# Fraction Operations

## Objective

Make a line plot (dot plot) representation to display a data set of measurements in fractions of a unit.

## Common Core Standards

### Core Standards

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• 4.MD.B.4 — Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots. For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection.

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• 3.MD.B.4

## Criteria for Success

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1. Construct a line plot by:
1. Determining the starting and ending value for the line plot by finding the largest and the smallest value in the data set,
2. Determining the interval for the line plot by determining the smallest fractional unit that is represented in the data,
3. Plotting Xs above the corresponding value for each value in the data set,
4. Creating a label for the number line that describes the unit that is represented by the data, and
5. Creating a title for the line plot that explains what the data set as a whole represents.
2. Understand the purpose of a line plot as a way to represent a data set to be able to see trends and analyze it more easily (MP.7).

## Tips for Teachers

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• The following materials are needed for today's lesson: rulers buttons
• Students will need an inch ruler for the Homework.
• Students will use the line plots on this Problem Set and Homework to solve problems in Lesson 22’s Problem Set and Homework. So, make sure students hold on to this lesson's work for Lesson 22.

#### Remote Learning Guidance

If you need to adapt or shorten this lesson for remote learning, we suggest prioritizing Anchor Task 3 (benefits from worked example). Find more guidance on adapting our math curriculum for remote learning here.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

The table below shows the distance that Ms. Smith's fourth graders were able to run before stopping for a rest.

 Student Distance (in miles) Joe ${2{1\over2}}$ Arianna ${1{3\over4}}$ Bobbi ${2{1\over8}}$ Morgan ${1{{5\over8}}}$ Jack ${2{{5\over8}}}$ Sasha ${2{1\over4}}$ Tyler ${2{2\over4}}$ Jenny ${{5\over8}}$ Anson ${2{2\over8}}$ Chandra ${2{4\over8}}$

Using the information in the table, answer the following questions:

1. Who ran the longest distance?
2. Who ran the shortest distance?
3. What was the most common distance that students ran?

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic E > Lesson 28Concept Development

Grade 4 Mathematics > Module 5 > Topic E > Lesson 28 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Use the data from Anchor Task #1 to create a line plot.

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 5 > Topic E > Lesson 28Concept Development

Grade 4 Mathematics > Module 5 > Topic E > Lesson 28 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 3

1. With a partner or group, gather a handful of round buttons from a diverse collection and use a ruler to measure the diameter of each button to the nearest eighth inch.
2. Make a dot plot of button diameters, marking your scale in eighth-inch increments.
3. What is the most common diameter in your collection? How does that compare with the collection from another group?
4. Now measure the diameters of these same buttons to the nearest quarter inch.
5. Make a dot plot of button diameters, marking your scale in quarter-inch increments.
6. Describe the differences between the two dot plots you created. Which one gives you more information? Which one is easier to read?

#### References

Illustrative Mathematics Button Diameters

Button Diameters, accessed on July 18, 2018, 4:54 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

## Problem Set & Homework

#### Discussion of Problem Set

• How were #1 and #2 different? What made #2 a bit more challenging than #1?
• What did you notice about the heights of football players once you created the line plot that you didn’t initially notice in the table?
• How did the line plot make answering #4 easier compared to if you just had this data listed out of order in a table?
• What objects did you measure in #5? What was their total length?
• How is a line plot useful in showing data? What might be some reasons to use a line plot to display data rather than using a chart or table?

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Mr. O'Neil asked his students to record the length of time they read over the weekend. The times are listed in the table.

Make a line plot of the data below. Include a title and the correct labels.

 Student Length of time (in hours) Robin ${{1\over2}}$ Bill $1$ Katrina ${{3\over4}}$ Kelly $1{{{3\over4}}}$ Mary $1{{{1\over2}}}$ Gail $2{1\over4}$ Scott $1{{{3\over4}}}$ Ben ${2{2\over4}}$

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