# What are Fractions?

### Learning Module

• Creator(s):

#### Abstract

This learning module will help students with basic fraction knowledge. They will learn how to write fractions, use unit fractions, place fractions on a number line and compare fractions. Each update will provide an explanation video, online games and practice problems. There will also be a collaboration aspect during each update. The final update contains a peer reviewed project where students will demonstrate their fraction knowledge learning during this module.

#### Keywords

parts, whole, numerator, denominator, unit fraction, comparing fractions, equivalent fractions, number line, whole numbers

# Course Alignment

This course has focused on community learning. The purpose of this module is to provide information about fractions, and then, allow students to collaborate and extend their understanding with each other.  The goal of this module is to create a reflective pedagogy through the use of social scaffolds because social learning is essential for learning (Kalantzis & Cope, 2020).

# Experiential Alignment

I have been an elementary teacher for six years now. Fractions are a concept that is quite tricky for students when first introduced. It takes a lot of work with manipulatives, pictorial drawings, and real work connections to get the concept to be deeply understood. I created this module to help guide the learners from a basic understanding to a deep conceptual understanding of fractions. Each update adds upon the next with a gradual teacher release with students interacting with their peers more as the updates progress. Overall, a module like this would help my current third-grade students to better grasp fractions in their entirety.

# Overview

This learning module contains seven updates to be posted to Scholar => Community covering the topics of:

1. Partitioning shapes into two, three or four equal shares calling halves, thirds, fourths
2. The meaning of fractions and fraction notation

3. Unit Fractions

4. The number line and number line diagrams

5. Equivalent Fractions

6. Express whole numbers as fractions

7. Compare fractions with the same numerator or same denominator

This learning module uses media to engage students in learning about the concept of fractions. Each update adds another layer to the workings of fractions. Students will utilize technology-based activities that will improve their overall understanding of basic faction skills. The goal of this module is for students to learn the meaning of a fraction, identify fractions on a numberline, find equivalent fractions and compare fractions with the same numerator or denominator. Students will use their learning to create a project that demonstrates this understanding. These updates fit perfectly into the standards expected of third-grade students. It can be modified for younger or older students, but the target audience is third-grade students.

The assessments within this module are both peer and teacher feedback as well as comments made during the activities.

# Learning Outcomes

## For Student

Student Success Criteria

• Can I split shapes into equal parts?
• Can I identify if the parts of the whole are halves, thirds, or fourths?
• Can I explain what the numerator and denominator represent?
• Can I form fractions when referencing a shape split into equal parts?
• Can I locate a fraction on a numberline? Can I create a number line to represent a fraction?
• Can I express whole numbers as fractions?
• Can I recognize equivalent fractions by using models?
• Can I create equivalent fractions using models?
• Can I compare fractions that have the same numerator or denominator to determine which is larger?

## For Teacher

Teacher’s Learning Progressions

By the end of the module students should be able to:

Divide shapes into equal parts and use these shapes to identify halves, thirds and fourths

Understand the meaning of numerator and denominator and use fraction representations to create written fractions

Students understand a unit fraction is one part of the whole and can recognize that ½ is greater than ⅓ and so on.

Students can both identify fractions on a numberline and create number lines to place fractions on.

Students are able to use models, or fraction strips, to identify equivalent fractions.

Students will understand that whole numbers are made up of “sneaky, hidden” fractions. For example, 2 can be represented as 6/3.

Students can identify the larger fraction from the smaller fraction when given fractions that either have the same numerator or the same denominator.

Standards

CCSS.MATH.CONTENT.2.G.A.3

CCSS.MATH.CONTENT.3N.F.A.1

CCSS.MATH.CONTENT.3N.F.A.2

CCSS.MATH.CONTENT.3N.F.A.3.a

CCSS.MATH.CONTENT.3N.F.A.3.b

CCSS.MATH.CONTENT.3N.F.A.3.c

CCSS.MATH.CONTENT.3N.F.A.3.d

By the end of each lesson, students should be able to answer yes to their success criteria. The Learning Goal of each lesson is what the teacher knows the students should be able to accomplish.

# Update 1: Partitioning shapes into two, three or four equal shares calling halves, thirds, fourths

## For Student

Success Criteria:

• Can I split shapes into equal parts?
• Can I identify if the parts of the whole are halves, thirds or fourths?
Figure 1 Open Up Resources. (2022, January 19).

Claire ate three pieces of pizza and her friends got upset with her. Why do you think that is?

That's right, she ate the whole pizza!

She ate three-thirds of the pizza, and now, none of the pizza is left for anyone else. We can now see why her friends were upset with her.

