= = The number system. Module. Glossary Math Tools... 33

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2 - > + > < - %. < + a = - = = b in. F - - Module The number sstem Lesson Rational and Irrational Numbers NS. Lesson ompare and Order Numbers NS., 8.NS. Lesson Estimate the Value of Epressions NS. Lesson Eponents EE. Lesson Square Roots and ube Roots NS., 8.EE. Lesson Scientific Notation EE. Lesson 7 Solve Problems Using Scientific Notation EE., 8.EE. Glossar Math Tools ommon ore State Standards

3 - in. + > < = cm a - +. in. = = b ft < rational and irrational numbers cm = > ft Ke Words irrational number rational number % A rational number is a number that can be epressed as a ratio in the form a, where a and b are both integers and b is not zero.,., %, and b are eamples of rational numbers. Numbers that cannot be epressed as a ratio of two integers are called irrational numbers. p and are eamples of irrational numbers. The decimal epansion of a rational number terminates in zeros or in a repeated pattern. When a decimal epansion repeats a pattern, draw a line over the repeating portion. For eample,... The decimal epansion of an irrational number does not terminate and does not repeat. Eample Find the decimal epansion of 9 8. Divide the numerator b the denominator The decimal epansion terminates APPLY Provide an eample of a rational number in fraction form along with its decimal epansion.

4 - > + > < - %. < + a = - = = b in. F - - Guided Practice Find the decimal epansion of. Divide the numerator b the denominator. Step Divide b using long division... Step Recognize a repeating pattern. Rewrite the decimal epansion.. RememBeR The decimal epansion of a rational number will terminate in zeros or in a repeating pattern. RememBeR A repeating pattern is denoted with a line over the repeating portion of the decimal. Is.98 a rational number? Step Decide if the decimal epansion terminates and if it repeats..98 does / does not (circle one) terminate..98 does / does not (circle one) have repeating patterns. Step Determine if the number is rational or irrational..98 does not and does not, so it is a /an.98 is. number. THINK The decimal has no repeating digits.

5 . in. - in.. < = = = > = -... ft Lesson : Rational and Irrational Numbers independent Practice > = cm %. What is a rational number?. What is an irrational number?. What are the two possibilities for the decimal epansion of a rational number? alculate the decimal epansion of each number. Indicate repeating decimals with the correct notation. Ask Yourself How do ou know if a decimal is rational or irrational? How do ou change a fraction to a decimal? - + = < ft > lassif each number as rational or irrational..... Solve % 9.. Ian and seven of his friends earn a total of $9 shoveling snow from all of the drivewas on their block. The split the mone equall 8 was. Epress Ian s share, 9, as a decimal and round to the nearest cent. 8

6 - - + = > + > % - < = - = in. < Epress each rational number in decimal form. - The Number Sstem % Eplain wh each of the following is a rational number Solve each problem.. Lnnette earns a total of $7 for 7 hours of work. alculate the value of 7 to decimal places to determine Lnnette s hourl wage. 7 dollars. David divides a -mile drive into equal-length segments. Epress the length of each segment as a decimal. miles 7

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8 - > + > < - %. < + a = - = = b in. F - - Module Epressions and Equations Lesson Slope EE., 8.EE. Lesson Proportional Relationships EE. Lesson Linear Equations and Graphs EE. Lesson Slope as Rate of hange EE., 8.EE. Lesson Solve Linear Equations in One Variable EE.7.a, 8.EE.7.b Lesson Pairs of Linear Equations EE.8 Lesson 7 Use Graphs to Solve Sstems EE.8.a, 8.EE.8.b ommon ore State Standards Lesson 8 Use Substitution to Solve Sstems EE.8.a, 8.EE.8.b, 8.EE.8.c Lesson 9 Use Elimination to Solve Sstems EE.8.a, 8.EE.8.b, 8.EE.8.c Lesson Use Sstems to Solve Problems EE.8.c Glossar Math Tools

9 - in. + > < = cm -. = a = < + b Slope = > ft Ke Words rise run slope % The slope of a line is a measure of its steepness. For an two points on a line, the rise is the vertical distance between the two points and the run is the horizontal distance. The slope, m, between an two points on a line (, ) and (, ) is given b the formula: m rise run Lines with a positive slope slant upward as the move to the right. Lines with a negative slope slant downward. Horizontal lines have a slope of. The slope of vertical line is undefined. (, ) run (, ) rise Eample alculate the slope of the line through points A and B. A (, ) 7 B (, ) Determine the coordinates of the points. Point A has coordinates (, ). Point B has coordinates (, ). Appl the slope formula. m () m The slope of the line is. DRAW Sketch a line with a zero slope on a pair of coordinate aes.

