SESSION 14 OGAP FRACTION OPERATIONS INTRODUCTION 2018 OGAPMath

SESSION 14: OGAP FRACTION OPERATIONS INTRODUCTION © 2018 OGAPMath LLC. For non-commercial use only. 1

The Ongoing Assessment Project (OGAP) ● OGAP is an intentional, systematic, and ongoing formative assessment system designed to gather evidence as students learn specific mathematics concepts (Additive Reasoning, Multiplicative Reasoning, Fractions, Proportions). ● OGAP is grounded in the math education research on how students learn math concepts – Learning Progressions © 2018 OGAPMath LLC. For non-commercial use only. 2

The Essence of formative assessment is… • …“the relentless attention to evidence of student thinking” (p. ix) and the systematic and intentional use of this information to inform instruction and student learning (Popham, 2012). • To be considered formative assessment the evidence must be ‘elicited, interpreted, and used by teachers and learners” (Wiliam 2011, 43). © 2018 OGAPMath LLC. For non-commercial use only. 3

OGAP Cycle Gather Evidence Make Instructional Decisions © 2018 OGAPMath LLC. For non-commercial use only. Analyze Evidence 4

OGAP – Knowledge-based decision making… Knowledge of math education research Deepened content knowledge Tools and strategies to gather evidence Informed instructional decision making © 2018 OGAPMath LLC. For non-commercial use only. 5

OGAP Fraction Professional Development © 2018 OGAPMath LLC. For non-commercial use only. 6

Operation Workshop Goals To understand the importance of developing procedural fluency with understanding for fraction operations in order to for students to engage in the mathematics expected in middle school. To understand how to use visual models, estimation, understanding of magnitude, unit fraction understanding, properties of operations, problem context, and reasoning to develop procedural fluency with understanding. © 2018 OGAPMath LLC. For non-commercial use only. 7

Procedural Fluency If you were in a meeting with your fellow teachers and asked what they thought it meant for students to be procedurally fluent, what do you think they would say? © 2018 OGAPMath LLC. For non-commercial use only. 8

Procedural fluency “refers to the knowledge of procedures, knowledge of when and how to use them appropriately, and skill in performing them flexibly, accurately and efficiently. ” (Adding It Up! NRC (2000)) © 2018 OGAPMath LLC. For non-commercial use only. 9

The CCSSM and Fractions Grades 1 - 3 Grades 3 - 6 Grades 6 -8 Develop meaning of fractions through partitioning shapes into equal shares. Develop understanding of equivalence, magnitude and procedural fluency using models and reasoning. Extend understanding and fluency to all rational numbers (including positive and negative fractions). Apply when solving problems involving: 1) Area, volume and surface area 2) Percents 3) Equations and expressions 4) Proportions 5) Units rates with ratios of fractions 6) Coordinate plane 7) Scaling 8) Transformations 9) Measures of central tendency 10) Probability 11) Functions 12) Other © 2018 OGAPMath LLC. For non-commercial use only. 10

OGAP Fraction Progression © 2018 OGAPMath LLC. For non-commercial use only. Develop conceptual understanding and procedural fluency using visual models, equipartitioning, unit fraction understanding, equivalence, and properties of operations. 11

Fraction Big Ideas • Emphasize fractions as numbers. • Use number lines and other visual models. • Use meaningful contexts. • Use unit fraction reasoning and strategies. • Apply properties of operations. © 2018 OGAPMath LLC. For non-commercial use only. 12