Course Description
Algebra I with Probability is a newly-designed course which builds upon algebraic concepts studied in the middle grades. It provides students with the necessary knowledge of algebra and probability for use in everyday life and in the subsequent study of mathematics. This is one of three courses required for all students. Students can obtain the essential content from this course either by taking the course after completing Geometry with Data Analysis in Grade 9 or by completing the middle school accelerated pathway. Alternatively, students who did not take the accelerated pathway in middle school may choose to accelerate in high school by taking Algebra I with Probability in Grade 9 along with Geometry with Data Analysis.
If students need additional support while taking Algebra I with Probability, schools are encouraged to offer a concurrent “lab course” to meet their specific needs. The lab course might review prior knowledge needed for upcoming lessons, reinforce content from previous lessons, or preview upcoming content to ensure that students can fully participate in the required class. Since the lab course does not cover additional mathematical standards, students can receive only an elective credit for each lab course, not a mathematics credit. See further details on the lab courses in the High School Overview. School systems will not offer Algebra I with Probability as “A” and “B” courses in which the content is spread over two courses.
Algebra I with Probability builds essential concepts necessary for students to meet their postsecondary goals (whether they pursue additional study or enter the workforce), to function as effective citizens, and to recognize the wonder, joy, and beauty of mathematics (NCTM, 2018). Algebra is important and useful in most careers. It is one of the most common and malleable types of mathematics, because it is valuable in a range of activities from ordinary decision-making to advanced training in scientific and technological fields. The ability to understand and apply algebraic thinking is a crucial stepping stone on a successful journey in life.
Algebra is a collection of unifying concepts that enable one to solve problems flexibly. The study of algebra is inextricably linked to the study of functions, which are fundamental objects in mathematics that model many life situations involving change. This course provides experiences for students to see how mathematics can be used systematically to represent patterns and relationships among numbers and other objects, analyze change, and model everyday events and problems of life and society.
Algebra I with Probability emphasizes functions including linear (as introduced in Grades 7 and 8), absolute value, quadratic, and exponential; and functions as explicit (relation between input and output) and recursive (relation between successive values). Properties of algebra are applied to convert between forms of expressions and to solve equations (factoring, completing the square, rules of powers, and radicals).
Graphing is an important component of study in Algebra I with Probability. Graphs of equations and inequalities consist of all points (discrete or continuous) whose ordered pairs satisfy the relationship within the domain and range. Students find points of intersection between two graphed functions that correspond to the solutions of the equations of the two functions, and transform graphs of functions (through translation, reflection, rotation, and dilation) by performing operations on the input or output.
Probability is important because it educates one in the logic of uncertainty and randomness, which occur in almost every aspect of daily life. Therefore, studying probability structures will enhance students’ ability to organize information and improve decision-making. The study of probability undergirds the understanding of ratio and proportion in algebra and encourages inferential reasoning about the likelihood of real-life events. Categorical data are represented as marginal and conditional distributions. Parallels are drawn between conditions and events in probability and inputs and outputs of functions.
A focus on mathematical modeling and real-world statistical problem-solving is included across the course; see Appendix E for more information on the modeling cycles for mathematics and statistics. It is essential for students to use technology and other mathematical tools such as graphing calculators, online graphing software, and spreadsheets to explore functions, equations, and probability.
The eight Student Mathematical Practices listed in the chart below represent what students are doing as they learn mathematics. Students should regularly engage in these processes and proficiencies at every level throughout their mathematical studies. Proficiency with these practices is critical in using mathematics, both in the classroom and in everyday life. The Student Mathematical Practices are standards to be incorporated across all grades.
The standards indicating what students should know or be able to do are listed in the right columns of the content area tables. The essential concepts are described in the left columns of the content area tables. In some cases, focus areas are indicated within the tables. Only those focus areas which are appropriate for this course are included.
Statements in bold print indicate the scope of the standard and align the standard to related content in other courses. The full scope of every standard should be addressed during instruction.
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