Program Model B' Pacing Guide
Blended Model for High School Mathematics
(For students intending to take calculus, see
Model B)
Traditionally, high school mathematics has been compartmentalized into separate
courses for Algebra I, Geometry, and Algebra II. In the Ohio Academic Content Standards,
however, the algebra and geometry standards appear side-by-side through all the
grades, along with standards for number, measurement, and data analysis. This model
is designed to blend all five standards in a two-year program that exploits connections
among those different branches of mathematics.
In the first year, the primary focus of the course is linear mathematics, with non-linear
topics emphasized in the second year. The entry point each year is through the first
two levels of the data analysis standard, namely identifying a problem to be investigated
and collecting data. With that introduction, students should understand the advantage
gained by applying algebraic and geometric tools in solving these problems. The
second year concludes with an in-depth study that involves the analysis and interpretation
of data both linear and non-linear. This should provide students with an opportunity
to consolidate concepts and skills in number, algebra, and geometry that they have
acquired over the two years and use them to solve realistic problems.
The model assumes that students will be engaged with rich problems in each course.
This experience is essential to assuring that students understand the mathematics
fully and that they develop creative problem solving and reasoning skills. Students
should also be expected to communicate mathematical ideas using formal mathematical
language.
Model B' is an adaptation of Model B that allows additional time for students who are preparing
for postsecondary education in programs that do not include calculus. This adaptation prepares
students for OGT requirements by the end of the second year course and meets the Ohio Board of
Regents expectations for students to be prepared for a non-remedial college mathematics course
by the end of the third year course.
First and Second Year Courses
First and Second Year Course Rationale
This first two years of this model can be viewed as a single two-year course that over the two years, meets the
mathematics content standards for grades 9 and 10. It weaves the five content strands (number, measurement, geometry,
algebra, and data analysis) into a coherent pair of courses that builds on the mathematics of grades 7 and 8. In the
first year the primary emphasis is on linear mathematics; non-linear topics are emphasized in year two.
First and Second Year Course Description
Each year the course opens with data analysis and relates mathematical ideas and methods to real-world problem
situations. This is followed by a systematic study of the relevant mathematical functions and equations (linear
and some polynomial in year one, quadratic, more polynomial, exponential, and logarithmic in year two). Topics from
geometry, trigonometry, and measurement are integrated with the algebra and data analysis. A survey of properties of
geometric figures and transformations in year one leads to formal proofs of geometric theorems in year two.
| Second Year Chapter List for Model B' | Instructional Days
(suggested) |
| 2.1 Quadratic Functions | 25 - 34 |
| 2.2 Functions (with emphasis on polynomials) | 29 - 35 |
| 2.3 Synthetic Geometry | 80 - 91 |
| 2.4 Data Analysis Revisited | 16 - 19 |
Third Year Course
Third Year Course Rationale
This course introduces additional basic mathematical topics not addressed in the first and second years. The emphasis is
on in-depth investigations using data analysis, supplemented by topics involving number, algebra, and trigonometry.
Third Year Course Description
Following Ohio’s grade eleven standard for data analysis and probability, this course requires students to design a
statistical study for a problem, collecting and interpreting data with appropriate graphical displays and descriptive
statistics. Relating this project to students’ studies in science or social studies provides connections between disciplines
and relevancy for students. The course begins with an in-depth study
of functions not considered earlier and then moves to a discussion of data analysis topics relevant to student projects. The
rest of the course concerns mathematical topics that are important for all students to know, but not directly related to this
data analysis strand. While the class is engaged in learning these topics, small groups will work on their data
projects, which will be presented in class as the culmination of the course.
Fourth Year Course
Fourth Year Course Rationale
With the advent of the new core requirements for Ohio, all students must take mathematics
in their senior year. Two options are offered as possible courses following the three-year sequence above: Fourth Year Topics or the Modeling and Quantitative
Reasoning course.
Fourth Year Course, Option 1
Fourth Year Topics
Fourth Year, Option 1, Course Rationale
Topics in this course include applications of algebra and trigonometry for students not planning to take calculus.
Fourth Year, Option 1, Course Description
The course includes systems of equations, exponential and logarithmic functions, infinite series and trigonometry.
Fourth Year Course, Option 2
Modeling and Quantitative Reasoning
Fourth Year, Option 2, Course Rationale
One purpose of secondary education in the United States has always been preparing students for their roles
as citizens, as well as preparing them for future study and the workplace. Today numbers and data are
critical parts of public and private decision making. Decisions about health care, finances, science policy,
and the environment are decisions that require citizens to understand information presented in numerical form,
in tables, diagrams, and graphs. Students must develop skills to analyze complex issues using quantitative tools.
In addition to a textbook, teachers will want to use on-line resources, newspapers, and magazines to identify
problems that are appropriate for the course. Students should be encouraged to find issues that can be
represented in a quantitative way and shape them for investigation. Appropriate use of available technology is
essential as students explore quantitative ways of representing and presenting the results of their investigations.
Fourth Year, Option 2, Course Description
This course prepares students to investigate contemporary issues mathematically and to apply the mathematics
learned in earlier courses to answer questions that are relevant to their civic and personal lives. The course
reinforces student understanding of:
- percent
- functions and their graphs
- probability and statistics
- multiple representations of data and data analysis
This course also introduces functions of two variables and graphs in three dimensions. The applications in all
sections should provide an opportunity for deeper understanding and extension of the material from earlier courses.
This course should also show the connections between different mathematics topics and between the mathematics and
the areas in which applied.
| Modeling and Quantitative Reasoning Chapter List for Model B' | Instructional Days
(suggested) |
| 4M.1 Use of Percent | 15 - 18 |
| 4M.2 Statistics and Probability | 29 - 32 |
| 4M.3 Functions and Their Graphs | 54 - 65 |
| 4M.4 Functions of More Than One Variable | 10 - 15 |
| 4M.5 Geometry | 40 - 48 |
| 4M.6 Exploration of Data (integrated throughout the course) | |