Mathematically Connected Communities. PARCC Practice Test Items Grade 4 Mathematics
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1 Mathematically Connected Communities PARCC Practice Test Items Grade 4 Mathematics Excerpted in fall 2017 from: Item Packets-Preparing for Spring Item Packets-Spring Illustrative Mathematics under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. PARCC Computer-Based Practice Tests
2 Contents MC 2 Thinking Protocol... 3 User s Guide Difficulty (Most to Least) CCSS-M Page Numbers 1 4.G.2 4.G.A C.2 OGL MD MD.A C.5-5 OGL C.1-2 OGL C.6-2 OGL G.1 4.G.A C.7-2 OGL MD MD.B Int.6 4.MD.A C.5-2 OGL MD.1 4.MD.A C.4-5 OGL C.5-1 OGL NBT NBT.B C.7-3 OGL OA OA.A C.7-1 OGL OA OA.B Int.4 4.MD.A MD.3 4.MD.A C.6-1 OGL NF.5 4.NF.C C.5-6 SHK D.2 SHK MD MD.A C.4-2 OGL G.3 4.G.A D.1 OGL C.4-1 OGL NF.3c 4.NF.B.3.C NBT NBT.B NF.Int.1 Multiple NF NF.A Int.5 4.NBT.A.1 4.OA.A OA.2 4.OA.A NF.4b-2 4.NF.B.4.B OA.5 4.OA.C NF.7 4.NF.C NBT.1 4.NBT.A NF.4b-1 4.NF.B.4.B Int.2 4.NBT.B MD.7 4.MD.C NBT NBT.B NF.4a 4.NF.B.4.A NF.3d 4.NF.B.3.D NF.A.Int.1 4.NF.A NF.4c 4.NF.A.2 4.NF.B.4.C NBT.Int.1 Multiple MD.5 4.MD.C OA MD.C.5.A 4.OA.A NF.Int.2 4.NF.A.1 4.NF.C.5 4.NF.C NF NF.A Int.3 4.NBT.B.5 4.OA.A MD.6 4.MD.C NF.3a 4.NF.B.3.A OA OA.A NBT NBT.B NBT.2 4.NBTA Int.7 4.NBT.A.1 4.NBT.B OA OA.A Int.8 4.NBT.B.4 4.OA.A NF.6 4.NF.C OA OA.B C.5-4 OGL NBT NBT.B NBT NBT.B NF.3b-1 4.NF.B.3.B 86 2
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 4.G.2 4.G.A.2 Geometry MC 2 excerpted test items, Fall
5 1 4.G.2 4.G.A.2 Geometry MC 2 excerpted practice test items, Fall
6 2 4.C.2 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
7 3 4.MD MD.A.2 Measurement & Data Illustrative Mathematics MC 2 excerpted practice test items, Fall
8 s s 4 4.C.5-5 OGL Reasoning PARCC Computer-Based Practice Test, Unit 1 MC 2 excerpted practice test items, Fall
9 s s 5 4.C.1-2 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
10 s 6 4.C.6-2 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
11 s 7 4.G.1 4.G.A.1 Geometry Illustrative Mathematics MC 2 excerpted practice test items, Fall
12 Difficulty s s 8 4.C.7-2 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
13 9 4.MD MD.B.4 Measurement & Data Illustrative Mathematics MC 2 excerpted practice test items, Fall
14 10 4.Int.6 4.MD.A.3 4.NF.B.3 Measurement & Data Number & Operations-Fractions MC 2 excerpted practice test items, Fall
15 11 4.C.5-2 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
16 12 4.MD.1 4.MD.A.1 Measurement & Data MC 2 excerpted practice test items, Fall
17 13 4.C.4-5 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
18 14 4.C.5-1 OGL Reasoning MC 2 excerpted practice test items, Fall
19 15 4.NBT NBT.B.5 Number & Operations in Base Ten Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
20 16 4.C.7-3 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
21 17 4.OA OA.A.3 Operations & Algebraic Thinking Item Packets-Spring 2017 MC 2 excerpted practice test items, Fall
22 17 4.OA OA.A.3 Operations & Algebraic Thinking Item Packets-Spring 2017 MC 2 excerpted practice test items, Fall
23 17 4.OA OA.A.3 Operations & Algebraic Thinking MC 2 excerpted practice test items, Fall
24 17 4.OA OA.A.3 Operations & Algebraic Thinking MC 2 excerpted practice test items, Fall
25 18 4.C.7-1 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
