This learning module relies on the use of media to engage students in mathematics learning that is all about the basics of working with fractions. Within each update students will participate in technology-based activities to gain in understanding of basic fraction skills. The goal of the learning module is for students to learn visual strategies for working with fractions when making equivalent fractions and adding, subtracting, comparing, and multiplying fractions. Students will then use their learning to create a project that demonstrates their understanding of these concepts.

As a fourth grade teacher, I have taught fractions for the past ten years. Much of our grade level math curriculum is focused on fractions. We use the Bridges in Mathematics curriculum which relies heavily on using visuals to teach and to understand math concepts. The lessons have students creating their own visual representations using a variety of math tools and evaluating the visual representations of others.

The assessment within this learning module is in the form of peer and teacher feedback, as well as the comments made and shared throughout the activities. This approach was selected based on a philosophy that students can represent their understandings in ways other than a paper-and-pencil test. Instead, the creation of a final product incorporates the knowledge and skills gained through the learning activities (Cope & Kalantzis, 2010).

Learning Outcomes

Teacher

By the end of this learning module students will be able to:

-identify the numerator and denominator of a fraction

-create models of fractions

-use visual models to create equivalent fractions

-add fractions with like denominators

-subtract fractions with like denominators

-compare fractions with like denominators or numerators

-multiply a fraction by a whole number

Standards:

CCSS.MATH.CONTENT.4.NF.A.1

CCSS.MATH.CONTENT.4.NF.A.2

CCSS.MATH.CONTENT.4.NF.B.3

CCSS.MATH.CONTENT.4.NF.B.3.A

CCSS.MATH.CONTENT.4.NF.B.3.B

CCSS.MATH.CONTENT.4.NF.B.3.C

Students

By the end of this learning module students will be able to:

-identify the numerator and denominator of a fraction

-create models of fractions

-use visual models to create equivalent fractions

-add fractions with like denominators

-subtract fractions with like denominators

-compare fractions with like denominators or numerators

-multiply a fraction by a whole number

Finding Equivalent Fractions

Teacher

Learning Objectives:

Students will be able to

-identify the numerator and denominator of a fraction

-create models of fractions

-use visual models to create equivalent fractions

Time: 1 hour

1. Discuss the concept of equivalent fractions, building on students’ prior knowledge. Use the visuals to explain what equivalent fractions are. (include images from student side)

2. Have students view the video and play the online games in order to practice creating equivalent fractions with models and equations.

3. Students will create an update to demonstrate their understanding of today’s concept. They will use the Pieces Basic app to show their thinking using words, numbers, and pictures.

4. Students should also comment on two classmates’ posts.

Students

Learning Objectives:

You will be able to

-identify the numerator and denominator of a fraction

-create models of fractions

-use visual models to create equivalent fractions

What are equivalent fractions?

Equivalent fractions are fractions that have different numerators and denominators, but stand for the same number. Below is an example of equivalent fractions.

Teachable Math. (2017, August 15). Teaching Equivalent Fractions [Chart]. Teachable Math. https://teachablemath.com/teaching-equivalent-fractions/

Even though each fraction has different numbers each fraction still represents the same amount of a whole. Notice that the same amount of each circle is colored in.

The fraction bars in the image below show equivalent fractions as well. Notice that 1/3 and 2/6 are the same length. You can take a piece of paper and line it up at the end of 1/3 and 2/6 will line up with it as well.

The Teachers Cafe Educational Resources. (n.d.). Fraction Bars [Chart]. The Teachers Cafe. https://theteacherscafe.com/teaching-4-nf-a-1-equivalent-fractions-using-visual-fraction-models/

Your Work

1. Watch the video below to learn about using models and equations to find equivalent fractions.

Media embedded February 14, 2021

TenMarks Amazon. (2017, October 3). Finding Equivalent Fractions with Models and Equations [Video]. YouTube. https://www.youtube.com/watch?v=Hsy_i8s60ME

2. Play the following games to practice creating equivalent fractions.

Game 1: Equivalent Fractions Using Models

Game 2: Multiply and Generate Equivalent Fractions

Game 3: Select the Correct Pair of Fractions

3. Create an update that shows your understanding of equivalent fractions and how to create them using models and equations. Use the Pieces Basic app to show two equivalent fractions. Use numbers, words, and pictures to explain how you know the two fractions are equivalent. Post your update and comment on at least two classmates’ updates.

