1 / 48

EPISD 9 th Grade TEKS Tech Cards

EPISD 9 th Grade TEKS Tech Cards. Which point on the grid satisfies the conditions x ≥ 5 and y < −1?. A W B X C Y D Z. [ TEKS 8.14C : 2004 #48 ] Student expectation

long
Download Presentation

EPISD 9 th Grade TEKS Tech Cards

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. EPISD 9th Grade TEKS TechCards Which point on the grid satisfies the conditions x ≥ 5 and y < −1? A W B X C Y D Z [TEKS 8.14C : 2004 #48 ]Student expectation Select or developan appropriate problem-solving strategyfrom a variety of different types, including drawing a picture, looking for a pattern, systematic guessing and checking, acting it out, making a table, working a simpler problem, or working backwards to solve a problem.

  2. First, plot the points TEKS 8.14C (Objective 10) AcademicVocabulary: • point • horizontal line • vertical line Draw a vertical line to represent x>5 hold right arrow and scroll to the right until you get to x=5 Answer: A Only points x and w are at or to the right of the vertical line Draw a horizontal line to represent y<-1 hold down arrow and scroll down until you get to y=-1 Point x is not below the line y= -1 but point w is. Thus, letter A is the answer.

  3. EPISD 9th Grade TEKS TechCards Sue wants to write an expressionthat will always produce an eveninteger. Which of the following will always produce an even integer for any given integer, n? A 2n + 1 B 2n – 1 C n + 2 D 2n [TekS a.3b : 2004 #43] Student expectation The studentlooksfor patterns and represents generalizations algebraically.

  4. Input the first expression using x instead of n. TEKS A. 3B (Objective 2) Look at the table of values. AcademicVocabulary: • expression • integer • even integer • table of values Your calculator should display a screen like the one below. 2n +1 Did your expression produce even integers? NO Repeat the process for the rest of the expressions. You may input all expressions at the same time as shown below Answer: D • Look and compare the tables of values. The last expression, Y4, is the only one that produces even integers for any given integer x. Therefore, letter D is the correct answer.

  5. EPISD 9th Grade TEKS TechCards • Which is the best representation of the function y = x? [TEKS A.2A : 2003 #7 ]Student expectation The student identifies [and sketches] the general forms of linear, y=x, and quadratic, y=x²,parent functions.

  6. Begin by graphing the given equation, y=x. TEKS A.2A (Objective 2) AcademicVocabulary: • function • parent function • equation It is easy to see that letter B, the linear parent function, is the correct answer. Guide students to come up with examples for the rest of the answer choices. Some examples are shown below: A) y = 5 Answer: B C) y =|x| D) y = 0.5x²

  7. EPISD 9th Grade TEKS Tech Cards Which equation describes a line that has a y-intercept of 5 and a slope of ½ ? F y=5 + ½ x G y=(5+x) ½ H y=5x + ½ J y=(5x + 1) ½ [TEKS A.6D : 2004 #10 ]Student expectation The student graphsand writes equations of lines given characteristics such as two points, a point and a slope, or a slope and y–intercept.

  8. Input the first answer choice into the calculator TEKS A.6D (Objective 3) • Academic Vocabulary: • equation • line • y-intercept • slope • ordered pair Notice how the first answer choice, F, includes the ordered pair (0, 5) on the table of values. Therefore, the y-intercept of that line is 5. Similarly, answer choices G, H, and J do not include the point (0, 5) as shown below. Thus, the y-intercept for those lines cannot be 5 and those three answers can be eliminated. Answer: F Delete the three wrong answers from the and find the slope for the first line to ensure the answer is correct The slope is dy/dx = .5 = 1/2

  9. EPISD 9th Grade TEKS TechCards The graph of a line that contains the points (–1, −5) and (4, 5) is shown to the right. Which best represents this line if the slope is doubled and the y-intercept remains constant? [TEKS A.6C : 2003 #18 ]Student expectation The student investigates, describes, and predicts the effects of changes in m and b on the graph of y=mx+b

  10. TEKS A.6C (Objective 3) Plot the given points (-1, -5) and (4, 5) using the function AcademicVocabulary: • line • point • slope • y-intercept • doubled • constant • steeper Find the slope and y-intercept of the equation of the line that passes through those two points: Answer: G So, b=-3 m=2 • Double the original slope (2x2=4) and let the y-intercept (0, -3) remain the same. Then, graph the new line: y=4x-3. Thenew line is steeper and has the same y-intercept as the original one. Thus, the correct answer is G.

