MathematicsK-5

FDRESA June 2013

Supporting CCGPS

Leadership Academy

How can school leader familiarity with the Standards for Mathematical Practice, Standards for Mathematical Content, content emphases, and instructional shifts impact successful implementation of CCGPS?

Essential Question

“It is literally true that you can succeed best and quickest by helping others to succeed.”

Napoleon Hill American author 1883-1970

Monitoring Collaborating

A Partnership

Common Core State Standards

Growing Mathematically Proficient Students

A Response

Mathematics is the economy of information. The central idea of all mathematics is to

discover how knowing some things well, via reasoning, permits students to know much else…without having to commit the information to memory as a separate fact.

It is the connections…the reasoned, logical connections…that make mathematics manageable.

Common Core Georgia Performance Standards place a greater emphasis on problem solving, reasoning, representation, connections, and communication.

Theory

There is a shift toward the student applying mathematical concepts and skills in the context of authentic problems and understanding concepts rather than merely following a sequence of procedures.

In mathematics classrooms, students will learn to think critically in a mathematical way with an understanding that there are many different ways to a solution and sometimes more than one right answer in applied mathematics.

Theory

Those content standards which set an expectation of understanding are potential “points of intersection” between the Standards for Mathematical Content and the Standards for Mathematical Practice.

These points of intersection are weighted toward central and generative

concepts. merit the most time, resources, innovative

energies, and focus. qualitatively improve the curriculum,

instruction, assessment, professional development, and student achievement in mathematics.

Theory

The standards define what students should understand and be able to do in their study of mathematics.

Asking a student to understand something means asking a teacher to assess whether the student has understood it.

Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient rigor.

Assessment

The Georgia Mathematics Curriculum focuses on actively engaging the students in the development of mathematical understanding by using manipulatives and a variety of

representations, working independently and cooperatively to solve

problems, estimating and computing efficiently, and conducting investigations and recording findings.

Engagement

Standards for Mathematical Practice Eight standards crossing all grade levels and

applied in conjunction with content standards

Standards for Mathematical Content Multiple standards categorized in domains

Six Shifts Teacher practices

Common Core GPS

Standards for Mathematical Practice

K 1 2 3 4 5 6 7 8 9 - 12

Modeling

Geometry

Measurement and Data

The Number SystemNumber and Operations in Base Ten

Operations and Algebraic Thinking

Geometry

Number and Operations Fractions

Expressions and Equations

Statistics and Probability

Algebra

Number and Quantity

Functions

Statistics and Probability

Ratios & Proportional Relationships

FunctionsCounting

and Cardinality

© Copyright 2011 Institute for Mathematics and Education

Standards for Mathematical Content

Six Shifts

FOCUS: PrioritiesCOHERENCE: Vertical Scope

FLUENCY: Intensity/FrequencyDEEP UNDERSTANDING:

Variety/SMPAPPLICATION: Relevance

DUAL INTENSITY:Balance in Practice/Understanding

MCC5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them.

MCC7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it are related. For example, a+0.05a=1.05a means that “increase by 5%” is the same as “multiply by1.05.”

MCC9-12.A.SSE.1 Interpret expressions that represent a quantity in terms of its context.

MCC9-12.A.SSE.1a Interpret parts of an expression, such as terms, factors, and coefficients.

MCC9-12.A.SSE.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.

Coherence

Grade 3From Grade 2

Fluent addition and subtraction to 18; foundational ideas about addition and subtraction

Foundational place value understanding

Foundational ideas about shape and position in space

Ability to compare and categorize

Understanding of quantities to 1000

Measurement as unit iteration

Foundational data ideas

Later Deep understanding of

addition and subtraction, multiplication and division

Useful place value understanding

Understanding of defining attributes about shape, comparison of shape

Foundational fractional relationships

Continuation of fluency/algebraic thinking

Measurement, addition, subtraction relationships

Data analysis

Coherence

Where to look…Frameworks Concepts and Skills to Maintain

Enduring Understandings Previous Unit Current Unit

Evidence of Learning in Current Unit

Coherence / Focus

Grade Priorities in Support of Rich Instruction and Expectations of Fluency and Conceptual Understanding

K-2 Addition and subtraction; measurement using whole number quantities

3-5 Multiplication and division of whole numbers and fractions

6 Ratios and proportional reasoning; early expressions and equations

7 Ratios and proportional reasoning; arithmetic of rational numbers

8 Linear algebra

9-12 Modeling

Focus

Grade

Required Fluency

K Add/subtract within 5

1 Add/subtract within 10

2 Add/subtract within 20; add/subtract within 100 (pencil and paper)

3 Multiply/divide within 100 ; add/subtract within 1000

4 Add/subtract within 1,000,000

5 Multi-digit multiplication

6 Multi-digit division ; multi-digit decimal operations

7 Solve px + q = r, p(x + q) = r

8 Solve simple 2x2 systems by inspection

9-12 Algebraic manipulation in which to understand structure.Writing a rule to represent a relationship between two quantities.Seeing mathematics as a tool to model real-world situations.Understanding quantities and their relationships.

Fluency

Kindergarten

3+2=55-1=4

Grade 1

6+4=108-2=6

Grade 3

5X7=35 12÷4=3

132+256=388

675-38=637

Grade4

3,276+5,428=8,704

358,732-126,325=

232,407

Grade 5

2,378 X 42=

99,876

Grade 2

8+7=15 16-9=7 22+7=2

9 67-

18=49

Fluency

Grade 6

6(4-y)= 32

Grade 7

Solve the system of equations.

3x+2y=7 x-4y=-7

Grade 8

Fluency

Write the equation of the line 3x+2y=7 so that it can easily be graphed

using the y-intercept and slope.

Write the rule to express the relationship

between the area of a square and

its inscribed circle.

Fluency

High School

FLEXIBILITY ACCURACY EFFICIENCY APPROPRIATENESS

Accuracy Appropriateness

Flexibility

Efficiency

FLUENTPROBLEMSOLVER

Fluency

Two Approaches Word problems: Assigned after explanation of

operations, algorithms, or rules; and students are expected to apply these procedures to the problems.

Problematic situations: Used at the beginning… for construction of understanding, for generation and exploration of mathematical ideas and strategies…offering multiple entry levels, and supportive of mathematization.

(Young Mathematicians at Work, Fosnot, 2002)

Application

A Delicate BalanceTeachers must…

…ritualize skills practice

…normalize productive

struggle

Dual Intensity

INSTRUCTION

Teacher-Focused

Content Delivery Strategies

HOMEWORK

Distributed Practice

PROCESSING

Student-Focused

Linked to Delivery Strategy

DRILL

Basic facts recall

Fluency

APPLICATION

Making content relevant,

purposeful, and meaningful

REVIEW/PREVIEW

Maintaining old learning

Building foundations for new learning

Six Elements

How can school leader familiarity with the Standards for Mathematical Practice, Standards for Mathematical Content, content emphases, and instructional shifts impact successful implementation of CCGPS?

Essential Question

Ensuring Success

Leaders Supporting CCGPS

A Solution

Success