Bellwood-Antis School District Curriculum Revised on 11/08/12

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1 Course: Alg I Grade Level(s): 8 Bellwood-Antis School District Curriculum Revised on 11/08/12 Month Duration Common Core Standards/Anchors Content Assessment Instructional Activities Pre-Requisite Skills Resources Aug-Sept Sept I: 1 4 days I: 2 4 days M08.B-E Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive number. Evaluate square roots of perfect squares (up to and including 12^2) and cube roots of perfect cubes (up to and including 5^3) without a calculator Example: If x^2 = 25, then x=+/- square root of 25 M08.A-N Determine whether a number is rational or irrational. For rational numbers, show that the decimal expansion terminates or repeats (limit repeating decimals to thousandths). M08.A-N Convert a terminating or repeating decimal into a rational number (limit repeating decimals to thousandths). Unit I: Expressions and Equations Chap.1: The Language of Algebra A: Variables and Expressions B: Order of Operations C: Open Sentences D: Identity and Equality Properties E: The Distributive Property F: Commutative and Associative Properties G: Logical Reasoning H: Graphs and Functions I: Statistics: Analyzing Data by Using Tables Chap. 2: Real Numbers A: Rational Numbers on the Number Line B: Adding & Subtracting Rational Numbers C: Multiplying Rational Numbers D Dividing Rational Numbers E: Statistics: Displaying & Analyzing Data F: Probability: Simple Probability & Odds G: Square Roots and Real Numbers Includes a minimum of 10 grades per marking period from any of the following: listening, and thinking. Suggested strategies will include but are not limited to the following: Warm-ups, Do Now and/or Ticket Out the Door Word Wall Activities Collins Writing Type 1 and/or Type 2

2 M0.B-F Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch or determine a graph that exhibits the qualitative features of a function that has been described verbally. Sept-Oct I: 3 21 days M0.B-E Write and identify linear equations in one variable with one solution, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms x=a, a=a, or a=b results (where a and b are different numbers). Chap. 3: Solving Linear Equations A: Writing Equations B: Solving Equations by Using Addition and Subtraction C Solving Equations by Using Multiplication and Division D: Solving Multi-Step Equations F: Solving Equations with the Variable on Both Sides G: Ratios and Proportions H: Percent of Change I: Solving Equations and Formulas J: Weighted Averages Door

3 3 days Unit I Benchmark Test Quarterly Benchmark Assessment 32 days total time Oct-Nov- Dec Nov-Dec- Jan II:4 16 days II:5 16 M0.C-G Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures, using coordinates. M08.B-E Use similar right triangles to show and explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane. M0.B-E Derive the equation y=mx for a line through the origin and the equation y=mx+b for a line intercepting the vertical axis at b. M0.8.B-E Solve real-world and mathematical leading to two linear equations in two variables. Example: Unit II Chap.4: Graphing Relations and functions A: The Coordinate Plane B: Transformations on the Coordinate Plane C: Relations D: Equations as Relations E: Graphing Linear Equations F: Functions G: Arithmetic Sequences H: Writing equations from Patterns Chap. 5: Analyzing Linear Equations A: Slope B: Slope and Direct Variation C: Slope-Intercept form D: Writing Equations in Slope- Intercept form E: Writing Equations in Point- Slope form F: Geometry: Parallel and Perpendicular lines G: Statistics: Scatter Plots and Lines of fit Door

4 Jan-Feb II:6 14 Given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. M08.B-F Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function for a description of a relationship or from two (x, y) values, including reading these from a table or graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models and in term of its graph or a table of values. Chap. 6: Solving Linear Inequalities A: Solving Inequalities by Addition and Subtraction B: Solving Inequalities by Multiplication and Division C: Solving Multi-Step Inequalities D: Solving Compound Inequalities E: Solving Open Sentences Involving Absolute Value F: Graphing Inequalities in Two Variables Door Bnmk Test 3 days M08.D-S For scatter plots that suggest a linear association, identify a line of best fit by judging the closeness of data points to the line. Unit II Benchmark Test Quarterly Benchmark Assessment 49 Total time M08.B-F Interpret the equation y=mx+b as defining a linear function whose graph is a straight line; give examples of functions that are not linear. M08.D-S Use the equation of a linear model to solve

