End of Course (EoC) / School Year
2012–2013
Preface
The information contained within this document supports the summative, Endof Course (EoC) assessment of student content knowledge developed by New Mexico educators in August 2012. The EoC examinations can be administered to all high school students upon completion of the applicable course. In some cases, students that do not meet the exit criteria for graduation can use the results as an alternative demonstration of competency (ADC) as prescribed by the New Mexico Public Education Department (PED) policy. Additional policy information is available on the PED’s website at
In Section I, the EoC’s purpose statement and targeted New Mexico content standards are provided. Section II details the EoC’s design in a series of specification tables along with providing administration guidelines to high school educators. Finally, an Appendix is provided for additional material/information needed to administer the EoC. This document is in public domain and does not compromise the security of the EoC assessment’s final operational forms or scoring keys.
TableofContents
Preface...... 2
Section I: FocusandContentStandards
1.1 Purpose Statement
1.2 Targeted Content Standards
Section II: DesignandAdministration...... 8
2.1 Specification Tables...... 8
2.2 Administrative Guidelines...... 10
Appendix A—Reference Materials...... 12
Section I
FocusandContentStandards
Section I contains the purpose statement and those New Mexico content standards selected by the design team. The purpose statement outlines the reason this assessment was developed and how it will be used. The targeted standards identify those academic content standards applicable to the EoCassessment. EoC results are designed as one measure of what students completing a course of study are able to demonstrate on an on-demand, paper-and-pencil assessment.
1.1 Purpose Statement
The Integrated Math III EoC assessment measures student proficiency of the course content aligned to the New Mexico math standards. This EoC assessment is given to all students to measure student proficiency. There will be a standardized assessment for all students across the state for Integrated Math III. This EoC assessment serves as an accountability measure for the teaching of Integrated Math III and for consistency across the state.
1.2 Targeted Content Standards
Content ID / Content Statement9–12 Benchmark.A.1: Represent and analyze mathematical situations and structures using algebraic symbols. / 9–12.A.1.7 Translate verbal statements into algebraic expressions or equations.
9–12.A.1.9 Solve quadratic equations in one variable.
9–12A.1.10 Solve radical equations involving oneradical.
9–12.A.1.14 Evaluate polynomial, rational, radical, and absolute value expressions for one or more variables.
9–12.A.1.16 Factor polynomials of various types (e.g., difference of squares, perfect square trinomials, sum and difference of cubes).
9–12.A.1.18 Use the four basic operations (+, -, ×, ÷) with linear, polynomial, and rational expressions in contextual situations.
Content ID / Content Statement
9–12 Benchmark A.2: Understand patterns, relations, functions, and graphs. / 9–12.A.2.2 Determine whether a relation defined by a graph, a set of ordered pairs, a table of values, an equation, or a rule is a function.
9–12.A.2.3 Translate among tabular, symbolic, and graphical representations of functions and relations.
9–12.A.2.5 Explain and use function notation in both abstract and contextual situations and evaluate a function at a specific point in its domain.
9–12.A.2.6 Graph a linear equation and demonstrate that it has a constant rate of change.
9–12.A.2.7 Graph a linear inequality in two variables.
9–12.A.2.8 Graph a quadratic function and understand the relationship between its real zeros and the x-intercepts of its graph.
9–12.A.2.9 Graph exponential functions and identify their key characteristics as related to contextual situations.
9–12.A.2.11 Use the quadratic formula and factoring techniques to determine whether the graph of a quadratic function will intersect
9–12.A.2.12 Explain the meaning of the real and complex roots of quadratic functions in contextual situations.
9–12.A.2.13 Read information and draw conclusions from graphs, and identify properties of a graph that provide useful information about the original problem.
9–12.A.2.15 Evaluate estimated rate of change in a contextual situations.
9–12 Benchmark A.3: Use mathematical models to represent and understand quantitative relationships. / 9–12.A.3.2 Model real-world phenomena using quadratic equations, interpret resulting solutions, and use estimation to detect errors.
