# Decimal and Percentages Application

### Learning Module

• Creator(s):

Background:

During the school year, I’ve spent the past 6 years teaching 6th-grade and 7th-grade math in a Title I school in California. Some of the questions and prompts are adapted from existing resources while others are newly designed by me. This module is completely new and hasn't been taught before. This learning module is intended for virtual learning with both asynchronous (comments/updates) and synchronous content (discussions).

Content:

Decimal and percentages are everywhere in real life. When mastered, there are terrific applications of decimals and percentages that can help students make informed decisions in the real world, from finding the best deal at a store sale to budgeting for a wedding.

This module gives students a brief overview on how to perform operations with decimals and percentages, and then asks students to apply their skills to complete a summative project and assessment. Within the modules, students play an active and social role where they not only are given access to content, but are required to comment, post updates on related topics, and interact with the updates from their peers. The basis of this module uses CGScholar, an example of a technology-mediated environment to help students explore topics relevant to their interests, learn from their peers, and receive feedback in a prompt manner. Dr. Bill Cope and Dr. Mary Kalantzis from the University of Illinois College of Education talk about the elements and benefits of this module format in learning:

Media embedded September 24, 2022

Video 1. Social Learning in Scholar (Education at Illinois, 2017)

As mentioned in the video, the purpose of this type of this technology-mediated environment is to encourage students to learn from their peers, not just the instructor. Therefore, there will be many aspects of prompts to comments and write updates about in the following sections. This format is inspired by the seven affordances, mentioned by Cope and Kalantzis (2013).

Caption: Figure 1. Seven Affordances (Cope & Kalantzis, 2013)

Cope and Kalantzis defined these seven affordances as “pedagogical openings” for a new form of learning that encourages collaborative intelligence, intrinsic motivation, and differentiated learning (Cope & Kalantzis, 2013). The following decimal and percentages module is designed with these seven affordances in mind.

By the end of this learning module, students will have engaged in hands-on exploration to discover the intricate connection between decimals and percentages so that they can apply their knowledge to future real-world contexts. Depending on time availability and student performance levels, thist module can take between 6-8 days. I would suggest having an extra 1-3 days of buffer in case reteaching or mini-review sessions may be necessary if misconceptions are spotted during the learning modules.

In update 1, students will be given a pre-survey to learn about their prior knowledge on decimals and percentages, in addition to the regular comments and updates. The purpose of this pre survey is to obtain an initial benchmark of students' knowledge in decimals and percentages. This data will allow instructors to more flexibly adapt and modify existing lessons and activities in the learning module. In update 7, students will also be given a peer review project (with a rubric) where they would complete the project and peer review the work of two students in the class. They would then receive peer feedback from two other students, be given a chance to revise and improve their work. They would also complete a post survey to compare their results against the pre-survey to paint a picture of their progression throughout the learning modules. Instructors can use these additional data points to improve the learning modules for future years.

# Intended Learning Outcomes

## For the Learner

The primary goal of this decimal and percentages module is to help students master decimal operations and finding percentages of numbers. Then, students would apply their knowledge to solve real world problems. This module is broken down into seven sections, with a pre-survey (section 1), post-survey (section 7), and peer review project (section 7).

The knowledge objectives are as follows.

Students will be able to:

• Compare decimals using decimal place values and take the pre-survey.
• Add and subtract decimals.
• Multiply and divide decimals.
• Apply decimal operations to a real life situation in the vending machine activity.
• Identify what percentages are and how they are related to decimals.
• Find the percentage of a number.
• Apply knowledge of decimal and percentages to find the better deal at a store with potential discounts.
• Complete a peer review project to apply their knowledge of decimal and percentages in real life.

Materials needed:

• Computer
• Paper and pencil
• Access to CGScholar
• Zoom/video conferencing software for synchronous discussions

## For the Instructor

Target Learner:

• 6th grade students in a Common Core aligned class.

Assumptions About Prior Learning:

Students are expected to have knowledge in comparing decimal place values and brief overview of operations with decimals using place value and models, as these are 5th grade Common Core math standards. However, students are not expected to be able to perform all four operations with decimals fluently and apply it to solve word problems yet. There will be a pre-survey to get more information on the knowledge levels of the students so that the module can be adjusted based on instructor evaluation.

