CCGPS Review Packet Math 8 ~ per unit ~

Transcription

1 CCGPS Review Packet Math 8 ~ per unit ~ Common Core Georgia Performance Standards

2 CCGPS Review Packet Math 8 UNIT 1

3 Geometry Standard: MCC8.G.1 Verify experimentally the properties of rotations, reflections, and translations; a. Lines are taken to lines, and line segments to line segments of the same length. b. Angles are taken to angles of the same measure. c. Parallel lines are taken to parallel lines. Meaningful Vocabulary Transformation: A change in position or size Congruent: Same size and shape Reflection: A transformation that "flips" a figure over a line of reflection. Rotation: A transformation that turns a figure about a fixed point through a given angle and a given direction. Translation: A transformation that slides a figure Rigid: Unchanging; Congruent Graph the triangle ABC at A(-2,3), B(-2,8), and C(-6,3). Translate using (x+10,y-2); then, rotate 90 degrees clockwise about the origin; last, reflect over the y-axis. Label all points appropriately. How does the original figure relate to the transformed figure? Include details about side lengths and angles.

4 Geometry Standard: MCC8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Meaningful Vocabulary Transformation: A change in position or size Congruent: Same size and shape Reflection: A transformation that "flips" a figure over a line of reflection. Rotation: A transformation that turns a figure about a fixed point through a given angle and a given direction. Translation: A transformation that slides a figure Rigid: Unchanging; Congruent Graph triangle XYZ at X(1,5), Y(5,8), and Z(4,3). Reflect it over the x- axis and translate 2 units down. Label all points appropriately. Starting Coordinates: Ending Coordinates: Are the two figures congruent? Explain.

5 Geometry Standard MCC8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them. Meaningful Vocabulary Transformation: A change in position or size Congruent: Same size and shape Reflection: A transformation that "flips" a figure over a line of reflection. Rotation: A transformation that turns a figure about a fixed point through a given angle and a given direction. Translation: A transformation that slides a figure Rigid: Unchanging; Congruent Graph the original figure: A(-2,-8), B(-10,-6) C(-5,3). Graph the transformed figure: A (2,-5), B (10,-3), C (5,6). What transformation(s) are necessary to go from the original figure to the transformed figure? Are the two figures congruent? Explain.

6 Geometry Standard MCC8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. Starting Coordinates: Meaningful Vocabulary Transformation: A change in position or size Congruent: Same size and shape Reflection: A transformation that "flips" a figure over a line of reflection. Rotation: A transformation that turns a figure about a fixed point through a given angle and a given direction. Translation: A transformation that slides a figure Rigid: Unchanging; Congruent Ending Coordinates: X(2,-3), Y(7,-8), Z(5,-4) Rotation of 180 degrees about the origin Starting Coordinates: Ending Coordinates: A(1,4) B(1,1), C(5,3) Translation rule: (x+2, y-8)

7 Geometry Standard MCC8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Meaningful Vocabulary Transformation: A change in position or size Dilation: enlarging or shrinking an image; produces a similar figure Graph A(-6,-2), B(2,8), C(4,-2) and dilate with a scale factor of 1/2. Label all points appropriately. Starting Coordinates: Ending Coordinates: Are the two figures congruent? Explain.

8 Geometry Standard MCC8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Meaningful Vocabulary Congruent: Same size and shape Dilation: enlarging or shrinking an image; produces a similar figure Reflection: A transformation that "flips" a figure over a line of reflection. Rigid: Unchanging; Congruent Rotation: A transformation that turns a figure about a fixed point through a given angle and a given direction. Transformation: A change in position or size Translation: A transformation that slides a figure Graph the original figure: X(-2,-8), Y(-6,-6), Z(-4,4). Graph the transformed figure: X (-1,-4), Y (-3,-3), Z (-2,2). What transformation(s) are necessary to go from the pre-image to the image? Are the two figures similar? Explain.

9 Geometry Standard MCC8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Meaningful Vocabulary Alternate Exterior Angles: a pair of angles on opposite sides of the transversal but outside the parallel lines Alternate Interior Angles: a pair of angles on opposite sides of the transversal but inside the parallel lines Corresponding Angles: angles that are in the same position when parallel lines are cut by a transversal Parallel Lines: lines that are the same distance apart Similar: having the same shape, but not necessarily the same size Supplementary Angles: angles whose sum is 180 degrees Transversal: a lines that cuts across two or more lines Lines m and n are parallel cut by transversal, t. t Lines m and n are parallel cut by transversal, t. t m n m n Name all pairs of corresponding angles. Are they congruent or supplementary? Name all pairs of vertical angles. Are they congruent or supplementary?

