integrated math
Int. 1 is an integrated (algebra, geometry, statistics) course and. Int. 2 is an integrated (algebra, geometry, trigonometry, probability) course.
In high school, these are 9th and 10th grade level math courses.
Overview of Integrated 1 from the e-book:
It aims to deepen and extend student understanding built in previous courses by focusing on developing fluency with solving linear equations, inequalities, and systems. These skills are extended to solving simple exponential equations, exploring linear and exponential functions graphically, numerically, symbolically, and as sequences, and by using regression techniques to analyze the fit of models to distributions of data.
On a daily basis, students in Core Connections Integrated I 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 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 are:
Representations of linear, quadratic, and exponential relationships using graphs, tables, equations, and contexts.
Symbolic manipulation of expressions in order to solve problems, such as factoring, distributing, multiplying polynomials, expanding exponential expressions, etc.
Analysis of the slope of a line multiple ways, including graphically, numerically, contextually (as a rate of change), and algebraically.
Solving equations and inequalities using a variety of strategies, including rewriting (such as factoring, distributing, or completing the square), undoing (such as extracting the square root or subtracting a term from both sides of an equation), and looking inside (such as determining the possible values of the argument of an absolute value expression).
Solving systems of two equations and inequalities with two variables using a variety of strategies, both graphically and algebraically.
Use of rigid transformations (reflection, rotation, translation) and symmetry to demonstrate congruence and develop triangle congruence theorems.
Using coordinates to prove geometric theorems.
Geometric constructions (with compass and straightedge).
Simple geometric proofs (investigate patterns to make conjectures, and formally prove them).
Representations of arithmetic and geometric sequences, including using tables, graphs, and explicit or recursive formulas.
Use of exponential models to solve problems, and to compare to linear models.
Use of function notation.
Statistical analysis of two-variable data, including determining regression lines, correlation coefficients, and creating residual plots.
The differences between association and causation, and interpretation of correlation in context.
Comparison of distributions of one-variable data.
https://ebooks.cpm.org/bookdb.php?title=cc4&name=intro.oview&type=sectionoview
Overview of Integrated 2 from the e-book:
Core Connections Integrated II is the second course in a five-year sequence of college preparatory mathematics courses that starts with Core Connections Integrated I and continues through Calculus Third Edition. 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- and three-dimensional objects, work within the rectangular coordinate system to verify geometric relationships and prove basic theorems about circles. Students also use the language of set theory to compute and interpret probabilities for compound events.
On a daily basis, students in Core Connections Integrated II 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 between procedural fluency (algorithms and basic skills), deep conceptual understanding, strategic competence (problem solving), and adaptive reasoning (extension and transference). The lessons in the course meet all of the content standards, including the “plus” 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 are:
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).
Theorems about circles, including arc lengths and areas of sectors.
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).
Investigation of a variety of functions including square root, cube root, absolute value, piecewise-defined, step, and simple inverse functions.
Representations of quadratic functions with a graphs, tables, equations, and contexts.
Solve quadratic equations using a variety of methods such as the zero product property, completing the square, and the quadratic formula.
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.
https://ebooks.cpm.org/bookdb.php?title=int2&name=intro.oview&type=sectionoview