Mathematically Connected Communities. PARCC Practice Test Items Grade 5 Mathematics

Transcription

1 Mathematically Connected Communities PARCC Practice Test Items Grade 5 Mathematics Excerpted from: Packets-Preparing for Spring Packets-Preparing for Spring Illustrative Mathematics (Under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License) PARCC Released Items-Spring

2 Contents MC 2 Thinking Protocol... 3 User s Guide Difficulty (Most to Least) CCSS-M Page Numbers 1 5.MD MD.B NF NF.B C.4-1 OGL NF.7a 5.NF.B.7.A C.5-2 OGL C.2-2 OGL C MD.C.5.C; OGL C.2-3 OGL C.4-3 OGL MD MD.A C NBT.B C.7-3 OGL NBT NBT.B D.1 OGL C.3 OGL NF.5a 5.NF.B.5.A NBT.A.Int.1 5.NBT.A.2; 5.NBT.A.3.A ; 5.NBT.A.3.B; 5.NBT.A D.2 SHK MD MD.A C.4-4 OGL NBT.4 5.NBT.A NF NF.B G.3 5.G.B Int.2 5.MD.C.5; 5.NBT.B.5; 5.OA.A NBT.1 5.NBT.A NF NF.A OA OA.A NF NF.A C.1-1 OGL G.4 5.G.B C.5-1 OGL NBT NBT.B NBT.Int.1 5.NBT.A.2; 5.NBT.B.5; 5.NBT.B NF NF.A MD.5c 5.MD.C.5.C NF NF.B C NBT.B.5; 4.NF.B.3.A; SHK NBT NBT.B Int.1 5.NBT.B NBT NBT.A NF.4b-1 5.NF.B.4.B NBT.3a 5.NBT.A.3.A NF.7c 5.NF.B.7.C NF NF.A NF.7b 5.NF.B.7.B G.1 5.G.A NBT.6 5.NBT.B NF.A.Int.1 5.NF.A.1; 5.NF.A NF NF.A NF.4a-1 5.NF.B.4.A OA.3 5.OA.B MD.5b 5.MD.C.5.B MD.3 5.MD.C MD.4 5.MD.C NBT.3b 5.NBT.A.3.B NBT.5 5.NBT.B NF.4a-2 5.NF.B.4.A G.2 5.G.A NBT NBT.B NF NF.B OA OA.A OA.1 5.OA.A

3 MC 2 Thinking Protocol: PARCC Test Prep Using Mathematical Practice Prompts Use the MC 2 Thinking Protocol and follow the process below in working with the PARCC practice test items found in this packet: 1. Choose items from this packet that relate to math concepts studied in the current or previous curriculum units during your math instruction. Each item may be used as a practice item worksheet. 2. Choose a set of Thinking/Writing Prompts below based on the math practice the class is working to develop. 3. Add the prompts to the practice item worksheet or display the prompts for the students to respond to. 4. Continue using the same set of prompts for an extended period of time so children develop competence and confidence in describing their mathematical thinking related to the math practice. The questions below were intentionally not included on each MC 2 PARCC practice test item worksheet in this packet. These are intended to help students move beyond answer getting to fully making sense of test item questions and their own mathematical thinking. Thinking/Writing Prompts to Promote Mathematical Practices Math Practice 1: Make sense of problems and persevere in solving them. 1. What do you know about the problem? 2. What questions do you have? 3. Explain your reasoning or thinking in solving the problem. Math Practice 3: Construct viable arguments and critique the reasoning of others. 1. What are the assumptions, definitions, and previous knowledge to help in thinking about this problem? 2. What are some possible conjectures that you have about the problem? 3. Explain your mathematical argument so that somebody else can make sense of your thinking. Math Practice 4: Model with mathematics. 1. What are the important quantities in the problem that are needed to solve it? 2. What mathematical operation(s) or representation(s) will you use to solve the problem? 3. Explain how you know your answer makes sense in the context of the situation. Math Practice 6: Attend to precision. 1. What are the important units in the problem? (What are we measuring or counting?) 2. What relationship between the units/quantities do you need to know in order to solve the problem? 3. Use appropriate and precise mathematical language, units, labels and computations to clearly describe your mathematical reasoning. Copyright 2014 Mathematically Connected Communities (MC 2 ) Project. All rights reserve 3

