C o m m o n C o r e E d i t i o n New York CCLS Practice 8 Teacher Guide Mathematics Addresses latest NYS Test updates from 11/20/12 Replaces Practice Test 3
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Table of Contents For the Teacher 2 Completed Answer Form 4 Answers to Short- and Extended-Response Questions 5 Mathematics Rubrics for Scoring 7 Correlation Charts Common Core Learning Standards Coverage by the Ready Program 9 Ready New York CCLS Practice Answer Key and Correlations 12 Common Core State Standards 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. New York Common Core Learning Standards: http://engageny.org/resource/new-york-state-p-12-common-corelearning-standards-for-mathematics 1
For the Teacher What is Ready New York CCLS Practice? Ready New York CCLS Practice is a review program for the Common Core Learning Standards for Mathematics. By completing this book, students develop mastery of the Common Core Learning Standards for Mathematics. To develop this mastery, students answer comprehension questions that correlate to the Mathematical content strands of the Common Core Learning Standards. How does Ready New York CCLS Practice correlate to the Common Core Learning Standards for Mathematics? The test has 78 questions (68 multiple-choice, 6 shortresponse, and 4 extended-response) that address the key skills in the Mathematics strands of the CCLS: Expressions and Equations Functions Geometry Statistics and Probability How should I use Ready New York CCLS Practice? This book can be used in various ways. To simulate the test-taking procedures of the New York State Testing Program, have students complete each part of the practice test in one sitting on three consecutive days. (See the timetable to the right.) After students have completed the entire practice test, correct and review answers with them. Prior to administration of the statewide Mathematics assessment, use this test to evaluate progress and identify students areas of weakness. How do I introduce my students to Ready New York CCLS Practice? Provide each student with a student book and two sharpened No. 2 pencils with good erasers. Have students read the introduction on the inside front cover of the student book. Tell students to pay particular attention to the tips for answering multiplechoice questions. Before having students begin work, inform them of the amount of time they will have to complete each part of the practice test. You may choose either to follow or to adapt the following timetable for administering the practice test: Day 1 Book 1 (questions 1 34) 50* minutes Day 2 Book 2 (questions 35 68) 50* minutes Day 3 Book 3 (questions 69 78) 70* minutes * Each Testing Day will be scheduled to allow 90 minutes for completion. Where do students record their answers? Students record their answers to the multiple-choice questions on the answer form at the back of the student book. Have students remove the answer form and fill in the personal information section. Ensure that each student knows how to fill in the answer bubbles. Remind students that if they change an answer, they should fully erase their first answer. A completed answer form is on page 4 of this teacher guide. Students will complete the short- and extendedresponse items in their student books. 2
What is the correction procedure? Correct and review the answers to multiple-choice questions as soon as possible after students have completed the practice test. As you review the answers, explain concepts that students may not fully understand. Encourage students to discuss the thought processes they used to answer the questions. When answers are incorrect, help students understand why their reasoning was faulty. Students sometimes answer incorrectly because of a range of misconceptions about the strategy required to answer the question. Discussing why choices are incorrect will help students understand the correct answer. Use the 2-Point Holistic Rubric Short-Response (page 7) to score the short-response items. Use the 3-Point Holistic Rubric Extended-Response (page 8) to score the extended-response items. If you wish to familiarize students with the use of a rubric, provide them with copies. Discuss the criteria with them. Then show students some responses that you have evaluated using the rubrics. Explain your evaluations. How should I use the results of Ready New York CCLS Practice? Ready New York CCLS Practice provides a quick review of a student s understanding of the Common Core Learning Standards for Mathematics. It can be a useful diagnostic tool to identify standards that need further study and reinforcement. Use the Ready New York CCLS Practice Answer Keys and Correlations, beginning on page 12, to identify the standard that each question has been designed to evaluate. For students who answer a question incorrectly, provide additional instruction and practice through Ready New York CCLS Instruction. For a list of the Common Core Learning Standards that Ready New York CCLS Practice assesses, see the Common Core Learning Standards Coverage by the Ready Program chart beginning on page 9. 3
