Integrated Math 2
Integrated Math 2 is the second course in a three-year sequence of college preparatory mathematics courses leading to Pre-Calculus or AP Statistics. It aims to formalize and extend the geometry that students have learned in previous courses. It does this by focusing on establishing triangle congruence criteria using rigid motions and formal constructions and building a formal understanding of similarity based on dilations and proportional reasoning. It also helps students develop the concepts of formal proof, explore the properties of two-dimensional objects, and work within the rectangular coordinate system to verify geometric relationships. Students also use the language of set theory to compute and interpret probabilities for compound events.
On a daily basis, students in Integrated Math 2 use problem-solving strategies, questioning, investigating, analyzing critically, gathering and constructing evidence, and communicating rigorous arguments justifying their thinking. 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:
- Geometric transformations (reflection, rotation, translation, and dilation) and symmetry.
- Relationships between figures (such as similarity and congruence) in terms of rigid motions and similarity transformations.
- Properties of plane figures.
- Proofs of geometric theorems (investigate patterns to make conjectures, and formally prove them).
- Modeling with geometry.
- Measurements of plane figures (such as area, perimeter, and angle measure).
- Measurements of three-dimensional solids (such as volume and surface area).
- Tools for analyzing and measuring right triangles, general triangles, and complex shapes (such as the Pythagorean Theorem, and trigonometric ratios).
- Probability (independence and conditional probability, compound events, expected value, and permutations and combinations).
- Representations of quadratic functions with a graphs, tables, equations, and contexts.
- Symbolic manipulation of expressions in order to solve problems, such as factoring, distributing, multiplying polynomials, expanding exponential expressions, etc.
- Using algebra to write and solve equations arising from geometric situations.
- Investigation of a variety of functions including square root, cube root, absolute value, piecewise-defined, step, and simple inverse functions.