### Table of Contents

- Content Home
- Welcome
- Module Overview
- Pre-Assessment
- Unit 1: Teaching and Learning the Standards for Mathematical Practice
- Unit 2: Overarching Habits of Mind: MP1 and MP6
- Unit 3: Reasoning and Explaining (MP2 and MP3)
- 3.0 Unpacking MP2 and MP3
- 3.1 Beginning to Reason: Definitions and Conjectures
- 3.2 Explaining and Justifying
- Taxonomy of Questions in Mathematical Discourse
- 3.3 Identifying Flaws in Reasoning
- 3.4 Making Arguments More Viable
- 3.5 Summary

- Unit 4: Modeling and Using Tools (MP4 and MP5)
- 4.0 Unpacking MP4 and MP5
- 4.1 Introduction to Modeling with Mathematics (MP4)
- 4.1.1 Examples of Modeling with Mathematics
- 4.1.2 Summary and Reflection

- 4.2 Modeling with Mathematics at Different Grade Level Spans
- 4.3 Introduction to Using Appropriate Tools Strategically (MP5)
- 4.4 Use of Tools at Different Grade Level Spans
- 4.5 Summary and Reflection

- Unit 5: Seeing Structure and Generalizing (MP7 and MP8)
- Unit 6: Summary and Next Steps
- Post-Assessment
- Certificate of Completion
- Glossary
- Resources
- Acknowledgements
- Module Evaluation

#### Bookmarks (1)

Unit 4: Modeling and Using Tools (MP4 and MP5)

# 4.1.1 Examples of Modeling with Mathematics

Select your grade level span below and complete the task titled, Tiling Pool Problem. This task will allow you to experience modeling with mathematics appropriate for the grade level you teach.

As it is written, the Tiling Pool Problem represents a level 2 modeling problem (with the exception of grade level spans 6–8 and 9–12 which each contain a level 3 question). The same problem is used for each grade level span.

Mathematics: Kindergarten through Grade Twelve (K–12) Standards for Mathematical Practice. Brought to you by the California Department of Education, the Regents of the University of California, and the California Mathematics Project.

For questions or feedback, please e-mail commoncoreteam@cde.ca.gov.