Program Model A' Pacing Guide
Applications-Driven Model for High School Mathematics
(For students intending to take calculus, see
Model A)
Every citizen is deluged with numbers: claims and counter-claims, polls and statistics,
measures of risk, and promises of certainty. Each student must attain a level of
quantitative sophistication sufficient to decide what to believe and what to challenge.
The model presented here uses applications, including probability and data, to motivate
student learning of algebra and geometry. An approach that combines applications,
computation, and theory will engage students throughout their studies and will help
prepare them for employment or further education.
This model requires that students have frequent experience with rich problems in
order to understand the mathematical topics fully. Students must be challenged throughout
the sequence with tasks that require creative problem solving and reasoning skills.
They must also learn to communicate mathematical ideas using formal mathematical
language.
Model A' is an adaptation of Model A 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 Year Course
Model A' is an adaptation of Model A 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 Year Course Rationale
Every citizen is deluged with numbers: claims and counter-claims, polls and statistics,
measures of risk, and promises of certainty. Each student must attain a level of
quantitative sophistication sufficient to decide what to believe and what to challenge.
The model presented here uses applications, including probability and data, to motivate
student learning of algebra and geometry. An approach that combines applications,
computation, and theory will engage students throughout their studies and will help
prepare them for employment or further education.
This model requires that students have frequent experience with rich problems in
order to understand the mathematical topics fully. Students must be challenged throughout
the sequence with tasks that require creative problem solving and reasoning skills.
They must also learn to communicate mathematical ideas using formal mathematical
language.
First Year Course Description
This course is designed to be a first-year algebra course with applications-driven
development of the content. The early emphasis is on linear expressions and relationships.
The curriculum begins with the study of bivariate data that have a linear relationship.
Intuition is developed before linear functions and equations are formally presented.
Classical topics from algebra are emphasized, such as solutions and graphs of linear
functions and solutions of linear equations, arithmetic of polynomials, and factorization
of trinomials. Fluency with numerical computation
(decimals, fractions, scientific notation, radicals, etc) with and without technology
will be reinforced throughout the curriculum.
Second Year Course
Second Year Course Rationale
Geometry was developed in the ancient world for surveying, architecture, astronomy,
and navigation. However, the main thrust of the second year course is the logical
development of geometry and the beginnings of abstract mathematical thought. For
more than 2300 years Euclid’s Elements has served as the model for instruction in
mathematics and logic. The study of Euclidean geometry is necessary for anyone interested
in understanding the foundations of western civilization. This second course moves
from concrete applications, through the logical beauty of Euclidean geometry, to
geometric ideas used in contemporary mathematics.
Second Year Course Description
The course begins with quadratic polynomials, functions, and equations and uses coordinate geometry to connect algebra learned in Year 1 to
geometric topics learned in earlier grades and in this course. Geometry is introduced
informally, in the context of the coordinate plane. Subsequently students learn
the core ideas of logic and deduction in more formal Euclidean geometry, while also
understanding geometric interpretations of results in the preceding algebra course.
Geometry software such as Geometer’s Sketchpad or Cabri can be used to advantage.
The main part of the course emphasizes logic, proofs, and classical synthetic Euclidean
plane geometry. This section should occupy more than half of the year. The course
concludes with right triangle trigonometry. Measurement topics of units and scaling should receive
attention throughout the course including units, conversion between units, and scale
factors.
Third Year Course
Third Year Course Rationale
This course allows for a deeper study of some topics included in previous courses
and introduces new topics necessary for students who will continue their mathematical
studies. A variety of teaching strategies should be used, with the underlying theme
of applications-driven, exploratory activities and real-world applications.
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 equations and inequalities,
and absolute value and distance. The third year course begins with data analysis,
statistics, and probability. These topics are data-driven and can be introduced
and expanded through classroom experiments and observations. By observing different
trends in bivariate data, students are introduced to linear, quadratic, cubic, exponential,
and logarithmic functions. Students discuss various properties of those functions,
including their symmetry and inverses. Real-world applications
and technology should be used to promote a better understanding of the topics.
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 (ranging from trigonometry to finance) or the Modeling and
Quantitative Reasoning course.
Fourth Year Course, Option 1
Fourth Year Topics
Fourth Year, Option 1, Course Rationale
Topics covered in a fourth year course can have many applications to a variety of
post-high school pathways. In order to enable all students to be successful in such
topics, a variety of teaching styles is encouraged, with the depth of theory and
application fitted to student needs.
Fourth Year, Option 1, Course Description
As presented here, the fourth course is primarily a course in trigonometry and its
geometric applications, together with discussion of series and applications to finance.
| Fourth Year Chapter List for Model A' | Instructional Days
(suggested) |
| |
| 4.1 Trigonometry | 41 - 50 |
| 4.2 Review: Exponential and Logarithmic Functions | 18 - 24 |
| 4.3 Sequences, Series, and Mathematical Induction | 28 - 37 |
| 4.4 Personal Finance | 21 - 27 |
| 4.5 Matrices | 28 - 36 |
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 A' | 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) | |