4 1 5.MD MD.B.2 Measurement & Data PARCC Released Items Spring 2017 MC 2 excerpted test items, Fall

5 2 5.NF NF.B.6 Number & Operations - Fractions Packets-Preparing for Spring

6 3 5.C.4-1 OGL Reasoning PARCC Released Items Spring

7 4 5.NF.7a 5.NF.B.7.A Number & Operations - Fractions Illustrative Mathematics 7

8 5 s s 5.C.5-2 OGL Reasoning PARCC Released Items Spring

9 s s 6 5.C.2-2 OGL Reasoning Pending New PARCC Released Test Items 9

10 7 5.C.8-2 s 5.MD.C.5.C OGL Reasoning Pending New PARCC Released Test Items 10

11 s 8 5.C.2-3 OGL Reasoning PARCC Released Items Spring

12 s 9 5.C.4-3 OGL Reasoning Packets-Preparing for Spring

13 10 5.MD MD.A.1 Measurement & Data Packets-Preparing for Spring

14 10 5.MD MD.A.1 Measurement & Data PARCC Released Items Spring

15 11 5.C NBT.B.6 Reasoning Packets-Preparing for Spring

16 12 5.C.7-3 OGL Reasoning Pending New PARCC Released Test Items 16

17 13 5.NBT NBT.B.7 Number & Operations in Base Ten Pending New PARCC Released Test Items 17

18 14 5.D.1 OGL Modeling Packets-Preparing for Spring

19 14 5.D.1 OGL Modeling Packets-Preparing for Spring

20 14 5.D.1 OGL Modeling PARCC Released Items Spring

21 14 5.D.1 OGL Modeling PARCC Released Items Spring

22 15 5.C.3 OGL Reasoning Pending New PARCC Released Test Items 22

23 16 5.NF.5a 5.NF.B.5.A Number & Operations - Fractions Packets-Preparing for Spring

24 16 5.NF.5a 5.NF.B.5.A Number & Operations - Fractions Packets-Preparing for Spring

25 16 5.NF.5a 5.NF.B.5.A Number & Operations - Fractions PARCC Released Items Spring

26 17 5.NBT.A.Int.1 5.NBT.A.2 5.NBT.A.3.A 5.NBT.A.3.B 5.NBT.A.4 Number & Operations in Base Ten Packets-Preparing for Spring

27 17 5.NBT.A.Int.1 5.NBT.A.2 5.NBT.A.3.A 5.NBT.A.3.B 5.NBT.A.4 Number & Operations in Base Ten Packets-Preparing for Spring

28 18 5.D.2 SHK Modeling Packets-Preparing for Spring

29 19 5.MD MD.A.1 Measurement & Data Packets-Preparing for Spring

30 20 5.C.4-4 OGL Reasoning Pending New PARCC Released Test Items 30

31 21 5.NBT.4 5.NBT.A.4 Number & Operations in Base Ten Packets-Preparing for Spring

32 21 5.NBT.4 5.NBT.A.4 Number & Operations in Base Ten Packets-Preparing for Spring

33 22 5.NF NF.B.6 Number & Operations - Fractions Packets-Preparing for Spring

34 22 5.NF NF.B.6 Number & Operations - Fractions Packets-Preparing for Spring

35 23 5.G.3 5.G.B.3 Geometry Packets-Preparing for Spring

36 23 5.G.3 5.G.B.3 Geometry PARCC Released Items Spring

37 24 5.Int.2 5.MD.C.5 5.NBT.B.5 5.OA.A.2 s Measurement & Data Number & Operations in Base Ten Operations & Algebraic Thinking Packets-Preparing for Spring

38 25 5.NBT.1 5.NBT.A.1 Number & Operations in Base Ten Packets-Preparing for Spring

39 25 5.NBT.1 5.NBT.A.1 Number & Operations in Base Ten Packets-Preparing for Spring /10 10 times 1/ times 1/10 10 times 1/ times 39

40 25 5.NBT.1 5.NBT.A.1 Number & Operations in Base Ten PARCC Released Items Spring

