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Math Models – Semester – 2

 
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Math Models – Semester – 2

Recommended Grade Level: 11 - 12

This course focuses on modeling with mathematics and problem-solving. Students conduct and analyze research and study the applications of mathematical modeling in finance, purchases, and investments. Students understand models and how to use them to solve real-life problems. Students learn about patterns and transformations and use music as a field of example to study this concept.

Credit: 0.5

Prerequisites:

Math Models Semester 1

Syllabus:

Unit 6 – Finance 

Objectives:

  • Determine salary.
  • Evaluate and determine the value of other types of compensation, such as benefits.
  • Know how to create and calculate budgets.
  • Calculate deductions, withholdings, and state taxes using income tax tables.
  • Estimate unemployment benefits, such as Social Security and Medicare.
  • Calculate sales tax.
  • Understand banking terminology.
  • Understand how to write checks and balance a checkbook.
  • Examine the differences between simple and compound interest, and know how to calculate both.
  • Write equations and solve problems involving investments.

Lessons:

  • Salary
  • Other Forms of Compensation
  • Budgeting
  • Deductions, Withholdings, State Taxes
  • Unemployment Insurance and Social Security
  • Sales Tax
  • Checking Accounts
  • Savings Accounts and Simple Interest
  • Compound Interest
  • Money Applications 

Unit 7 – Purchases

Objectives:

  • Determine wholesale, retail, and markup prices.
  • Estimate the cost of credit cards.
  • Calculate installment loan payments and cost.
  • Determine rental costs.
  • Determine buying costs, including closing costs and property taxes.
  • Calculate the cost and interest of different types of mortgages.
  • Understand what an amortization schedule is.
  • Compare renting property to buying property.
  • Understand the terminology involved in automobile purchases.
  • Compare and calculate used vehicle costs, new vehicle costs, and leasing costs.
  • Understand and calculate cost of ownership.

Lessons:

  • Sales Prices
  • Credit Cards
  • Installment Payments
  • Renting Costs
  • Buying costs
  • Type of Mortgages
  • Renting vs Buying
  • Buying a Vehicle
  • Leasing a Vehicle
  • The cost of Ownership

Unit 8 – Investments

Objectives:

  • Examine savings investment options.
  • Calculate simple and compound interest.
  • Compare simple, compound, and continuously compounded interest in relation to investments.
  • Examine different types of insurance.
  • Understand various insurance terminology.
  • Calculate the costs and benefits of insurance, including copayments and deductibles.
  • Understand investment terminology, including terminology associated with annuities and bonds.
  • Calculate stock values.
  • Examine annuity and bond investments.
  • Calculate retirement funds.
  • Examine the risks and benefits of various investments.

Lessons:

  • Simple Interest
  • Compound Interest
  • Life Insurance
  • Health Insurance
  • Deductibles and Copayments
  • Stocks
  • Annuities
  • Bonds
  • Retirement Plans

Unit 9 – Solving Problems Using Models

Objectives:

  • Understand growth and decay models.
  • Evaluate growth and decay.
  • Apply growth and decay models to real-life situations.
  • Understand trigonometric functions and ratios, including inverse functions.
  • Use trigonometric functions to solve real-life problems.
  • Convert radians to degrees and degrees to radians.
  • Model periodic motion using sine, cosine, and tangent.
  • Understand direct, inverse, and joint variation.
  • Connect variation to science concepts and laws of physics.
  • Evaluate variation problems.

Lessons:

  • Growth Models
  • Decay Models
  • Modeling Real-life Situations
  • Trigonometric Ratios
  • Inverse Functions and Trigonometric Proportions
  • Periodic Motion
  • Direct Variation
  • Inverse Variation
  • Variation in Science
  • Joint Variation

Unit 10 – Transformations, Patterns, and Music

Objectives:

  • Identify the types of transformations and their properties.
  • Transform geometric shapes through translation, rotation, and reflection.
  • Determine whether a figure has reflection or rotational symmetry.
  • Understand perspective and patterns in art and architecture.
  • Determine scale factor.
  • Understand mathematical patterns, including the golden ratio and tessellation.
  • Identify and understand transformations in music.
  • Calculate proportional relationships in music.
  • Understand that ratios can indicate consonance or dissonance in music.
  • Model harmonic motion.

Lessons:

  • Transformations
  • Translations
  • Rotation
  • Reflections
  • Symmetry
  • Perspective
  • Patterns in Art and Architecture
  • Transformations in Music
  • Proportional Relationships in Music
  • Harmonic Music

 

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