9–12.A.3.3 Model real-world phenomena using exponential equations, interpret resulting solutions, and use estimation to detect errors.
9–12.A.3.4 Solve systems of linear equations in two variables algebraically and graphically
9–12.A.3.5 Solve applications involving systems of two equations in two variables.
Content ID / Content Statement
9–12 Benchmark G.1: Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop / 9–12.G.1.2 Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles with just edges in common.
9–12.G.1.3 Draw three-dimensional objects and calculate the surface areas and volumes of these figures (Examples: prisms, cylinders, pyramids, cones, spheres) as well as figures constructed from unions of prisms with faces in common, given the formulas for these figures.
9–12.G.1.4 Identify the hypothesis and conclusion in examples of conditional statements.
9–12.G.1.9 Write geometric proofs, including proofs by contradiction, and perform and explain basic geometric constructionsrelated to: theorems involving the properties of parallel and perpendicular lines, circles, and polygons; theorems involving complementary, supplementary, and congruent angles; theorems involving congruence and similarity; and the Pythagorean theorem.
9–12 Benchmark G.2: Specify locations and describe spatial relationships using coordinate geometry and other representational systems. / 9–12.G.2.1 Identify the origin, coordinate axes, and four quadrants on the Cartesiancoordinate plane, and draw and label them correctly.
9–12.G.2.2 Determine the midpoint and distance between two points within a coordinate system and relate these ideas to geometricfigures in the plane (e.g., find the center of a circle given the two points of a diameter of the circle).
9–12.G.2.3 Use basic geometric ideas (e.g., the Pythagorean theorem, area and perimeter) in the context of the Cartesian coordinate plane (e.g., calculate the perimeter of a rectangle with integer coordinates and with sides parallel to the coordinate axes, and of a rectangle with sides not parallel).
Content ID / Content Statement
9–12 Benchmark G.4: Use visualization, spatial reasoning, and geometric modeling to solve problems. / 9–12.G.4.1 Solve contextual problems using congruence and similarity relationships of triangles (e.g., find the height of a pole given the length of its shadow).
9–12.G.4.3 Know that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively.
9–12.G.4.5 Understand how similarity of right triangles allows the trigonometric functions sine, cosine and tangent to be defined as ratios of sides and be able to use these functions to solve problems.
9–12.G.4.6 Apply basic trigonometric functions to solve right-triangle problems.
9–12.G.4.7 Use angle and side relationships in problems with special right triangles (e.g., 30-, 60-, 90-, and 45-, 45-, 90- degree triangles).
9–12 Benchmark D.1: Formulate questions that can be addressed with data and collect, organize, and display relevant data to analysis, and the validity of conclusions. / 9–12.D.1.1 Explain the differences between various methods of data collection.
9–12.D.1.2 Describe the characteristics of a well-designed and well-conducted survey by differentiating between sampling and census, and a biased and unbiased sample.
9–12.D.1.3 Describe the characteristics of a well-designed and well-conducted experiment by differentiating between experiments and observational studies, and recognizing the sources of bias in poorly designed experiments.
9–12.D.1.4 Explain the role of randomization in well-designed surveys and experiments.
Content ID / Content Statement
9–12 Benchmark D.2: Select and use appropriate statistical methods to analyze data and make predictions. / 9–12.D.2.8 Describe the shape of a scatterplot.
9–12.D.2.9 Use linear patterns in data to make predictions.
9–12.D.2.12 Explain why correlation does not imply a cause-and-effect relationship.
9–12.D.2.14 Describe how sample statistics, including the law of large numbers, reflect the values of population parameters and use sampling distributions as the basis for informal inference
9–12.D.2.15 Evaluate published reports that are based on data by examining the design of the study, the appropriateness of the data
9–12 Benchmark D.3: Understand and apply basic concepts of probability. / 9–12.D.3.1 Explain the concept of a random variable.
9–12.D.3.3 Use the results of simulations to compute the expected value and probabilities of random variables in simple cases.