Name Teacher School Ready New York CCLS Mathematics Practice, Grade 8 Answer Form City Grade Book 1 Book 2 Book 3 1. A B D 2. A B D 3. B C D 4. A C D 5. A B C 6. A B D 7. A C D 8. A B D 9. A C D 10. A B D 11. A B C 12. A B D 13. B C D 14. A B D 15. B C D 16. A C D 17. B C D 18. A C D 19. A B D 20. A B C 21. A C D 22. B C D 23. A B D 24. A C D 25. A B D 26. A B D 27. A B C 28. A B D 29. B C D 30. A C D 31. A B C 32. B C D 33. A C D 34. A C D 35. B C D 36. A C D 37. A B C 38. B C D 39. A B C 40. B C D 41. A C D 42. A C D 43. B C D 44. B C D 45. A C D 46. A B C 47. A B D 48. A B C 49. A C D 50. A B D 51. A B C 52. A B D 53. A B C 54. B C D 55. A B D 56. A B C 57. A C D 58. A C D 59. A B D 60. B C D 61. A B C 62. A B C 63. A B C 64. A C D 65. A B D 66. A B D 67. A B D 68. A C D For questions 69 through 78, write your answers in the book. 69. See page 5. 70. See page 5. 71. See page 5. 72. See page 5. 73. See page 5. 74. See page 6. 75. See page 6. 76. See page 6. 77. See page 6. 78. See page 6. 4
Answers to Short- and Extended-Response Questions Book 3 pages 46 56 For scoring of questions 69 78, see also Mathematics Rubrics for Scoring, pages 7 and 8. 69. (short response) Part A: 6.0434 3 10 24 kilograms Part B: about 8.1 3 10 1 70. (short response) Part A: y 10 9 8 7 6 5 4 3 2 1-10 -9-8 -7-6 -5-4 -3-2 -1 0 1 2 3 4 5 6 7 8 9 10-1 -2-3 -4-5 -6-7 -8-9 -10 Part B: (2, 21) x 71. (extended response) Part A: Possible table: Figure Number Number of Blocks 1 1 2 3 3 6 4 10 5 15 Part B: Number of Blocks 20 18 16 14 12 10 8 6 4 2 0 y 1 2 3 4 5 6 7 8 9 10 Figure Number Part C: No; Possible explanation: The pattern is not a linear function because the points on the graph do not form a straight line. 72. (short response) Part A: nabc and nxby Part B: Possible explanation: nabc is similar to nxby because the parallel lines create two pairs of congruent angles: /BXY is congruent to /BAC and /BYX is congruent to /BCA. 73. (extended response) Part A: 99 square feet Part B: 24 square feet Part C: 75 square feet x 5
74. (extended response) Part A: distributive property Part B: 19 5 x 5 52 or x 5 5 3 4 5 10 2 5 Part C: x 5 52 or 2 14 19 19 75. (short response) Part A: Possible scatter plot: Sales (in dollars) y 170 165 160 155 150 145 140 135 130 125 120 115 110 0 58 LEMONADE SALES VS. TEMPERATURE 60 62 64 66 68 70 72 74 76 78 80 Temperature (in degrees Fahrenheit) Part B: linear association; Possible explanation: All points lie on or around the line of best fit for the scatter plot. 76. (extended response) Part A: Possible answer: The number 12 is twice that of 6. Part B: infinitely many solutions; Possible explanation: The equations are the same, so all values of x and y that are substituted into both equations will result in two true equations. Part C: Possible explanation: Multiply each term of the second equation by 2. Then, subtract the corresponding terms of the second equation from the first equation. The result is 0 5 0, which means there are an infinite number of solutions. x 77. (short response) Part A: y 5 5x 1 25 Part B: Possible explanation: A canoe costs $5 for each hour rented. 78. (short response) Part A: b 5 6; m 5 22 Part B: y 5 22x 1 6 6
Mathematics Rubrics for Scoring 2-Point Holistic Rubric (for Short-Response Questions)* 2 Points A 2-point response answers the question correctly. This response demonstrates a thorough understanding of the mathematical concepts but may contain errors that do not detract from the demonstration of understanding indicates that the student has completed the task correctly using mathematically sound procedures 1 Point A 1-point response is only partially correct. This response indicates that the student has demonstrated only a partial understanding of the mathematical concepts and/or procedures in the task correctly addresses some elements of the task may contain an incorrect solution but applies a mathematically appropriate process may contain correct numerical answer(s) but required work is not provided 0 Points A 0-point response is incorrect, irrelevant, incoherent, or contains a correct response arrived at using an obviously incorrect procedure. Although some parts may contain correct mathematical procedures, holistically they are not sufficient to demonstrate even a limited understanding of the mathematical concepts embodied in the task. *Reprinted courtesy of New York State Education Department. 7
