A Story of Units

1. A Story of Units Betty Chin

2. Standards for Mathematical Practices Make sense of problems and persevere in solving them. Reason abstractly and quantitatively. Construct viable arguments and critique the reasoning of others. Model with mathematics. Use appropriate tools strategically. Attend to precision. Look for and make use of structure. Look for and express regularity in repeated reasoning.

3. Framework

4. Review of Module Structure

5. Debrief Problem Set Exit Ticket Concept Development Application Fluency Homework

6. Balanced, Rigorous Instruction

7. Key Points • Modules Overviews and Topic Openers provide essential information about the instructional path of the module and are key tools in planning for successful implementation. • Each of the lesson components are necessary in order to achieve balanced, rigorous instruction and to bring the Standards to life. • The Exit Ticket is an essential piece of the Student Debrief and provides daily formative assessment. • Opportunities to nurture the Standards for Mathematical Practice are embedded throughout the lesson.

8. A Story of Units Fluency in Practice

9. Implementation of a Fluency Routine • Fluency activities serve a variety of purposes: • Maintenance: Staying sharp on previously learned skills • Preparation: Targeted practice for the current lesson • Anticipation: Building skills to prepare students for the in-depth work of future lessons • In fluency work, all students are actively engaged with familiar content. This provides a daily opportunity for continuous improvement and individual success.

10. Required Fluencies

11. Fluency Exercises in A Story of Units • Three general categories of fluency work support student learning in A Story of Units: • Counting Exercises • Choral and White Board Exchanges • Sprints

12. Key Foundational Skills in A Story of Units Module 1 • K – Counting to 5, counting consecutively, and recognizing numerals • 1 – Counting a set of objects or pictures and assigning a numeral, and counting on in a number sequence • 2 – Adding and subtracting units such as tens and centimeters, and using rulers to count, add, and subtract • 3 – Group counting (skip counting) to lay the foundation for • understanding multiplication as repeated addition • 4 – Multiplying and dividing by 10, and decomposing numbers into units • 5 – Renaming decimals in various place value units (3.14 = 3 ones 14 hundredths = 31 tenths 4 hundredths = 314 hundredths)

13. Differentiation in Fluency Practice • Some possibilities for adapting fluency exercises include: • Modeling with visual tools • Adapting the length and pace of exercise • Using content from lower or higher grades • Varying between independent, partner, small group, and whole class activities

14. A Story of Units Application and Concept Development in Practice

15. Application Problems • Application involves using relevant conceptual understandings and appropriate strategies even when not prompted to do so. • Time allotted to application varies, but is commonly 10-20 minutes of the lesson. • The Read, Draw, Write (RDW) process is modeled and encouraged through daily problem solving.

16. Concept Development • Constitutes the major portion of instruction and generally comprises at least 20 minutes of the total lesson time.  • Builds toward new learning through intentional sequencing within the lesson and across the module. • Often utilizes the deliberate progression from concrete to pictorial to abstract, whichcompliments and supports an increasingly complex understanding of concepts. • Accompanied by thoughtfully sequenced problem sets and reproducible student sheets.

17. Differentiation in Application Problems and Concept Development

18. A Story of Units Student Debrief in Practice

19. Another Look at Problem Sets • Generally embedded within the Concept Development. • May be completed independently or with teacher guidance, and are reviewed in class as part of the Student Debrief. • Provide an opportunity for students to apply understanding(s) from the lesson. • Directions introducing the Problem Set give guidance about how to differentiate

20. Another Look at Problem Sets

21. The Student Debrief • Includes sample dialogue or suggested lists of questions to invite the reflection and active processing of the totality of the lesson experience. • Encourages students to articulate the focus of the lesson and the learning that has occurred. • Promotes mathematical conversation with and among students. • Allows student work to be shared and analyzed. • Closes the lesson with daily informal assessment known as Exit Tickets.

22. Differentiation in the Student Debrief • Have students restate their learning for the day. Ask for a different representation in the restatement. Would you restate that answer in a different way or show me by using a diagram? • Encourage students to explain their reasoning both orally and in writing. • Let students use pictures and gestures to calculate and explain.