1. GMU COMPLETE Center Arranging Chairs Lesson Plan A VDOE SPONSORED MSP PROFESSIONAL DEVELOPMENT OPPORTUNITY THROUGH GEORGE MASON UNIVERSITY Fiona Cobb Clare Daly Anita Magrath Rolling Valley ESSpringfield Estates ES Springfield Estates ES Fairfax County Fairfax County Fairfax County Tanya Matyi Jennifer Moore Lynbrook ES Kings Park ES Fairfax County Mary Randolph Pat Schreiber Springfield Estates ESKings Park ESFairfax County

2. Arranging Chairs Lesson Study – Rolling Valley ES Fiona Cobb, Host Teacher Third Grade

3. WG Lesson Goals  Professional Learning Goals: Effectively teach multiple approaches to problem solving Learn to anticipate the individual needs of students and plan guided responses Work collaboratively to understand and apply the process of Lesson Study  Lesson goals: (both immediate and long term) Students will understand build the foundation for the communicative property Introduce students to rectangular arrays Long term – these concepts will be the foundations for learning about area, multiplication, multiple arrays (factors)

4. WG Related SOL Objectives (2009)  Lesson Objectives: SOL 3.6 Students will represent multiplication and division using area models and sets, and number line models, and create and solve problems that involve multiplication of two whole numbers, one factor 99 or less and the second factor five or less.

5. EK Arranging Chairs Puzzle  Students were asked to arrange 12 tiles into straight rows for an audience to watch a play  Students drew and labeled arrangements on graph paper

6. CN Students Mathematizing

8. TF Example of Students’ Work This example of student work shows all of the arrangements labeled. Students worked in pairs to find the arrangements.

9. Analysis of student learning Three levels of understanding: Level One:  Missing arrays  One-by-one counting or skip counting

10. Analysis of student learning Level Two:  Breaking tiles into groups

11. Analysis of student learning Level Three:  All arrays  Multiplication

12. EK Modifications and Enhancements  Using sticky notes instead of SmartBoard tiles  Modeling task with actual chairs  Extended time  Emphasize key vocabulary (rectangle, down, across)

13. What We Learned  collaborative planning process  assessment to focus instruction  revisions led to a better lesson  students enjoyed making mathematical connections  student conversation led to deeper understanding

14. Further Questions to Explore  Do bigger numbers have more arrays?  Is a 6 by 2 array the same as a 2 by 6 array?  Is there a way to predict how many arrays a number will have?