Adding Fractions

Teacher

Learning Objectives:

Students will be able to

-identify the numerator and denominator of a fraction

-create models of fractions

-add fractions with like denominators

Time: 1 hour

1. Discuss the concept of fraction addition, building on students’ prior knowledge. Use the visual to explain the basics of adding fractions. (include image from student side)

2. Have students view the video and play the online games in order to practice adding fractions with like denominators.

3. Students will create an update to demonstrate their understanding of today’s concept. They will use the Pieces Basic app to show their thinking using words, numbers, and pictures.

4. Students should also comment on two classmates’ posts.

Students

Learning Objectives:

You will be able to:

-identify the numerator and denominator of a fraction

-create models of fractions

-add fractions with like denominators

How do you add factions?

When two fractions have the same denominator (the number on the bottom of the fraction) it is possible to add them together. The number on the bottom stays the same when adding because the size of the pieces is not changing. Only the numerator (the top number) changes. The top half of the image below shows visuals to help explain why this works.

Hays, A. (n.d.). How Can I [Chart]. Pinterest. https://www.pinterest.com/pin/185210603401605583/

Your Work

1. Watch the video below to learn about adding fractions.

Media embedded February 14, 2021

Freckle by Renaissance. (2015, January 26). Intro to Fraction Addition - Common Core Standard [Video]. YouTube. https://www.youtube.com/watch?v=08gqrqKp7LM&feature=emb_logo

2. Play the following games to practice adding fractions.

Game 1: Represent Addition Using Models

Game 2: Add Like Fractions

Game 3: Complete the Addition

3. Create an update that shows your understanding of fraction addition. Use the Pieces Basic app to show how to add two fractions. Use numbers, words, and pictures to explain how the fractions can be added together. Post your update and comment on at least two classmates’ updates.

Subtracting Fractions

Teacher

Learning Objectives:

Students will be able to

-identify the numerator and denominator of a fraction

-create models of fractions

-subtract fractions with like denominators

Time: 1 hour

1. Ask students to complete the survey.

2. Discuss the concept of fraction subtraction, building on students’ prior knowledge. Use the visual to explain the basics of subtracting fractions. (include image from student side)

3. Have students view the video and play the online games in order to practice subtracting fractions with like denominators.

4. Students will create an update to demonstrate their understanding of today’s concept. They will use the Pieces Basic app to show their thinking using words, numbers, and pictures.

5. Students should also comment on two classmates’ posts.

Students

Learning Objectives:

You will be able to

-identify the numerator and denominator of a fraction

-create models of fractions

-subtract fractions with like denominators

How do you subtract factions?

When two fractions have the same denominator (the number on the bottom of the fraction) it is possible to subtract them. The number on the bottom stays the same when subtracting because the size of the pieces is not changing. Only the numerator (the top number) changes. The bottom half of the image below shows visuals to help explain why this works.

Hays, A. (n.d.). How Can I [Chart]. Pinterest. https://www.pinterest.com/pin/185210603401605583/

Your Work

1. Take the survey.

2. Watch the video below to learn about subtracting fractions.

Media embedded February 14, 2021

Math with Mr. J. (2020, June 17). Subtracting Fractions with Common Denominators [Video]. YouTube. https://www.youtube.com/watch?v=VTCOHFJOAA8&feature=emb_logo

3. Play the following games to practice subtracting fractions.

Game 1: Represent Subtraction Using Models

Game 2: Subtract Like Fractions

Game 3: Complete the Subtraction

4. Create an update that shows your understanding of fraction subtraction. Use the Pieces Basic app to show how to subtract two fractions. Use numbers, words, and pictures to explain how the fractions can be subtracted. Post your update and comment on at least two classmates’ updates.

Comparing Fractions

Teacher

Learning Objectives:

Students will be able to

-identify the numerator and denominator of a fraction

-create models of fractions

-compare fractions with like denominators or numerators

Time: 1 hour

1. Discuss the concept of comparing fractions, building on students’ prior knowledge. Use the visual to explain the basics of comparing fractions. (include image from student side)

2. Have students view the video and play the online games in order to practice comparing fractions with like denominators.

3. Students will create an update to demonstrate their understanding of today’s concept. They will use the Pieces Basic app to show their thinking using words, numbers, and pictures.

4. Students should also comment on two classmates’ posts.

Students

Learning Objectives:

You will be able to

-identify the numerator and denominator of a fraction

-create models of fractions

-compare fractions with like denominators or numerators

How do you compare fractions?

When comparing fractions, you are really thinking about the size of the pieces and how much of a whole each fraction represents.

If the two fractions have the same denominator, then you compare the numerators. Because both fractions have the same size pieces (because the denominators are the same), whichever fraction has the bigger numerator is the bigger fraction.

