Word (.docx)
Acrobat (.pdf)
Examples
Rain was collected and measured daily to the nearest inch for the past week. The recorded amounts are 1,0,3,1,0,0 and 1. The range is 3 inches, the modes are 0 and 1 inches and the mean value can be determined as
which is equivalent to 
of an inch. This mean would be the same if it rained of an inch each day.
Clarifications
Clarification 1: Instruction includes interpreting the mean in real-world problems as a leveling out, a balance point or an equal share.Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
- Line Plots
- Mean
- Median
- Mode
- Range
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
The purpose of this benchmark is to interpret numerical data by using the mean, mode, median and range. This work builds on the previous understanding of mode, median, and range in Grade 4 (MA.4.DP.1.2). In Grade 6, a focus will be on comparing the advantages and disadvantages of the mean and median.- When finding median and mode, it is important for students to organize their data, putting it in order from least to greatest.
- With the data organized, students can determine:
- range by subtracting the least value from the greatest value in the set.
- mode by finding the value that occurs most often.
- median by finding the value in middle of the set.
- mean by finding the average of the set of numbers.
Common Misconceptions or Errors
- Students may confuse the mean and median of a data set. During instruction, teachers should provide students with examples where the median and mean of a data set are not close in value.
Strategies to Support Tiered Instruction
- Instruction includes examples where the mean and the median are not close in value and uses a data set to explain the difference between mean and median.
- For example, the data set shown has a median of 4 and a mean of 7. The teacher uses the data to model how the mean is calculated and how the median is found.
- Instruction includes writing the data on index cards or sticky notes. Students can then easily arrange the data in order from least to greatest. This will assist in finding the median of the data set.
- For example, students use the data shown to explain the difference between mean (which is 7) and median (which is 4) and to model how the mean is calculated and how the median is found.
Instructional Tasks
Instructional Task 1 (MTR.7.1)
Bobbie is a fifth grader who competes in the 100-meter hurdles. In her 8 track meets during the season, she recorded the following times to the nearest second.
- Part A. What is the mean time, in seconds, of Bobbie’s 100-meter hurdles?
- Part B. What is the median time, in seconds, of Bobbie’s 100-meter hurdles?
- Part C. What is the mode time, in seconds, of Bobbie’s 100-meter hurdles?
- Part D. If you were Bobbie, which of these results would you report to your friend?
Instructional Items
Instructional Item 1
There was a pie-eating contest at the county fair. The line plot below shows the number of pies each of the 10 contestants ate. Use the line plot to determine the mean, mode, median and range of the data.
*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.
Related Courses
Related Access Points
Related Resources
Lesson Plans
Perspectives Video: Teaching Idea
Teaching Ideas
Tutorials
STEM Lessons - Model Eliciting Activity
In this Model Eliciting Activity, MEA, the students' will determine the best canteen for an outdoor hiking company.
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 process. 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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
Students will rank fast food restaurants from best to worst based on their nutrition, price, and distance to sport field. Students will have to make tradeoffs for nutrition or price.
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 process. 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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
In this Model Eliciting Activity, MEA, the students will determine the best ad for a tennis shoe company.
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 process. 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 MEA’s visit: https://www.cpalms.org/cpalms/mea.aspx
This MEA asks the students to compare hand drying products based on: initial cost, replacement cost and absorbency. Students will provide the "top choice" to the principal of the school and explain how they arrived at the solution. In the twist, students will be asked to consider the environmental impact of the products and reevaluate their conclusions.
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
This MEA asks students to decide which factors are important in developing a successful frozen yogurt (froyo) store in order to compete with and become the best store in the area. Students will provide feedback to an entrepreneur who is looking to open a frozen yogurt store. They will rank order their choices of the most successful to least successful store. Students will provide a detailed written explanation for how they decided to rank factors and their solution rating existing stores from best to worst.
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
Student Resources
Tutorials
This Khan Academy tutorial video presents a strategy for solving the following problem: given a dot plot with different measurements of trail mix in bags, find the amount of trail mix each bag would contain, if the total amount in all the bags was equally redistributed.
Type: Tutorial
In this video, we organize data into frequency tables and dot plots (sometimes called line plots).
Type: Tutorial