41 26 5.NF NF.A.1 Number & Operations - Fractions Illustrative Mathematics 41

42 26 5.NF NF.A.1 Number & Operations - Fractions PARCC Released Items Spring

43 27 5.OA OA.A.2 Operations & Algebraic Thinking Packets-Preparing for Spring

44 27 5.OA OA.A.2 Operations & Algebraic Thinking Packets-Preparing for Spring

45 28 5.NF NF.A.2 Number & Operations - Fractions Packets-Preparing for Spring

46 28 5.NF NF.A.2 Number & Operations - Fractions Packets-Preparing for Spring

47 28 5.NF NF.A.2 Number & Operations - Fractions PARCC Released Items Spring

48 29 5.C.1-1 OGL Reasoning Pending New PARCC Released Test Items 48

49 30 5.G.4 5.G.B.4 Geometry Packets-Preparing for Spring

50 30 5.G.4 5.G.B.4 Geometry Packets-Preparing for Spring

51 31 5.C.5-1 OGL Reasoning Packets-Preparing for Spring

52 32 5.NBT NBT.B.7 Number & Operations in Base Ten Pending New PARCC Released Test Items 52

53 33 5.NBT.Int.1 5.NBT.A.2 5.NBT.B.5 5.NBT.B.7 Number & Operations in Base Ten Packets-Preparing for Spring

54 33 5.NBT.Int.1 5.NBT.A.2 5.NBT.B.5 5.NBT.B.7 Number & Operations in Base Ten PARCC Released Items Spring

55 34 5.NF NF.A.2 Number & Operations - Fractions Packets-Preparing for Spring

56 34 5.NF NF.A.2 Number & Operations - Fractions Packets-Preparing for Spring

57 35 5.MD.5c 5.MD.C.5.C Measurement & Data Packets-Preparing for Spring

58 35 5.MD.5c 5.MD.C.5.C Measurement & Data PARCC Released Items Spring

59 36 5.NF NF.B.3 Number & Operations - Fractions Packets-Preparing for Spring

60 36 5.NF NF.B.3 Number & Operations - Fractions Packets-Preparing for Spring

61 36 5.NF NF.B.3 Number & Operations - Fractions PARCC Released Items Spring

62 36 5.NF NF.B.3 Number & Operations - Fractions PARCC Released Items Spring

63 37 5.C NBT.B.5 4.NF.B.3.A SHK s Number & Operation in Base Ten Number & Operations-Fractions Reasoning MC 2 PARCC Practice Test Item Packets-Preparing for Spring

64 37 5.C NBT.B.5 4.NF.B.3.A SHK s Number & Operation in Base Ten Number & Operations-Fractions Reasoning PARCC Released Items Spring 2017 Continued on next page. 64

65 37 5.C NBT.B.5 4.NF.B.3.A SHK s Number & Operation in Base Ten Number & Operations-Fractions Reasoning PARCC Released Items Spring

66 38 5.NBT NBT.B.7 Number & Operations in Base Ten Packets-Preparing for Spring

67 39 5.Int.1 5.NBT.B.5 Number & Operations in Base Ten Packets-Preparing for Spring

68 39 5.Int.1 5.NBT.B.5 Number & Operations in Base Ten PARCC Released Items Spring

69 40 5.NBT NBT.A.2 Number & Operations in Base Ten Illustrative Mathematics 69

70 40 5.NBT NBT.A.2 Number & Operations in Base Ten PARCC Released Items Spring

71 41 5.NF.4b-1 5.NF.B.4.B Number & Operations - Fractions Packets-Preparing for Spring

72 41 5.NF.4b-1 5.NF.B.4.B Number & Operations - Fractions Packets-Preparing for Spring

73 41 5.NF.4b-1 5.NF.B.4.B Number & Operations - Fractions PARCC Released Items Spring

74 41 5.NF.4b-1 5.NF.B.4.B Number & Operations - Fractions PARCC Released Items Spring

75 42 5.NBT.3a 5.NBT.A.3.A Number & Operations in Base Ten Packets-Preparing for Spring

76 42 5.NBT.3a 5.NBT.A.3.A Number & Operations in Base Ten PARCC Released Items Spring

77 43 5.NF.7c 5.NF.B.7.C Number & Operations - Fractions Packets-Preparing for Spring

78 43 5.NF.7c 5.NF.B.7.C Number & Operations - Fractions Packets-Preparing for Spring

79 43 5.NF.7c 5.NF.B.7.C Number & Operations - Fractions PARCC Released Items Spring

80 44 5.NF NF.A.1 Number & Operations -Fractions Packets-Preparing for Spring

81 45 5.NF.7b 5.NF.B.7.B Number & Operations - Fractions Illustrative Mathematics 81

