Integrated Math 3
Integrated Math 3 is the third course in a three-year sequence of college preparatory mathematics courses leading to Pre-Calculus or AP Statistics. It aims to apply and extend what students have learned in previous courses by focusing on exploring the properties of three-dimensional objects, proving basic theorems about circles, finding connections between multiple representations of functions, transformations of different function families, solving systems of equations and inequalities, and understanding the role of randomness and the normal distribution in drawing statistical conclusions.
On a daily basis, students in Integrated Math 3 use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. Under teacher guidance, students learn in collaboration with others while sharing information, expertise, and ideas.
The course is well balanced among procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (extension and application). The lessons in the course sequence meet all of the content standards of Appendix A of the Common Core State Standards for Mathematics. The course embeds the CCSS Standards for Mathematical Practice as an integral part of the lessons in the course.
Key concepts addressed in this course include:
- Theorems about circles, including arc lengths and areas of sectors.
- Visualize, express, interpret and describe, and graph functions (and their inverses, in many cases). Given a graph, students will be able to represent the function with an equation, and vice-versa, and transform the graph, including the following function families:
- absolute value
- square root
- Use of variables and functions to represent relationships given in tables, graphs, situations, and geometric diagrams, and recognize the connections among these multiple representations.
- Application of multiple algebraic representations to model and solve problems presented as real world situations or simulations.
- Solving linear or quadratic equations in one variable, systems of equations in two variables, and linear systems of equations in three or more variables.
- Use of algebra to rewrite complicated algebraic expressions and equations in more useful forms.
- Applications of the Law of Sines and Law of Cosines.
- Concepts of randomness and bias in survey design and interpretation of the results.
- Use of a normal distribution to model outcomes and to make inferences as appropriate.
- Use of computers to simulate and determine complex probabilities.
- Use of margin of error and sample-to-sample variability to evaluate statistical decisions