# Ohio’s Learning Standards Mathematics

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Ohio’s Learning StandardsMathematicsAlgebra 1DRAFT 2018

ALGEBRA 1 STANDARDS DRAFT 2018Table of ContentsTable of Contents . 2Introduction . 3STANDARDS FOR MATHEMATICAL PRACTICE . 4Mathematical Content Standards for High School . 7How to Read the High School Content Standards . 8ALGEBRA 1 CRITICAL AREAS OF FOCUS . 10ALGEBRA 1 COURSE OVERVIEW . 11High School—Modeling . 12High School—Number and Quantity. 14Number and Quantity Standards . 15High School—Algebra . 16Algebra Standards . 18High School—Functions . 20Functions Standards . 21High School—Statistics and Probablity . 23Statistics and Probability Standards . 24Glossary. 25Table 3. The Properties of Operations. . 29Table 4. The Properties of Equality. . 29Table 5. The Properties of Inequality. . 30Acknowledgements . 312

ALGEBRA 1 STANDARDS DRAFT 20186Standards for Mathematical Practice,continued8. Look for and express regularity in repeated reasoning.Mathematically proficient students notice if calculations are repeated, and lookboth for general methods and for shortcuts. Upper elementary students mightnotice when dividing 25 by 11 that they are repeating the same calculationsover and over again, and conclude they have a repeating decimal. By payingattention to the calculation of slope as they repeatedly check whether pointsare on the line through (1, 2) with slope 3, students might abstract the equation(y 2)/(x 1) 3. Noticing the regularity in the way terms cancel when expanding(x 1)(x 1), (x 1)(x2 x 1), and (x 1)(x3 x2 x 1) might lead themto the general formula for the sum of a geometric series. As they work to solvea problem, mathematically proficient students maintain oversight of theprocess, while attending to the details. They continually evaluate thereasonableness of their intermediate results.CONNECTING THE STANDARDS FOR MATHEMATICAL PRACTICE TOTHE STANDARDS FOR MATHEMATICAL CONTENTThe Standards for Mathematical Practice describe ways in which developingstudent practitioners of the discipline of mathematics increasingly ought toengage with the subject matter as they grow in mathematical maturity andexpertise throughout the elementary, middle, and high school years.Designers of curricula, assessments, and professional development shouldall attend to the need to connect the mathematical practices to mathematicalcontent in mathematics instruction.The Standards for Mathematical Content are a balanced combination ofprocedure and understanding. Expectations that begin with the word“understand” are often especially good opportunities to connect the practicesto the content. Students who lack understanding of a topic may rely onprocedures too heavily. Without a flexible base from which to work, they maybe less likely to consider analogous problems, represent problems coherently,justify conclusions, apply the mathematics to practical situations, usetechnology mindfully to work with the mathematics, explain the mathematicsaccurately to other students, step back for an overview, or deviate from aknown procedure to find a shortcut. In short, a lack of understanding effectivelyprevents a student from engaging in the mathematical practices. In thisrespect, those content standards which set an expectation of understandingare potential “points of intersection” between the Standards for MathematicalContent and the Standards for Mathematical Practice. These points ofintersection are intended to be weighted toward central and generativeconcepts in the school mathematics curriculum that most merit the time,resources, innovative energies, and focus necessary to qualitatively improvethe curriculum, instruction, assessment, professional development, andstudent achievement in mathematics.

ALGEBRA 1 STANDARDS DRAFT 20187Mathematical Content Standards for High SchoolPROCESSThe high school standards specify the mathematics that all studentsshould study in order to be college and career ready. Additionalmathematics that students should learn in order to take advancedcourses such as calculus, advanced statistics, or discretemathematics is indicated by ( ), as in this example:( ) Represent complex numbers on the complex plane inrectangular and polar form (including real and imaginarynumbers).All standards without a ( ) symbol should be in the commonmathematics curriculum for all college and career ready students.Standards with a ( ) symbol may also appear in courses intended forall students. However, standards with a ( ) symbol will not appear onOhio’s State Tests.The high school standards are listed in conceptual categories: Modeling Number and Quantity Algebra Functions Geometry Statistics and ProbabilityConceptual categories portray a coherent view of high schoolmathematics; a student’s work with functions, for example, crosses anumber of traditional course boundaries, potentially up through andincluding calculus.Modeling is best interpreted not as a collection of isolated topics but inrelation to other standards. Making mathematical models is aStandard for Mathematical Practice, and specific modeling standardsappear throughout the high school standards indicated by a starsymbol ( ).Proofs in high school mathematics should not be limited to geometry.Mathematically proficient high school students employ multiple proofmethods, including algebraic derivations, proofs using coordinates,and proofs based on geometric transformations, includingsymmetries. These proofs are supported by the use of diagrams anddynamic software and are written in multiple formats including not justtwo-column proofs but also proofs in paragraph form, includingmathematical symbols. In statistics, rather than using mathematicalproofs, arguments are made based on empirical evidence within aproperly designed statistical investigation.

ALGEBRA 1 STANDARDS DRAFT 2018HOW TO READ THE HIGH SCHOOL CONTENT STANDARDSConceptual Categories are areas of mathematics that cross throughvarious course boundaries.Domains are larger groups of related standards. Standards fromdifferent domains may sometimes be closely related.Clusters are groups of related standards. Note that standards fromdifferent clusters may sometimes be closely related, becausemathematics is a connected subject.Standards define what students should understand and be able todo.Gshows there is a definition in the glossa

mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these arethe NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections.

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