  11. EPISD 9th Grade TEKS TechCards • What is the slope of the linear function shown in the graph? [TEKS A.6A : 2004 #19 ]Student expectation The student developsthe concept of slope as rate of change and determinesslopes from graphs, tables, and algebraic representations.

  12. TEKS A.6A (Objective 3) Write linear equations in slope intercept form for all answer choices using the y-intercept (0, 14) and adjust the window to match the one on the graph. A) -7/4 x + 14 B) -4/7 x +14 C) 4/7 x + 14 D) 7/4 x +14 AcademicVocabulary: • slope • linear function • equation • slope-intercept form • y-intercept Graph all equations Similarly, B) Answer: B C) D) Notice how only the graph from answer choice B matches with the given one. Therefore, the correct answer is B.

  13. EPISD 9th Grade TEKS TechCards • The graph of a linear function is shown on the coordinate grid below. If the y-intercept is changed to (0, 5) and the slope becomes −4, which statement best describes the relationship between the two lines when they are graphed on the same coordinate grid? A The y-intercepts are 1 unit apart, and the linesare parallel. B The y-intercepts are 1 unit apart, and the lines intersect at (1, 1). C The y-intercepts are 1 unit apart, and the lines are perpendicular. D The y-intercepts are 1 unit apart, and the lines intersect at (1, 0). [TEKS A.6C : 2006 #12 ]Student expectation The student investigates, describes, and predicts the effects of changes in m and b on the graph of y=mx+b

  14. TEKS A.6C (Objective 3) First, find the equation of the given line using two points. AcademicVocabulary: • linear function • coordinate grid • y-intercept • slope • relationship • parallel • intersect y = - 5 x + 6 If the slope changes from -5 to -4 and the y-intercept from (0, 6) to (0, 5), the new equation will be y= -4x + 5. Graph both equations. Answer: B The lines are not parallel nor perpendicular. Therefore, A and C cannot be the correct answers. So, we need to find where the lines intersect. Since the lines intersect at (1, 1), the correct answer is B

  15. EPISD 9th Grade TEKS TechCards The table below shows various values for x and y. Which equation best describes the relationship between x and y? F y = −3x + 5 G y = −5x – 7 H y = −x + 17 J y = 3x + 41 [TEKS A.5C : 2006 #15 ]Student expectation The student translates among and uses algebraic, tabular, graphical, or verbal descriptions of linear functions.

  16. TEKS A.5C (Objective 3) First, input the equations into the calculator using the function AcademicVocabulary: • equation • relationship • table of values • orderedpair Look at the tables of values for all equations: Answer: F • Check the first ordered pair (-6, 23) from the original table. As you can see, that point is included in all four tables. • Continue checking the rest of the ordered pairs. • Only Y1 includes all points from the table. Thus, letter F is the correct answer.

  17. EPISD 9th Grade TEKS TechCards • What is the slope of the line that contains the coordinate points (8, −3) and (−2, 7)? • -1 • -9/11 • -5/3 • -2/5 [TEKS A.6A : 2006 #17 ]Student expectation The student develops the concept of slope as rate of change and determinesslopes from graphs, tables, and algebraic representations.