Anticipated Timeline for this Learning Module:

• 7 school days (recommended: 1-3 days of buffer room if needed)
• It is highly encouraged that instructors offer short office hours (i.e. 15-30 min during dedicated time blocks) to support students who may need additional clarification on the assignments.

Alignment with Common Core Standards:

The following standards will be covered in this learning module. These standards will be referenced in the instructor section of each lesson.

• CCSS.MATH.CONTENT.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.
• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
• CCSS.MATH.CONTENT.6.RP.A.3.C Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.
• CCSS.MATH.CONTENT.5.NBT.A.3 Read, write, and compare decimals to thousandths.
• CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

(Common Core State Standards Initiative, 2022)

# Update 1: Activating Prior Knowledge (Pre-Survey) & Decimal Place Value Review

## For the Learner

Learning Outcome

Students will be able to compare decimal values based on place value and explain real-life application of place values.

Directions

1) Take Pre-Module Survey

Since this is the first update in the learning module, please take this pre-module survey to show what you know about decimals. If you do not know the answer to a question, you can type “I’m not sure” or make your best guess. This survey is not used to grade your performance but rather for the teacher to know what prior knowledge you have about this topic. For any questions that require explanations or examples, feel free to use bullet points or complete sentences.

2) Watch This Video:

Watch the following video on decimal place value.

Media embedded September 24, 2022

Video 2. Decimal Place Value (Math Antics, 2016)

Discuss:

Comment Below: How is decimal place value related to whole number place value? Explain in your own words. Feel free to use an example.

Post an Update: Write about one real-life application of decimal place value. Why is it important and how can you use it to help make real life decisions? Attach at least one media to showcase this application (video, infographic, image, attached documents, etc.). The media can be things you photographed or videographed in real life or something you searched online.

Comment on Peers’ Updates: After posting your update, comment on 2 updates created by your peers on whether you agree/disagree or are curious about their updates.

## For the Instructor

Aligns with Common Core Standards

These are the standards that are covered in this update.

• CCSS.MATH.CONTENT.5.NBT.A.3 Read, write, and compare decimals to thousandths.
• CCSS.MATH.CONTENT.5.NBT.A.3.A Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).

(Common Core State Standards Initiative, 2022)

Rationale

For activating prior knowledge:

This first update aims to activate prior knowledge about decimal place value, which the students had learned last year. This concept is essential in connecting to new content, decimal operations. Research shows that connecting new knowledge to prior knowledge reduces cognitive load and improves learning retention (Myhill & Brackley, 2004). After reviewing and activating their knowledge on place values, students can use this information to understand why it's important to line up the decimal point (and therefore place value) when adding and subtracting decimals in the next lesson.

For pre-module survey:

The purpose of the pre-module survey is to gauge students’ prior knowledge about decimals and percentages so the teacher can better tailor their lessons to fit the needs of the students. I often administer these pre-module surveys and tell the students to not be stressed if they do not know the answer to the questions. Most of the questions are open-ended to give students more freedom to express what they know and don’t know. After students take the pre-module survey, teachers can analyze the results and take quick notes on any major misconceptions I need to address. You can address the misconceptions as a whole class through making video assignments or holding synchronous discussions. Alternatively, you can also modify the discussion question for the next update to address any major misconceptions if pertaining to the majority of the class.

Here is a series of screenshots of the pre-module survey for your reference. The survey is built using the survey tool within Scholar. Click post to have the link appear on the student side.

Screenshots of Pre-Survey

Extra (optional) supplementary resources:

If students struggle with finding real-life applications of decimal place value, one supplementary source you can point them to is the number dyslexia blog (Number Dyslexia, 2022). Alternatively, you can also have students do a mini-reseach session and share out the findings through the updates.

For real-life applications:

This lesson’s update is focused around making a real life application of decimal place value so students can see what they are learning in the classroom is meaningful to their lives. Additionally, student responses serve as valuable insights for instructors to learn about their interests, experiences. Perhaps best stated by Luukkonen (2003),

“Teachers need to be aware of what the students are doing, listening to, reading, and watching. When we better understand what is going on students’ lives, we can better serve them in our instruction.”

(Luukkonen, 2003)

# Update 2: Adding and Subtracting Decimals

## For the Learner

Learning Outcome

Students will be able to add and subtract decimals to the thousandths place.

Directions

1) Watch This Video:

Watch the following video on adding and subtracting decimals.

