Academic Standards for Mathematics

1 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 ofcollege and career readiness by demanding that students develop a depth ofunderstanding 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 ofactivities, school entities will use them to develop a local school curriculum that will meet local students' needs.

2 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 111,: [ Il'i"il:I 111' j 111'''i' l1 ] 1:]!'1i111111']'I l"H i.'.'i UI.':: '!1lll'i'IJ:]rl ]rj'l:ii' J,l '11i l:l l !':11, :i': il1'Jii[1!l1 IJH 1,: 11,H I 1 J: : :I j11 :1j:111 i ,111 rl1 :: I I '. :-1 n'i l 'li 'I i i : ,.1, i111 lli1'1'1 i'1i1111,,11,11 1 1111 :1 ':1111: ' I i i 111 iH,1',,1i 11 1 1 111 111 :111\! :1:1r1n1:i:1r :!: i: 1I11 1111 JtJI 1 , 1,: 11, ,IJ1J"11:: 1:1:1iF: 11':1 ::111,i::11:11111111i11:1,::1:1::;11:::1 :~!: :!: 1:1:: :1 i :ii.!11 1 11:: 1i!'i!ii!i:: 1 11111 11 1 11 1111h1 i il1,,11,,l,,1 . 11 111 111 'I' I 1I -'.I 1'l'JI '1' 1 "1' ': illl 1j1:1 r, ,]1',i1l'l''l' I'1[I II i[l"1 ''' ' 1 1 I11 1 1 1 11111 1!

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6 These revised Standards reflect instructional shifts that cannot occur without the integrated emphasis on content and practice. Standards are overarching statements ofwhat a proficient math student should know and be able to do. The pennsylvania Assessment Anchors and Eligible Content closely align with the revised Standards and are an invaluable source for greater detail. Key Points in Mathematics The Standards stress both procedural skills and conceptual understanding to ensure students are learning and applying the critical information they need to succeed at higher levels. K-5 Standards , which provide students with a solidfoundation in whole numbers, addition, subtraction, multiplication, division, fractions, and decimals, help young students build the foundation to successfully apply more demanding math concepts and procedures, and move into application. They also provide detailed guidance to teachers on how to navigate their way through topics such as fractions, negative numbers, and geometry, and do so by maintaining a continuous progression from grade to grade.

7 Having built a strong foundation at K-5, students can do hands-on learning in geometry, algebra, and probability and statistics. Students who have mastered the content and skills through the seventh grade will be well-preparedfor algebra in grade 8. High school Standards emphasize practicing applying mathematical ways ofthinking to real world issues and challenges. !Page3 january2013 pennsylvania Core Standards Mathematics The PA Core Standards for Mathematics detail four standard areas: Numbers and Operations, Algebraic Concepts, Geometry, and Measurement, Data, and Probability. These standard areas are reflective reporting categories in the PA Core Assessment Anchors and Eligible Content. The intent ofthis document is to provide a useful tool for designing curriculum, instruction, and assessment. The grade level curriculum and instructional shifts in Mathematics cannot occur without the integrated emphasis on content and practice. The chart below illustrates the four standard areas and the development and progression ofthe strands, with an understanding that all is framed around the Standards for Mathematical Practice.

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