S

Mathematics Progressions – Common Core

Elizabeth Gamino, Fresno Unified Public SchoolsDenise Walston, Council of the Great City Schools

Purpose

Review and take a closer look at the Mathematics Progressions Focus, Coherence, and Rigor Instructional implications

Scaffolding Explain their thinking; critique the reasoning of others Developing mathematical arguments Reading and interpreting real-world problems Technical language of the discipline

S

Instructional ShiftsMathematics

A Look Back

Mathematics Instructional Shifts

Focus Coherence Rigor

Conceptual understanding Procedural skill and fluency Applications

Focus

Significantly narrow and deepen the way that time and energy is spent in the math classroom Communicate focus so that it is manageable in instruction; it is more

than merely writing a standard a day Focus deeply on those concepts emphasized in the standards

Provide the time for students to transfer mathematical skills and understanding across concepts and grade levels Deep conceptual understanding Connect conceptual and procedural understanding

Transitions from concrete↔pictorial↔language↔abstract

Coherence

Coherence provides the opportunity for students to make connections between mathematical ideas and across content areas Connects the learning both within a grade and across grades Thinking across grades Each standard is not a new event, but an extension of previous

learning Allows students to see mathematics as inter-connected ideas

Mathematics instruction cannot be relegated to merely a checklist of topics to cover, but instead must be centered around a set of interrelated and powerful ideas, rather than a series of disconnected topics

Rigor

Conceptual Understanding Involves more than getting the right answer Access concepts from multiple perspectives

Transitions from concrete↔pictorial↔language↔abstract

Procedural Skill and Fluency Study algorithms as a way to see the structure of mathematics (organization, patterns,

predictability) or apply a variety of appropriate procedure flexibly to solve problems Students are expected to achieve speed and accuracy with simple calculations (at

specific grade levels) Fluent is used in the Standards to mean “efficient and accurate”

Class time and/or homework should be structured for students to practice core functions such as single-digit multiplications

Application Expectation that students apply math and choose the appropriate concept for application,

even when not prompted to do so Apply math concepts in real-world situations Mathematical modeling

With equal intensity

S

Common Core State Standards

Mathematics

Closer Look at Fractions

Fraction Concepts

Grade One: Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrase half of,

fourth of, and quarter of. Describe the whole as two of or four of the

shares. Understand for these examples that decomposing into more equal shares

creates smaller shares.

Fraction Concepts

Grade Two Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the

whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Coherence – strengthens foundations

Progression involving fractional concepts (conceptual understanding) and operations (multiplication and division of fractions):

Grade Three: Develop understanding of fractions as numbersDevelop understanding of fractions as part of a whole and as a number on the number line

Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size

Grade Four: Extend understanding of fraction equivalence and ordering

Build fractions from unit fractions by applying and extending previous understandings on whole numbers

(decompose a fraction into a sum of fractions with the same denominator)

Coherence: Number and Operations - Fractions

Grade Four: Multiply a fraction by a whole number Grade Five: Multiply a fraction by a fraction

Divide unit fractions by a whole number; and whole

numbers by unit fractions

Grade Six: Interpret and compute quotients of fractions and solve word problems

S

The Mathematics Progressions

Developing a deep understanding of focus,

coherence, and rigor

• Mathematics Progressions• Common Core State Standards in

Mathematics• Informed by research on children’s

cognitive development and the logical structure of mathematics • Narrative documents• Progression of concepts across several

grade bands

Closer Look – Fraction Progression

Fraction as number

Linking content to the Mathematical Practices

District Perspective

Read and analyze the progressions (book study, close read) Through the lens of focus, coherence and rigor

Need to look at the standards in their entirety K-12 Determine what happens prior to students entering

your door and where they need to go - beyond the grade level below and above.

and

S

Problems for consideration

Exploring the Fraction Progression using illustrative tasks

Questions to consider

What are some things that you had to attend to? What are some things that ELLs need to be aware

of? What are the implications for planning for

instruction? How might you assess student understanding

specifically related to ELLs? What are the implications for professional

development?

S

Online ResourcesFraction Professional Development Module

Fraction Progression Online Module

Goals/Purpose: Deepen educators content knowledge, specifically around the

mathematics “Fractions” progression; Engage practicing educators in the development of CCSS-aligned

professional development; and Provide consistent, high-quality professional development that can

be used at large scale and online across PARCC states to inform elementary teachers and instructional leaders

Partnership with CGCS, Institute for Mathematics & Education, University of Arizona, and Achieve

Design within Edmodo

Features of the module Online and interactive Based on a framework developed collaboratively with CGCS Illustrative of the Fractions Progression in the CCSSM Seven units anchored by a 3-5 minute video Three to four illustrative tasks associated with the

progression Built-in, interactive checks for understanding Interactive-check for understandings – Quiz – linked to the

commentary

Online Professional Development Module

http://commoncoreworks.org/domain/121