82 46 5.G.1 5.G.A.1 Geometry Packets-Preparing for Spring

83 46 5.G.1 5.G.A.1 Geometry Packets-Preparing for Spring

84 46 5.G.1 5.G.A.1 Geometry Packets-Preparing for Spring

85 46 5.G.1 5.G.A.1 Geometry PARCC Released Items Spring

86 47 5.NBT.6 5.NBT.B.6 Number & Operations in Base Ten Packets-Preparing for Spring

87 47 5.NBT.6 5.NBT.B.6 Number & Operations in Base Ten Packets-Preparing for Spring

88 47 5.NBT.6 5.NBT.B.6 Number & Operations in Base Ten PARCC Released Items Spring

89 48 5.NF.A.Int.1 5.NF.A.1 5.NF.A.2 Number & Operations - Fractions Packets-Preparing for Spring

90 48 5.NF.A.Int.1 5.NF.A.1 5.NF.A.2 Number & Operations - Fractions PARCC Released Items Spring

91 49 5.NF NF.A.1 Number & Operations - Fractions Packets-Preparing for Spring

92 49 5.NF NF.A.1 Number & Operations - Fractions Packets-Preparing for Spring

93 49 5.NF NF.A.1 Number & Operations - Fractions PARCC Released Items Spring

94 50 5.NF.4a-1 5.NF.B.4.A Number & Operations - Fractions Packets-Preparing for Spring

95 51 5.OA.3 5.OA.B.3 Operations & Algebraic Thinking Packets-Preparing for Spring

96 52 5.MD.5b 5.MD.C.5.B Measurement & Data Packets-Preparing for Spring

97 53 5.MD.3 5.MD.C.3 Measurement & Data Packets-Preparing for Spring

98 53 5.MD.3 5.MD.C.3 Measurement & Data PARCC Released Items Spring

99 54 5.MD.4 5.MD.C.4 Measurement & Data Packets-Preparing for Spring

100 55 5.NBT.3b 5.NBT.A.3.B Number & Operations in Base Ten Packets-Preparing for Spring

101 56 5.NBT.5 5.NBT.B.5 Number & Operations in Base Ten Packets-Preparing for Spring

102 56 5.NBT.5 5.NBT.B.5 Number & Operations in Base Ten Packets-Preparing for Spring

103 56 5.NBT.5 5.NBT.B.5 Number & Operations in Base Ten PARCC Released Items Spring

104 56 5.NBT.5 5.NBT.B.5 Number & Operations in Base Ten PARCC Released Items Spring

105 57 5.NF.4a-2 5.NF.B.4.A Number & Operations - Fractions Packets-Preparing for Spring

106 57 5.NF.4a-2 5.NF.B.4.A Number & Operations - Fractions PARCC Released Items Spring

107 58 5.G.2 5.G.A.2 Geometry Packets-Preparing for Spring

108 58 5.G.2 5.G.A.2 Geometry PARCC Released Items Spring 2017 Continued on next page. 108

109 58 5.G.2 5.G.A.2 Geometry PARCC Released Items Spring

110 59 5.NBT NBT.B.7 Number & Operations in Base Ten Packets-Preparing for Spring

111 59 5.NBT NBT.B.7 Number & Operations in Base Ten PARCC Released Items Spring

112 60 5.NF NF.B.3 Number & Operations - Fractions Packets-Preparing for Spring

113 61 5.OA OA.A.2 Operations & Algebraic Thinking Illustrative Mathematics 113

114 62 5.OA.1 5.OA.A.1 Number & Operations in Base Ten Packets-Preparing for Spring

115 62 5.OA.1 5.OA.A.1 Number & Operations in Base Ten PARCC Released Items Spring

116 User s Guide To support New Mexico educators in preparing students for the Spring 2018 PARCC Assessment, Mathematically Connected Communities (MC 2 ) has again compiled Practice Test Item Packets posted on the MC 2 website. Each packet is organized in order of difficulty (most to least) based on the Spring 2017 Analysis at the cross-state level used for all reports. Each grade-level/subject analysis contains a graph (see sample below) representing the following data: Average percent correct for each item represented by cross-state (aggregation of all states in PARCC consortium), state, district, and for the school report, at school level (see legend below) s are located along the bottom and left blank on the district/school report if not tested in that particular location (see below) LEGEND SAMPLE EVIDENCE STATEMENTS : Spring 2017 PARCC Interpretation Guide Each page contains only one problem and identifies the following for that item: The practice test items are presented in order from most to least difficult based on the Difficulty Spring 2017 Analysis at the cross-state level used for all reports. Since the harder problems are found at the beginning of the document, teachers may want to start with the easier items at the end. 116

