A LGEBRA 1 AND THE C OMMON C ORE S TANDARDS

W HAT ARE THE C OMMON C ORE S TATE S TANDARDS ? The standards are... aligned with college and work expectations. focused and coherent. rigorous in content and application of knowledge through high-order thinking skills. built upon the strengths and lessons of current state standards. internationally benchmarked so that all students are prepared to succeed in our global economy and society. based on evidence and research. state led – coordinated by National Governors Association Center for Best Practices and the Council of Chief State School Officers.

Overview of 8 th Grade Content Standards

8 TH G RADE C OMMON C ORE S TATE S TANDARDS FOR M ATHEMATICS What’s Moved Effect of changing one or more dimensions on perimeter, area, or volume (to Geometry) Indirect measurement (to Geometry) Misuses of data (to AP Stats) Linear Inequalities (to Algebra I)

W HAT ’ S S TILL T HERE Irrational Numbers – approximate, compare and order, evaluate square roots and cube roots of perfect squares and cubes Pythagorean Theorem Dilations Collect, organize, and display data (bivariate only) Describing correlation (positive or negative association) Informally fit a line to a set of data; interpret slope and yintercept; solve problems; make predictions Four forms of functions – graphical, verbal, tabular, algebraic Relations and functions Linear vs. non-linear functions Linear function y = mx + b Find the rate of change (slope) and initial value (yintercept) from any form; write the equation; interpret constants in context Solving one-variable equations

W HAT ’ S N EW Moved from 6th grade: Express numbers in scientific notation and convert to standard form and vice versa Interpret scientific notation on the calculator Translations, rotations, reflections Moved from 7th grade: Volume of cylinders Outliers Moved from AP Statistics: Association between categorical variables Clusters in data Other Compare numbers expressed as powers of ten Express congruence and similarity between two figures as a series of transformations

W HAT ’ S N EW Moved from Algebra I: Negative exponents Operations with scientific notation Use the Pythagorean Theorem to find the distance between two points Describing a set of data as having a linear or nonlinear association Solve a system of linear equations graphically and algebraically Proportional relationships (direct variation) Geometric connection to constant rate of change (similar triangles) Sketch a graph that exhibits the features of a function described verbally Describe features of a functional relationship between two quantities by analyzing the graph

W HAT ’ S N EW Moved from Geometry: Volume of cones & spheres Understand the properties of congruence motions Informally prove angle sum and exterior angle theorems and angle pair theorems when two parallel lines are cut by a transversal Prove the Pythagorean Theorem and its converse

Overview of Algebra 1 Content Standards

M OVED O UT OF A LGEBRA 1: To 7th grade: Direct Variation To Geometry: Parallel and Perpendicular Lines To 4th math course: Matrices

M OVED O UT OF A LGEBRA 1: To 8th grade: Negative exponents Operations with scientific notation Use the Pythagorean Theorem to find the distance between two points Describing a set of data as having a linear or nonlinear association Solve a system of linear equations graphically and algebraically Proportional relationships (direct variation) Geometric connection to constant rate of change (similar triangles) Sketch a graph that exhibits the features of a function described verbally Describe features of a functional relationship between two quantities by analyzing the graph

W HAT ’ S S TILL T HERE : Add, subtract, and multiply polynomials (linear and quadratic) Factoring Arithmetic and geometric sequences – both recursive and explicit forms; recursive function notation Linear, quadratic, and exponential models; interpret in context Calculate correlation coefficient & interpret Solve one-variable equations and inequalities – linear; exponential with integer inputs Solve quadratic equations with real solutions – using square roots, factoring Functions – linear, exponential; Function notation Arithmetic and geometric sequences Applications of systems of linear equations Linear inequalities System of linear inequalities Graph linear, exponential, and quadratic functions

W HAT ’ S N EW : More emphasis on key features of functions From Middle School: Univariate data From Algebra II: Rational exponents Properties of irrational numbers Derive the formula for the sum of a finite geometric series and use it to solve problems (e.g. calculate mortgage payments) Residuals; residual plots to assess goodness-of-fit

W HAT ’ S N EW : From Algebra II (Cont.) Solve quadratic equations with real solutions – by completing the square and the quadratic formula Systems of linear and quadratic equations Complete the square to find the vertex of a quadratic function Rewrite exponential expressions to find rate of growth or decay Graph absolute value, step, and piecewise-defined functions From AP Statistics: Distinguish between correlation and causation Categorical data