# 7-12 Mathematics

## Support Success in High School Math Courses through Careful Placement in 9th Grade

Success in 9th grade math is critical to prepare students for success in college and career, particularly for students pursuing the fields of science, technology, engineering, and mathematics (STEM).

Oakdale Joint Unified School District offers 4 Math Pathways. Successful completion of pathways 1-3 meets admission requirements for CSU/UC admission. Use the tabs below to learn more about the pathways, their courses, and the School Board Policy.

Parents may request that their child be placed in a more rigorous pathway than the one suggested by the district by printing out the Parent Contract (tab below), reviewing it, and then scheduling an appointment with an Oakdale High School Counselor.

Understanding the Progression of Math Courses in OJUSD

Use the following guide to make an informed decision about your students. Math Course Pathway

• High School Graduation Math Requirements: Completion of 3 math courses. Must meet or exceed Integrated
Math I or equivalent.

• CSU/UC Math Requirements: Integrated Math I, Integrated Math II and Integrated Math III meet the a-g requirements. A 4th year of math is recommended.

Middle School Courses

Math 7:Grade 7 Mathematics - Common Core

In grade seven instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships, including percentages; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples:Students also work towards fluently solving equations of the formpx + q = r and p(x + q) = r.

Math 8:Grade 8 Mathematics - Common Core

In grade eight, instructional time should focus on three critical areas: (1) formulating and reasoning about expressions and equations, including modeling an association in bivariate data with a linear equation, and solving linear equations and systems of linear equations; (2) grasping the concept of a function and using functions to describe quantitative relationships; (3) analyzing two- and three-dimensional space and figures using distance, angle, similarity, and congruence and understanding and applying the Pythagorean Theorem. Students also work towards fluency with solving simple sets of two equations with two unknowns by inspection.

Integrated Mathematics I - Common Core

The fundamental purpose of Mathematics I is to formalize and extend students understanding of linear functions and their applications. The critical topics of study deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Students build on their prior experiences with data, developing more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit. Mathematics I uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades.

High School Courses

Integrated Mathematics I - Common Core

The fundamental purpose of Mathematics I is to formalize and extend students understanding of linear functions and their applications. The critical topics of study deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Students build on their prior experiences with data, developing more formal means of assessing how a model fits data. Students use regression techniques to describe approximately linear relationships between quantities. They use graphical representations and knowledge of the context to make judgments about the appropriateness of linear models. With linear models, they look at residuals to analyze the goodness of fit. Mathematics I uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades.

Integrated Mathematics II - Common Core

The focus of Mathematics II is on quadratic expressions, equations, and functions, and comparing their characteristics and behavior to those of linear and exponential relationships from Mathematics I. The need for extending the set of rational numbers arises and real and complex numbers are introduced. The link between probability and data is explored through conditional probability and counting methods, including their use in making and evaluating decisions. The study of similarity leads to an understanding of right triangle trigonometry and connects to quadratics through Pythagorean relationships. Circles, with their quadratic algebraic representations, round out the course.

Integrated Mathematics III - Common Core

The standards in the integrated Mathematics III course come from the following conceptual categories: Modeling, Functions, Number and Quantity, Algebra, Geometry, and Statistics and Probability. Students expand their repertoire of functions to include polynomial, rational, and radical functions. Students perform all four operations on polynomials. Students identify zeros of polynomials and make connections between zeros of polynomials and solutions of polynomial equations. They expand their study of right triangle trigonometry to include general triangles. And, finally, students bring together all of their experience with functions and geometry to create models and solve contextual problems.

PreCalculus - Common Core

In Precalculus, students extend their work with complex numbers begun in Mathematics III or Algebra II to see that the complex numbers can be represented in the Cartesian plane and that operations with complex numbers have a geometric interpretation. They connect their understanding of trigonometry and the geometry of the plane to express complex numbers in polar form. Students begin working with vectors. Students also work with matrices, their operations, and find inverse matrices. They see the connection between matrices and transformations of the plane. Students use matrices to represent and solve linear systems. Students extend their work with trigonometric functions, investigating the reciprocal functions secant, cosecant, and cotangent and their graphs and properties. They find inverse trigonometric functions by appropriately restricting the domains of the standard trigonometric functions and use them to solve problems that arise in modeling contexts. Students add ellipses and hyperbolas to their work. They also work with polar coordinates and curves defined parametrically and connect these to their other work with trigonometry and complex numbers. Finally, students work with more complicated rational functions, graphing them and determining zeros, y-intercepts, symmetry, asymptotes, intervals for which the function is increasing or decreasing, and maximum or minimum points.

Statistics and Probability - Common Core

Students extend their work in statistics and probability by applying statistics ideas to real-world situations. They link classroom mathematics and statistics to everyday life, work, and decision-making, by applying these standards in modeling situations. They choose and use appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions.

Students in Statistics and Probability take their understanding of probability further by studying expected values, interpreting them as long-term relative means of a random variable. They use this understanding to make decisions about both probability games and real-life examples using empirical probabilities.

AP Calculus AB

Following the College Board suggested curriculum designed to parallel college-level calculus courses, AP Calculus AB provides students with an understanding of the concepts of calculus and experience with its methods and applications. These courses introduce calculus and include the following topics: functions, graphs, limits, and continuity; differential calculus (including definition, application, and computation of the derivative; derivative at a point; derivative as a function; and second derivatives); and integral calculus (including definite integrals and antidifferentiation).

AP Calculus BC

Following the College Board suggested curriculum designed to parallel college-level calculus courses, AP Calculus BC courses provide students with an understanding of the concepts of calculus and experience with its methods and applications. These courses cover all of the calculus topics in AP Calculus AB as well as the following topics: parametric, polar, and vector functions; applications of integrals; and polynomial approximations and series, including series of constants and Taylor series.

AP Statistics

Following the College Board's suggested curriculum designed to parallel college-level statistics courses, AP Statistics courses introduce students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. Students are exposed to four broad conceptual themes: exploring data, sampling and experimentation, anticipating patterns, and statistical inference.

February/March 2018

## Brochures for Parents/Guardians in English and Spanish

These brochures on the mathematics standards showcase example problems and highlight the progression of learning through the grade levels. The brochures also offer suggestions for parents/guardians to support their students learning and a list of additional resources. (Source: California Department of Education: Curriculum Frameworks)

Math Framework Glossary

Eureka Math

Common Core Map | Khan Academy