Mathematics Curriculum

  Curriculum

Standards and Instructional Objectives
      The secondary math program is based on a set of specific standards and course objectives. The district math standards are the Nebraska State Math Standards and specific course objectives have been designed to ensure students have the opportunity to acquire the knowledge and skills outlined in the Nebraska State Math Standards.
      Course outlines contain specific course objectives, student assessment information, Nebraska State Standards and NeSA-M correlations, and furnish useful information to students, teachers, administrators, and parents.

Graduation Requirement
    The high school graduation requirement is 30 hours of mathematics, including coursework in algebra and geometry. The 30 hours of mathematics credit must come from courses beginning with Algebra/Algebra Block (special education students will graduate according to requirements outlined in their IEP). This does not mean that a student has to pass each semester of algebra and geometry to graduate, only that a student’s 30 hours of mathematics must include, at a minimum, 5 hours of algebra credit and 5 hours of geometry credit.

Grading
  • In all courses in grades 6-12, the grading template is 80% summative and 20% formative.
  • Only chapter/Big Idea assessments, cumulative assessments, and finals count in the summative category.
  • Quizzes and homework count in the formative category.

Assessment and Reteaching (Middle Level and High School)
    Reteaching and relearning is a research-based instructional strategy to improve student learning. The National Mathematics Advisory Panel recommended the use of assessments for the purpose of modifying instruction based on student progress (NMAP, 2008). Research indicates that when the results of assessment are used to provide students additional instruction, practice, and reinforcement in the skills and/or concepts with which they struggle, that student achievement is improved (Baker, Gersten, & Lee, 2002). Therefore, reteaching and re-assessment is now a required district expectation in mathematics from Kindergarten through Differentiated Precalculus. In order to prepare students for possible coursework beyond high school, there is a steady decline in the amount of re-assessment that takes place as students progress through the curriculum as outlined below:
  • Middle School Math Courses (grades 6-8): Retesting occurs on either individual unit retention quizzes or cumulative assessments. Retesting is used for grade replacement. Please see individual course information for specific retesting opportunities.
  • Algebra: Retesting occurs on both chapter tests and cumulative assessments. Retesting is used for grade replacement.
  • Geometry: Retesting occurs only on cumulative assessments. Retesting is used for grade replacement.
  • Advanced Algebra: Retesting occurs only on cumulative assessments.
  • Precalculus: Retesting occurs only on first and third quarter cumulative assessments.
  • Calculus: No retesting.

Format of District Assessments
    The NeSA-M emphasizes the application of mathematics. Specifically, many of the assessment items on the NeSA-M require students to draw on a variety of mathematical topics and apply these topics to novel problems that students may have never previously seen. This places an emphasis on student mathematical understanding, as opposed to rote procedural skill, so that students can make appropriate connections among mathematical topics and draw on their understanding to solve problems. Therefore, all secondary math objectives and assessments through precalculus are organized around connected “Big Ideas.” It is a district expectation that common unit assessments, cumulative assessments, and finals will be used to ensure consistency and that they will not be modified (beyond special education requirements) to adjust the cognitive demand.

Re-assessment Procedures
    Re-teaching (not just additional practice) and re-learning must take place prior to re-assessment for the strategy to be effective at improving student learning. It is assumed that all teachers will provide all students an opportunity to continue to master topics they have not yet mastered through appropriate re-teaching either inside or outside of the regular instructional time. Because re-assessment is embedded within formal and required district assessments, all students will have access to re-assessment opportunities regardless of their compliance with behavioral expectations, e.g. homework completion.
    Re-assessment on Chapter Assessments in Algebra and Algebra Block
  • Chapter tests which do not begin a semester or follow a cumulative assessment may include a re-assessment of one big idea from the previous chapter. This is determined in part by what is assessed by NeSA-M and in part based on what is most essential for students to know moving forward in the curriculum.
  • Assessment sections (Big Ideas) from chapter tests will be entered in the district gradebook as individual scores.
  • The length of the re-assessment section may not match the original assessment.
  • A score is replaced only if the student improves because re-assessment is more likely to prove a positive than a negative.
  • Although the opportunity to re-learn should be a significant motivator, the reality is that for many students the opportunity to replace a low score serves as a motivation to engage in the re-learning process.
  • Because retention and understanding are essential goals, the re-assessment section of a chapter test or cumulative assessment is used not only for the purpose of re-assessment and grade replacement, but also constitutes a new score in a student’s grade.

Cumulative Assessments

  • Cumulative assessments are used as a way to emphasize the importance of retention as well as an additional vehicle for students to demonstrate re-learning.
  • Cumulative assessments are administered periodically following 2-3 chapters of instruction with the exception of Geometry Plus.
  • Cumulative assessments will assess all big ideas from the previous chapters (since the time of the last cumulative assessment).
  • In Algebra, Geometry and Advanced Algebra courses, the last chapter of each semester will not be included on a cumulative assessment. This provides teachers with additional time to process cumulative exams and create instructional space prior to the final exam.
  • Cumulative assessments focus on assessment of students’ retention of critical concepts. The rigor of a cumulative assessment resides in the retention. It is not possible to re-assess every concept or skill as it was assessed on the original assessment, nor at its original depth.
  • The cumulative assessment also counts as a single new score in a student’s grade. This serves to motivate students to retain previous learning.

Final Exam
  • The final exam serves to assess student learning across a semester’s big ideas, but can only survey essential topics – it cannot re-assess every big idea at the level done on individual chapter tests.
  • The final exam will account for approximately 10% of a student’s grade.