If the two fractions have the same numerator, then you look at the denominators and decide which has smaller pieces. The bigger the denominator, the smaller the pieces. So…when comparing fractions with the same numerator, whichever fraction has a smaller denominator is actually the bigger fraction.

The image below shows examples of comparing fractions with the same denominator and the same numerator.

Samuels, S. (n.d.). Comparing Fractions [Chart]. Pinterest. https://www.pinterest.com/ssamuels1/comparing-fractions/

Your Work

1. Watch the video below to learn about comparing fractions.

Media embedded February 14, 2021

TenMarks Amazon. (2017, October 3). Comparing Fractions Using Common Numerators [Video]. YouTube. https://www.youtube.com/watch?v=S-kD9NtZwNo&feature=emb_logo

2. Play the following games to practice comparing fractions.

Game 1: Compare Fractions Using 1 as Benchmark

Game 2: Compare Fractions Using Half as Benchmark

3. Create an update that shows your understanding of comparing fractions. Use the Pieces Basic app to show how to compare two fractions. Use numbers, words, and pictures to explain your thinking. Post your update and comment on at least two classmates’ updates.

Multiplying Fractions by Whole Numbers

Teacher

Learning Objectives:

Students will be able to

-identify the numerator and denominator of a fraction

-create models of fractions

-multiply a fraction by a whole number

Time: 1 hour

1. Discuss the concept of multiplying fractions by whole numbers, building on students’ prior knowledge. Use the visual to explain the basics of multiplying fractions by whole numbers. (include image from student side)

2. Have students view the video and play the online games in order to practice multiplying fractions by whole numbers.

3. Students will create an update to demonstrate their understanding of today’s concept. They will use the Pieces Basic app to show their thinking using words, numbers, and pictures.

4. Students should also comment on two classmates’ posts.

Students

Learning Objectives:

You will be able to:

-identify the numerator and denominator of a fraction

-create models of fractions

-multiply a fraction by a whole number

How do you multiply fractions by whole numbers?

The image below shows how you can write out or visualize multiplying a fraction by a whole number. The example shows 2/7 x 3.

Mashup Math. (2020, March 23). Multiplying Fractions by Whole Numbers [Chart]. Mashup Math. https://www.mashupmath.com/blog/multiplying-fractions-by-whole-numbers-examples

Your Work

1. Watch the video below to learn about multiplying fraction by whole numbers.

Media embedded February 14, 2021

TenMarka Amazon. (2017, October 5). Visualizing the Multiplication of a Fraction by a Whole Number [Video]. YouTube. https://www.youtube.com/watch?v=9cvpA3Ov6Rw&feature=emb_logo

2. Play the following games to practice multiplying fractions by whole numbers.

Game 1: Represent Multiplication Using Models

Game 2: Represent Multiplication On a Number Line

Game 3: Find the Product

3. Create an update that shows your understanding of multiplying fractions by whole numbers. Use the Pieces Basic app to show how to multiply 1/4 x 3. Use numbers, words, and pictures to explain your thinking. Post your update and comment on at least two classmates’ updates.

Peer-Reviewed Project

Teacher

Students will create an informative presentation about the fraction skills they have learned. Your presentation will share with the audience how to create equivalent fractions, how to add and subtract fractions, how to compare fractions, and how to multiply a fraction by a whole number.

The presentation must include:

Visual representations that show your understanding of how to perform these skills
Explanations of your thinking and how you connected this new knowledge to what you understood about fractions before completing this learning module

• A related video clip or audio clip

*Any other digital or written components that are important to your topic (i.e. drawings, sketches, explanations, examples, graphics, etc.)

Project Options:

*multimedia slideshow

*video

*website

*propose another idea!

Each student will be asked to provide feedback on classmates' presentations.

Peer Feedback

Students

Your challenge is to create an informative presentation about the fraction skills you have learned. Your presentation will share with the audience how to create equivalent fractions, how to add and subtract fractions, how to compare fractions, and how to multiply a fraction by a whole number.

The presentation must include:

• A related video clip or audio clip

*Any other digital or written components that are important to your topic (i.e. drawings, sketches, explanations, examples, graphics, etc.)

Project Options:

*multimedia slideshow

*video

*website

*propose another idea!

You will be asked to provide feedback on classmates' presentations. Use the attached rubric to rate the work of your classmates. Feedback will also be provided to you by your classmates and your teacher.

Peer Feedback

References

Cope, B. & Kalantzis, M. (2010). The teacher as designer: Pedagogy in the new media age. E-Learning and Digital Media, 7(3).