26 19 4.OA OA.B.4 Operations & Algebraic Thinking Illustrative Mathematics MC 2 excerpted practice test items, Fall
27 20 4.Int.4 4.MD.A.2 4.NBT.B.6 Measurement & Data Number & Operations in Base Ten Item Packets-Spring 2017 MC 2 excerpted practice test items, Fall
28 21 4.MD.3 4.MD.A.3 Measurement & Data MC 2 excerpted practice test items, Fall
29 22 4.C.6-1 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
30 23 4.NF.5 4.NF.C.5 Number & Operations - Fractions Illustrative Mathematics MC 2 excerpted practice test items, Fall
31 24 4.C.5-6 SHK Reasoning MC 2 excerpted practice test items, Fall
32 25 4.D.2 SHK Modeling Continued on next page. MC 2 excerpted practice test items, Fall
33 25 (Cont.) 4.D.2 SHK Modeling MC 2 excerpted practice test items, Fall
34 26 4.MD MD.A.2 Measurement & Data Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
35 27 4.C.4-2 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
36 28 4.G.3 4.G.A.3 Geometry Illustrative Mathematics Continued on next page. MC 2 excerpted practice test items, Fall
37 28 (Cont.) 4.G.3 4.G.A.3 Geometry Illustrative Mathematics Continued on next page. MC 2 excerpted practice test items, Fall
38 28 (Cont.) 4.G.3 4.G.A.3 Geometry Illustrative Mathematics MC 2 excerpted practice test items, Fall
39 29 4.D.1 OGL Modeling MC 2 excerpted practice test items, Fall
40 29 4.D.1 OGL Modeling MC 2 excerpted practice test items, Fall
41 29 4.D.1 OGL Modeling MC 2 excerpted practice test items, Fall
42 30 4.C.4-1 OGL Reasoning PARCC Computer-Based Practice Test, Unit 3 MC 2 excerpted practice test items, Fall
43 31 4.NF.3c 4.NF.B.3.C Number & Operations - Fractions Illustrative Mathematics MC 2 excerpted practice test items, Fall
44 31 4.NF.3c 4.NF.B.3.C Number & Operations - Fractions Illustrative Mathematics MC 2 excerpted practice test items, Fall
45 32 4.NBT NBT.B.6 Number & Operations in Base Ten Illustrative Mathematics MC 2 excerpted practice test items, Fall
46 33 4.NF.Int.1 Multiple Number & Operations - Fractions MC 2 excerpted practice test items, Fall
47 33 4.NF.Int.1 Multiple Number & Operations - Fractions MC 2 excerpted practice test items, Fall
48 34 4.NF NF.A.2 Number & Operations - Fractions MC 2 excerpted practice test items, Fall
49 35 4.Int.5 4.NBT.A.1 4.OA.A.3 Multiple MC 2 excerpted practice test items, Fall
50 36 4.OA.2 4.OA.A.2 Operations & Algebraic Thinking MC 2 excerpted practice test items, Fall
51 36 4.OA.2 4.OA.A.2 Operations & Algebraic Thinking MC 2 excerpted practice test items, Fall
52 37 4.NF.4b-2 4.NF.B.4.B Number & Operations - Fractions Illustrative Mathematics MC 2 excerpted practice test items, Fall
53 38 4.OA.5 4.OA.C.5 Operations & Algebraic Thinking Illustrative Mathematics MC 2 excerpted practice test items, Fall
54 39 4.NF.7 4.NF.C.7 Number & Operations - Fractions MC 2 excerpted practice test items, Fall
55 40 4.NBT.1 4.NBT.A.1 Number & Operations in Base Ten MC 2 excerpted practice test items, Fall
56 41 4.NF.4b-1 4.NF.B.4.B Number & Operations - Fractions MC 2 excerpted practice test items, Fall
57 42 4.Int.2 4.NBT.B.5 Number & Operations in Base Ten MC 2 excerpted practice test items, Fall
58 43 4.MD.7 4.MD.C.7 Measurement & Data MC 2 excerpted practice test items, Fall
59 44 4.NBT NBT.B.6 Number & Operations in Base Ten 12. Enter your answer in the box = MC 2 excerpted practice test items, Fall