10 Geometry Standard MCC8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. Meaningful Vocabulary Angle Sum: the sum of the interior angles in a shape Exterior Angle: an angle formed outside a polygon when one side is extended. Similar: having the same shape, but not necessarily the same size Supplementary Angles: angles whose sum is 180 degrees Transversal: a lines that cuts across two or more lines Given triangle: Given triangle: Angle 1 = 50⁰ Angle 2 = 90⁰ Angle 3 = 40⁰ What does this diagram tell us about the sum of the interior angles of a triangle? What is the value of angle 4 in the diagram?

11 CCGPS Review Packet Math 8 UNIT 2

12 Expressions and Equations Standard MCC8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 x 3-5 = 3-3 = 1/3 3 = 1/27. Meaningful Vocabulary Equivalent: having same value Exponent: the small number used to show the number of times the base is multiplied by itself Integer: positive or negative number or zero (no fractions or decimals) Laws of Exponents: rules used to simplify expressions containing exponents Simplify: to reduce the complexity Simplify using the law of exponents. (Show work here.) Simplify using the law of exponents. (Show work here.) Simplified expression: Simplified expression:

13 Expressions and Equations Standard MCC8.EE.2 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 rational number; evaluate square roots of small perfect squares and cube roots of small perfect cubes; know that the square root of 2 is irrational. Meaningful Vocabulary Cube Root: one of three identical factors of a number Irrational Number: number that cannot be written as a fraction Perfect Cube: a result of multiplying a number by itself 3 times Perfect Square: a result of multiplying a number by itself 2 times Rational Number: a number that can be written as a fraction Square Root: one of two identical factors of a number Evaluate the square roots. Evaluate the cube roots. Evaluate the perfect squares. Evaluate the perfect cubes.

14 Expressions and Equations Standard MCC8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is more than the other. For example, estimate the population of the United States as 3 x 10 8 and the population of the world as 7 x 10 9, and determine that the world population is more than 20 times larger. Meaningful Vocabulary Scientific Notation: a way of writing a very large or very small number using a number between 1 and 10 multiplied by a power of 10 Standard Form: writing a number as a single term Express the above number in scientific notation. Express the above number in standard form. Is this number very large or very small? Justify. Is this number very large or very small? Justify.

15 Expressions and Equations Standard MCC8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used; use 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. Meaningful Vocabulary Scientific Notation: a way of writing a very large or very small number using a number between 1 and 10 multiplied by a power of 10 Standard Form: writing a number as a single term Given problem/word problem: (information given is fiction) A gnat has about 43,000,000 cells. A fly has about 1.7 x 10 3 times as many cells as a gnat. About how many cells does a fly have? Given problem/word problem: The population of Laos is 6.64 x The population of Vietnam is 8.8 x The population of Thailand is 6.68 x What is the total population of the three countries? Solve. Solve. What does the solution mean within the context of the problem? What does the solution mean within the context of the problem?

16 Expressions and Equations Standard MCC8.EE.7.a Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions; show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x=a, a=a, or a=b results (where a and b are different numbers). Meaningful Vocabulary Coefficient- a number that is multiplied by a variable Distributive Property- simplifying an expression by multiplying a number by each term inside the parenthesis Like Terms- terms where the variable is raised to the same power Solve the equation. Solve the equation. Show all steps. How many solutions does this equation have? Justify. How many solutions does this equation have? Justify.

17 Expressions and Equations Standard 8.EE.7.b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting the terms. Meaningful Vocabulary Coefficient- a number that is multiplied by a variable Distributive Property- simplifying an expression by multiplying a number by each term inside the parenthesis Like Terms- terms where the variable is raised to the same power Solve the linear equation. Show all steps. Solve the linear equation. Show all steps.

18 The Number System Standard 8.NS.1 Know that numbers are rational are irrational; understand informally that every number has a decimal expansion; for rational numbers show that a decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number. Meaningful Vocabulary: Irrational Number- a number that cannot be written as a fraction Rational Number- a number that can be written as a ratio Characteristics of rational numbers: Characteristics of irrational numbers: Rational numbers: Irrational numbers:

19 The Number System Standard MCC8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g., pi squared). For example, by truncating the decimal expansion of the square root of 2, show that the square root of 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Meaning Vocabulary: Approximate- to estimate a number, often rounding it of Estimate- to make a rough or approximate calculation Irrational Number- a number that cannot be written as a fraction Number Line- a line marked with numbers that are evenly spaced Rational Number- a number that can be written as a fraction Square Root- one of two identical factors of a number Place the given irrational numbers on the number line.