Figure 2. Open Up Resources. (2022, January 19).

In problem two, there are three friends in the group. If Priya eats a piece, she eats one-third of the pizza. Since the pizza is divided into thirds, each slice that is eaten represents one-third. If all three friends each have one slice, they will eat three-thirds of the pizza.

Figure 3. Open Up Resources. (2022, January 19).

In problem 3, there are two slices of pizza. If the pizza is divided into two equal parts, each part represents one half of the pizza. Therefore, each girl will eat one half of the pizza, and together, they will eat the whole pizza.

Figure 4. Open Up Resources. (2022, January 19).

Since the pizza is divided into four pieces, each slice is worth one fourth. Each of the members in the group will eat one fourth of the pizza. Since there are four members in the group, they will eat four fourths of the pizza.

Figure 5. Open Up Resources. (2022, January 19).

Letter A matched the number 2 visual. There is one quarter (or one fourth) of the pie left.

Letter B matched the number 1 visual. One half of the pie is left.

Letter C matched the number 4 visual. One quarter (or one fourth) of the pie is eaten, so three fourths are left.

Letter D matched the number 3 visual. The pie is cut into three equal pieces to be shared by the three friends.

1. Watch this video.

Media embedded November 13, 2022

2. Play this game to practice your understanding of halves, thirds, and fourths.

3. Comment with a story to describe this fraction.

4. Post an update using a circle. Explain two ways you could divide it equally. Use this link to create and divide the circle. Make two stories that would explain the way you divided the circle. Comment on two peers' updates by describing why their stories match the way they divided the circle.

## For Teacher

Learning Goal of Lesson:

Divide shapes into equal parts and use these shapes to identify halves, thirds and fourths.

Standard:

CCSS.MATH.CONTENT.2.G.A.3

This is a second grade standard and hopefully, will be a simple review for many students. This is a good jumping off point to help students grasp the idea and purpose of a fraction. The purpose of this lesson is for the students to learn that when you divide a shape into 2, 3, and four equal pieces, the whole shape can be named as 2 halves, 3 thirds and 4 fourths. You used the idea of the pizza and the pie to help students grasp the idea of a whole in the situation.

The students explore four different problems that introduce the idea of splitting a pizza, or circle into equal parts. Then, the students need to engage with stories that explain different fractions visually. Next, the students are asked to watch a video that explains the idea of dividing into halves, thirds, and fourths. They also practice this skill with a game to reinforce their understanding. The students are asked to comment with a story that describes five fifths. Additionally, the students need to create their own circle fraction using the attached link. They need to create two stories that go along with that fraction. Finally, the student needs to comment on at least two student updates explaining how the updater's stories match their fraction.

Additional Activities if the learner is still finding the concept difficult:

They can watch this additional video.

Media embedded December 3, 2022

MCCS Teachers. (2020). Equal Parts. YouTube. Retrieved December 3, 2022, from https://www.youtube.com/watch?v=HC8Kavk1-tg.

Ask them to visual the following questions:

"I have half a sandwich..."

"You have eaten a third of your chocolate!"

"Can you cut me a fourth of this cheese?"

These are things that we say all the time. There are actual fractions to represent these sayings.

Have the students think of other real world saying that they could use to match halves, thirds, and fourths.

# Update 2: The meaning of fractions and fraction notation

## For Student

Success Criteria:

• Can I explain what the numerator and denominator represent?
Figure 6. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

The denominator is the bottom portion of a fraction, and it represents how many parts in the whole. In the example above, there are four parts of the whole. Therefore, a four is placed on the bottom of the fraction.

Figure 7. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

The numerator is the top portion of the fraction, and it represents how many parts of the whole you have. In the example above five parts are shaded out of six. Therefore, the five is placed on the top.

Figure 8. Open Up Resources. (2022, January 19).

In the above figure, there are a total of four pieces, so four is in the denominator. There are three shaded pieces, so three is the numerator. The fraction is 3/4.

What does this figure represent? There are 6 pieces total and 5 pieces are shaded.

The fraction shown is 5/6.

1. Watch these two videos.

Media embedded November 13, 2022
Media embedded November 13, 2022
Media embedded November 13, 2022

MathAntics. (2012). Fractions Are Parts. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=CA9XLJpQp3c.

KidsLearningVideo. (2015). Let's Learn Fractions! YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=n0FZhQ_GkKw&t=2s.

2. Play this game to practice your understanding of numerator and denominator.

3. Create an update filling in all the missing parts of this chart. In four to five sentences, explain your reasoning.

4. Comment on this post creating a definition for numerator and denominator in your own words. How can you determine which is which from looking at a figure?

