3rd Grade Math – Model, Compare, Order Fractions
What is your subject, level of instruction, and intended audience?
The subject that I am teaching is 3rd grade math where we will be focusing on learning how to model, compare, and order fractions. This topic involves logical reasoning, problem solving, and critical application skills. The intended audience will be my students, and their parents, as a possible support system at home.
What are the key institutional documents (i.e. syllabus, outline, accreditation standards, etc.) that will influence your design process?
As a teacher in HaysCISD I follow the TEKS, or Texas Essential Knowledge and Skills, which are the state academic standards on what students should know and be able to do. I also use our district’s pacing guide, and Schoology, our school’s LMS, to structure lessons and provide resources. Unit Checks and CBAs are created around these objects to set the standards that we are meeting.
What design approach have you chosen? Why?
I have chosen to use a blended learning flex model approach because I plan to combine online, self-paced resources in Schoology, project based learning, and small group guided instruction. This combination will promote active student engagement, and personalized learning opportunities for students to be self-directed learners that exhibit student agency, and use COVA, which ensures that all students have choice, ownership, voice, and authentic learning experiences. In return, this type of support and infrastructure will supply a productive and positive learning environment for the learners.
Who controls the learning?
Students will have a hands-on approach and control their own learning. They will use COVA, and set the pace of their learning, and the teacher will be a facilitator that is available to support and guide the students through the learning process and journey. Also, more one on one attention can be provided in a small group guided instruction setting, as needed. Additionally, students will have constant access to Hays Class Link, in which they can login to use Schoology, Progress Learning, StemsScopes, Padlet, or any other apps to enrich their learning from home, and complete projects at their own time, pace, and in their own way. This tunes in on the individual’s differences of growth, or achievements, and allows learners to be connected to a learning environment that uses digital tools to create a hybrid learning experience.
Are you using competency-based education (CBE) or outcome-based education (OBE)? Why?
I have chosen to integrate both competency-based education and outcome-based education because I feel like they will both be essential to this significant learning environment. CBE allows students to work at their own pace and achieve mastery skills, such as modeling and comparing fractions. Whereas OBE gives students opportunities to focus on the overall outcomes, meet clear goals, and solve real word problems or scenarios that involve fractions, which in essence supports ways to gain deeper understanding of the concepts learned.
How will you balance assessment Of/For/As learning?
Assessment Of Learning – formal assessments, such as quizzes, unit checks, and tests
Assessment For Learning – Formative checks, like exit tickets, and class discussions
Assessment As Learning – Self-reflections and peer reviews where growth is evaluated
Are you moving your learners into deeper learning? If not, why not?
Yes, students will have deeper learning experiences because they will be given opportunities to apply fractions to real world scenarios where they can explore, and make connections to what they are learning and how it can be used in everyday life situations, meanwhile reinforcing essential concepts that they have gained. They will develop foundational knowledge that they will use in future situations and learning environments, and learn to apply their understanding and skills to practical situations in life.
Big Hairy Audacious Goal:
At the end of this unit, 3rd grade students will be able to model, compare, and order fractions using real-life situations and demonstrate problem solving skills, critical thinking abilities, and logical reasoning. Also, parents can reinforce these concepts at home to support a collaborative learning environment that ensures all students can be successful.
