Pre-Algebra Curriculum Crawford Central School District

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1 Concept Competency Resources Larson Pre- Algebra Resource Vocabulary Strategy PA Core Eligible Content PA Core Standards PA Core Standards Scope and Sequence Number System identify numbers as either rational or irrational Holt 2010: Ch 2 & 4; Pearson: Ch 2 & 3; Holt 2012: Ch 3 How do we classify numbers in the real number system? Performance Coach page 23-24; A Million Dollars Task (MDC) Real numbers; rational numbers; irrational numbers; relatively prime N CC E.1 8.NS weeks convert, compare and order real numbers Holt 2010: Ch 2 & 4; Pearson: Ch 2 & 3; Holt 2012: Ch 3 Ch 5 & 9 Real numbers; rational numbers; irrational numbers; relatively prime N.1.1.2; N.1.1.4; N CC E.1, CC E.4 8.NS.1 estimate values of irrational numbers Ch 2 & 3; Holt 2012: Ch 3 Real numbers; rational numbers; irrational numbers; relatively prime N CC E.4 8.NS.2 complete rational number operations Holt 2010: Ch 2; Pearson: Ch 2 & 3; Holt 2012: Ch 1 Ch 5 least common denominator; reciprocal; multiplicative inverses M07.A- N CC E.4 8.NS.2 How do mathematical properites allow us to work with expression and equations in algebra? Buying Chips and Candy Task (MDC)

2 Solving Equations Holt 2010: Ch 1, 2 & 11; Pearson: Ch 6; Holt 2012: Ch 1 & 7 Ch 3 inverse operation; Algebra tiles equation; solution; variable; constant; Distributive Property; like terms; literal equation; term; simplify solve linear equations in onevariable E.3.1.1; E EE weeks state special types of solutions to linear equations Holt 2010: Ch 11; Pearson: Ch 6; Holt 2012: Ch 7 Ch 2 & 3 MDC Lesson Solving Linear Equations in One Variable or Building and Solving Linear Equations E.3.1.1; E EE.7 solve systems of linear equations algebraically (8th grade) Holt 2010: Ch 11; Pearson: Ch 6; Holt 2012: Ch 7 system of equations; solution to a system; elimination method; substitution show more than one way to solving systems at the same time E EE.7 Integer Exponents and Pythagorean Theorem How and when can the Pythagorean Theorem help us to calculate the length of a segment without directly measuring it? evaluate expressions with integer exponents simplify expressions using laws of exponents Ch 1 & 4 Ch 4 Jane's TV MDC Task negative exponent, power of zero product of powers MDC Properties Laws of with the same base, Exponents quotient of powers with the same base, power of a power E E EE weeks 8.EE.1 evaluate square and cube roots rational number; irrational number; perfect square; perfect cube Engage NY E EE.2 write and compare numbers in scientific notation Ch 4 scientific notation; standard notation E.1.1.3; 8.EE.3

3 perform operations with numbers in scientific notation explain a proof of the Pythagorean Theorem and its converse use the Pythagorean Theorem to determine unknown lengths in right apply the Pythagorean Theorem to real-world problems use the Pythagorean Theorem to find the distance between two points in a Pre-Algebra Curriculum Ch 4 Pythagorean Theorem, hypotenuse, legs, right triangle, converse E.1.1.3; G G television screens G distance formula G How do we recognize when it is appropriate to use a linear model to represent a real world situation, and what are the benefits of using a linear model to answer questions about the situation? Performance Coach page EE.4 8.G.6 8.G.7 8.G.7 8.G.8 Functions define a function Holt 2010: Ch 3 & 12; graph a function Holt 2010: Ch 3 & 12; relation; function; domain; range; independent variable; dependent function, linear equation F F CC C.1 8.F weeks CC C.1 8.F.1 compare function in various forms (tables, graphically, algebraically, verbal descriptions) Holt 2010: Ch 3 & 12; table of values, graph F CC C.1 8.F.2 identify if functions are linear Holt 2010: Ch 3 & 12; linear, non-linear F CC C.1 8.F.3

4 write a function from a table, graph or situation Holt 2010: Ch 3 & 12; slope-intercept form F.1.1.2; F CC C.2 8.F.4 describe a functional relationship from a graph or verbal description Holt 2010: Ch 3 & 12; F.1.1.2; F CC C.2 8.F.5 How do we recognize when it is appropriate to use a linear model to represent a real world situation, and what are the benefits of using a linear model to answer questions about the situation? Performance Coach page Graphing Equations (8th grade) calculate the slope of a line on a coordinate plane 2012: slope, rate of change, rise, run, linear equation E CC B weeks graph proportional relationships and compare slopes 2012: E.2.1.1;M08. B-E CC B.2 create an equation using slope-intercept form from a graph 2012: slope-intercept form; y-intercept; point-slope form E CC B.2 solve systems of linear equations graphically 2012: system of equations; solution to a system E solve systems of linear equations for real-world applications 2012: Fencing MDC Task E How can we use tables and graphs to organize and make conclusions with data? Performance Coach

5 Data Analysis create scatter plots Ch 1 scatter plot, x-axis, y-axis S SP weeks determine relationships between two sets of data Ch 1 types of correlation S SP.1 draw a line of best fit on a scatter plot line of best fit; slopeintercept form S SP.2 write an equation for the line of best fit of a scatter plot use linear models to solve problems and make predictions for data apply the concept of correlation to real-world applications graph data in various forms slope-intercept form; y-intercept; point-slope form S linear model S stem-and-leaf; histogram; box-andwhisker plot; circle graph; line graph, bar graph; frequency table; quartiles, median collect two types of data from the same set of people and see if they are S S CC B.2 8.SP.3 8.SP.3 8.SP.4 calculate measures of central tendency mean, median, mode, range, outlier S How do transformations affect the congruence and similarity of images? Performance Coach page Geometry understand the congruence of images to the original after rotations, reflections and translations congruence; rotation, reflection, translation; image G CC A.1 8.G.1, 8.G weeks

6 given two congruent figures, desribe a sequence of transformations verifying the congruence G CC A.1 8.G.1, 8.G.2 describe the effect of transformations on twodimensional figures in the coordinate plane Representing and Combining Transformations MDC Lesson G CC A.1 8.G.3 understand and describe similarity using transformations dilation; similarity; corresponding angles; corresponding sides G.1.1.1; G CC A.1 8.G.4 use the formulas for volume of space figures to solve mathematical problems Ch 10 volume, cone, cylinder, sphere, rectangular prism, cube, pi, radius, diameter Performance Coach pg 260 G CC A.3 8.G.9

Students will understand 1. use numerical bases and the laws of exponents

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