117 Describe the knowledge and skills that the assessment item/task elicits from s students and are derived from the s for Mathematics (CCSS-M). s for grades 3 through 8 will begin with the grade number. High School s begin with HS or with the label for a conceptual category. Numbers at the end of Integrated s and those focused on Reasoning and Modeling are added for assessment clarification and tracking purposes. documents are available at: An might: 1. Use exact language as the CCSS-M. For example, 8.EE.1 uses the exact language as standard 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, = 3-3 = 1/33 = 1/ Be derived by focusing on specific parts of a standard. For example, CCSS-M 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 was split into the following two s: 8.F.5-1 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). 8.F.5-2 Sketch a graph that exhibits qualitative features of a function that has been described verbally. Together these two evidence statements are CCSS-M 8.F Be integrative (Int). Integrative s allow for the testing of more than one of the Standards and can be integrated across all content within a grade/course, all standards in a high school conceptual category, all standards in a domain, or all standards in a cluster. For example: Grade/Course 4.Int.2 (Integrated across Grade 4) Conceptual Category F.Int.1 (Integrated across the Functions Conceptual Category) 4.NBT.Int.1 (Integrated across the Number and Operations in Base Ten ) Cluster 3.NF.A.Int.1 (Integrated across the Number and Operations Fractions, Cluster A) 4. Focus on mathematical reasoning. A Reasoning (keyed with C as per PARCC Claims Structure, see pg. 4) will state the type of reasoning that an item/task will require and content scope from the CCSS-M that the item/task will require students to reason about. Such as, 3.C.2 Type of Reasoning: Base explanations/reasoning on the relationship between addition and subtraction or the relationship between multiplication and division. Content Scope: Knowledge and skills are articulated in 3.OA.6 When the focus is on reasoning, the may also require the student to reason about securely held knowledge (SHK-see pg. 4) from a previous grade. 5. Focus on mathematical modeling. A Modeling (keyed with D as per PARCC Claims Structure, see pg. 4) will state the type of modeling that an item/task will require and the content scope from the CCSS-M that the item/task will require students to model about. For example, HS.D.5: Type of Modeling: Given an equation or system of equations, reason about the number or nature of the solutions. Content Scope: A-REI.11, involving any of the function types measured in the standards. 4.D.2 below is of an example in which an item/task aligned to the evidence statement will require the student to model on grade level (OGL), using securely held knowledge from a previous grade. Type of Modeling: Solve multi-step contextual problems with degree of difficulty appropriate to Gr. 4 Securely Held Knowledge: requiring application of knowledge and skills articulated in 3.OA.A, 3.OA.8, 3.NBT, and/or 3.MD. 117

118 Sub-Claim C (expressing mathematical reasoning) and Sub-Claim D (modeling/application) in the PARCC Claims Structure are not explicitly found in the CCSS-M as domains but are included in the Mathematical Practices. s An focusing on Reasoning or Modeling will not indicate a specific standard in the Common Core column because these are not explicitly found in the CCSS-M as a domain. Instead it will indicate: OGL-On Grade Level Securely Held Knowledge (SHK)-Ability to flexibly apply what one already knows to a non-routine or complex problem. For example, modeling is a sophisticated practice. This means that modeling and other complex tasks will naturally draw upon securely held knowledge and skills. Some tasks may demand flexible application of content knowledge first gained in previous grades to solve complex problems. Examples of standards which refer to securely held knowledge begin with the words Apply and Extend. s Operations & Algebraic Thinking (OA) Number & Operations in Base Ten (NBT) Number & Operations-Fractions (NF) Measurement & Data (MD) Geometry (G) s Identifies where the practice test items were excerpted from (e.g., MC2 PARCC Practice Test Item Packets; Illustrative Mathematics) 118

119 For more information, Funded by: US Department of Education/Math-Science Partnership (MSP) New Mexico Public Education Department (PED) Higher Education Department (HED) Participating School Districts Cost Share 2018 Mathematically Connected Communities (MC 2 ) Project. All Rights Reserved. 119