Academic Standards for Mathematics

Academic Standards for

Mathematics

Grades PreK-High School

January 2013

Pennsylvania Department ofEducation

Pennsylvania Core Standards

Mathematics

INTRODUCTION

The Co=on Core Standards in Mathematics in grades PreK-5 lay a solid foundation in whole numbers, addition, subtraction, multiplication, division, fractions, and decimals. Taken together, these elements support a student's ability to learn and apply more demanding math concepts and procedures. The middle school and high school standards call on students to practice applying mathematical ways ofthinking to real world issues and challenges; they prepare students to think and reason mathematically. Additionally, they set a rigorous definition of college and career readiness by demanding that students develop a depth of understanding and ability to apply mathematics to novel situations, as college students and employees regularly do. Although the standards are not a curriculum or a prescribed series of activities, school entities will use them to develop a local school curriculum that will meet local students' needs.

This document includes PA Core Standards for Mathematical Content and Mathematical Practice. The mathematics standards define what students should understand and be able to do. Mathematical Practice Standards describes the habits ofmind required to reach_a level ofmathematical proficiency.

PA Core Standards

Standards for Mathematical Practice

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Grade4

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equivalency to add and

fractions as numbers.

fractions to show

snbtract fractions.

equivalence .and

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

numbers.

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Apply and extend previo?s understandings ofmultiplication and division to multiply and divide fractions.

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Connect decimal notation to fractions, and compare decimal. fractions (base 10 denominator, e.g.,

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1Page6 January 2013

Pennsylvania Core Standards

Mathematics

2.2 Algebraic Concepts

The Standards ofMathematical Practices

Make sense of problems and persevere in solVingthem.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Attend to precision.

Look for and make use ofstructure.

Look for and Pvnress re!rulari -;v in reoeated reasonini .

GradePreK 2.2.PreK

GradeK 2.2.K

Gradel 2.2.1

Grade2 Z.2.2

Grade3 2.2.3

Grade4 2.2.4

Grades 2.2.5

Pennsylvania's public schools shall teach, challenge, andsupport every student to realize his or her maximum potential and to acquire the knowledge and ski.Ifs needed to:

CC.Z.2.l'reKA.1 Understand addition as putting together and adding to, and understand subtraction astakingapartand taking from.

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CC.2.2.KA.1 Extend the concepts of putting together and taking apart to add and subtract Within 10.

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Represent and solve

Represent and solve

Represent and solve

Represent and solve

Interpret and evaluate

problems involviDg

problems involving

problems involving

problems involving tbt;: numerical expressions

addition and subtraction addition and

multiplication and

Within20.

subtraction Within 100. division.

four.o.perations.

using order ofoperations.

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Understand and apply

Use mental strategies to Understand properties of Develop and/or apply

properties of operations add and subtract Within multiplication and the

number tbeozy concepts

and the relationship

20.

relationship between

to find factors and

betvveen addition and subtraction.

multiplication and division.

multiples.

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WorkWitb equal groups Demonstrate

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multiplication and

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foundations for

division fluency.

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Solve problems involving Generate and analyze Analyze patterns and

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IPage7

January 2013

Pennsylvania Core Standards

Mathematics

2.3 Geometry

The Standards of Mathematical Practices

Make sense of problems and persevere in solving them.

Reason abstractly and quantitatively.

Construct viable arguments and critique the reasoning of others.

Model with mathematics.

Use appropriate tools strategically.

Look for and make use of structure.

Attend to precision. Look for and exuress regularitv in reueated reasonin .

GradePreK

GradeK

Grade 1

GradeZ

Grade3

Grade4

Grades

2.3.PreK

2.3.l(

Z.3.1

Z.3.Z

2.3.3

Z.3.4

2.3.5

Pennsylvania's public schools shall teach, challenge, and support every student to realize his or hermaximum potential and to acquire the lmowledge and skills needed to:

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Identify and describe Identify and descnbe

Compose and distinguish Analyze and draw two- Identify,colllpare,and Draw lines and angles Graph points in the first

shapes.

two- and three-

between ruro- and three- and three...ffimensional classifyshapes and their and identify these in

quadrant on the

dimensional shapes.

dimensional shapes

shapes having specified attributes.

tvvo-dimensional

coordinate plane and

based on their attrihu.tes. attnOutes.

figures.

interpret these points

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when solving real world

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and mathematical

problems.

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Attalyze, compare,

Analyze, compare, create, Use the understanding of Use the understanding Use the understanding of Classify two-

Glassey two,.ditnensional

?: create, and compose

and compose two? and fractions to partition

of fractions to partition fractionstopartition

dimensional figures by figures into categories

shapes.

three-dimensional

shapes into halves and shapes into halves,

shapes into parts with properties oftheir llnes based on an

shapes.

quarters.

quarters, and thirds.

equal areas and express and angles.

understanding oftheir

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properties.

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:Recognize symmetric shapes and draw lines of symmetry.

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[Pages January2013

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