# Math Models – Semester – 2

## 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