In course 1 instructional time should focus on four critical areas: (1) connecting ratio and rate to whole number multiplication and division and using concepts of ratio and rate to solve problems; (2) completing understanding of division of fractions and extending the notion of number to the system of rational numbers, which includes negative numbers; (3) writing, interpreting, and using expressions and equations; and (4) developing understanding of statistical thinking.
This math course will prepare the student for the Pre- Algebra course. Students will build on their knowledge of mental math and estimation strategies as they compute with decimals, fractions, integers, and metric units. They will use algebraic properties and number sense to compare, order, and compute with rational numbers. Order of operations will be extended to simplify expressions with exponents.
Students will solve simple one-step equations with all rational numbers. Ratio, proportion, and percent are applied to real-world problems. They will extend their work in 2-dimensional geometry by learning properties of lines, angles, and polygons, and by finding area and perimeter of polygons. The 3-dimensional geometry will include recognizing solid shapes and their parts, knowing their properties, and finding surface area and volume. The data analysis and probability units will now include more analysis of statistics, charts, and graphs. Throughout the course, technology, interdisciplinary activities, and global perspectives will be integrated.
This one-year course has been designed to equip students with the skills needed for Foundations of Algebra. Students will solidify their computation skills with rational numbers and integers, applying both number sets to algebraic and real-world problems. In addition to satisfying grade level requirements**, students will be expected to write and solve one-step equations with rational coefficients, solve and graph one-step inequalities with integer and rational coefficients, transform geometric figures in the coordinate plane, and simplify algebraic expressions using exponent rules. Using algebraic properties, students will solve equations and inequalities in one variable. They will explore transformational geometry and gain an understanding of how the three basic types of transformations may be used individually as well as in conjunction with one another.
Students will extend their work in 2-dimensional geometry by finding areas of more complex polygons (beyond the basic quadrilaterals and triangles). Students will identify figures produced from slicing a 3-dimensional figure and calculate areas of those shapes. The statistics and probability unit has been expanded to include more work with random sampling, comparison of theoretical and experimental data, and analysis of various statistics in real-world situations. Throughout the course, technology, interdisciplinary activities, media literacy and global perspectives will be integrated.
This course represents the first part of a two-year course. It has been designed to offer a rigorous and comprehensive foundation that addresses the newly expanded core content standards for Algebra 1. It will also provide students the opportunity to truly master algebraic and mathematics skills that will lead to greater achievement in subsequent courses. Students will create and use numerical, algebraic, graphical, and verbal representations and analyze sophisticated patterns, relations, and functions. They will represent linear functions numerically, algebraically, graphically and verbally and work with and interpret these representations. They will deepen their understanding of relations and functions and expand their repertoire in working with them.
Students will develop insight and understanding of the algebraic properties that govern the manipulation of symbols in expressions, equations, and inequalities. Functions will be introduced as mathematical modeling tools providing students with a versatile and powerful means for analyzing and solving complex, multi-step, real world problems. Students will also learn the appropriate use of technology, such as graphing calculators and spreadsheet utilities to model and analyze a wide range of mathematical relationships.