Finks 3-COLUMN TABLE
| Learning Goals/Outcomes | Learning Activities | Assessments |
| Foundational Knowledge: Model fractions using manipulatives, visuals, and vocabulary words to understand basic fraction concepts, like parts of a whole | Interactive videos and lessons using Schoology, guided practice, hands-on objects, such as various fraction pieces or fraction bars | Formative assessment: exit ticket with simple fraction identification |
| Application: Compare fractions, share knowledge, and explain logical reasoning, use real world examples | Group activities (sharing and comparing food, like pizza,pie, cake, chocolate bar) and teacher led small group sessions, students create their own word problems | Summative Assessment: students solve a fraction word problem showing their use of modeling and equations, to demonstrate their critical thinking skills |
| Integration: Apply fractions to real world scenarios and use problem solving skills and strategies | Project based learning activities to collaborate in a team, integrate activities on Schoology to show problem solving abilities | Project Completion and Student Presentations, Make Connections, and Peer Review |
| Human Dimension/Self – students grow and gain confidence in their own abilities and problem solving skills, and they will learn to collaborate with others | Students have pair and share activities where they show their understanding of modeling fractions and problem solving. They can journal about their learning experiences. | Teachers make observations and make note of students’ growth and learning progress as they collaborate with their peers, and show their level of confidence with group projects. |
| Caring – Students will make connections on how math and using fractions connects to their daily lives and how it is important to problem solve and develop critical thinking skills. | Class discussions of how fractions are used on a daily basis in the real world , such as with cooking, and using recipes, or sharing food, or using measurement to build things. | Students make reflections and share one thing that they use fractions outside of school, or at home with their own families. |
| How to Keep on Learning – Students will learn how to use tools like Schoology, or other digital tools to enhance their learning and collaborate with others. They will learn tools for self assessment strategies to measure their own growth or level of understanding. | Practice ways to have self-paced learning. Students will learn how to ask clarifying questions and seek help when needed. | Students will set a goal to improve, be able to track their own progress, and track their progress in a learning journal. |
Implementation schedule:
Week 1 – Introduce fractions using videos, anchor charts, and new vocabulary words in Schoology. Guided instruction in a small group setting, including manipulatives.
Week 2 – Explore fraction comparisons, use interactive games, project based learning activity with a real life example, like creating a garden, or running a pizza parlor.
Week 3 – Continue to apply fractions in a collaborative team setting where students can relate it to practical usage in real life and work as a group with different roles to collectively use the knowledge and skills that they have learned and make it applicable to the real world so that they can have opportunities to problem solve, and use critical thinking skills
Week 4 – Students should finalize and present their projects to their peers, then allow peer review, and read their classmate’s reflections for peer feedback, so that this will help them make improvements to their work.
Week 5 – Students are journaling along the way and making self reflections of their projects and group work that led up to what they have done. They can share their personal experiences and what they have learned through this entire process. What were some of the pros and cons? And, what would they do differently for next time?
ADDIE MODEL: Instructional Design
Analysis – Identify learning environment, learner characteristics, and instruction
3rd graders will learn to model, compare, and order fractions, then apply their understanding to real-life scenarios.They will build logical reasoning, problem solving, and critical thinking skills. They will be challenged with understanding that fractions are parts of a whole, and not just a separate number.
Design – Create a plan for the learning experience
Students will begin by using fraction tiles, or manipulatives. They will also use visuals, like pie charts, fraction bars, and number lines. They will apply their understanding by playing interactive games, completing assignments, and quizzes. Examples like sharing pizza or baking will be provided, and this will be used as a guide for parents to give support from home.
Develop – Create the learning materials
Students will make charts and number lines using project based learning activities that link to real world scenarios, such as gardening, cooking, or sharing. They can create their own real life examples, and complete online quizzes from Schoology or Progress Learning. They can also create their own fraction tiles, and cutouts to represent their understanding. They will collaborate on projects and work as a team to have extra hands-on practice of the lessons being learned.
Implement – Put the learning materials into action
In a small group, the teacher can use fraction charts, and number lines as examples to facilitate the learning. Fraction pieces or tiles can also be used to have a hands-on approach to understanding the concepts. Students can create their own learning games to share with their peers, or play interactive games, and complete lessons as a small group. Together, they can solve word problems that relate to real world situations. Videos and guides can be shared with parents for at home practice.
