property insurance rates may include newer home, sturdy construction meeting updated codes, low risk location, no major claims, no risk factors on property, and high credit score, etc.
    • Auto insurance
      • Factors that increase auto insurance rates may include traffic tickets, accident claims, location, driving habits, new vehicle, male under the age of 25, lapses in coverage, auto theft, low credit score, etc.
      • Factors that lower auto insurance rates may include clean driving record (no tickets or accidents), location, married, used or less expensive vehicle, age between 50 and 65, no lapses in coverage, high credit score, etc.

Note(s):

  • Grade Level(s)
    • Grade 5 studied the multiplication of decimals.
    • Grade 8 identified and explained the advantages and disadvantages of different payment methods.
    • Algebra I studied the linear parent function f(x) = x.
    • Mathematical Models with Applications introduces insurance, premiums and making decisions about coverage.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxCCRS
    • I. Numeric Reasoning
      • B1 – Perform computations with real and complex numbers.
    • II. Algebraic reasoning
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
M.4B Investigate and compare investment options, including stocks, bonds, annuities, certificates of deposit, and retirement plans.

Investigate, Compare

INVESTMENT OPTIONS, INCLUDING STOCKS, BONDS, ANNUITIES, CERTFICATES OF DEPOSIT, AND RETIREMENT PLANS

Including, but not limited to:

  • Stocks – shares or pieces of ownership of a corporation's assets and earnings
  • Bonds – investments made as a loan to a government entity, company, non-profit organization, for a stated amount of time and on which the investor (bond buyer) receives interest. Interest is usually paid periodically over the pre-determined time.
  • Annuities – contracts sold, usually by insurance companies, for which the buyer pays regular premiums for a specified time, and then receives a stated amount of money per month or year for life, usually beginning with the time of retirement
  • Certificates of deposit (CD) – a specified amount deposited with a bank for a specified amount of time that earns interest at a set rate. At the end of the specified time, on the maturity date, the deposited amount accrues the interest for the entire time.
  • Savings account – a bank or credit union account in which the money deposited earns interest on the principal over time. The owner of the account can make deposits and withdrawals at any time without penalty.   
  • Retirement plans
    • Employer pension programs – a retirement plan through which an employer puts a portion of an employee's earnings into an investment account set aside to grow for the employee's retirement. These funds are usually tax exempt at the time of deposit.
    • Individual retirement account (Traditional IRA)
    • Individual Roth IRA

 

Note(s):

  • Grade Level(s)
    • Algebra I studied the linear parent function, f(x) = x and the exponential parent function f(x) = abx.
    • Mathematical Models with Applications introduces investment and savings options and decisions.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxCCRS
    • I. Numeric Reasoning
      • B1 – Perform computations with real and complex numbers.
    • II. Algebraic reasoning
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
    • VII. Functions
      • A2 – Recognize and distinguish between different types of functions.
    • VIII. Problem Solving and Reasoning
    • IX. Communication and Representation
    • X. Connections
M.4C Analyze types of savings options involving simple and compound interest and compare relative advantages of these options.

Analyze

TYPES OF SAVINGS OPTIONS INVOLVING SIMPLE AND COMPOUND INTEREST

Including, but not limited to:

  • Simple interest – interest paid on the original principal in an account, disregarding any previously earned interest
    • Simple interest formula: A = P(1 + rt), where A is the total accrued amount (principal and interest), P is the original principal amount, r is the rate of interest per year, and t is the number of years.
  • Compound interest – interest that is computed on the latest balance, including any previously earned interest that has been added to the original principal 
    • Compound interest formula: , where A is the total accrued amount (principal and interest), P is the original principal amount, r is the interest rate per year, n is the number of times per year the interest is paid (the compounding interval), and t is the number of years. The more often interest is compounded, the faster the balance grows.
      • Quarterly (four times per year): 
      • Monthly (12 times per year): 
      • Daily (365 times per year): 

Compare

RELATIVE ADVANTAGES OF SAVINGS OPTIONS

Including, but not limited to:

  • Savings account – a bank or credit union account in which the money deposited earns interest on the principal over time. The owner of the account can make deposits and withdrawals at any time without penalty.
  • Certificates of deposit (CD) – a specified amount deposited with a bank for a specified amount of time that earns interest at a set rate. At the end of the specified time, on the maturity date, the deposited amount accrues the interest for the entire time.  
  • Money market account – a savings account that pays interest based on current interest rates. Money market accounts pay higher interest rates than other savings options and usually require a higher minimum balance.
  • Annual percentage yield (APY) – the effective annual rate of return taking into account the effect of compounding interest 
  • Simple and compound interest
  • Bank service fees – bank charges for different services for different types of accounts
  • Available balance – the amount available in an account for a person, business, or organization to spend. Some types of savings accounts have limitations on time and amount of withdrawals allowed without penalty.

Note(s):

  • Grade Level(s)
    • Grade 7 calculated and compared simple interest and compound interest earnings.
    • Grade 8 introduced the compound interest formula without using multiple compounding in a year.
    • Algebra I studied the exponential parent function f(x) = abx.
    • Mathematical Models with Applications introduces students to investment and savings options and decisions.
    • Various mathematical process standards will be applied to this student expectation as appropriate.
  • TxCCRS
    • I. Numeric Reasoning
      • B1 – Perform computations with real and complex numbers.
    • II. Algebraic reasoning
      • B1 – Recognize and use algebraic (field) properties, concepts, procedures, and algorithms to combine, transform, and evaluate expressions.
    • VII. Functions
      • A2 – Recognize and distinguish between different types of functions.
    • VIII. Problem Solving and Reasoning
    • 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 09/01/2016
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