10 - > + > < - %. < + a = - = = b in. F - - Guided Practice What is the slope of the line shown below? D Determine the coordinates of two points on the line and calculate the slope. Step Find the coordinates of points and D. Step The coordinates of point are. The coordinates of point D are. Appl the formula for the slope of a line between two points. THINK Point is units to the left of the origin. Point D is units to the right of the origin and unit up. The formula for the slope is m. For points and D, m. The slope of the line is. Remember The slope is given b rise run.

11 in. < Lesson : Slope - in. - =.. + > = = -. ft Independent Practice. What does the slope of a line measure? > = cm %. Describe how to calculate the slope of a line when the coordinates of two points are given. lassif the slope of each line shown below as positive, negative, zero, or undefined. Ask Yourself How do I subtract a negative number? - + = < ft > Line D Line Line B Line A. Line A:. Line B:. Line :. Line D: alculate the slope of the line through each pair of points. 7. (, ), (9, ) 8. (, ), (, ) slope slope 9. (, ), (, 8). (7, ), (, ) slope slope

12 - - + = > + > % - < = alculate the slope of each line. - = in. < Epressions and Equations. Line through (, 9) and (, ). Line through (, 8) and (, 8) slope slope slope slope Solve each problem.. A line with slope passes through the point (, ). Use the 8 definition of slope to find another point on the same line.. A line with slope. passes through the point (, ). Use the definition of slope to find another point on the same line. 7. Julia plots the points (, ), (, ), and (8, ) on a coordinate grid. Do all three points lie on the same line? Eplain our reasoning. 7

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14 - > + > < - %. < + a = - = = b in. F - - Module Functions, Statistics, and Probabilit Lesson Introduction to Functions F., 8.F. Lesson Interpret Linear Functions F., 8.F. Lesson Use Linear Functions to Solve Problems F. Lesson Use Graphs to Describe Relationships F. Lesson ompare Properties of Functions EE., 8.F. Lesson Scatter Plots SP., 8.SP. Lesson 7 Trend Lines SP., 8.SP. Lesson 8 Interpret Linear Models SP. Lesson 9 Patterns in Data SP. Glossar Math Tools ommon ore State Standards

15 - in. + > < = cm -. = a = < + b Introduction to Functions = > ft Ke Words function linear function nonlinear function % A function is a rule that assigns to each input eactl one output. In a function, the value of the input determines the value of the output. A rule that assigns more than one output to an input value is not a function. Functions can be represented as a set of ordered pairs, as a table of values, as an equation, as a verbal description, or as a graph. Since ever input value can have onl one output value, the graph of a function cannot intersect an -coordinate at more than one point. An equation of the form m b represents a linear function. The graph of a linear function is a straight line. The slope of the line, given b m in the equation, represents the rate of change of the function. A nonlinear function has an equation that cannot be put in m b form. The graph of a non-linear function is not a straight line. Eample Does the table of values represent a function? Is it linear? 9 Each -value corresponds to onl one -value, so the relation is a function. Graph the relationship. The table gives four points (, ), (, ), (, ), (9, ) The graph is a straight line. The table represents a linear function. LASSIFY Is a linear function? Wh or wh not?

16 - > + > < - %. < + a = - = = b in. F - - Guided Practice Does the set of ordered pairs below represent a function? Is it linear? {(, ), (, ), (, ), (, 9)} Step ompare the inputs and outputs. Ever input value has output. The set of ordered pairs is a. THINK No input values are repeated. Step Plot the coordinate pairs. The points straight line. The relationship is not a The set of ordered pairs represents a function. Does the equation represent a linear or nonlinear function? be joined b a function Step Solve the equation for. Subtract from both sides. 8 Divide both sides b. Step Decide if the function is linear. 8 is in m b form. The equation is a function. The equation represents a function. Remember A linear function can be written in m b form.

17 in. - in. < Lesson : Introduction to Functions - =.. + > = = -. ft Independent Practice. What is a function? > = cm %. Describe two characteristics of a linear function. Determine if each set of ordered pairs represents a function.. (7, ), (, ), (, ), (, 8). (, ), (, ), (, ), (, ). (, ), (, ), (, ), (, ). (, ), (, ), (, ), (, ) Determine if each graph represents a function Ask Yourself How can I tell if a relation is a function from its graph? - + = < ft > Function? Function?

