Program Model B Pacing Guide
Blended Model for High School Mathematics
(For students not 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.
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.
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 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 continue to 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: Pre-Calculus or the Modeling and Quantitative
Reasoning course.
Fourth Year Course, Option 1
Pre-Calculus
Fourth Year, Option 1, Course Rationale
Calculus is the gateway to many of the more advanced mathematics courses and to careers or majors in mathematics,
engineering, physical sciences, biological sciences, medical sciences, social sciences, and business. To succeed in
calculus, students need to have mastery of the many facets of algebra as discussed in earlier courses, and of the more
advanced topics here.
Fourth Year, Option 1, Course Description
The course includes the study of vectors, polar coordinates, complex numbers, functions, solving equations, and
trigonometric identities.
| Pre-Calculus Chapter List For Model B | Instructional Days
(suggested) |
| 4.1 Equations and Applications | 28 -36 |
| 4.2 Trigonometric Identities | 20 - 27 |
| 4.3 Vectors | 20 - 26 |
| 4.4 Polar Coordinates | 14 - 18 |
| 4.5 Complex Numbers | 24 - 32 |
| 4.6 Mathematical Induction, Sequences, and Series | 33 - 40 |
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) | |
Fifth Year Course
Fifth Year Course Rationale
Students in a fifth year high school mathematics course have been accelerated at
some point in their study. This might involve starting with the first year high
school course in eighth grade, doubling up on courses at some point, or another
form of acceleration. Any student who has been successful in the pre-calculus course
is prepared for college-level calculus or statistics courses, and students who have
been successful in either of the other year 4 courses will be prepared for college-level
statistics.
Fifth Year Course Description
The fifth year of high school mathematics will be a calculus course for most accelerated
students. When a calculus course is offered in the high school curriculum, the course
should be taught at the college level and students should expect it to replace a
first year calculus course in college. This can be assured by using one of the College
Board’s Advanced Placement calculus courses and requiring students to take the AP
exam at the end of the course. In some locations, accelerated students are able
to enroll in a mathematics course at an area college or to take a college level
course through distance education, concurrent with their high school studies. The
Program Models also prepare accelerated students to take the College Board’s Advanced
Placement statistics course. For many accelerated students, AP Statistics can be
an exciting and appropriate option.
Syllabi for AP Calculus and AP Statistics are provided by the College Board.