High School Math Materials Evaluation Tool (Integrated .
High School Math Materials Evaluation Tool (Integrated Pathway)To evaluate math materials for high school for alignment with the CCSS, analyze the materials against the non-negotiable criteria* in the table below. Instructionalsubmissions must meet all of the relevant non-negotiable criteria and metrics to align with the CCSS. Criteria labeled as indicators of critical at the end of the tool are differentfrom the non-negotiable criteria. Although instructional materials may be aligned without meeting these indicators of critical quality, submissions that do reflect theseindicators are likely higher quality. Note: Materials must align with the letter and spirit of the CCSS and must be available in Spanish to be considered.Section 1: Non-Negotiable CriteriaNon-Negotiable Criteria: Alignment to Focus on Major WorkInstructional Materials will be scored on the following scale and applied in the appropriate weight for each indicator and applied in the appropriate weights for each indicator.N-Less than 80 days are devoted to the major work of the grade. (0 pts); M-Between 80 and 115 days are devoted to the major work of the grade. (2 pts)H-115 or more days are devoted to the major work of the grade. (4 pts)CriteriaMetricsStudents and teachers using theCourseMajor ClustersTally of Days Spent on ClusterDaysNotesScorematerials as designed devote the largeSpent onmajority of time in each grade to theClustermajor work of the grade.Math IMath IIMath -CO.B.6-8HS.G-CO.C.9-11HS.S-ID.C.7-9Major -8Major ED.A.1-2HS.A-REI.A.1-2/4/4/4*Criteria derived from Instructional Materials Evaluation Tool, EQuiP Rubric, and tools from the Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project1
High School Math Materials Evaluation Tool (Integrated Pathway)HS.A-REI.D.11HS.F-IF.B.4, 6HS.G-GPE.B.4-7HS.G-MG.A.1-3HS.S-IC.B.3-6Major Total:Non-negotiable Criteria: Alignment to the Depth of the CCSS ContentInstructional Materials will be scored on the following scale and applied in the appropriate weight for each indicator.N (not found) - The mathematics content was not found. (0 pts)L (low) - Major gaps in the mathematics content were found; content was not developed or developed superficially. (3 pts)M (moderate) - Gaps in the mathematics content, as described in CCSS, were found and may not be easily filled; content focused primarily on procedural skills and minimally on mathematicalunderstanding, or ignored procedural skills. (6 pts)A (acceptable)- Few gaps in the mathematics content, as described in CCSS, were found and may be easily filled; content was developed with a balance of mathematical understanding andprocedural skills consistent with CCSS, but connections between the two were not developed. (9 pts)H (high)- The mathematics content was fully formed as described in CCSS; content was developed with a balance of mathematical understanding and procedural skills consistent with CCSS, andconnections between the two were developed. (12 pts)CriteriaMetricsNotesScore1) Materials target grade-level CCSS standards to the full depth of the standards for teaching and1a) Lessons and units targeting the major worklearning.of the grade provide an in-depth treatment,Mathematics Iwith high expectations.Reasoning with Equations and Inequalities – A-REI1b) Content develops through reasoning aboutSolve equations and inequalities in one variable. (A-REI.B)the new concepts on the basis of previous3.Solve linear equations and inequalities in one variable, including equations with coefficientsunderstandings. Where appropriate, provides/12represented by letters.opportunities for students to connectInterpreting Functions – F-IFknowledge and skills within or across clustersInterpret functions that arise in applications in terms of the context. (F-IF.B)and domains.4.For a function that models a relationship between two quantities, interpret key features of1c) Lessons and units provide opportunities forgraphs and tables in terms of the quantities, and sketch graphs showing key features given astudents to independently apply mathematicalverbal description of the relationship. Key features include: intercepts; intervals where theconcepts in real-world situations and solvefunction is increasing, decreasing, positive, or negative; relative maximums and minimums;challenging problems with persistence,choosing and applying an appropriate model orsymmetries; end behavior; and periodicity. strategy to new situations.5.Relate the domain of a function to its graph and, where applicable, to the quantitative1d) Lessons and units develop students’relationship it describes. For example, if the function h(n) gives the number of person-hours itconceptual understanding through tasks, brieftakes to assemble n engines in a factory, then the positive integers would be an appropriateproblems, questions, multiple representationsdomain for the function. and opportunities for students to write and6.Calculate and interpret the average rate of change of a function (presented symbolically or