20 CCGPS Review Packet Math 8 UNIT 3

21 Geometry Standard MCC8.G.6 Explain a proof of the Pythagorean Theorem and its converse. Use the 3, 4, 5 right triangle given. Use the grid to illustrate the squares of the sides to prove the Pythagorean Theorem. Meaningful Vocabulary: Converse- opposite statement Proof- the process of showing that something is true Pythagorean Theorem- a formula relating the three side lengths of a right triangle Right Triangle- a triangle with one 90 degree angle Explain how the diagram to the left illustrates the Pythagorean Theorem and its converse.

22 Geometry Standard MCC8.G.6; MCC8.G.7 Apply the Pythagorean Theorem and its converse to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Given problem: Solve for the missing side length in the given right triangle. Meaningful Vocabulary: Pythagorean Theorem- a formula relating the three side lengths of a right triangle Right Triangle- a triangle with one 90 degree angle Three-dimensional- having three dimensions: length, width and height Two-dimensional- having two dimensions: length and width Given problem: Triangle ABC has side lengths of 5 centimeters, 8 centimeters, and 10 centimeters. Is it a right triangle? Figure: Sketch: b Solve. Solve.

23 Geometry Standard MCC8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. Meaningful Vocabulary: Pythagorean Theorem- a formula relating the three side lengths of a right triangle Right Triangle- a triangle with one 90 degree angle Find the distance between the two points: Use the space below to find the distance between given locations/points.

24 Geometry Standard MCC8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Meaningful Vocabulary: Volume- the amount of space occupied by a 3D object, measured in cubic units 10cm 6cm 12 in 8 in 12 in Formula: Formula: Formula: Solve. Solve. Solve.

25 Expressions and Equations Standard MCC8.EE.2 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 rational number; evaluate square roots of small perfect squares and cube roots of small perfect cubes; know that the square root of 2 is irrational. Meaningful Vocabulary: Cube Root- one of three identical factors of a number that is the product of those factors Perfect Cube- a number that results from multiplying an integer by itself twice Perfect Square- a number that results from multiplying an integer by itself Rational Numbers- any number that can be written as a ratio Square Root- one of two identical factors of a number that is the product of those factors Evaluate the square roots. Evaluate the cube roots.

26 CCGPS Review Packet Math 8 UNIT 4

27 Functions Standard MCC8.F.1 Understand that a function is a rule that assigns to each input exactly one output; the graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Meaningful Vocabulary: Function- a rule that determines a relationship between 2 variables Function Table- a set of inputs with corresponding outputs in a chart Input values- x-values; domain Ordered Pair- a pair of numbers to show a position on a coordinate plane Output values- y-value; range Given function: f(x) = -2x + 3 [Remember f(x) means the same as y.] Function Table: x y Graph:

28 Distance (in meters) Functions Standard MCC8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a table of values and an algebraic expression, determine which function has the greater rate of change. Meaningful Vocabulary: Compare- to note similarities (and/or differences) Function- a rule that determines a relationship between 2 variables Ordered Pair- a pair of numbers to show a position on a coordinate plane Rate of Change- slope; the change in the y value divided by the change in the x value Verbal description and graph: A brother and sister are racing 30 meters to the end of the street. Since Blake is younger, his sister Jenny lets him have a 6 meter head start. The graph show the distance that Blake runs during the race. Jenny s Race: Number of Seconds The equation y = 3x can be used to represent y, the total distance in meters that Jenny has run after x seconds have passed. Who is running at a faster speed? How much faster? Blake s Race Compare the verbal description to the graph: What is Blake s speed? What is Jenny s speed? Table and graph: Compare the rates of change for the two linear functions. Which function has a greater rate of change, or are they the same? Function 1 Function 2 x y Compare the table to the graph: Function 1 has a rate of change of and Function 2 has a rate of change of, so which function has a greater rate of change or are they the same?

29 CCGPS Review Packet Math 8 UNIT 5

30 Total Distance (miles) Expressions and Equations Standard MCC8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph; compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distancetime equation to determine which of two moving objects has greater speed. PART 1 Interpret unit rate as slope: Meaningful Vocabulary: Interpret- to explain Linear Equation- a function that produces a line on a coordinate grid Proportional Relationship- when two quantities vary directly with one another Slope- rate of change; the change in the y value divided by the change in the x value Unit Rate- a comparison of two measurements in which one term has a value of one PART 2 Compare two different proportional relationships: Two trains, North Train and South Train, are traveling at a constant rate of speed. The equation y = 130x shows the total distance in miles, y, traveled by North Train over x hours. The graph shows the relationship between time and distance for South Train. y 480 South Train What is the speed of North Train? Time (hours) x What is the speed of South Train? Interpret unit rate as slope: Slope = Which train is traveling faster? How do you know?