Figure 9. Open Up Resources. (2022, January 19).

## For Teacher

Learning Goal of Lesson:

Understand the meaning of numerator and denominator and use fraction representations to create written fractions.

Standard

CCSS.MATH.CONTENT.3N.F.A.1

In this module, the students are learning to understand that the numerator is the number of pieces that are shaded, and the denominator is the number of pieces in the whole. They will watch two videos, both explain in detail about the parts of a fraction and what the numerator and denominator represent. Then, the students will play a game where they practice locating and identifying the numerator and denominators of fractions. Finally, they will create an update filling in a chart to help them see the patterns of fractions and numerators and denominators. Finally, they will comment on this update with their personal definition for numerator and denominator, and how they determine which is which from looking at a fraction figure.

Additional Activities if the learner is still finding the concept difficult:

Show the student this graphic.

Then, remind the students of the component of a fractions using this table.

Have them practice filling the rest of this chart in.

# Update 3: Unit Fractions

## For Student

Success Criteria:

• Can I form fractions when referencing a shape split into equal parts?

Unit fractions are fractions that have one in the numerator. Above you can see 1/2, 1/3, and 1/4.

Above are even more examples of unit fractions.

1. Watch this video.

Media embedded November 13, 2022

Alex Lochoff. (2020). Intro to Fractions Visually (Unit-Fractions). YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=7lz9qfUPtPY&t=1s.

2. Play this game to practice your understanding of unit fractions.

3. Comment answering these questions: What could be an example sentence that matches this fraction? What is this unit fraction?

4. Make an Update using this link to create a fraction that is divided into eight pieces and 1/8 are shaded. Take a screenshot and show it on your update. Explain how you knew how to shade that shape. Create an example sentence that would represent 1/8. Look at one of your classmates' updates. Comment how they could improve their example sentence.

## For Teacher

Learning Goal of Lesson:

Students understand a unit fraction is one part of the whole and can recognize that ½ is greater than ⅓ and so on.

Standard

CCSS.MATH.CONTENT.3N.F.A.1

In this lesson, students will engage with common unit fractions. First, they will look at several unit fractions. there will understand that a unit fraction as a 1 in the numerator. They will think about how these fractions relate to each other. They will start to compare these fractions in subsequent lessons. Then, they will watch a video that describes this further. Next, they will play a game to hone their skills. Additionally, they will comment on this update answering some questions related to unit fractions. Finally, they will make an Update creating a fraction that is divided into eight pieces and 1/8 are shaded. They will explain how you knew how to shade that shape and create an example sentence that would represent 1/8. Also, they will comment on one of their classmates' updates on how to improve their example sentences.

Additional Activities if the learner is still finding the concept difficult:

Remind the students that a unit fraction is always one part of the whole.

Practice counting how many parts are in this whole.

Then, make the unit fraction. You know the numerator is always 1. You counted three parts. The unit fraction here would be 1/3.

Have the student practice the same reasoning with the next four problems.

# Update 4: The number line and number line diagrams

## For Student

Success Criteria:

• Can I locate a fraction on a numberline?
• Can I create a number line to represent a fraction?

Which of the letters below doesn't belong?

Figure 11. Open Up Resources. (2022, January 19).

You guessed it! Letter D. All the others represent 1/3.

Below are all ways to represent 1/4. Today, we are going to learn how to locate fractions on a numberline.

Figure 12. Open Up Resources. (2022, January 19).

You break up the number line the same way you break up a fraction strip. You make the number of spaces that you have in the denominator. The figure below represents 3/4 because it is on the line just past the third space.

Figure 13. Open Up Resources. (2022, January 19).

1. Watch this video.

Media embedded November 13, 2022

Math with Mr. J. (2020). Fractions on a Number Line | Place a Fraction on a Number Line. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=TLktfswm54A&t=3s.

2. Play this game to help practice identifying fractions on a numberline.

3. Comment naming this fraction, and explain how you know in your own words.

4. Update using this link to place a fraction on a number line. Explain what your fraction is and why it is located at that place on the numberline.

## For Teacher

Learning Goal of Lesson:

Students can both identify fractions on a numberline and create number lines to place fractions on.

Standard

CCSS.MATH.CONTENT.3N.F.A.2

CCSS.MATH.CONTENT.3N.F.A.3.a

Students deepen their understanding of fractions on a numberline. They learn to locate and label non-unit fractions. This lesson focuses on numbers between 0 and 1. They also learn how to partition a number line to create fractions. Students will watch a video to help with understanding and play a game to deepen their skills. Furthermore, students will comment naming the fraction on the numberline and explain in their own words how they knew. Finally, the students will use their understanding to make an update of their own. In this update, they will place a fraction on a numberline and explain why it is located on that place on the numberline.