5 Jan-Feb Jan-Feb Feb-Mar V:13 8 V:14 8 IV: Total in the context of bivariate measurement data, interpreting the slope and intersect. Example: In a linear model for a biology experiment, interpret a slope of 1.5cm/hr. as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. M08.C-G Given two congruent figures, describe a sequence of transformations that exhibits the congruence between them. M08.C-G Given two similar twodimensional figures, describe a sequence of transformations that exhibits the similarity between them. M08.C-G Apply the converse of the Pythagorean theorem to show a triangle is a right triangle. M08.C-G Apply the Pythagorean theorem to determine unknown side lengths in Unit V Chap. 13: Statistics C: Histograms D: Measures of Variation E: Box- and- Whisker plots Chap. 14: Probability A: Counting Outcomes B: Permutations and Combinations C: Probability of Compound Events D: Probability Simulations Unit IV Chap. 11: Radical and Rational Functions D: The Pythagorean Theorem F: Similar Triangles Door

6 Sep-Mar 14 days right triangles in two and three dimensions. (Figures provided for in three dimensions will be consistent with Eligible Content in grade 8 and below.) M08.C-G Apply the Pythagorean theorem to find the distance between two points in a coordinate system. M08.C-G Apply formulas for the volumes of cones, cylinders, and spheres to solve real-world and mathematical. Formulas will be provided. M08.B-E Perform operations with numbers expressed with scientific notation, including where both decimal and scientific notation are used. Express answers in scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology (e.g., interpret 4.7EE9 displayed on a calculator as 4.7x10^9). M08.B-E PSSA Preparation & Review A variety of teacher compiled and constructed materials to review the standards and anchors. Door

7 Sept-Mar Estimate very large or very small quantities by using numbers expressed in the form of a single digit times an integer power of 10, and express how many times larger or smaller one number is than another. M08.B-E Use square root and cube root symbols to represent solutions to equations of the form x^2 = p and x^3 = p, where p is a positive number. Evaluate square roots of perfect squares (up to and including 12^2) and cube roots of perfect cubes (up to and including 5^3) without a calculator Example: If x^2 = 25, then x=+/- square root of 25 PSSA Preparation & Review A variety of teacher compiled and constructed materials to review the standards and anchors. Door Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible associations between the two variables. Example: Given data on whether students have a curfew on school nights and whether they have assigned chores at home, is there evidence that those who have a curfew also tend to have chores?

8 Sept-Mar PSSA Preparation & Review A variety of teacher compiled and constructed materials to review the standards and anchors. Door 3 days Benchmark III Test Quarterly Benchmark Assessment Testing Total PSSA Testing Window

9 Apr-May- Jun II:7 10 III:8 20 Unit II (Continued) Chap. 7: Solving Systems of Linear Equations and Inequalities A: Graphing Systems of Equations B: Substitution C: Elimination Using Addition and Subtraction D: Elimination Using Multiplication E: Graphing Systems of Inequalities Unit III Chap. 8: Polynomials and Nonlinear Functions A: Multiplying Monomials B: Dividing Monomials C: Scientific Notation D: Polynomials E: Adding and Subtracting Polynomials F: Multiplying Polynomials by a Monomial G: Multiplying Polynomials H: Special Products Door

10 III:9 12 Chap. 9: Factoring A: Factors and Greatest Common Factors B: Factoring Using the Distributive Property C: Factoring Trinomials: x 2 + bx + c D: Factoring Trinomials: ax 2 + bx + c E: Factoring Differences of Squares F: Perfect Squares and Factoring Door IV:11 8 Unit IV Chap. 11: Radical and Rational Functions G: Trigonometric Ratios Total Time 50