Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Percent of change
- Percent error
- Simple interest
Purpose and Instructional Strategies
In middle grades, students worked with operations of fractions, percentages and decimals to solve real-world problems. In Math for Data and Financial Literacy, students utilize their understanding of operations and problem solving to solve real-world problems involving money and business. Throughout instruction, it will be important to help students connect the mathematical concepts to everyday experiences (MTR.7.1)
as they validate conclusions by comparing them to a given situation.
- Instruction includes discounts, markups, simple interest, tax, tips, fees, percent increase, percent decrease and percent error (MTR.7.1).
- Markdown/discount is a percentage taken off of an original price. Instruction includes showing the connection between subtracting the calculated discount or taking the difference between 100% and the discount and multiplying that by the original price.
- For example, if there was a 15% discount on an item that costs $15.99, students could take 85% of $15.99 or take 15% of $15.99 and subtract that value from the original price of $15.99.
- Markup showcases adding a charge to the initial price. Markups are often shown in retail situations.
- Simple interest refers to money you can earn by initially investing some money (the principal). The percentage of the principal (interest) is added to the principal making your initial investment grow. The simple interest formula ( = )
calculates only the interest earned over time. Each year’s interest is calculated
from the initial principal, not the total value of the investment of that point in time. The simple interest amount formula ( = (1 + )) calculates the total value of an investment over time. When using simple interest, provide the formula as students should not be expected to memorize this.
- Tax, tips and fees are an additional charge added to the initial price. Students can add the calculated tax, tip or fee to the original price or add 1 to the tax, tip or fee and multiply it by the original price to reach the final cost.
- For example, if there was a 6% sales tax on clothing and a t-shirt costs $7.99. Students can add 100% to the 6% and multiply that value to $7.99, or students can find 6% of the $7.99 and add that to the original value of the t-shirt.
- For example, if the bill is $54.83, students can find 18% of the total and then add it back to the original.
- Percent increase/decrease asks students to look for a percentage instead of a dollar amount. Percent error is a way to express the relative size of the error (or deviation) between two measurements.
Common Misconceptions or Errors
- Students may incorrectly truncate repeating decimals when problem solving.
- Students may incorrectly divide when the quotient is not a whole number.
- For example, students may use the remainder of a problem as a decimal representation.
- Students may incorrectly place the decimal point when calculating with percentages. If students have discovered the shortcut of moving the decimal point twice, instruction includes understanding of how a percent relates to fractions and decimals.
- Students may forget to change the percent amount into decimal form (divide the percent by 100) when setting up an equation (MTR.3.1).
- Students may incorrectly believe all percentages must be between 1 and 100%. To address this misconception, provide examples of percentages below 1% and over 100%.
- Students may incorrectly believe a percent containing a decimal is already in decimal form.
- For example, emphasize that 43.5% is 43.5 out of 100 and dividing by 100 will provide the decimal form.
- In multiple discount problems, students may incorrectly combine the discounts instead of working them sequentially (MTR.5.1).
- For example, 25% off, then 10% off could incorrectly lead to 35% off rather than finding 25% off before calculating the additional 10% off.
Instructional Task 1 (MTR.6.1)
- Video Pro Shop and The Video Store both sold game systems for $450. In February, Video Pro Shop wanted to increase their profits so they increased the prices of their game systems by 15%. When this increase failed to bring in more money, they decreased their price by 10% in November. To beat their competitor who had increased prices, The Video Store decided to decrease their price of video games by 10% in March. However, when they started to lose money on the new pricing scheme, they increased the price of the game system in November by 15%.
- Part A. If no other changes were made after November, which store now has the better price for the game system?
- Part B. What is the difference between their prices?
Instructional Task 2 (MTR.7.1)
- Sherri goes to dinner with 3 friends at a local restaurant in Floral City. The total bill was $82.45. The tax rate where the restaurant is located is 7.5% and they want to leave a 20% tip on the original total bill.
- Part A. If they split the bill evenly, how much will each person pay, including tax and tip?
- Part B. One of Sherri’s friends has a $20 gift card and wants to use it to help with the dinner costs. If the gift card is applied to the entire bill before payment, how much will each person pay?
Instructional Item 1
- Joseph sells internet plans through phone call sales. He receives 11% commission on any sales up to $500. If he sells any plans over the $500 sales, he will earn 15% commission on those sales. If he sold $5,250 in one month, what was his commission for that month?
Instructional Item 2
- A new clothing company has 30 employees, 40% of which are women. After 22 new employees joined the team; the percentage of women was increased to 50%. How many of the new employees are women?
Instructional Item 3
- Part A. Mika takes out a loan that adds interest each year on the initial amount. What is the interest Mika will pay on the loan if he borrowed $15,000 at an annual interest rate of 4.5% for 15 years? (Use the formula = , where is the interest, is the principal or initial investment, is the interest rate per year and is the number of years.)
- Part B. What will be the total amount Mika will have to pay back if the loan provider charges an additional $500 fee?
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.