District Common Assessments
    District Common Assessments (DCAs) are a critical component of the district’s NeSA-M preparation program. DCAs must be administered in designated courses at designated times. Instructional time is not spent reviewing for or studying for DCAs. The goal is to gauge retention and application of concepts and skills in order to identify intervention needs. Results must be used to plan intentional review and re-teaching of critical NeSA math standards.
  Course Descriptions

Math 6
    This course includes work with Integers, Factors and Multiples, Operations with Positive Rational Numbers, Equivalent Expressions, One Step Equations, Introduction to Inequalities, Relationships in Geometry, Coordinate Plane Geometry, Measurement and Data, Percent, and Rates, Ratios and Percents. Throughout the class, exploration and technology is utilized in problem solving.

Math 6D
    This course includes work with Factors and Multiples, Operations with Positive Rational Numbers, Operations with Integers, Equivalent Expressions, Two Step Equations, Introduction to Inequalities, Relationships in two variables, Relationships in Geometry, Coordinate Plane Geometry, Measurement and Data, Percent, and Rates, Ratios and Percents. Throughout the class, exploration and technology is utilized in problem solving. Students successful in Math 6D will be enrolled in Pre-Algebra.

Math 7
    This course includes Integer Operations, Rational Number Operations, Percent Relationships, Expressions and Equations, Solving Inequalities, Statistics, Probability, Geometric Figures, Ratios and Proportional Relationships. Throughout the class, exploration and technology is utilized in problem solving.

Pre-Algebra
    This course includes Integer Operations, Rational Number Operations, Percent, Simplify Expressions and Solve Linear Equations, Solve Inequalities, Scientific Notation, Real Numbers, Probability, Geometry, Transformational Geometry, 3-D Geometry, and Angle Relationships. Throughout the class, exploration and technology is utilized in problem solving. Students successful in Pre-Algebra and Pre-Algebra D will be able to enroll in Algebra in 8th grade.

Math 8
    This course includes Operations with Rational Numbers, Solve Equations, Solve Inequalities, Real Numbers, Angle Relationships, Pythagorean Theorem, Transformational Geometry, Surface Area and Volume, Proportional Relationships and Scatter Plots. Throughout the class, exploration and technology is utilized in problem solving.

Algebra/Geometry/Advanced Algebra Support
    Support classes are taken in addition to a regular math course to provide additional instructional support. Students must be enrolled in the appropriate math course at the same time as the Support class. The grade for the Support class will take into consideration the student’s grade in their regular math course. In order to earn credit for the Support class, students must pass both the regular math course and the Support class.

Accelerated Math
    Accelerated Math provides individualized and compacted instruction focused on essential concepts from the pre-Algebra curriculum . The purpose is to prepare students for success in first year Algebra.

Algebra/Algebra Block
    Algebra is the first class in the traditional college preparatory sequence. The class explores the solutions of open sentences using the basic operations, linear sentences, lines and distance, slopes and distance, exponents and powers, polynomials, systems of equations, quadratic equations, functions, statistics, and informal geometry. Throughout the class, appropriate applications are explored and technology utilized in problem solving.

Geometry/GeometryPlus/Geometry Block
    Technology and cooperative investigations are the vehicles by which students discover angle relationships and properties of triangles, quadrilaterals, regular polygons, parallel lines and planes, perpendicular lines, ratio and proportion, similar polygons, special properties of right triangles, circles, solid figures, areas, and transformations. Applications of geometry are emphasized throughout the class. After students have developed a geometric knowledge base using inductive reasoning, they verify their discoveries using deductive reasoning.

Elements of Advanced Algebra
    This semester is a review of algebra, statistics, probability, and geometry concepts. Students will preview skills required for advanced algebra.

Advanced Algebra
    In Advanced Algebra, the core topics are again explored through the use of higher-level applications. Practical applications become the basis for the further investigation of linear and quadratic equations and inequalities, absolute value, fractions, linear systems in two and three variables, graphs and exponents. In addition, the class includes the study of applications of relations, functions, irrational and complex numbers, quadratic systems, matrices, logarithms, binomial expansions, sequences, and series.

Precalculus
    Precalculus is designed for those students who intend to continue their study of mathematics in the traditional calculus sequence. This includes students interested in mathematics, the sciences, and engineering. This class includes a thorough study of elementary trigonometric functions and their properties; the limits of functions and sequences; properties of algebraic, exponential and logarithmic functions; and polar coordinates.

AP Calculus
    AP Calculus is a college-level class covering topics that are normally studied during the first semester of the three semester college calculus course. This course goes at a slower pace than the Differentiated Calculus course. Students who successfully complete this course may enroll in the second semester of the calculus sequence at the University of Nebraska-Lincoln, and may qualify for university credit (half of the credit students who successfully complete the differentiated calculus course may earn).

AP Calculus D
    AP Calculus is a college-level class covering topics that are normally studied during the first two calculus classes in college. Topics include conics, limits, continuity, derivatives, applications of differentials, the definite integral, trigonometric and exponential functions, vectors, methods of integration, and applications of the integral. Students who successfully complete two semesters of calculus may enroll in the third class of the calculus sequence at the University of Nebraska, Lincoln, and may qualify for university credit.

AP Statistics
    The purpose of AP Statistics is to introduce students to the major concepts and tools for collecting, analyzing and drawing conclusions from data. Students are exposed to four broad conceptual themes:1. Exploring Data: Describing patterns and departures from patterns. 2. Sampling and Experimentation: Planning and conducting a study. 3. Anticipating Patterns: Exploring random phenomena using probability and simulation. 4. Statistical Inference: Estimating population parameters and testing hypotheses. Students who successfully complete the course and exam may receive credit, advanced placement or both, for a one-semester introductory college statistics course.
  Course Objectives and Outlines