  18. TEKS A.6A (Objective 3) Guide students to write the slope formula, which can be found in their formula chart: m =y2-y1 x2-x1 Identify the x and y values of the given points: (8, −3) (−2, 7) Calculate y2-y1: =10 Calculate x2-x1: =-10 AcademicVocabulary: • Slope • line • coordinate points • equation x1 y1 x2 y2 Find the slope: So, m=-1 Extend by finding the equation of the line that goes through the given points and has the obtained slope. Answer: A Graph the equation

  19. EPISD 9th Grade TEKS TechCards • Find the slope of the given line. • A 9 • B 3 •  C  • D -3 [TEKS A.6A ]Student expectation The student develops the concept of slope as rate of change and determinesslopes from graphs, tables, and algebraic representations

  20. TEKS A.6A (Objective 3) Begin by plotting two points from the graph (0, 2) and (-2, -4) AcademicVocabulary: • slope • line • parallel If letter A is the correct answer, then the slope of the line must be 9. So, we can graph the equation y=9x and see if such line passes through the points or seems parallel to the line that would go through those points. Answer: B It doesn't. Thus, letter A is not the correct answer If we continue this process, we can see that letter B is the right answer (Look at the graphs below). B) y=3x C) y=1/3 x D) y= -3x

  21. EPISD 9th Grade TEKS TechCards • What are the x- and y-intercepts of the function graphed below? A (4, 0) and (5, 0) B (4, 0) and (0, 5) C (0, 4) and (5, 0) D (0, 4) and (0, 5) [TEKS A.3B : 2004 #42 ]Student expectation Given situations, the student looks for patternsand represents generalizations algebraically.

  22. TEKS A.3B (Objective 3) Find the equations of the lines passing through the given points in the answer choices and graph them: AcademicVocabulary: • x-intercept • y-intercept • function • line • points A) (4,0) & (5,0) We continue the same process using the rest of the answer choices B) (4,0) & (0,5) C) (0,4) & (5,0) Answer: B D) (0,4) & (0,5) We can see that letter B is correct because: 1) The graphs match 2) (4,0) is the x-intercept on the graph, and 3) (0,5) is the y-intercept on the graph.

  23. EPISD 9th Grade TEKS TechCards • Which linear function includes the points (–3, 1) and (–2, 4)? A f(x) = 3x + 10 B f(x) = ⅓ x + 2 C f(x) = 3x − 6 D f(x) = −3x + 1 [TEKS A.6D : 2003#44 ]Student expectation The student graphsand writes equations of lines given characteristics such as two points, a point and a slope, or a slope and -intercept.

  24. TEKS A.6D (Objective 3) Begin by plotting the given points (-3, 1) and (-2, 4). AcademicVocabulary: • linear function • point • equation Graph each function to examine which one passes through the plotted points. A. f(x) = 3x + 10 y = 3x + 10 Answer: A Similarly: B. y = ⅓ x + 2 C. y= 3x − 6 D y= −3x + 1 Thus, the correct answer is letter A.

  25. EPISD 9th Grade TEKS TechCards • The graphs of the linear equations y = 2x – 3 and y = 3x − 7 are shown below. If 2x − 3 = 3x − 7, what is the value of x? A 4 B 5 C 9 D 10 [TEKS A.7B : 2004 #36 ]Student expectation The student investigates methods for solving linear equationsand inequalities using [concrete] models, graphs, and the properties of equality, selects a method, and solves the equations and inequalities.

  26. TEKS A.7B (Objective 4) The correct value of x will make the equation 2x-3 = 3x -7 true. Guess and check to see which answer choice will do that. A) x=4 AcademicVocabulary: • graph • linear equation • true statement A 1 represents a true statement. Therefore, A is the correct answer. However, to confirm that A is the right choice, we must test the rest of the answer choices: Notice how the calculator produced a 0 for this choice. Thus, this answer cannot represent the correct value for x. B) x=5 Answer: A Similarly, C) x=9 D) x=10