# Update 5: Equivalent Fractions

## For Student

Success Criteria:

• Can I recognize equivalent fractions by using models?
• Can I create equivalent fractions using models?
Figure 14. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).
Figure 15. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

1/2 is equal to two 1/4 fraction strips. Therefore, 1/2 and 2/4 are equivalent. Equivalent means equal to each other in amount of the whole.

Figure 16. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

1/2 is equal to three 1/6 fraction strips. Therefore, 1/2  and 3/6 are equivalent.

Figure 17. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

1/2 is equal to four 1/8 fraction strips. Therefore, 1/2 and 4/8 are equivalent.

Figure 18. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

How many 1/12 strips would equal 1/6?

• Yes! 2/12 = 1/6
Figure 19. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

How many 1/12 strips would equal 1/4?

• Yes! 3/12 = 1/4

Which fractions are equivalent?

Figure 20. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).
Figure 21. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).
Figure 22. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

1. Watch this video.

Media embedded November 14, 2022

LearnZillion. (2021). Identify equivalent fractions using fraction strips. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=m5XltroBYKY.

2. Comment on this update. In your own words, how can you determine if two fractions are equivalent?

3. Use this link and create as many equivalent fractions as you can. Then, create an update explaining what was challenging about creating equivalent fractions. What was less challenging?

## For Teacher

Learning Goal of Lesson:

Students are able to use models, or fraction strips, to identify equivalent fractions.

Standard

CCSS.MATH.CONTENT.3N.F.A.3.b

In this update, students will compare fractions using fraction strips to see if they are equivalent. They will recognize that the larger the denominator, the more parts are needed to make it equivalent to a fraction with a smaller denominator. They will watch a video to help their understanding of equivalent fractions. Then, they will comment on this update explaining how to determine if two fractions are equivalent. Finally, they will explore equivalent fractions on their own.

Additional Activities if the learner is still finding the concept difficult:

Have the student take out a piece of notebook or computer paper. Then, have the students fold the paper in half, then quarters, then eighths and finally sixteens. As them questions like:

What do you notice?
Is there a pattern?
Is there a rule?

Guide them towards understanding that some fractions are worth the same amount.

# Update 6: Express whole numbers as fractions

## For Student

Success Criteria:

• Can I express whole numbers as fractions?
Figure 22. Open Up Resources. (2022, January 19).

What do you wonder about the above fractions? What do you notice?

Figure 23. Open Up Resources. (2022, January 19).

What does it mean to have a denominator of 1?

Figure 24. Open Up Resources. (2022, January 19).
Figure 25. Open Up Resources. (2022, January 19).

All the circled fractions are equilvalent to whole numbers. What patterns do you notice and see?

1. Watch this video.

Media embedded November 17, 2022

2. Comment what are two ways you can write this number. Make sure to include the "sneaky" fraction.

3. Create an update using this link. Place a whole number as a fraction on a numberline. Explain what "sneaky" fraction is represented by the whole number and explain how you know.

## For Teacher

Learning Goal of Lesson:

Students will understand that whole numbers are made up of “sneaky, hidden” fractions. For example, 2 can be represented as 6/3.

Standard
CCSS.MATH.CONTENT.3N.F.A.3.c

In this lesson, students will be learning that whole numbers can be represented by fractions. They will learn what the denominator of 1 represents. They will also see how every whole number can be written as a fraction. Additionally, they will watch a video to further their understanding. Then, they will comment explaining how that 2 on the numberline can be represented as a fraction. Finally, they will use a numberline creation link to create their own "sneaky" fraction on a numberline. They will explain what the fraction represents and how they know.

# Update 7: Compare fractions with the same numerator or same denominator

## For Student

Success Criteria:

• Can I compare fractions that have the same numerator or denominator to determine which is larger?
Figure 26. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

5/6 Is greater than 4/6 because it has 5 pieces.

To compare fractions with the same denominators, just compare their numerators. For fractions with the same denominator, the fraction with the larger numerator is larger!

Figure 27. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).
Figure 28. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

Each of the above fractions have 5 pieces, but the figure on the right has 5/6 shaded. The figure on the left has 5/8 shaded. Therefore, more parts of the whole are shaded in 5/6 than in 5/8.

For fractions with the same numerator but different denominators, the fraction with the smaller denominator is actually the larger fraction.

Figure 29. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

The bigger the denominator, the smaller the parts become.

Figure 30. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

See how 1/8 is smaller because the pieces are smaller than the 1/6 pieces?