3-Point Holistic Rubric (for Extended-Response Questions)* 3 Points A 3-point response answers the question correctly. This response demonstrates a thorough understanding of the mathematical concepts but may contain errors that do not detract from the demonstration of understanding indicates that the student has completed the task correctly, using mathematically sound procedures 2 Points A 2-point response is partially correct. This response demonstrates partial understanding of the mathematical concepts and/or procedures embodied in the task addresses most aspects of the task, using mathematically sound procedures may contain an incorrect solution but provides complete procedures, reasoning, and/or explanations may reflect some misunderstanding of the underlying mathematical concepts and/or procedures 1 Point A 1-point response is incomplete and exhibits many flaws but is not completely incorrect. This response demonstrates only a limited understanding of the mathematical concepts and/or procedures embodied in the task may address some elements of the task correctly but reaches an inadequate solution and/ or provides reasoning that is faulty or incomplete exhibits multiple flaws related to misunderstanding of important aspects of the task, misuse of mathematical procedures, or faulty mathematical reasoning reflects a lack of essential understanding of the underlying mathematical concepts may contain correct numerical answer(s) but required work is not provided 0 Points A 0-point response is incorrect, irrelevant, incoherent, or contains a correct response arrived at using an obviously incorrect procedure. Although some parts may contain correct mathematical procedures, holistically they are not sufficient to demonstrate even a limited understanding of the mathematical concepts embodied in the task. *Reprinted courtesy of New York State Education Department. 8
Correlation Charts Common Core Learning Standards Coverage by the Ready Program The chart below correlates each Common Core Learning Standard to the Ready New York CCLS Practice item(s) that assess it, and to the instruction lesson(s) that offer(s) comprehensive instruction on that standard. Use this chart to determine which lessons your students should complete based on their mastery of each standard. Common Core Learning Standards for Grade 8 Mathematics Standards Ready New York CCLS Instruction and Practice Practice Item Numbers Instruction Lesson(s) The Number System 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal 3 expansion which repeats eventually into a rational number. 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, Tested in Grade 9 and estimate the value of expressions (e.g., p 2 ). For example, by truncating the 3 decimal expansion of Ï 2, show that Ï 2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get better approximations. Expressions and Equations 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 3 3 5 5 3 3 5 1 3 3 5 1 27. 32, 66 1 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 5 p and x 3 5 p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that Ï 2 is irrational. Tested in Grade 9 2 8.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 than the other. For example, estimate the population of the United States as 3 3 10 8 and the population of the world as 7 3 10 9, and determine that the world population is more than 20 times larger. 1, 36, 58 4 8.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. 2, 8, 15, 46, 69 5 8.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 distance-time equation to determine which of two moving objects has greater speed. 21, 23, 52, 68 11 8.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 5 mx for a line through the origin and the equation y 5 mx 1 b for a line intercepting the vertical axis at b. 17, 49, 78 12 The Standards for Mathematical Practice are integrated throughout the instructional lessons. Common Core State Standards 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. New York Common Core Learning Standards: http://engageny.org/resource/new-york-state-p-12-common-corelearning-standards-for-mathematics 9
Common Core Learning Standards for Grade 8 Mathematics Standards Expressions and Equations (continued) Ready New York CCLS Instruction and Practice Practice Item Numbers Instruction Lesson(s) 8.EE.7 Solve linear equations in one variable. 5, 27, 40, 63, 74 13, 14 8.EE.8 8.EE.7.a 8.EE.7.b 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 5 a, a 5 a, or a 5 b results (where a and b are different numbers). Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and collecting like terms. Analyze and solve pairs of simultaneous linear equations. 8.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. 8.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. For example, 3x 1 2y 5 5 and 3x 1 2y 5 6 have no solution because 3x 1 2y cannot simultaneously be 5 and 6. 8.EE.8.c Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair. Functions 8.