| Module 10: Developing Conceptual Understanding through Tables and Proportional Reasoning | |
| Task Introduction | |
| "Welcome to the final module in this series! In this module, you’ll watch a video of a lesson on proportional reasoning involving tables. You’ll reflect on the teacher’s practices, how students connect their reasoning, and the ways these practices address Common Core standards. Let’s dive in!" | |
| Video: | |
| "Watch the video provided at this link. Before watching how students approach the task, solve it yourself to reflect on your own reasoning." | |
| Pre-Video Task Prompt | |
| Before watching the video, let's start by solving the problem. | |
| 1. How did you approach solving the problem? | |
| - What strategies did you use? | |
| - Did you recognize proportional relationships within the table? | |
| Hints if Needed: | |
| - Think about the relationships both horizontally (within rows) and vertically (between columns) in the table. | |
| - How might unit rate play a role in reasoning proportionally? | |
| After you solve the problem, let me know, and we’ll move to the next step! | |
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| Post-Video Reflection Prompts | |
| Now that you’ve watched the video and solved the problem, let’s reflect on different aspects of the lesson one by one: | |
| Step 1: Observing Creativity-Directed Practices | |
| - What creativity-directed practices did you notice the teacher implementing during the lesson? | |
| - Reflect on how these practices supported students’ reasoning and collaboration. | |
| Hints if Needed: | |
| - Consider whether the teacher encouraged mathematical connections, collaborative problem-solving, or extended students’ thinking beyond the unit rate. | |
| When you're ready, share your thoughts, and we'll move to the next reflection. | |
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| Step 2: Student Reasoning and Connections | |
| - How did students connect the relationship between price and container size? | |
| - How did their reasoning evolve as they worked through the task? | |
| Hints if Needed: | |
| - Did students start with the given information (e.g., the 24-ounce container costing $3)? | |
| - How did they use this information to reason proportionally? | |
| Once you respond, we’ll move on! | |
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| Step 3: Teacher Actions in Small Groups | |
| - How did the teacher’s actions during small group interactions reflect the students’ reasoning? | |
| - How did the teacher use these interactions to inform whole-class discussions? | |
| Hints if Needed: | |
| - Think about how the teacher listened to students’ reasoning and used their ideas to guide the next steps. | |
| - What types of questions did the teacher ask? | |
| Once you're ready, let’s move forward! | |
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| Step 4: Initial Prompts and Sense-Making | |
| - How did the teacher prompt students to initially make sense of the task? | |
| - What role did these prompts play in guiding students’ reasoning? | |
| Hints if Needed: | |
| - Did the teacher ask open-ended questions? | |
| - How did these prompts help students engage with the task? | |
| Share your response, and we’ll continue! | |
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| Step 5: Common Core Practice Standards | |
| - What Common Core practice standards do you think the teacher emphasized during the lesson? | |
| - Choose four and explain how you observed these practices in action. | |
| Hints if Needed: | |
| - Consider whether the teacher emphasized reasoning, collaboration, or modeling with mathematics. | |
| - How did the students demonstrate these practices? | |
| When you’re ready, let’s move to the final steps! | |
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| Step 6: Problem Posing Activity | |
| Based on what you observed, pose a problem that encourages students to use visuals and proportional reasoning. | |
| - What real-world context will you use? | |
| - How will students use visuals like bar models or tables to represent proportional relationships? | |
| - Does your problem encourage multiple solution paths? | |
| Hints if Needed: | |
| - Try to design a problem where students can approach it differently but still apply proportional reasoning. | |
| Once you've created your problem, let me know! | |
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| Step 7: Summary and Final Reflection | |
| - What’s one change you will make in your own teaching based on this module? | |
| - Reflect on a specific strategy, question type, or approach to representation that you want to implement. | |
| Encouraging Closing Statement: | |
| "Great work completing all the modules! We hope you’ve gained valuable insights into fostering creativity, connecting mathematical ideas, and engaging students in meaningful learning experiences. It was a pleasure working with you—see you in the next professional development series!" | |