1. Watch this video about same denominator and same numerator.

Media embedded November 14, 2022
Media embedded November 14, 2022

MATH-N-ROLL. (2020). Compare Fractions with the Same Denominator. Grade 3. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=TPwgVpoujLA&t=2s.

MATH-N-ROLL. (2020). Compare Fractions with the Same Numerator. Grade 3. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=hXn95-HNmH0&t=2s.

2. Play this game.

3. Comment on these fraction strips. Choose two fractions with like denominators to compare, and two fractions with like numerators to compare.

Figure 31. Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.).

## For Teacher

Learning Goal of Lesson:

Students can identify the larger fraction from the smaller fraction when given fractions that either have the same numerator or same denominator.

Standard

CCSS.MATH.CONTENT.3N.F.A.3.d

For this lesson, students will learn to compare fractions that have either the same numerator or denominator. For the same numerator, the smaller the denominator the larger the fraction. For the same denominator, the larger the numerator the larger the fraction. They will practice these skills by watching two separate videos. One covers same numerator examples, and one covers same denominator examples. Then, they will practice with a game. Finally, they will comment comparing several fractions using a fraction strip.

Additional Activities if the learner is still finding the concept difficult:

Typically, students quickly understand the same denominator because it is easy to visualize that more pieces of the whole are larger. Students often have difficulty understanding that if two fractions have the same numerator, the fraction with the smaller denominator is actually larger pieces of the whole. This feels very counterintuitive to many young learners. They might need additional practice with the concept to reach mastery.

Have the students use fraction strips to visualize having 3 out of 4 pieces is greater than having 3 out of 8 pieces.

Additionally, have them use fraction strips to see that having 2 out of 6 pieces is more than having 2 out of 8 pieces.

# Peer-Reviewed Project

## For Student

Your final activity is to use all the skills you learned about fractions and create a presentation. In your presentation you need to share about the meaning of fractions, fractions on a numberline, creation of equivalent fractions and comparing fractions.

• visuals representing how you perform these skills
• connect this material to anything you knew about fractions prior (hint partitioning shapes)
• video or audio clip related to this topic
• other forms of media to explain your thinking (i.e. graphs, drawings, fraction strips, numerlines etc.

• Slideshow
• Video
• Poster (that you explain in a video)
• propose any other idea

Peer_20Feedback.pdf

## For Teacher

Students will be asked to create an activity based on the skills they learned about fractions. In their presentation they will need to share about the meaning of fractions, fractions on a numberline, creation of equivalent fractions and comparing fractions.

The students' presentations need to include:

1. visuals representing how you perform these skills
3. connect this material to anything you knew about fractions prior (hint partitioning shapes)
4. video or audio clip related to this topic
5. other forms of media to explain your thinking (i.e. graphs, drawings, fraction strips, numerlines etc.)

Ways they can create the project:

• Slideshow
• Video
• Poster (that you explain in a video)
• propose any other idea

Each student will be asked to provide feedback on classmates' presentations. The teacher will also provide feedback on each project.

Peer_20Feedback.pdf

# References

Alex Lochoff. (2020). Intro to Fractions Visually (Unit-Fractions). YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=7lz9qfUPtPY&t=1s.

Fractions as numbers - intensive intervention. intensiveintervention.org. (n.d.). Retrieved November 20, 2022, from https://intensiveintervention.org/sites/default/files/Fractions_as_Numbers_508.pdf

Kalantzis, Mary and Bill Cope. 2020. "The Digital Learner: Towards a Reflexive Pedagogy." Pp. xviii-xxxi in Handbook of Research on Digital Learning, edited by M. Montebello. Hershey PA: IGI Global.

KidsLearningVideo. (2015). Let's Learn Fractions! YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=n0FZhQ_GkKw&t=2s.

LearnZillion. (2021). Identify equivalent fractions using fraction strips. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=m5XltroBYKY.

MathAntics. (2012). Fractions Are Parts. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=CA9XLJpQp3c.

MATH-N-ROLL. (2020). Compare Fractions with the Same Denominator. Grade 3. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=TPwgVpoujLA&t=2s.

MATH-N-ROLL. (2020). Compare Fractions with the Same Numerator. Grade 3. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=hXn95-HNmH0&t=2s.

Math with Mr. J. (2020). Fractions on a Number Line | Place a Fraction on a Number Line. YouTube. Retrieved November 20, 2022, from https://www.youtube.com/watch?v=TLktfswm54A&t=3s.

MCCS Teachers. (2020). Equal Parts. YouTube. Retrieved December 3, 2022, from https://www.youtube.com/watch?v=HC8Kavk1-tg.