  27. EPISD 9th Grade TEKS TechCards Alonso’s family rented a car when they flew to Orlando for a 4-day vacation. They paid $39 per day and $0.09 for each mile driven. How much did it cost to rent thecar for 4 days and drive 350 miles, not including tax? A $70.50 B $124.50 C $156.00 D $187.50 [TEKS 8.14B: 2003 #5 ]Student expectation The student uses a problem-solving model that incorporates understanding the problem, making a plan, carrying out the plan, and evaluating the solution for reasonableness

  28. TEKS 8.14B (Objective 10) Begin by writing an equation that describes the situation: C = 39 d + 0.09 m C  Total Cost d  Number of days m  Miles driven AcademicVocabulary: • equation • given values • solution Store the given values for d and m: Answer: D Enter the equation and find a solution: Therefore, the correct answer is letter D.

  29. EPISD 9th Grade TEKS TechCards Jake made a map of his neighborhood for a school project. He placed a grid over the map. Which coordinate point best represents the post office? A (6, 12) B (12, 6) C (1.2, 0.6) D (0.6, 1.2) [TEKS 8.7D: 2003#43 ]Student expectation The student will locate and namepoints on a coordinate plane using ordered pairs of rational numbers

  30. TEKS 8.7D (Objective 6) Adjust the window to match the one on the given grid: AcademicVocabulary: • point • coordinate • grid • orderedpair Plot the ordered pairs for each answer choice: A) Answer: D Similarly, B) C) D) The answer choice that shows a point representing the post office is letter D.

  31. EPISD 9th Grade TEKS TechCards • Which inequality best describes the graph shown below? A y ≥ −2x B y ≥ −x − 2 C y ≥ −2x − 2 D y ≥ x – 2 [TEKS A.7A ]Student expectation The student analyzes situations involving linear functions and formulates linear equations or inequalities to solve problems.

  32. TEKS A.7A (Objective 4) Graph each inequality: A) B) AcademicVocabulary: • inequality • table of values • intercepts D) C) Answer: C You can eliminate answer choices A and D Check the tables of values for choices B and C: B) C) Choice C does include the intercepts (-2, 0) and (0, -2). Thus, C is the correct answer.

  33. EPISD 9th Grade TEKS TechCards • Which inequality best describes the graph shown below? F y > − ¾x + 5 G y < − 4⁄3x + 5 H y < − ¾x + 5 J y > − 4⁄3x + 5 [TEKS A.1D : 2006 #5 ]Student expectation The student represents relationships among quantities using [concrete] models, tables, graphs, diagrams, verbal descriptions, equations, and inequalities.

  34. TEKS A.1D (Objective 1) Begin by selecting a point from the shaded area. For example (8, -2) Store the corresponding x and y values. AcademicVocabulary: • inequality • point • shaded area • correspondingvalues Test each inequality: F) G) H) J) Answer: J F and G produced a 0 (False statements!) We repeat the process for H and J, only, using a different point: H produced a false statement. Therefore, letter J is the correct answer. (5, 3) H) J)

  35. EPISD 9th Grade TEKS TechCards • Which expression describes the area in square • units of a rectangle that has a width of 4x 3y 2 • and alength of 3x 2y 3? A 12x 6y6 B 12x 5y 5 C 7x 6y 6 D 7x 5y 5 [TEKS A.11A : 2003 #10 ]Student expectation The student uses[patterns to generate] the laws of exponents and applies them in problem solving situations.

  36. TEKS A.11A (Objective 5) Begin by storing a value for both x and y: AcademicVocabulary: • expression • area • square units • rectangle • width • length Find the area of the rectangle by multiplying the given expressions: A= (L)(W) A= Answer: B Input all choices and compare to the value obtained in step 2: A) B) C) D) The correct answer is letter B since =

  37. EPISD 9th Grade TEKS TechCards • Which expression is equivalent to A 4x 9 B 4x 2 C 2x 8 D 2x 4 [TEKS A.11A : 2006 #9 ]Student expectation The student uses[patterns to generate] thelaws of exponents and applies them in problem solving situations.