asspeak about their understanding.1e) After developing conceptually, lessons anda table) over a specified interval. Estimate the rate of change from a graph. units support and provide guidelines forCongruence – G-COprocedural skills and fluency with coreUnderstand congruence in terms of rigid motions. (G-CO.B)calculations and mathematical procedures.6.Use geometric descriptions of rigid motions to transform figures and to predict the effect of a7.given rigid motion on a given figure; given two figures, use the definition of congruence interms of rigid motions to decide if they are congruent.Use the definition of congruence in terms of rigid motions to show that two triangles arecongruent if and only if corresponding pairs of sides and corresponding pairs of angles arecongruent.*Criteria derived from Instructional Materials Evaluation Tool, EQuiP Rubric, and tools from the Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project2
High School Math Materials Evaluation Tool (Integrated Pathway)8.Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definitionof congruence in terms of rigid motions.Interpreting Categorical and Quantitative Data – S-ID.Interpret Linear Models. (S-ID.C)7.Interpret the slope (rate of change) and the intercept (constant term) of a linear model in thecontext of the data.8.Compute (using technology) and interpret the correlation coefficient of a linear fit.9.Distinguish between correlation and causation.Non-negotiable Criteria: Alignment to the Depth of the CCSS ContentInstructional Materials will be scored on the following scale and applied in the appropriate weight for each indicator.N (not found) - The mathematics content was not found. (0 pts)L (low) - Major gaps in the mathematics content were found; content was not developed or developed superficially. (3 pts)M (moderate) - Gaps in the mathematics content, as described in CCSS, were found and may not be easily filled; content focused primarily on procedural skills and minimally on mathematicalunderstanding, or ignored procedural skills. (6 pts)A (acceptable)- Few gaps in the mathematics content, as described in CCSS, were found and may be easily filled; content was developed with a balance of mathematical understanding andprocedural skills consistent with CCSS, but connections between the two were not developed. (9 pts)H (high)- The mathematics content was fully formed as described in CCSS; content was developed with a balance of mathematical understanding and procedural skills consistent with CCSS, andconnections between the two were developed. (12 pts)CriteriaMetricsNotesScore1) Materials target grade-level CCSS standards to the full depth of the standards for teaching and1a) Lessons and units targeting the major worklearning.of the grade provide an in-depth treatment,Mathematics IIwith high expectations.The Real Number System — N-RN1b) Content develops through reasoning aboutExtend the properties of exponents to rational exponents. (N-RN.A)the new concepts on the basis of previous/121.Explain how the definition of the meaning of rational exponents follows from extending theunderstandings. Where appropriate, providesproperties of integer exponents to those values, allowing for a notation for radicals in terms ofopportunities for students to connectrational exponents. For example, we define 51/3 to be the cube root of 5 because we want (51/3)3knowledge and skills within or across clusters 5(1/3)3 to hold, so (51/3)3 must equal 5.and domains.2.Rewrite expressions involving radicals and rational exponents using the properties of1c) Lessons and units provide opportunities forexponents.students to independently apply mathematicalReasoning with Equations and Inequalities – A-REIconcepts in real-world situations and solveSolve equations and inequalities in one variable. (A-REI.B)challenging problems with persistence,4.Solve quadratic equations in one variable.choosing and applying an appropriate model ora.Use the method of completing the square to transform any quadratic equation in x intostrategy to new situations.an equation of the form (x – p)2 q that has the same solutions. Derive the quadratic1d) Lessons and units develop students’formula from this form.conceptual understanding through tasks, briefb.Solve quadratic equations by inspection (e.g., for x2 49), taking square roots,problems, questions, multiple representationscompleting the square, the quadratic formula and factoring, as appropriate to the initial and opportunities for students to write andform of the equation. Recognize when the quadratic formula gives complex solutionsspeak about their understanding.and write them as a bi for real numbers a and b.1e) After developing conceptually, lessons andInterpreting Functions – F-IFunits support and provide guidelines forInterpret functions that arise in applications in terms of the context. (F-IF.B)procedural skills and fluency with core4.For a function that models a relationship between two quantities, interpret key features ofcalculations and mathematical procedures.graphs and tables in terms of the quantities, and sketch graphs showing key features given averbal description of the relationship. Key features include: intercepts; intervals where thefunction is increasing, decreasing, positive, or negative; relative maximums and minimums;symmetries; end behavior; and periodicity. *Criteria derived from Instructional Materials Evaluation Tool, EQuiP Rubric, and tools from the Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project3
