### 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.

**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.

- 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)

- 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 *

**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

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

## 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