# 8.4 - Proportional Reasoning

8.4  The student will solve practical problems involving consumer applications.

### BIG IDEAS

• I can figure the value of my grandmother’s jewelry which will increase with time, determine what to sell the farm tractor for which decreases in value as it gets older, calculate how much my pay check will be after a percentage raise, and I will have enough money with me after predicting amount of purchases with discount, tax, and tip.
• I will understand percent of change is the relationship between an old value and a new value of the same variable.

### UNDERSTANDING THE STANDARD

2016 VDOE Curriculum Framework - 8.4 Understanding

·  Rational numbers may be expressed as whole numbers, integers, fractions, percents, and numbers written in scientific notation.

·  Practical problems may include, but are not limited to, those related to economics, sports, science, social science, transportation, and health. Some examples include problems involving the amount of a pay check per month, commissions, fees, the discount price on a product, temperature, simple interest, sales tax and installment buying.

·  A percent is a ratio with a denominator of 100.

·  Reconciling an account is a process used to verify that two sets of records (usually the balances of two accounts) are in agreement. Reconciliation is used to ensure that the balance of an account matches the actual amount of money deposited and/or withdrawn from the account.

·  A discount is a percent of the original price. The discount price is the original price minus the discount.

·  Simple interest (I) for a number of years is determined by finding the product of the principal (p), the annual rate of interest (r), and the number of years (t) of the loan or investment using the formula I = prt.

·  The total value of an investment is equal to the sum of the original investment and the interest earned.

·  The total cost of a loan is equal to the sum of the original cost and the interest paid.

·  Percent increase and percent decrease are both percents of change measuring the percent a quantity increases or decreases.

### ESSENTIALS

• What is a percent?  A percent is a special ratio with a denominator of  100.

• What is the difference between percent increase and percent decrease?
Percent increase and percent decrease are both percents of change measuring the percent a quantity increases or decreases. Percent increase shows a growing change in the quantity while percent decrease shows a lessening change.

The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to

·  8.41  Solve practical problems involving consumer applications by using proportional reasoning and computation procedures for rational numbers.

·  8.42  Reconcile an account balance given a statement with five or fewer transactions.

·  8.43  Compute a discount or markup and the resulting sale price for one discount or markup.

·  8.44  Compute the sales tax or tip and resulting total.

·  8.45  Compute the simple interest and new balance earned in an investment or on a loan given the principal amount, interest rate, and time period in years.

·  8.46  Compute the percent increase or decrease found in a practical situation.

### KEY VOCABULARY

proportion, ratio, equality, formula, check registry, discount, mark up, sale price, sales tax, percent of increase, percent of decrease, interest, principle, rate, time, balance, investment, loan

Updated: Nov 20, 2018