18 - - + = > + > % - < = - = in. < Determine if each equation represents a linear function. Functions, Statistics, and Probabilit 9. 7 Linear function?. Linear function?. 9 Linear function?. Linear function? Graph the table or set of ordered pairs. Determine if the relationship is a linear function. (You can use the grid below for both graphs.). Linear function?. (, ), (, ), (, ), (, ) Linear function? Solve.. A relation between two variables consists of ordered pairs. (, 8) (, 7) (, ) (a, b) a. hoose values of a and b that make the relation a linear function. a b b. hoose values of a and b that make the relation a nonlinear function. a b c. hoose values of a and b that make the relation not a function. a b 7

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20 > + > < - %. < + a = - = = b in. F Module Geometr ommon ore State Standards Lesson ongruence Transformations G..a, 8.G..b, 8.G..c, 8.G., 8.G. Lesson Dilations G., 8.G. Lesson Similar Triangles G., 8.G. Lesson Interior and Eterior Angles G. Lesson Parallel Lines and Transversals G. Lesson The Pthagorean Theorem G., 8.G.7 Lesson 7 Distance G.8 Lesson 8 Appl the Pthagorean Theorem G.7, 8.G.8 Lesson 9 Volume G.9 Glossar Math Tools

21 - in. + > < = cm a -. + b in. = = congruence Transformations ft < = > ft Ke Words congruence transformation congruent reflection rotation translation % A congruence transformation moves a figure in the coordinate plane to create another figure with the same size and shape. Angles are taken to angles of the same measure. Line segments are taken to line segments of the same length. The congruence transformations are translations (slides), reflections (flips), and rotations (spins). Two figures are congruent if the second can be obtained from the first b a sequence of rotations, reflections, and translations. ongruent figures have the same size and shape. Eample Translate the line segment 7 units down and units to the left. The endpoints of the line segment are (, 9) and (, ). To shift down, subtract 7 from the -coordinate. To shift left, subtract from the -coordinate. (, 9) (, 9 7) (, ) (, ) (, 7) (, ) The endpoints of the segment after translation are (, ) and (, ). Translate the endpoints and draw the new line segment. (, 9) (, ) 7 (, ) (, 9) (, ) 7 (, ) DESRIBE What happens to the coordinates of a point that is reflected across the -ais?

22 - > + > < - %. < + a = - = = b in. F - - Guided Practice Triangle AB has vertices (, 9), (9, 7), and (, ). Rotate n AB 8 around the origin. Then reflect it across the -ais. What are the coordinates of the final image? Step Rotate the figure 8º to create n A9B99. The vertices of the triangle are (, 9), (9, 7), and (, ). After rotating 8º, the new vertices of the triangle are:,, and. Plot the rotated triangle on the grid below and label the vertices A9, B9, and 9. REmEmBER To rotate 8º around the origin, switch the sign of the and coordinates. Step Reflect the figure across the -ais to create n AB. After rotation, the triangle has vertices (, 9), (9, 7), and (, ). After reflecting the object across the -ais, the new vertices of the triangle are:,, and. REmEmBER To reflect an object across the -ais, change the sign of the -coordinate. Plot the reflected triangle on the grid and label the vertices A, B, and. The resulting triangle is shown in Step. Its coordinates are,, and. A A 9 B 8 7 B B A

23 . in. - in.. < Lesson : ongruence Transformations. - =. + > = = -... ft independent Practice. What does it mean for two figures to be congruent? > = cm %. What is a translation? Perform the given transformation on each figure. Sketch the result on the provided aes. Ask Yourself Should a figure that has been translated, rotated, or reflected be congruent to the original figure? - + = < ft >. Rotate the figure 8º around the origin. (, ) (, ) (, ). Translate the figure units down and units to the left

24 - - + = > + > % - < = - = in. < An interior decorator uses a coordinate grid to design the laout of a room. Each unit on the grid represents foot. The rectangle to the right represents the location of a desk in the room. Sketch the result on the grid if the desk is moved feet to the right and feet up (, ) (, ) Geometr (, ) (, ) Solve each problem.. A line segment has endpoints (8, ) and (, ). What are the coordinates of the endpoints after the line segment is reflected across the -ais and translated 7 units down in that order? 7. The point (, ) is a verte of a triangle. What are the new coordinates of the verte if the triangle is rotated 8º around the origin, then translated units up and units to the left, in that order? 8. Rectangles and show the location of a car before and after it is moved. Each unit on the grid represents two meters. Describe the translation that moves the car. 8 8 N W E S 8 8 7