  38. TEKS A.11A (Objective 5) Enter the expression into the calculator using the y editor: AcademicVocabulary: • expression • equivalent • table of values Enter each answer choice and compare the tables of values A) B) Answer: B C) D)

  39. EPISD 9th Grade TEKS TechCards • Sean is an Algebra I student who believes that xy2 = (xy) 2. Rudy informs Sean that this theory is not always true. Which pair of values for x and y could Rudy use to disprove Sean’s theory? F x = 0 and y = 2 G x = 1 and y = 2 H x = 2 and y = 0 J x = 2 and y = 1 [TEKS 8.16B : 2004 #28 ]Student expectation The student validates his/her conclusions using mathematical properties and relationships.

  40. TEKS 8.16B (Objective 10) Substitute the x and y values from each answer choice into each side of the equation and compare. F) x=0 and y=2 AcademicVocabulary: • pair • values • substitute • equation xy2 (xy) 2 G) x=1 and y=2 H) x=2 and y=0 xy2 (xy) 2 Answer: J xy2 (xy) 2 J) x=2 and y=1 The only choice that Rudy could use to disprove Sean is letter J. xy2 (xy) 2

  41. EPISD 9th Grade TEKS TechCards • If y = x3, what is equivalent to x12 ? A y 36 B y15 C y 9 D y 4 [TEKS A.11A : 2004 #44 ]Student expectation The student uses[patterns to generate] the laws of exponents and applies them in problem solving situations.

  42. TEKS A.11A (Objective 5) Input both y=x3 and x12 using the y editor. AcademicVocabulary: • equation • equivalent • table of values Input the answer choices and compare their tables of values with that of x12 A) Answer: D Similarly, B) C) D)

  43. EPISD 9th Grade TEKS TechCards A 12- by 16-foot rectangular floor will be covered bysquare tiles that measure 2 feet on each side. If the tiles are not cut, how many of themwill be needed to cover the floor? A 192 B 96 C 48 D 14 [TEKS 8.7B : 2003 #31 ]Student expectation The student usesgeometric concepts and properties to solve problems in fields such as art and architecture.

  44. TEKS 8.7B (Objective 7) Adjust the window : AcademicVocabulary: • rectangular floor • square tiles • measure • cover • grid Turn on the grid and graph: Answer: C There are 6 “tiles” in each column and 8 “tiles” in each row. Therefore, the total number of tiles needed to cover the floor is: Thus, the correct answer is C.

  45. EPISD 9th Grade TEKS TechCards • Simplify the algebraic expression 3(x + 3) − 2(x + 3). A x + 3 B x − 3 C −6x2 − 54 D 6x2 + 3 [TEKS A.4B : 2004 #20 ]Student expectation The student uses the commutative, associative, and distributive properties to simplify algebraic expressions.

  46. Input the expression using the and graph: TEKS A.4B (Objective 2) AcademicVocabulary: • simplify • algebraic Expression Graph all choices: Similarly, A B Answer: A C D Notice how letter A is the only answer which graph matches the original one. Thus, letter A is the correct answer.

  47. EPISD 9th Grade TEKS TechCards • Which of the following ordered pairs is the x-intercept or the y-intercept of the function 2x − y = 8? F (8, 0) G (0, 4) H (4, 0) J (0, 8) [TEKS A.6E : 2006 #19 ]Student expectation The student determines the intercepts of linear functions from graphs, tables, and algebraic representations.

  48. TEKS A.6E (Objective 3) Find the x-intercept: Substitute a 0 for y 2x-0=8 Solve: AcademicVocabulary: • ordered pair • x-intercept • y-intercept • function • solve The x-intercept is at x=4, or (4, 0) Substitute a 0 for x 2(0)-y=8 Solve similarly. Continue to use x when you input the expression into the calculator Find the y-intercept: Answer: H Scroll up until you see y1=y2 So, The x-intercept is (4, 0), and The y-intercept is (0, -8) Therefore, the correct answer is letter H.

More Related