Standard #: MA.5.DP.1.2


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Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode, median or range.


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 begin mathsize 12px style fraction numerator open parentheses 1 plus 0 plus 3 plus 1 plus 0 plus 0 plus 1 close parentheses over denominator 7 end fraction end style which is equivalent to begin mathsize 12px style 6 over 7 end style of an inch. This mean would be the same if it rained begin mathsize 12px style 6 over 7 end style 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.

General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 5
Strand: Data Analysis and Probability
Standard: Collect, represent and interpret data and find the mean, mode, median or range of a data set.
Date Adopted or Revised: 08/20
Status: State Board Approved

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. 
line
  • 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.
numbers

 

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 Task 2

Create a table using the data below.
Andrew has a 400-acre piece of land.
He monitors the deer population on the land.
In 2015 he counted 100 deer, 125 in 2016, 250 in 2017, and 150 in 2018.In 2019 he counted 200, 225 in 2020, 350 in 2021, and 250 in 2022.
Part A. What patterns do you see in the population of deer as years increase?
Part B. What predictions can you make about deer populations in 2023-2026?
Part C. Find the mean, median, mode, and range of the deer population from 2015-2022.

Instructional Task 3

Diego is collecting boxes for a science experiment. The volume of the boxes, in cubic inches, is shown in the table below.

Table with numbers that represent volume in cubic inches

Part A. Find the mean, median, mode and range for the data set.
Part B. How will the mean, median, and mode for the data set change if Diego adds two more boxes that have a volume of 72 cubic inches?

 

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. 

line plot

 

Instructional Item 2 

Ada was given a Smart Watch as a gift.
She used the watch to monitor how much time she spent walking during the day.
She recorded her total minutes each day for eleven days.

Walking Minutes Recorded by Smart Watch Daily

Plot of minutes recorded

Use the data set above to find the following.
Mean _________
Median _________
Mode _________
Range _________

 

Instructional Item 3

 

Sam was collecting water in a rain gauge as part of a science experiment.
He collected water for eight days, the data is below.
Create a line plot of the data, including appropriate labels.

plot of data

Instructional Item 4

The line plot shows the number of minutes Teia read each day for the past 10 days.

Line plot

Part A. What is the mean of the data set?
Part B. Which statement correctly describes the data set?
a. The mode for the data set is 23.
b. The difference of the range and median is 18.
c. The range of the data set is greater than the median.
d. The difference of the range and median is 23.

 

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



Related Courses

Course Number1111 Course Title222
5012070: Grade Five Mathematics (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 - 2024, 2024 and beyond (current))
7712060: Access Mathematics Grade 5 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 - 2024, 2024 and beyond (current))


Related Access Points

Access Point Number Access Point Title
MA.5.DP.1.AP.2 Interpret numerical data, with whole-number values, represented with tables or line plots by determining the mean, mode or range. Line plot scales to include only whole numbers, halves and quarters.


Related Resources

Lesson Plans

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Practicing With Mean

In this lesson plan, students will practice finding the mean of a set of data and be able to connect that to how mean is used in real-life. Students will be able to collect data, create line plots, interpret the data, and find the mean.

Voter Task Force

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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. Click here to learn more about MEAs and how they can transform your classroom.

 

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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

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Perspectives Video: Teaching Idea

Name Description
Using Visual Models to Determine Mode, Median and Range

Unlock an effective teaching strategy for teaching median, mode, and range in this Teacher Perspectives Video for educators.

Teaching Ideas

Name Description
Ball Bounce Experiment

Students investigate different balls' abilities to bounce and represent the data they collect graphically.

Jump or Be Lunch! SeaWorld Classroom Activity

Students will predict how high they can jump and then compare the height of their jumps to how high a rockhopper penguin can jump out of the water. They will practice mathematical skills for determining averages.

Tutorials

Name Description
Redistributing Trail Mix

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.

Frequency tables and Dot Plots

In this video, we organize data into frequency tables and dot plots (sometimes called line plots).

Student Resources

Tutorials

Name Description
Redistributing Trail Mix:

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.

Frequency tables and Dot Plots:

In this video, we organize data into frequency tables and dot plots (sometimes called line plots).



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