Media embedded September 24, 2022

Video 3. Addition and Subtraction of Decimals (Math Antics, 2020)

Discuss:

Comment Below: List 1-2 strategies that are helpful to remember when adding or subtracting decimals.

Post an Update: Use Flipgrid to create a short video tutorial on how to add or subtract decimals. Your video should be:

• between 1-5 minutes
• at least one example of decimal addition or subtraction
• showcase step by step how you solved the problem
• showcase solution.

*You may choose to show or not show your face in the video. This video can be structured in any way you want, including but not limited to, whiteboard tutorial, notebook writing, slide shows.

*If you would like more help on creating this video or decimal support, please attend the office hour.

* If you need a refresher on how to use Flipgrid, watch the video below:

Media embedded September 24, 2022

Video 4. Student Version Getting Started with Flipgrid (Flip, 2021)

Comment on Peers’ Updates: After posting your update, comment on 1-2 Flipgrid videos created by your peers. You can discuss whether you agree/disagree or give feedback about their video presentation.

## For the Instructor

Aligns with Common Core Standards

These are the standard(s) that are covered in this update.

• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals

(Common Core State Standards Initiative, 2022)

Rationale:

For video updates:

Flipgrid is used for this lesson’s update to help students make sense of their learning. A six week study was conducted on middle and high school art students. The result showed an increase in student engagement and communication (Johnson & Skarphol, 2018).

Additional notes:

This lesson will follow closely with decimal place value, which was reviewed on the last lesson. Be prepared to hold additional office hours to help with tech related questions around Flipgrid. My experience as a teacher is that most of my students have been able to easily figure out how to record using school computers but there may be a few school devices that require updating or microphone repairs.

# Update 3: How to Multiply and Divide Decimals

## For the Learner

Learning Outcome

Students will be able to multiply and divide decimals to the thousandths place.

Directions

1) Watch This Video:

Watch the following video on multiplying and dividing decimals.

Media embedded September 24, 2022

Video 5. Decimal Multiplication and Division (Math Antics, 2019)

Comment Below: According to the video, what are some important tips that you can remember when multiplying or dividing decimals?

Post an Update: Choose one of the two options below for your updates. Both options will give you the same points.

Note: You may produce a written response for this update or create a video using Flipgrid, like the last update.

1. According to the video, how do you multiply decimals? How is this related to whole number multiplication?
2. According to the video, how do you divide decimals? How is this related to whole number division?

Comment on Peers’ Updates:

After posting your update, comment on 2 updates created by your peers on whether you agree/disagree or are curious about their updates.

## For the Instructor

Aligns with Common Core Standards

These are the standards that are covered in this update.

• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals
• CCSS.MATH.CONTENT.6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.

Extra supplementary resources:

If students struggle with long division of whole numbers from previous years, here is a resource that may help them, in addition to inviting them to office hours to help them fill the gaps that they may have developed from the last few years.

Media embedded September 24, 2022

Video 6. Long Division with Whole Numbers (Math Antics, 2013)

Rationale:

The purpose of this update is to help students connect decimal multiplication and division to whole number multiplication and division.

As mentioned before, connecting new knowledge to prior knowledge improves learning outcomes (Myhill & Brackley, 2004).

This week’s update intentionally provided students with two choices of update prompt as well as two choices of presentation. Study conducted with 207 high school students showed that students reported higher intrinsic motivation and performed better on unit tests when they were given a choice in homework assignment selection (Patall et al., 2010).

# Update 4: Real-Life Application of Decimals - Vending Machine Activity

## For the Learner

Learning Outcome

Students will be able to apply decimal operations to a real life situation in the vending machine activity.

Directions:

For this lesson, you will complete the vending machine activity, which is composed of 5 separate tasks with a self-created vending machine as the final product.

1) Download & print the pdf below.

Student Vending Machine Activity PDF (Congruent Math, 2022)

2) Review the rubric below for this activity.

Rubric (Congruent Math, 2022)

Create an update:

Upload a picture of Task 5 (create your own vending machines)

Take a picture and email the entire machine activity (Task 1-5) to the instructor.

Comment on Peer Update:

After posting your update, comment on 2 vending machine pictures created by your peers on whether you agree/disagree or are curious about their creation.

## For the Instructor

Aligns with Common Core Standards

These are the standards that are covered in this update.

• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals

(Common Core State Standards Initiative, 2022)

Teacher Resources:

Answer key and student samples for Vending Machine Activity available below. Note that each student vending machine (Task 5) may be slighlty different depending on which items they selected in the project. This will lead to a variety of possible answers to help the class see that decimals can be applied in many context in real life. If time permits, it may be fun to do a virtual gallery walk or post sample student projects from the class to help peers learn from the broader community.

Teacher Key Vending Machine Activity PDF (Congruent Math, 2022)

# Update 5: What are percentages? How is it related to decimals?

## For the Learner

Learning Outcome

Identify what percentages are and how it is related to decimals.

Directions:

Watch this video.

Media embedded September 24, 2022

Video 7. What are Percentages? (Math Antics, 2012)

Discuss:

Comment Below: How are percentages used in real life? Give two examples.

Post an Update: How is percentages related to decimals or fractions? Explain using one example.

Comment on Peers’ Updates: After posting your update, comment on 2 updates created by your peers on whether you agree/disagree or are curious about their updates.

## For the Instructor

Aligns with Common Core Standards

These are the standards that are covered in this update.

CCSS.MATH.CONTENT.6.RP.A.3.C Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

(Common Core State Standards Initiative, 2022)

Rationale:

This update also aims to connect percentages to prior knowledge of decimals to help enhance learning. The video explored the similarities of both percentages and decimals as part of a whole.

# Update 6: Find the percentage of a number.

## For the Learner

Learning Outcome

Find the percentage of a number.

Directions

Watch this video below.

Media embedded September 24, 2022

Video 8. Finding the Percentage of a Number (Math Antics, 2022)

Discuss:

Comment Below: In what situations would finding the percentage of a number help you make decisions? Give one example.

Post an update: Create your own real-life problem that can be solved by calculating the percentage of a number. Create the answer key to the real-life problem and upload the problem and answer key with your update. Alternatively, you can also record and upload a video using Flipgrid to present the question and solutions to your math problem.

Comment on Peers’ Updates: After posting your update, comment on 2 updates created by your peers on whether you agree/disagree or are curious about their updates.

## For the Instructor

Aligns with Common Core Standards

These are the standards that are covered in this update.

CCSS.MATH.CONTENT.6.RP.A.3.C Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

(Common Core State Standards Initiative, 2022)

Rationale:

When students create their own number and word problems, they connect math concepts to their background knowledge and lived experiences. Building this connection with the students is essential for meaningful learning (Luukkonen, 2003).

Below is an example of how a student may create and present a math problem related to content standard. This video showed lower grade levels but the same concept and rationale is applied when designing this week’s update.

Media embedded September 24, 2022

Video 9. Creating Our Own Math Story Problems (Meredith Phelan, 2017)

# Update 7: Which Is the Better Deal? (Peer Review Project and Post-Survey)

## For the Learner

Directions

This update will be a peer-reviewed project. Instead of posting your update publicly to the whole community, you will have to think and complete your project before you can view other students’ work.

Watch this video and read the scenario:

Video Scenario:

Video 10. Which is the better deal? (Congruent Math, 2022)

Post an Update:

1) Print and complete the PDF. Upload the PDF to the work section of Scholar.

Figure 5. Student Project 10% off or \$10 off? (Congruent Math, 2022)

Refer to the peer review rubrics for this project prior to submission.

Comment on Peers’ Updates:

After submitting your work, you will be assigned two peer reviewers. Compare your work with their work and then start a discussion by providing targeted feedback, comments, or questions for your assigned peers.

Revise Your Update After Receiving Peer Feedback:

You will also receive feedback, comments, and questions from two other peers in the class. After reflecting on the peer reviews, you can revise any part of your original update and submit your final draft. Please check the rubric embedded within the peer review project that your peer review and teacher will be using to grade you. This is your chance to improve and strengthen your mastery of decimals and percentages. If you would like more support for this project, please contact the instructor to schedule optional office hours.

Complete this Post-Module Survey:

Reflect on your experience working through this learning module. Please give honest and detailed feedback on your experiences with comments, updates, peer review projects so I can use it to improve this learning module for future years. This responses on the post- survey will not be used in your grade calculation. Thanks for taking the time to provide honest feedbacks.

## For the Instructor

Aligns with Common Core Standards

These are the standards that are covered in this update.

