Program Model C Pacing Guide
Traditional Model for High School Mathematics
For students not intending to take calculus, see Model C'.
This model features a classic sequence of courses that emphasizes connections across
content strands. Data analysis topics have been added to the familiar high school
mathematics curriculum. Topics are grouped so that Year 1 focuses on algebra and algebraic reasoning,
Year 2 focuses on geometry, and Year 3 returns to a focus on further algebraic topics leading to trigonometry and
pre-calculus. This sequence works well for many students, is familiar to teachers and parents, and fits the design of many
instructional materials. However, this does not mean that the status quo is working for all students. Even though course
topics and sequencing may look familiar, effective strategies for presenting the material must be implemented to make this
or any model curriculum successful. Students must be placed in a course for which they have the prerequisites and have
adequate time and support to fully understand the material. Students must be engaged with rich problems throughout each
course in order to understand the mathematics fully and develop creative problem solving and reasoning skills. Students
must also be expected to communicate mathematical ideas using formal mathematical language. Teachers in schools adopting
Model C will benefit from professional development that includes strategies for successfully teaching all students and
that familiarizes teachers with sources of problems to deepen student understanding of mathematical topics.
This model provides students with the basic mathematical knowledge they will need for future education and employment.
The design offers a progression for the development of mathematical thinking, with each course presenting the material in
a logical, efficient, and systematic way. Related topics are presented together whenever possible and learning builds
upon previously learned material. Connections between algebraic, numerical, and geometric representations are made
throughout the model to provide a coherent curricular model.
First Year Course
First Year Course Rationale
All students require a rigorous and demanding curriculum in order to develop sound reasoning and strong problem solving skills. The topics covered in Year 1 of this model can provide this rigor. Students progress from their informal middle school experience with number relationships, data analysis, and linear equations to more formal definitions, algebraic reasoning, and graphical representations, and they extend their study to polynomials and exponential functions. With this model, as with any model, different students may require different amounts of time and support to become proficient with the mathematics.
First Year Course Description
The focus of this course is the development of algebraic understanding, reasoning, and skills using mathematical language to express abstract ideas. The Year 1 course has four main themes:
- transition from generalized arithmetic to algebra;
- data analysis and probability;
- linear equations and functions;
- nonlinear equations and functions, with emphasis on quadratics.
More specifically, students will solve linear equations and inequalities and quadratic equations. They will graph a variety of functions and add the study of probability and statistics to the topics covered in a typical Algebra I course. Appropriate use of technology is encouraged to enhance the study of these topics.
Second Year Course
Second Year Course Rationale
The second year model develops formal logic and reasoning skills through the study of Euclidean geometry. Although geometry is a subject of importance and practical use, the main goal of the course is to develop students’ abilities to reason and to present coherent arguments. In addition to this deep involvement with logic and deduction, students discover connections between formal geometry and the algebraic techniques learned earlier, and they learn important practical applications of geometry. With mastery of the Year 1 and Year 2 courses, students will be prepared for further mathematical education and for understanding deeper connections between abstract mathematics and real world situations.
Second Year Course Description
The focus of this course is the development of logic and reasoning, along with basic ways to think geometrically. The two foci for the Year 2 course are formal reasoning and applications of geometry (constructions, calculating lengths, areas, and volumes). Geometric constructions should be woven through the course. Appropriate use of technology is encouraged to enhance the study of these topics.
Third Year Course
Third Year Course Rationale
The Third Year course includes content that is critical for all students. The third year continues to build mathematics essential for the workplace and future education, and exposes students to a wide variety of rich mathematics. Algebraic topics are a focus and are developed in relationship to the geometry and mathematical reasoning the students have previously studied.
Third Year Course Description
Prerequisite to this course is working knowledge of key topics from years one and two, including number line and interval notation, solving linear and quadratic equations and inequalities, and absolute value and distance. The thrust of the Year 3 course is to reinforce and extend the algebraic topics from the Year 1 course. Throughout this course, students should have frequent experiences with numeric, graphical, algebraic, and verbal examples of mathematics. Students should use graphing calculators and other technology as integral parts of the course to enhance the study of these topics.
Fourth Year Course
Fourth Year Course Rationale
With the advent of the 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
This course presents a mix of algebraic and geometric topics that will help develop students’ algebraic thinking. Throughout this course, students should have frequent experiences with numeric, graphical, algebraic, and verbal examples of mathematics. Mastery of the four courses in this model will provide students with the mathematical and reasoning skills needed to succeed in a rigorous college-level calculus course.
Fourth Year, Option 1, Course Description
The Year 4 course has several focus areas: (1) formal proofs by induction with applications, (2) modeling bivariate data, and (3) aspects of geometry. By studying these topics, the student will have completed a comprehensive pre-calculus curriculum. Students may use graphing calculators and other technology to enhance the study of these topics.
| Pre-Calculus Chapter List for Model C | Instructional Days
(suggested) |
| |
| 4.1 Mathematical Induction, Sequences, and Series | 24 - 30 |
| 4.2 Standard Functions | 27 - 33 |
| 4.3 Polar Coordinates | 15 - 18 |
| 4.4 Complex Numbers | 16 - 22 |
| 4.5 Conics | 19 - 23 |
| 4.6 Systems of Equations and Matrices | 25 - 29 |
| 4.7 Vectors | 21 - 27 |
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 online 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 C | 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) | |