Evaluate – Access learning experience and make improvements
The teacher gets feedback from students about what parts were hard or easy for them to understand, and apply. Observations can be made of how students used the given materials, and what challenges came up as they applied their knowledge and skills. Were the students focused and engaged on the material at hand? Reflections are made on lessons, assignments, and quizzes to check for learning gaps. The teacher can provide feedback or feedforward to students on completed projects. Furthermore, the teacher can get input from parents about what worked and didn’t work from home. In summary, the teacher can make modifications to make learning better for all students to have a personalized learning experience that fits what they need.
Syllabus
3rd Grade Math – Model, Compare, Order Fractions
Grade Level: 3rd grade Math
Course Title: Model, Compare, Order Fractions
Audience: Students and Parents (as a support system)
Course Overview:
In this course, students will learn the following:
- Model Fractions – using manipulatives, and visuals
- Compare Fractions – with denominators that are alike, and unlike
- Order Fractions – from least to greatest, and greatest to least
- Apply Fractions – relate to real-world scenarios, develop critical thinking skills, and problem solving abilities
Course Goals/Objectives
Students will be able to do the following:
- Develop foundational skills
- Represent fractions visually and numerically
- Use reasoning to compare fractions
- Arrange fractions on a number line
- Explore meaningful applications
- Apply knowledge to project based learning
- Connect fractions to the real-world
- Support lifelong learning
Standards and Tools
- Standards: TEKS, or Texas Essential Knowledge and Skills
- Resources: HaysCISD Pacing Guide, Unit Planner, and LMS, such as Schoology
- Assessments: Unit Checks, CBAs (Curriculum-Based Assessments), and project based activities
Course Structure
Blended Learning Flex Model Approach:
- Online Resources: lessons and activities in Schoology for self paced learning
- Project Based Learning: hands-on collaborative projects, promotes deeper understanding
- Small group/Guided Instruction: Teacher mentors/guides based on the needs of student
COVA Approach: Students will have the following on their learning journey –
- Choice – Students will choose how they learn, and demonstrate what they learn.
- Ownership – Students will take on responsibility for their learning.
- Voice – Students will express what they have learned
- Authentic learning opportunities – Students apply what they have learned to the real-world.
Control of Learning
- Teachers will act as facilitators, and provide guided support in small group sessions.
- Students will access Hays Class Link to enhance their learning at any time.
- Students will be self-directed and self-paced when using digital tools, or doing projects.
Competency-Based and Outcome-Based Education
- CBE: Students master skills to model, order, and compare fractions.
- OBE: Students focus on solving fractions using real world situations, with clear goals or outcomes.
Assessment Strategy
- Assessment Of Learning – Quizzes, Unit Checks, CBAs
- Assessment For Learning – Exit Tickets, classroom discussions (for immediate feedback)
- Assessment As Learning – Self-reflections, peer reviews (to evaluate own levels of growth)
Feedback from Collaborative Discussion Groups
Kelsi Martin
23 hours ago, at 2:35 PM
@jackie, I am not sure how to comment on Padlet, but your assignment is BEAUTIFUL! Feedback wise, I don’t think you should change a thing. It has EVERYTHING. Your assignment definitely motivated me to do better in the future!
Joseph Perrone
3 hours ago, at 10:34 AM
Jackie, your stuff is awesome.
Sarah Enger
I greatly enjoyed reviewing your work from this assignment. It is nice to see a fellow colleague working on content that is actually happening in the elementary classroom. Your material has given me some ideas for my own work. Your e-portfolio page is nicely organized and provides a clear presentation of the material for the week’s assignment. Just one note, your implementation schedule only has 4 weeks in it. I had emailed Dr. Bellard to ask specifically about how long a course would be. He mentioned that a “course” is usually at least 5 weeks. Maybe you could include a week where students are journaling reflections of their projects and work that led up to what they have and then reading their classmate’s reflections for more peer feedback? Just a thought.