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. 8.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 linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. 8.F.3 Interpret the equation y 5 mx 1 b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A 5 s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. 8.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. 8.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. Geometry 7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. 7.G.3 Describe the two-dimensional figures that result from slicing threedimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids. 27, 63 13 5, 40, 74 14 12, 19, 29, 38, 42, 50, 57, 60, 70, 76 15, 16, 17 19, 50, 70 15 29, 38, 42, 57, 76 16 12, 60 17 7, 28, 37, 64 6 13, 41 7 26, 59, 61, 71 8 3, 6, 53, 77 9 35, 55 10 4 33 20 37 10
Common Core Learning Standards for Grade 8 Mathematics Standards Geometry (continued) 7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and use them to solve simple equations for an unknown angle in a figure. 7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. 8.G.1 Verify experimentally the properties of rotations, reflections, and translations: 8.G.1.a Lines are taken to lines, and line segments to line segments of the same length. 8.G.1.b Angles are taken to angles of the same measure. 8.G.1.c Parallel lines are taken to parallel lines. 8.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. 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates. 8.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. 8.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. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so. 8.G.6 Explain a proof of the Pythagorean Theorem and its converse. 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system. 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Statistics and Probability 8.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. 8.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. 8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. 8.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 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 association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores? Ready New York CCLS Instruction and Practice Practice Item Numbers Instruction Lesson(s) 43 32 14, 67, 73 34, 35, 36 Classroom Activity 18 9, 34, 65 19 22, 24, 51, 56 19, 20 16, 33, 45 20 11, 44, 72 21, 22 Tested in Grade 9 23 24 25 47 26, 27 25, 31, 54, 62, 75 28 39 29 10, 30 30 18, 48 31 11
Ready New York CCLS Practice Answer Key and Correlations The chart below shows the answers to multiple-choice items in the Ready New York CCLS Practice test, plus the depth-of-knowledge (DOK) index, primary standard, additional standard(s), and corresponding Ready New York CCLS Instruction lesson(s) for every item. Use this information to adjust lesson plans and focus remediation. Practice Test Question Key DOK Primary Standard Additional Standard(s) Book 1 Book 2 Ready New York CCLS Instruction Lesson(s) 1 C 1 8.EE.3 4 2 C 2 8.EE.4 8.EE.3 5 3 A 2 8.F.4 8.F.1 9 4 B 2 7.G.2 33 5 D 2 8.EE.7.b 14 6 C 2 8.F.4 9 7 B 1 8.F.1 6 8 C 2 8.EE.4 8.EE.3 5 9 B 1 8.G.2 8.G.2 19 10 C 2 8.SP.3 8.F.4 30 11 D 3 8.G.5 7.G.5 21, 22 12 C 2 8.EE.8.c 17 13 A 2 8.F.2 8.F.1, 8.F.4 7 14 C 2 7.G.6 35 15 A 2 8.EE.4 8.EE.3 5 16 B 2 8.G.4 20 17 A 2 8.EE.6 8.F.1, 8.F.3 12 18 B 2 8.SP.4 31 19 C 2 8.EE.8.a 8.EE.7.a 15 20 D 1 7.G.3 37 21 B 2 8.EE.5 11 22 A 2 8.G.3 19 23 C 2 8.EE.5 11 24 B 2 8.G.3 19 25 C 1 8.SP.1 28 26 C 2 8.F.3 8.F.1 8 27 D 2 8.EE.7.a 13 28 C 2 8.F.1 6 29 A 2 8.EE.8.b 8.EE.8.a 16 30 B 2 8.SP.3 8.F.4 30 31 D 2 8.SP.1 28 32 A 1 8.EE.1 1 33 B 2 8.G.4 20 34 B 2 8.G.2 19 35 A 2 8.F.5 10 36 B 1 8.EE.3 8.EE.4 4 37 D 2 8.F.1 6 12
Practice Test (continued) Question Key DOK Primary Standard Additional Standard(s) Part 2 (continued) Book 3 Ready New York CCLS Instruction Lesson(s) 38 A 2 8.EE.8.b 8.EE.8.a 16 39 D 2 8.SP.2 29 40 A 2 8.EE.7.b 14 41 B 2 8.F.2 7 42 B 2 8.EE.8.b 16 43 A 1 7.G.5 32 44 A 2 8.G.5 7.G.5 21, 22 45 B 2 8.G.4 20 46 D 1 8.EE.4 8.EE.3 5 47 C 2 8.G.9 7.G.6 26, 27 48 D 1 8.SP.4 31 49 B 2 8.EE.6 12 50 C 2 8.EE.8.a 15 51 D 2 8.G.3 20 52 C 2 8.EE.5 8.F.2 11 53 D 2 8.F.4 8.EE.6 9 54 A 2 8.SP.1 28 55 C 2 8.F.5 10 56 D 2 8.G.3 19 57 B 2 8.EE.8.b 8.EE.7.a 16 58 B 2 8.EE.3 8.EE.3 4 59 C 2 8.F.3 8 60 A 2 8.EE.8.c 17 61 D 2 8.F.3 8.F.4 8 62 D 1 8.SP.1 28 63 D 2 8.EE.7.a 13 64 B 2 8.F.1 6 65 C 2 8.G.2 19 66 C 2 8.EE.1 1 67 C 2 7.G.6 36 68 B 2 8.EE.5 8.F.4 11 69 See Page 5 2 8.EE.4 8.EE.3 5 70 See Page 5 2 8.EE.8.a 8.EE.8.b 15 71 See Page 5 2 8.F.3 8 72 See Page 5 2 8.G.5 21, 22 73 See Page 5 2 7.G.6 34 74 See Page 6 2 8.EE.7.b 14 75 See Page 6 2 8.SP.1 28 76 See Page 6 2 8.EE.8.b 8.EE.7.a 16 77 See Page 6 2 8.F.4 9 78 See Page 6 2 8.EE.6 8.F.3 12 13
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