31 Expressions and Equations Standard MCC8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; 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. Meaningful Vocabulary: Origin- the coordinates of the origin are (0, 0). Proportional Relationships- a relationship between two equal ratios Slope- the steepness of a line; represented by the letter m; the ratio of the rise over run between two points on the graph. Evaluate the slope through similar triangles. Does the slope of a line change when using different points to to determine it? Find the ratio of the vertical and horizontal side lengths for each triangle. (Use the two similar triangles and the line graphed to help you answer the question.) (4, 5) 4 (8, 11) (2, 2) Use the coordinates of the points to find the rate of change. (You may use a table or the slope formula.)

32 Functions Standard MCC8.F.3 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. Meaningful Vocabulary: Equation- a mathematical statement containing an equal sign to show that two expressions are equal Function- a mathematical relationship between two values Interpret- to explain Linear- relating points to form a line Nonlinear- points that do not produce a line Linear Equations: Input (x) Output (y) Write an equation for the function and identify the rate of change and initial value. Non-linear Equations: A. y = ½ x + 2 B. y = x 2 C. y = 2x D. y = x - 2 Is the graph a function? Is the graph a linear function? Which equation does not represent a linear function? How do you know?

33 CCGPS Review Packet Math 8 UNIT 6

34 Functions Standard MCC8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x,y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Given problem: Meaningful Vocabulary: Construct- to make or create Equation- a mathematical statement containing an equal sign Function- a mathematical relationship between two values Function Table- outlining a set of inputs with corresponding outputs in a chart Initial Value- the starting quantity; beginning; y-intercept Model- to describe mathematically Rate of Change- slope; change in y value divided by the change in the x value To bowl at the local bowling alley, it costs $3 per game plus a $4 shoe rental. The total cost, y, in dollars depends on x, the number of games played. Write an equation to represent this situation and identify the slope and initial value (y-intercept). Then, make a table values to represent the situation. Graph the situation using the m and b values of your equation. Equation: Graph: Initial value: What does the initial value represent within the content of the problem? Rate of change: What does the rate of change represent within the context of the problem: Function Table: x y

35 Total Distance (miles) Functions Standard MCC8.F.5 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 a graph that exhibits the qualitative features of a function that has been described verbally. On Thursday, Luther went for a long walk, stopping to feed the ducks at one point. The graph below represents his walk Luther s Walk Meaningful Vocabulary: Analyze- to separate material into its parts or elements Exhibits- shows Function- a mathematical relationship between two quantities Qualitatively- relating to categories, variables, or real-world Quantity- amount; number of something Relationship- a connection What is the slope of segment from (0, 0) to (2, 6)? What does the slope of that segment represent? What is the slope of the segment from (2, 6) to (3, 6)? 8 What does the slope of that segment represent? Number of Hours What is the slope of the segment from (3, 6) to (5, 11)? What does the slope of that segment represent?

36 Distance from Home (in miles) Functions Standard MCC8.F.5 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 a graph that exhibits the qualitative features of a function that has been described verbally. Use the description to create a graph. Ben went rollerblading. He skated away from his home for 20 minutes for a total distance of 6 miles. He took a 10 minute break and skated back home for 30 minutes. Make a graph showing the distance he traveled away and back to his home. Describe the relationship between the two variables (relate it to the context of the problem) Meaningful Vocabulary: Analyze- to separate material into its parts or elements Exhibits- shows Function- a mathematical relationship between two quantities Qualitatively- relating to categories, variables, or real-world Quantity- amount; number of something Relationship- a connection Time (in minutes)

37 Statistics and Probability Standard MCC8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities; describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Use the given data to create a scatter plot. Be sure to include all appropriate labels. Bivariate- involving or relating to two variables Clustering- data points that tend to crowd together Construct- to make or create Interpret- to explain Negative Correlation- x increases while y decreases (opposite) Outlier- a data point far away from the majority of the other data points Positive Correlation- x increases and y increases also Scatter Plot- a graph with points to show a relationship between two variables Describe any patterns and/or relationships seen in the scatter plot. Day Sun. Mon. Tues. Wed. Thurs. Fri. Sat. Daily High Temp (in F) Bottles of Water Sold at a Baseball game