Reply | Hide Replies (1) • 1/31/25, 1:20 PM
Jackie Bittner
Thank you so much for your valuable feedback. I love your idea! And, yes, I will be sure to add a 5th Week. Journaling about the completed projects and group work is certainly a good way to self reflect on their work, and make improvements to what they have done. I also believe that students will find that to be very valuable. I appreciate it!
15 minutes ago, at 1:50 PM
Jeffrey Charles
Your alignment with TEKS and the district pacing guides shows a strong commitment to educational standards, essential for effective learning. Your blended learning flex model is impressive, as it combines online resources, project-based activities, and small group instruction, promoting student agency and ownership.
Integrating competency-based and outcome-based education is a great choice; It allows students to progress at their own pace while focusing on real-world applications. Your balanced assessment strategy featuring formal asses. It allows formative checks and self-reflections, comprehensively viewing student progress.
Lastly, I appreciate your emphasis on real-world applications, making the material relevant and practical for students. Your thoughtful design will create a positive and impactful learning experience for your students. Keep up the great work!
Reply | Hide Replies (1) • 4 hours ago, at 9:41 AM
Jackie Bittner
I truly appreciate your feedback, and really value your support. Thank you for that, as I feel confident that I am certainly on the right path, and enjoy seeing that others feel the same way as I do. Thank you!
7 minutes ago, at 1:58 PM
Melissa Richards
Hi Jackie,
I really liked watching your video that explained your goals and plans for your blended learning course. As another teacher who teaches elementary students, I enjoyed seeing both the face-to-face and online components of your plan. Having manipulatives available for your students to explore is so important in helping establish a strong foundation for understanding how fractions work. Although our goal should be to focus on outcome-based learning, I also feel that competency-based learning is needed to ensure that students have mastered a skill before applying it in real world settings. Your plan shows a great balance of both of these methods. On our campus, we use STEMscopes for science. I’m interested in how you feel about STEMscopes for Math. I’m curious about the digital learning options available! In addition to all of the learning and applying skills with their own assignments, I liked seeing how they will participate in peer reviews. I think this will establish great leadership skills in young learners where they are having to analyze the work of others and learn how to provide quality feedback in a respectful manner. I’m excited to hear how your plan continues to progress as you begin to implement this in your classroom! Thank you for sharing!
Reply | Hide Replies (1) • 4 hours ago, at 9:51 AM
Jackie Bittner
Thank you so much, Melissa! I really appreciate your supportive response. Using StemScopes has been so great for both Math and Science. However, we just started using this application for Math last year, and had to revamp all of our Math lesson plans to reflect the new format and activities. For math, some of those exploring assignments have been very tedious, and require a lot of printed out paper, which we are told to limit what we print. So, I have been using Schoology to project the questions, through facilitation slides, and have been having my students use notebook paper to make their responses on. It gives a lot of good lessons and practice, but we also use other resources to get a better mix or exposure. My favorite feature has been the technology enhanced questions and assessments.
a few seconds ago, at 2:05 PM
References
Bittner, J. (2024). Literature review: Promoting student agency using a flex model of blended learning. Retrieved October 22, 2024, from https://jackiebittnerdesigner.com/literature-review/
Finks Taxonomy & 3 Column Table Resources – https://drive.google.com/drive/folders/1gMqxX2SEtWmnQ37m4UxWUcWxy0w87rWj?usp=sharing
Harapnuik. D. (2021). Assessment Of/For/As learning. https://www.harapnuik.org/?page_id=8900
Harapnuik, D. (2018, July). COVA. https://www.harapnuik.org/?page_id=6991
Harapnuik, D. & Thibodeaux, T. (2023). COVA: Inspire Learning through Choice, Ownership, Voice, and Authentic Experiences. Amazon.com Services.
Harapnuik. D. (2020). Feedforward vs. Feedback. https://www.harapnuik.org/?p=8273
Top 7 Instructional Design Models to Help You Create Effective Learning Material. (2021). https://creately.com/blog/diagrams/instructional-design-models-process/
Jackie Bittner M.Ed. 