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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?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.
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$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.
- 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.
- 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.
- 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?
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Lesson Plans
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, students will analyze and use factors of various counties to recommend the top 3 to buy for a home given a client’s preferences. Students will use weighted averages, key statistics like median and mean, and correlation to conduct a thorough analysis of the data to justify their recommendations.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will analyze data sets to compare various job offers for a client. Students will also use weighted averages and normalize data in order to fairly compare job offers and make recommendations to the client.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity (MEA), students will analyze federal budget data to propose strategic allocations using mathematical skills like expected value calculations and data normalization to justify their recommendations.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will analyze and compare data from 4 different financial institutions to recommend the best fit for an accounting company. Students will apply mathematical skills such as basic arithmetic, averages, percentages, and weighted scoring to evaluate various banking characteristics including monthly fees, transaction costs, cash deposit costs, and stop-payment fees.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, students will apply basic arithmetic and averages to assess and rank the home field advantages of various baseball parks. They will analyze hitting statistics and use weighted averages and composite scores to determine rankings.
Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. MEAs resemble engineering problems and encourage students to create solutions in the form of mathematical and scientific models. Students work in teams to apply their knowledge of science and mathematics to solve an open-ended problem while considering constraints and tradeoffs. Students integrate their ELA skills into MEAs as they are asked to clearly document their thought processes. MEAs follow a problem-based, student-centered approach to learning, where students are encouraged to grapple with the problem while the teacher acts as a facilitator. To learn more about MEAs visit: https://www.cpalms.org/cpalms/mea.aspx
