MA.912.FL.1.3

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Solve real-world problems involving weighted averages using spreadsheets and other technology.

Examples

Example: Kiko wants to buy a new refrigerator and decides on the following rating system: capacity 50%, water filter life 30% and capability with technology 20%. One refrigerator gets 8 (out of 10) for capacity, 6 for water filter life and 7 for capability with technology. Another refrigerator gets 9 for capacity, 4 for water filter life and 6 for capability with technology. Which refrigerator is best based on the rating system?
General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Financial Literacy
Standard: Build mathematical foundations for financial literacy.
Date Adopted or Revised: 08/20
Status: State Board Approved

Benchmark Instructional Guide

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Purpose and Instructional Strategies

In middle grades, students have worked with the mean or average to solve real-world problems. In Geometry, students solved problems involving the weighted average of points on a line. In Math for Data and Financial Literacy, students use weighted averages in a variety of ways, including portfolios. 
  • To calculate the weighted average, one can begin by multiplying each value in the set by its assigned weight, then add up the products. Next, divide the products' sum by the total sum of all weights. 
    • For example, a smoothie consists of 5 ounces of milk, 3 ounces of bananas, 2.5 ounces of strawberries and 0.75 ounces of whey protein powder. Milk costs $0.04 per ounce, strawberries costs $0.20 per ounce, bananas costs $0.03 per ounce and whey protein costs $0.80 per ounce. To determine the costs of the smoothie, students can find the weighted average cost per ounce of the ingredients, using the quantity of ounces as the weighted value for each ingredient. 
      •  Expression
        $0.12 represents the cost per ounce of the ingredients for the smoothie. If the smoothie is 12 ounces, then the cost of the ingredients is $1.44. 
  • Students should understand that when determining the weighted averages and the weights are percentages, then the percentages should add up to one. In these cases, there is no need to divide by the sum of the weights. 
    • For example, a new employee has two evaluation performance ratings with their supervisor, one in April and one in December, with the April rating counting for 40% of their evaluation and the one in December counting for 60% of the evaluation. The April score is 78 and the December evaluation score is 96. 
      • To determine the weighted average, students can multiply each score by its weight, then find the sum. Next, students can divide by the sum of the weights. 
        Equation
  • A weighted average can be used evaluate something (i.e., an item, person’s performance, or investment earnings) whose value results from a combination of elements that have different significance. 
  • Weighted averages can be computed using the SUM function or the SUMPRODUCT function in a spreadsheet.
 

Common Misconceptions or Errors

  • Students may find the average versus the weighted average. 
  • Students may need support in understanding the varying weights for items in the data set. 
  • Students may incorrectly identify the cell ranges when using the spreadsheet to calculate the weighted average.
 

Instructional Tasks

Instructional Task 1 (MTR.3.1) 
  • Star Coffee has 3 varieties of coffee that were sold at their store this year. The coffee that is locally grown in Florida is $6.50 a pound and they sold 100 pounds. The coffee from South America is $7.50 and they sold 75 pounds. The coffee from Jamaica is $12.50 and they sold 50 pounds. Calculate the weighted average to determine cost per pound. How does this value compare to the unweighted average? 

Instructional Task 2 (MTR.4.1, MTR.7.1)
  • Ross just graduated from high school and decided to put his graduation money into four types of investments. He put: 
    • 40% of his money in online company investments with a return rate of 20%; 
    • 30% of his money in video gaming companies with a 5% return rate; 
    • 20% of his money in a startup company with a 5% return rate; and 
    • 10% of his money in a sports company with a 10% return rate. 
  • Part A. Calculate the weighted average rate of return Ross would receive. 
  • Part B. If Ross wanted to make a greater return, what suggestions would you give him?
 

Instructional Items

Instructional Item 1 
  • An employee at an online company receives his bonus based on the following work requirements. The employee’s score is listed with the percentage weight in the table below. In order to receive the bonus, the employee must have an overall weighted average of 95%, will the employee receive the bonus?
    Table
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.

Related Courses

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
1210305: Mathematics for College Statistics (Specifically in versions: 2022 and beyond (current))
1200388: Mathematics for Data and Financial Literacy Honors (Specifically in versions: 2022 and beyond (current))
1200384: Mathematics for Data and Financial Literacy (Specifically in versions: 2022 and beyond (current))

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Alternate version of this benchmark for students with significant cognitive disabilities.

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