## Building Fundamental Mathematics for Number Sense

Building Fundamental Mathematics for Number Sense: Enhancing Virginia K-2 Standards of Learning and Assessment is a K-2 mathematics partnership between Faculty from George Mason University (GMU) and school divisions in Northern Virginia (Alexandria, Fairfax County, Falls Church City, Manassas City and Prince William County). The mission of the COMPLETE Center is to promote excellence in mathematics teaching, learning and collaborative coaching in Northern Virginia through innovative and solution-oriented initiatives. Using a systemic and sustained approach to high quality teacher professional development through content-focused summer institute and content-focused coaching in the Fall Lesson Study for Kindergarten through second grade math teachers, special educators, and teachers of Limited English Proficient (LEP) students, we were able to engage the teachers in: a.Modeling Mathematics Ideas aligned to the 2009 Virginia Standards of Learning (SOL) for mathematics content, classroom strategies, and student assessment standards; b.Developing problem based assessment and performance based tasks for younger students in mathematics; c.Developing activities to differentiate instruction with parallel tasks that enrich critical thinking aimed at increasing the academic achievement of diverse populations (special education, gifted, ELL and economically disadvantaged students); d.Developing need-based on-site and e-learning professional and curricular resources (video clips of exemplar lessons, real-life math connections and concepts modeled using virtual manipulatives) to ensure that all teachers are able to participate in high-quality professional development that result in improved teaching practice and enhanced student learning.

# Description of the Project Activities

The goal of the Math Modeling Ideas in the Elementary Grades: Building Foundations for Number Sense (Grades K-2) is to impact student learning in mathematics by improving teachers' mathematics content knowledge and pedagogical strategies. The professional development will include two parts. Part I is a summer institute held in early August 2012 with a course entitled Math 600: Building Foundations for Number Sense (Grades K-2). This course covers the topics: ways of representing numbers, relationships between numbers, number systems, the meanings of operations and how they relate to one another, and computation within the number system as a foundation for algebra. Teachers will examine the developmental sequence and learning trajectory as children learn this material. There will be a focus on formative and performance based assessment and error analysis to improve student learning. By improving teachers' content-specific knowledge in mathematics, the project increases the potential for improving the math achievement of all students in the collaborating districts. Part II follow-up sessions include Collaborative Coaching and Lesson Study throughout the school year. Lesson Study will support teachers' needs in the classroom as they implement materials and strategies during the school year. Through the network, teachers will work on Lesson Study as a team with K-2 teachers, special educators, LEP teachers led by a mathematics educator and a math coach. The network will become the mechanism in place to sustain the learning and keep the focus on the content, helping teachers understand how the tasks they are using in their classrooms are intended to contribute to student understanding.
Does Order Matter?

Jake is building with cubes. He has a tower of 2 green cubes, a tower of 5 blue cubes, and tower of 3 yellow cubes. How many connecting cubes does he have?
Later, complete math stations with 4 similar problems using the numbers (5, 2, 3) (6,3,4) (6,8,5) (8,5,5)

Track Problem

There are 23 students in our class. We want to walk 230 laps on the track.
a) If each student walks the same amount, how many laps will each student walk?
b) What if the students do not have to walk the same amount, how could the class get to 230 laps?

Combinations Problem

Flat Stanley is going on vacation. He has 4 different colored pants (green, purple, pink and blue) and 3 different colored shirts (brown, orange, and blue). What are the combinations of different outfits that he could wear on his trip? Record your findings.

Arranging Chairs

Students were asked to arrange 12 tiles into straight rows for an audience to watch a play.

Feast for 10

There are 10 kids sitting at the lunch table at school. How many kids are boys and how many are girls? Show as many ways as you can.

Robots and Cell Phones

If three robots make 17 cell phones in 10 minutes, then 12 robots can make how many cell phones in 45 minutes?