ALGEBRA 1 AND THE COMMON CORE STANDARDS

WHAT ARE THE COMMON CORE STATESTANDARDS?

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 8th Grade Content Standards

8TH GRADE COMMON CORE STATESTANDARDS FOR MATHEMATICS

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)

WHAT’S STILL THERE 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

WHAT’S NEW

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

WHAT’S NEW

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

WHAT’S NEW

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

MOVED OUT OF ALGEBRA 1:

To 7th grade: Direct Variation

To Geometry: Parallel and Perpendicular Lines

To 4th math course: Matrices

MOVED OUT OF ALGEBRA 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

WHAT’S STILL THERE: 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

WHAT’S NEW:

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

WHAT’S NEW:

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