Focus On Fractions

1. Focus On Fractions Linking Content and Conceptual Knowledge Leading to Student Success in Algebra

2. Why Fractions? • “Understanding fractions is one of the most important outcomes of mathematics education because of the pervasive use of fractions throughout mathematics.” Dr. Randall Charles (primary author of enVisionMATH) in Math Across The Grades, 2011

3. The National Mathematics Advisory Panel (NMAP) (2008) • Offers recommendations for how we can best prepare elementary and middle school students for success in algebra, a gateway to mathematics in high school and beyond. http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

4. NMAP –On Preparation for Algebra… • Follow a focused, coherent progression of mathematics. • Achieve proficiency with whole numbers, fractions, and aspects of geometry and measurement. • Build deep understanding. • Emphasize fractions and related concepts. http://dww.ed.gov/topic/?T_ID=20

5. NMAP –Fraction Topic Benchmarks • By the end of Grade 4: • Identify and represent fractions and decimals and compare them on a number line or with other common representations • By the end of Grade 5: • Proficient with comparing fractions and decimals and common percents, and with the addition and subtraction of fractions and decimals • By the end of Grade 6: • Proficient with multiplication and division of fractions and decimals and all operations involving positive and negative integers

6. Institute of Education Sciences (IES) Practice Guide • Developing Effective Fractions Instruction for Kindergarten Through 8th Grade (2010) • “Fractions” refers to the full range of ways of expressing rational numbers, including decimals, percentages, and negative fractions. • All reflect the perspective that conceptual understanding is essential. • Provides five recommendations for improving students’ learning of fractions. http://ies.ed.gov/ncee/wwc/pdf/practiceguides/fractions_pg_093010.pdf

7. IES Recommendations: • Build on students’ informal understanding of sharing and proportionality to develop initial fraction concepts. • Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.

8. IESPG Recommendations: • Help students understand why procedures for computations with fractions make sense. • Develop students’ conceptual understanding of strategies for solving ratio, rate, and proportion problems before exposing them to cross-multiplication as a procedure to use to solve such problems. • Professional development programs should place a high priority on improving teachers’ understanding of fractions and of how to teach them.

9. The Project –Focus On Fractions • Project Goals: • Deepen teacher and student understanding of fraction concepts and operations. • Provide resources for best practices in teaching fractions. • Integrate new learning into enVisionMATH lessons. • Promote collaboration among team members and across schools. • Introduce Common Core Standards and Standards for Mathematical Practice.

10. The Project –Focus On Fractions • Teacher Outcomes: • Deeper understanding. • More effective instruction. • Improved use of enVision materials. • Increased collaboration among grade level teams. • Awareness of future directions in instruction and assessment.

11. All Leading To… • Increased student achievement in math.

12. The Project –Focus On Fractions • Expectations: • Participate in two professional development release days with colleagues on February 16th (Julie McNamara) & March 24th (Kate Gallaway). • Learn how to access and utilize Fraction Nation software by Scholastic. • Complete Fraction Nation’s 64 lessons and unit assessments online before Monday, March 21st.

13. The Project –Focus On Fractions • Expectations: • Study one related topic from Math Across The Grades, and complete the “Check Skills and Understanding” page. • Participate in a team meeting (ACE time) with principal to discuss project and school implications. • Earn $200 stipend or 7 hours PDA column advancement to be paid/credited at completion of project.

14. Focus On Fractions Day 1 - Agenda 8:00 – 11:30 Julie McNamara (w/10-minute break) 11:30 – 12:30 Lunch 12:30 – 2:15 Common Core Standards Q & A with Julie Fraction Nation software 2:15 – 2:30 Closing Comments/Day 1 Feedback Book raffles @ 7:45 AM, after break, 12:30 PM, & 2:30 PM.

15. Beyond Pizzas & PiesAuthor: Julie McNamara, Math Solutions

16. Math Across The Grades (MAG): enVision Math Content Development • Content resource for teachers • Addresses content and pedagogy • Attention to Big Ideas (Unifying Concepts) of mathematics “When you understand the Big Ideas of mathematics you no longer see mathematics as a set of disconnected concepts, skills, and facts. Rather, mathematics becomes a coherent set of ideas.” Dr. Randall Charles, Author.

17. MAGenVision Math Content Development • Four topics from which to choose: • Fraction Concepts • Fraction Operations • Decimals • Ratio, Proportion, and Percent

18. MAG: enVision Math Content Development • Three sections within each topic: • Overview • Mathematics Background • Check Skills and Understandings