• CCSS.MATH.CONTENT.6.NS.B.3 Fluently add, subtract, multiply, and divide multi-digit decimals
• CCSS.MATH.CONTENT.6.RP.A.3.C Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100 times the quantity); solve problems involving finding the whole, given a part and the percent.

(Common Core State Standards Initiative, 2022)

Rationale

The peer review project is a great summative assessment to gauge the mastery of content standards around percentages and decimals. This peer review project is interesting because shopping during sales is a relatable experience for most of my students. Deciding between deals to save money is a practical skill. In order to find the best deal, students need to find a percentage of a number and then perform decimal subtraction to find the value of the first coupon. For the second coupon, they would need to perform whole number subtraction to find the sale price. Lastly, they would need to compare the two decimals to determine the better deal.I think the questions in the project will stretch their critical thinking and application skills.

Students then receive feedback and comments from two peers, which gives them opportunities to fill in any gaps in their understanding and improve their final work. The rubrics provide a generalized expectation list that will set students up for success.

Here are screenshots of the peer assessment rubric that the student would be able to see when they are in the peer review project tab.

Screenshots of Peer Review Rubric

After the peer review project, the teacher can choose to discuss any further confusions or misconceptions (if they noticed any) if needed. The teacher can also target specific student groups for reteaching through the data collected from this peer review project. They may send struggling students an invitation to join small-group office hours or study sessions to help fill in the gaps needed. During the office hours, students can receive more support on misconceptions. Teacher could then give them another way to demonstrate mastery and then reassess from there.

Here are screenshots of the post-survey for your reference:

# References

Common Core State Standards Initiative. (2022). Common Core State Standards Initiative Grade 6. http://www.corestandards.org/Math/Content/6/NS/

Congruent Math. (2022). Real world math activities. https://congruentmath.com/

Cope, B., & Kalantzis, M. (2013). Towards a new learning: The scholar social knowledge workspace, in theory and practice. E-Learning and Digital Media, 10(4), 332–356. https://doi.org/10.2304/elea.2013.10.4.332

Education at Illinois (2017, April 12). Social learning in scholar: The learning module [Video]. https://www.youtube.com/watch?v=9YHWJQxSmiI

Flip (Director). (2021). Students version getting started with flipgrid [Video]. https://www.youtube.com/watch?v=kR1FxImNPSs

*Johnson, M., & Skarphol, M. (2018). The effects of digital portfolios and flipgrid on student engagement and communication in a connected learning secondary visual arts classroom. Masters of Arts in Education Action Research Papers. https://sophia.stkate.edu/maed/270

*Luukkonen, J. (2003). Relevancy in the classroom: Bringing the real world into school. Language Arts Journal of Michigan, 19(1). https://doi.org/10.9707/2168-149X.1283

Math Antics. (2012). Math antics—what are percentages? [Video]. https://www.youtube.com/watch?v=JeVSmq1Nrpw

Math Antics. (2013). Math antics— long Division [Video]. https://www.youtube.com/watch?v=LGqBQrUYua4

Math Antics. (2016). Decimal place value [Video]. https://www.youtube.com/watch?v=KG6ILNOiMgM

Math Antics (2019). Decimal multiplication & division [Video]. https://www.youtube.com/watch?v=Htt09rY9I_A

Math Antics. (2020). Addition and subtraction of decimals [Video]. https://www.youtube.com/watch?v=I4Xt136E1ZQ

Math Antics. (2022). Finding A Percent Of A Number [Video]. https://www.youtube.com/watch?v=rR95Cbc

Meredith Phelan. (2017). Creating Our Own Math Story Problems [Video]. https://www.youtube.com/watch?v=xw9WdhXp2VU

*Myhill, D., & Brackley, M. (2004). Making connections: Teacher’s use of children’s prior knowledge in whole class discourse. British Journal of Educational Studies, 52(3), 263–275. https://doi.org/10.1111/j.1467-8527.2004.00267.x

Number Dyslexia. (2022). 10 decimal examples and applications in real life to understand it better. https://numberdyslexia.com/decimal-examples-and-applications-in-real-life/

*Patall, E. A., Cooper, H., & Wynn, S. R. (2010). The effectiveness and relative importance of choice in the classroom. Journal of Educational Psychology, 102(4), 896–915. https://doi.org/10.1037/a0019545