High School Math Materials Evaluation Tool (Integrated Pathway)5.6.Relate the domain of a function to its graph and, where applicable, to the quantitativerelationship it describes. For example, if the function h(n) gives the number of person-hours ittakes to assemble n engines in a factory, then the positive integers would be an appropriatedomain for the function. Calculate and interpret the average rate of change of a function (presented symbolically or asa table) over a specified interval. Estimate the rate of change from a graph. Similarity, Right Triangles, and Trigonometry — G-SRTDefine trigonometric ratios and solve problems involving right triangles6.Understand that by similarity, side ratios in right triangles are properties of the angles in thetriangle, leading to definitions of trigonometric ratios for acute angles.7.Explain and use the relationship between the sine and cosine of complementary angles.8.Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in appliedproblems. Non-negotiable Criteria: Alignment to the Depth of the CCSS ContentInstructional Materials will be scored on the following scale and applied in the appropriate weight for each indicator.N (not found) - The mathematics content was not found. (0 pts)L (low) - Major gaps in the mathematics content were found; content was not developed or developed superficially. (3 pts)M (moderate) - Gaps in the mathematics content, as described in CCSS, were found and may not be easily filled; content focused primarily on procedural skills and minimally on mathematicalunderstanding, or ignored procedural skills. (6 pts)A (acceptable)- Few gaps in the mathematics content, as described in CCSS, were found and may be easily filled; content was developed with a balance of mathematical understanding andprocedural skills consistent with CCSS, but connections between the two were not developed. (9 pts)H (high)- The mathematics content was fully formed as described in CCSS; content was developed with a balance of mathematical understanding and procedural skills consistent with CCSS, andconnections between the two were developed. (12 pts)CriteriaMetricsNotesScore1) Materials target grade-level CCSS standards to the full depth of the standards for teaching and1a) Lessons and units targeting the major worklearning.of the grade provide an in-depth treatment,Mathematics IIIwith high expectations.Arithmetic with Polynomials and Rational Expressions — A-APR1b) Content develops through reasoning about/12Understand the relationship between zeros and factors of polynomials. (A-APR.B)the new concepts on the basis of previous2.Know and apply the Remainder Theorem: For a polynomial p(x) and a number a, theunderstandings. Where appropriate, providesremainder on division by x – a is p(a), so p(a) 0 if and only if (x – a) is a factor of p(x).opportunities for students to connect3.Identify zeros of polynomials when suitable factorizations are available, and use the zeros toknowledge and skills within or across clustersconstruct a rough graph of the function defined by the polynomial.and domains.Interpreting Functions – F-IF1c) Lessons and units provide opportunities forInterpret functions that arise in applications in terms of the context. (F-IF.B)students to independently apply mathematical4.For a function that models a relationship between two quantities, interpret key features ofconcepts in real-world situations and solvegraphs and tables in terms of the quantities, and sketch graphs showing key features given achallenging problems with persistence,verbal description of the relationship. Key features include: intercepts; intervals where thechoosing and applying an appropriate model orfunction is increasing, decreasing, positive, or negative; relative maximums and minimums;strategy to new situations.1d) Lessons and units develop students’ symmetries; end behavior; and periodicity.conceptual understanding through tasks, brief6.Calculate and interpret the average rate of change of a function (presented symbolically or asproblems, questions, multiple representationsa table) over a specified interval. Estimate the rate of change from a graph. and opportunities for students to write andExpressing Geometric Properties with Equations – G-GPEspeak about their understanding.Use coordinates to prove simple geometric theorems algebraically. (G-GPE.B)1e) After developing conceptually, lessons andunits support and provide guidelines for*Criteria derived from Instructional Materials Evaluation Tool, EQuiP Rubric, and tools from the Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project4