Section II
DesignandAdministration
Section II contains the specification tables which summarize the item types, item weights, and Depth of Knowledge (DoK) distribution of the EoC assessment. The specification tables provide educators with an understanding of the content range and patterns of emphasis within the general design of the assessment. The administration guidelines provide a standardized approach in administering the EoC to high school students. Accommodations afforded students with disabilities and English-language learners should reflect those provided to students on the statewide assessment and in classroom instruction.
The EoC design teams balanced: (a) the need for content coverage and depth, (b) administrative and scoring burden, and (c) current time/scheduling considerations. The resulting design affordshigh school students the opportunity to demonstrate content understanding within a suggested 90-minute testing window. This timeframe gives students the opportunity to respond to each of the 35 questions (some EoC have slight variations in the number of questions provided to students) on the assessment.
2.1 Specification Tables
The EoC assessments are a blend of three basic item types: (a) multiple choice (MC), (b) short-constructed response (SCR), and (c) extended-constructed response (ECR). Each item type is designed to assess knowledge, conceptual understanding, and application of skills associated with the targeted content standards. All MC items consist of a stem followed by four response options (A, B, C, D). MC items are scored as either correct or incorrect and contribute 1 point to the overall score. SCR items require students to develop an answer from a given stem/prompt. These items are assigned between 0 and 3 points using a scoring rubric provided in Appendix A of this document. Concurrently, ECR items require much more elaborate and detailed demonstrations of content knowledge. These items have point ranges from 4 points to higher. ECR items are designed to assess higher-order thinking skills. When combined, the blend of item types provides access points for all students that have completed the high school course, while minimizing items with low-cognitive demand.
Table 1.Item TypesContent Standards / MC / SCR / ECR / Total
Functions / 0 / 8 / 1 / 0 / 0 / 9
Trig/Geometry / 0 / 2 / 2 / 1 / 0 / 5
Data / 0 / 2 / 1 / 0 / 1 / 4
Grand Totals / 0
Items / 12
Items / 4
Items / 1
Items / 1
Items / 18
Items
Table 2. Item Points/Weights
Content Standards / MC / SCR / ECR / Total
Functions / 0 / 16 / 4 / 0 / 6 / 22
Trig/Geometry / 0 / 4 / 8 / 6 / 6 / 14
Data / 0 / 4 / 4 / 0 / 6 / 14
Grand Totals / 0
Points / 24
Points / 16
Points / 6
Points / 18
Points / 50
Points
* Questions 6, 10, 15, & 16 are 2 part questions each worth 2 points
* Question 7 is a 3 part question worth 2 points
Table 3. Depth of Knowledge (DoK) LevelsContent Standards / DoK 1 / DoK 2 / DoK 3 / Total
Functions / 2 / 7 / 0 / 11
Trig/Geometry / 1 / 3 / 1 / 7
Data / 3 / 1 / 0 / 7
Grand Totals / 5
Items / 11
Items / 1
Items / 18
Items
Appendix A
SCR Generic Rubric
Score / Description2 Points / The student’s response is as follows:
- offers a correct solution and is well supported by well-developed and accurate explanations
- gives evidence that an appropriate problem-solving strategy was selected and implemented, but may contain minor errors that do not detractfrom the overall quality of the student response
- is clearly organized and focused, and shows a mathematical understanding ofthe task or concept
- contains sufficient work to convey thorough understanding of the problem
1 Point / The student’s response is as follows:
- offers a correct solution with no supporting evidence or explanation
- offers a partially correct answer to the problem
- may contain flaws indicating an incomplete understanding of the task or concept
- may show faulty reasoning leading to weak answers or conclusions
- may demonstrate unclear communication in writing or diagrams
- may demonstrate a poor understanding of relevant mathematical procedure or concepts
0 Points / The student’s response is as follows:
- gives an incorrect response with no work shown
- offers no mathematical understanding of the problem
- does not address the problem
End-of-Course Assessment: Integrated Math III1
Public Education Department, October 2012