60 45 4.NF.4a 4.NF.B.4.A Number & Operations - Fractions Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
61 46 4.NF.3d 4.NF.B.3.D Number & Operations - Fractions MC 2 excerpted practice test items, Fall
62 46 4.NF.3d 4.NF.B.3.D Number & Operations - Fractions MC 2 excerpted practice test items, Fall
63 47 4.NF.A.Int.1 4.NF.A.1 4.NF.A.2 Number & Operations - Fractions MC 2 excerpted practice test items, Fall
64 47 4.NF.A.Int.1 4.NF.A.1 4.NF.A.2 Number & Operations - Fractions MC 2 excerpted practice test items, Fall
65 48 4.NF.4c 4.NF.B.4.C Number & Operations - Fractions MC 2 excerpted practice test items, Fall
66 48 4.NF.4c 4.NF.B.4.C Number & Operations - Fractions MC 2 excerpted practice test items, Fall
67 49 4.NBT.Int.1 Multiple Number & Operations in Base Ten MC 2 excerpted practice test items, Fall
68 50 4.MD.5 4.MD.C.5 4.MD.C.5.A Measurement & Data MC 2 excerpted practice test items, Fall
69 51 4.OA OA.A.3 Operations & Algebraic Thinking MC 2 excerpted practice test items, Fall
70 52 4.NF.Int.2 4.NF.A.1 4.NF.C.5 4.NF.C.6 Number & Operations - Fractions MC 2 excerpted practice test items, Fall
71 53 4.NF NF.A.1 Number & Operations - Fractions MC 2 excerpted practice test items, Fall
72 54 4.Int.3 4.NBT.B.5 4.OA.A.2 Number & Operations in Base Ten Operations in Algebraic Thinking Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
73 55 4.MD.6 4.MD.C.6 Measurement & Data MC 2 excerpted practice test items, Fall
74 56 4.NF.3a 4.NF.B.3.A Number & Operations - Fractions MC 2 excerpted practice test items, Fall
75 57 4.OA OA.A.1 Operations & Algebraic Thinking Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
76 58 4.NBT NBT.B.4 Number & Operations in Base Ten MC 2 excerpted practice test items, Fall
77 59 4.NBT.2 4.NBTA.2 Number & Operations in Base Ten MC 2 excerpted practice test items, Fall
78 60 4.Int.7 4.NBT.A.1 4.NBT.B.4 Number & Operations in Base Ten MC 2 excerpted practice test items, Fall
79 61 4.OA OA.A.1 Operations & Algebraic Thinking MC 2 excerpted practice test items, Fall
80 62 4.Int.8 4.NBT.B.4 4.OA.A.3 Number & Operations in Base Ten Operations & Algebraic Thinking Item Packets-Spring 2015 MC 2 excerpted practice test items, Fall
81 63 4.NF.6 4.NF.C.6 Number & Operations - Fractions Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
82 64 4.OA OA.B.4 Operations & Algebraic Thinking Illustrative Mathematics MC 2 excerpted practice test items, Fall
83 65 4.C.5-4 OGL Reasoning Pending New PARCC Released Test Items MC 2 excerpted practice test items, Fall
84 66 4.NBT NBT.B.5 Number & Operations in Base Ten MC 2 excerpted practice test items, Fall
85 67 4.NBT NBT.B.4 Number & Operations in Base Ten MC 2 excerpted practice test items, Fall
86 68 4.NF.3b-1 4.NF.B.3.B Number & Operations - Fractions MC 2 excerpted practice test items, Fall
87 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. MC 2 excerpted practice test items, Fall
88 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. MC 2 excerpted practice test items, Fall
89 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., Item Packets; Illustrative Mathematics) MC 2 excerpted practice test items, Fall
90 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 2017 Mathematically Connected Communities (MC 2 ) Project. All Rights Reserved. 90
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