High School Math Materials Evaluation Tool (Integrated Pathway)4.5.6.7.Use coordinates to prove simple geometric theorems algebraically. For example, prove ordisprove that a figure defined by four given points in the coordinate plane is a rectangle; proveor disprove that the point (1, 3) lies on the circle centered at the origin and containing thepoint (0, 2).Prove the slope criteria for parallel and perpendicular lines and use them to solve geometricproblems (e.g., find the equation of a line parallel or perpendicular to a given line that passesthrough a given point).Find the point on a directed line segment between two given points that partitions thesegment in a given ratio.Use coordinates to compute perimeters of polygons and areas of triangles and rectangles,procedural skills and fluency with corecalculations and mathematical procedures.e.g., using the distance formula. Modeling with Geometry-G-MGApply geometric concepts in modeling situations. (G-MG.A)1.Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling2.3.a tree trunk or a human torso as a cylinder). Apply concepts of density based on area and volume in modeling situations (e.g., persons persquare mile, BTUs per cubic foot). Apply geometric methods to solve design problems (e.g., designing an object or structure tosatisfy physical constraints or minimize cost; working with typographic grid systems based onratios). Making Inferences and Justifying Conclusions — S-ICMake inferences and justify conclusions from sample surveys, experiments, and observationalstudies. (S-IC.B)3.Recognize the purposes of and differences among sample surveys, experiments, andobservational studies; explain how randomization relates to each.4.Use data from a sample survey to estimate a population mean or proportion; develop amargin of error through the use of simulation models for random sampling.5.Use data from a randomized experiment to compare two treatments; use simulations todecide if differences between parameters are significant.6.Evaluate reports based on data.Non-Negotiable Criteria for Alignment to CCSS: Alignment to the Depth of the CCSS PracticesN (not found) (0 pts)L (low)-are not addressed or addressed superficially. (4 pts)M (moderate) -are addressed, but not consistently in a way that is embedded in the development of the Content Standards. (8 pts)A (acceptable)– Attention is embedded throughout the curriculum materials in ways that may help students to develop them as habits of mind. (12 pts)H (high)—Attention to the full meaning of each practice standard and explicitly attends to the development of the specialized language of mathematics. (16 pts)CriteriaMetricsNotes2) Standards for2a) Materials demand that students engage in the Standards for Mathematical Practice as the primary vehicle forMathematical Practice thatlearning the Content Standards.are central to the2b) Materials provide opportunities for students to develop the Standards for Mathematical Practice as “habits oflesson/unit are identifiedmind” (ways of thinking about mathematics that are rich, challenging, and useful) throughout the development of theand well connected to theContent Standards.content being addressed.2c) Materials include accompanying assessments of student learning (such as homework, observation checklists,portfolio recommendations, extended tasks, tests, and quizzes) that provide evidence regarding students’ proficiencywith respect to the Standards for Mathematical Practice.Score/16*Criteria derived from Instructional Materials Evaluation Tool, EQuiP Rubric, and tools from the Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project5
High School Math Materials Evaluation Tool (Integrated Pathway)Section II: Critical CriteriaCritical Criteria for Alignment to CCSSN (not found)--Materials do not support these criteria. (0 pts)L (low)—Materials contain limited support for this criteria but support is not embedded or consistent within/across grades. (2 pts)M (moderate)—Materials contain support for this criteria but support is not embedded or consistent within/across grades. (4 pts)H (high)—Curriculum materials contain embedded support for this element that is consistently present within/across grades. (6 pts)CriteriaMetrics3a) Materials provide teachers with strategies for meeting the needs of a r
High School Math Materials Evaluation Tool (Integrated Pathway) *Criteria derived from Instructional Materials Evaluation Tool, EQuiP Rubric, and tools from the Common Core State Standards (CCSS) Mathematics Curriculum Materials Analysis Project 1 To evaluate math materials for high school for alignment with the CCSS, analyze the materials against the non-
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2016 MCAS Results September 29, 2016 Page 4 8 Year Math CPI Results For State, District, and Schools Ranked by 2016 CPI School el 2009 Math MCAS 2010 Math MCAS 2011 Math MCAS 2012 Math MCAS 2013 Math MCAS 2014 Math MCAS 2015 Math MCAS 2016 Math PARCC Sewell-Anderson 1 80.0 78.7 76.7 84.2 88.3 89.0 89.3 92.5
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