38 Selling Price (dollars) Statistics and Probability Standard MCC8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables; for scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Use the given data on the scatter plot that has been created. Be sure to observe all labels (title, y -axis, x-axis). If a linear model is appropriate, sketch in a line of best fit. Meaningful Vocabulary: Bivariate- involving or relating to two variables Clustering- data points that tend to crowd around a particular point in a set of values Linear Model- representing a situation with a line on a graph Negative Correlation- x increases while y decreases (opposite) Outlier- a data point far away from the majority of the other data points Positive Correlation- x increases and y increases also Quantitative- data that can be counted or measured Scatter Plot- a graph with points to show a relationship between two variables Variable- a letter representing a quantity What type of correlation exists? Selling Price of Aging Cars Write a statement to justify the type of correlation. 36,000 32,000 28,000 24,000 20,000 16,000 12,000 8,000 4, Age (years) Does a linear model seem appropriate for this data? Why or why not?

39 Number of Views (thousands) Statistics and Probability Standard MCC8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and y-intercept. Bivariate- involving or relating to two variables Interpret- to explain Linear Equation- a function that produces a line on a coordinate grid Linear Model- representing a situation with a line on a graph Slope- rate of change; rise over run; initial value; beginning point y-intercept- the location where a line crosses the y axis On-Demand Movies Viewed Equation: Adding fertilizer to plants: Equation: Weeks Since Release Times fertilizer was added Number of Additional Blooms Define the variables. Define the variables. Identify the slope. Identify the slope. Interpret the slope within the context of the problem. Interpret the slope within the context of the problem. Identify the y-intercept. Interpret the y-intercept within the context of the problem. Identify the y-intercept. Interpret the y-intercept within the context of the problem.

40 Statistics and Probability Standard MCC8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table; construct and interpret a twoway table summarizing data on two categorical variables collected from the same subjects; use relative frequencies calculated for rows or columns to describe possible association between the two variables. Meaningful Vocabulary: Association- a connection or relationship Bivariate- involving or relating to two variables Categorical Variable- a variable that has a fixed number of values Frequency- the number of times a particular items appears in a set of data Two-Way Table- used to display data that pertains to two different categories Student Survey Student John George Hannah Javon Ciera Leila Nicole Kristin Lily Bryan Chores Yes Yes No No No Yes Yes Yes No Yes Allowance Yes Yes No No No Yes Yes No Yes No Two-way table: Figure Relative Frequency of each: Chores No Chores Total Allowance No Allowance Total Chores No Chores Total Allowance No Allowance Total

41 CCGPS Review Packet Math 8 UNIT 7

42 Expressions and Equations Standard MCC8.EE.8.a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Meaningful Vocabulary: Intersection- the location where two lines cross Equation- a mathematical statement containing an equal sign Linear Equation- a function that produces a line on a coordinate grid Satisfy- to make true Simultaneous- at the same time System of Equations- relating two linear equations to each other Variable- a letter representing a quantity Given system of equations: Solve the system by graphing each equation. Solve.

43 Expressions and Equations Standard MCC8.EE.8.b Solve systems of two linear equations in two variables algebraically, and estimate solutions by graphing the equations; solve simple cases by inspection. Meaningful Vocabulary: Intersection- the location where two lines cross Equation- a mathematical statement containing an equal sign Linear Equation- a function that produces a line on a coordinate grid Satisfy- to make true Simultaneous- at the same time System of Equations- relating two linear equations to each other Variable- a letter representing a quantity Given system of equations: How many solutions does this system have? Justify. Solve.

44 Expressions and Equations Standard MCC8.EE.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. Given ordered pairs: (-1, -3) (2, 3) Equation of the line through the above ordered pairs: Meaningful Vocabulary: Intersection- the location where two lines cross Equation- a mathematical statement containing an equal sign Linear Equation- a function that produces a line on a coordinate grid Satisfy- to make true Simultaneous- at the same time System of Equations- relating two linear equations to each other Variable- a letter representing a quantity Given ordered pairs: (-2, 4) (5, -3) Equation of the line through the above ordered pairs: Do these lines intersect? If so, at what point?

45 Expressions and Equations Standard MCC8.EE.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. Meaningful Vocabulary: Intersection- the location where two or more lines cross Equation- a mathematical statement containing an equal sign Linear Equations- a function that produces a line on a coordinate grid System of Equations- relating two linear equations to each other Variable- a letter representing a quantity Description of word problem. Timothy sold school festival tickets as a fundraiser. Adult and children bought 14 tickets from him. He collected a total of $38 from these ticket sales. Adult tickets cost $4 each, and child tickets cost $1 each. Create two equations that represent both situations. Solve the system. (You can use any method to solve that you choose.) What does the answer mean within the context of the problem?