January 2013 Louisville Municipal School District 3 Grade Math (MA) CCSS Pacing Guide 2nd Nine Weeks Common Core State Standards for MA Mississippi Competencies and Performance Level Objectives Descriptors rd Operations and Algebraic Thinking 3.OA.1. Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 × 7. Notes 3.1.f. Model multiplication using arrays, equal-sized groups, area models, and equal-sized moves on the number line. (DOK 2) 1.f. Proficient & Adv. Test 1: Question(s)- 14, 37 Test 2: Question(s)- 19, 26 Test 3: Question(s)- 11, 42,49 Interpreting products and modeling multiplication are not synonymous. However, in modeling multiplication, a student might demonstrate a total number of objects in n groups of n objects each. 3.1.f. Model multiplication using arrays, equal-sized groups, area models, and equal-sized moves on the number line. (DOK 2) 1.f. Proficient & Adv. Test 1: Question(s)- 14, 37 Test 2: Question(s)- 19, 26 Test 3: Question(s)- 11, 42,49 The MMFR does not specify that students use multiplication and division to solve word problems. I CAN: 3.OA.1. Apply multiplication to real life situations. 3.OA.1. Define the words product and factor. 3.OA.1. Draw an array. 3.OA.1. Explain an array using repeated addition and number lines. 3.OA.1. Find the product using objects in groups, arrays, number lines, or models. 3.OA.1. Multiply and name each number as a factor or product. 3.OA.1. Read an array. 3.OA.1. Tell in my own words what equal size groups are. 3.OA.3. Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. NOTE: Division is in 3rd 9 wks. I CAN: 1 January 2013 3.OA.3. Identify key words and relate words to operations. 3.OA.3. Use multiplication facts and strategies to solve word problems within 100 using arrays. 3.OA.3. Use multiplication facts and strategies to solve word problems within 100 using equations. 3.OA.3. Use multiplication facts and strategies to solve word problems within 100 using groups. 3.OA.3. Use multiplication facts and strategies to solve word problems within 100 using number lines. 3.OA.3. Explain that an unknown number is represented with a symbol/variable. 3.OA.4. Determine the unknown whole number in a multiplication or division equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 × ? = 48, 5 = ? ÷ 3, 6 × 6 = ?. NOTE: Division is in 3rd 9 wks. The MMFR does not specify that students determine the unknown whole number in a multiplication or division equation until grade 4.2.b. I CAN: 3.OA.4. Find the unknown number/variable/symbol to make a multiplication equation true. 3.OA.5. Apply properties of operations as strategies to multiply and divide. Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.) NOTE: Division is in 3rd 9 wks. 3.2.c. Use real number properties to develop multiple algorithms and to solve problems. (DOK 2) - Associative property of addition - Commutative property of addition - Identity property of addition 2.c. Proficient Test 1: Question(s)- 9, 25, 41 Test 2: Question(s)- 8 Test 3: Question(s)- 3, 13 The MMFR does not introduce the distributive property until grade 4.2.d. I CAN: 2 January 2013 3.OA.5. Create and model an example of Associative Property using multiplication facts. 3.OA.5. Create and model an example of Commutative Property using multiplication. (Students can use objects.) 3.OA.5. Create and model an example of Distributive Property using addition and/or multiplication. 3.OA.5. Create and model an example of the Multiplicative Identity Property of 1 using multiplication facts. 3.OA.5. Create and model an example of Zero Property using multiplication. 3.OA.5. Model the Distributive Property with the order of operations. 3.OA.7. Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of grade 3, know from memory all products of two one-digit numbers. NOTE: Division is in 3rd 9 wks. 3.1.f. Model multiplication using arrays, equal-sized groups, area models, and equal-sized moves on the number line. (DOK 2) 1.f. Proficient & Adv. Test 1: Question(s)- 14, 37 Test 2: Question(s)- 19, 26 Test 3: Question(s)- 11, 42,49 The MMFR does not specify that students know from memory all products of two one-digit numbers by the end of grade 3; however grade 4.1.i., “recall multiplication and division facts,” insinuates that students will be fluent by grade 4. 3.2.b. Determine the value of missing quantities or variables within equations or number sentences, and justify the process used. (DOK 2) 2.b. Proficient Test 1: Question(s)- 8, 40 Test 2: Question(s)- 27, 30, 32 Test 3: Question(s)- 2, 45 Grade 3.2.b objective does not specify that students solve two-step word problems. The MMFR does not specify Order of Operations until grade 7.1.a. I CAN: 3.OA.7. Fluently multiply numbers 0-5. 3.OA.7. Fluently multiply numbers 6-10 3.OA.7. Recall from memory all products of two 1digit numbers. 3.OA.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding. NOTE: Division is in 3rd 9 wks. I CAN: 3 January 2013 3.OA.8. Recognize key words to determine the number of steps in a word problem. 3.OA.8. Construct an equation with a letter (variable) for the unknown quantity. 3.OA.8. Explain or demonstrate how to solve twostep word problems using addition and subtraction (Of numbers within 1,000). 3.OA.8. Explain or demonstrate how to solve twostep word problems using multiplication (Of single digit products less than 100). 3.OA.8. Justify my answers using mental math and estimation. 3.OA.8. Read a word problem and interpret it into an equation using numbers and letters (variables). 3.OA.8. Solve two-step word problems which include multiple operations. 3.OA.8. Use mental math to estimate the answer of a single step word problem. 3.OA.8. Use mental math to estimate the answer of a two-step word problem. 3.OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends. 3.2.a. Create, describe, and extend growing and repeating patterns with physical materials and symbols including numbers. (DOK 2) I CAN: 3.1.a. Compose and decompose four-digit whole numbers with representations in words, physical models, and expanded and standard forms. (DOK 1) 3.OA.9. Explain and model the relationship of odd and even number patterns with addition facts. Examples: even. even. 2.a. Basic, Proficient, Advanced Test 1: Question(s)- 7, 54 Test 2: Question(s)- 9, 55 Test 3: Question(s)- 9, 19, 32 The MMFR does not specify that students explain patterns using properties of operations. 1.a. Proficient Test 1: Question(s)- 1, 20, 36 Test 2: Question(s)- 1, 4, 28 Test 3: Question(s)- 1, 17 number is odd. 3.OA.9. Explain and model the relationship of odd and even number patterns with multiplication facts. 4 January 2013 always even, using skip counting, repeated addition, arrays, etc. 3.OA.9. Use a multiplication table to locate examples of the commutative, identity, and zero properties of multiplication. 3.OA.9. Use an addition table to locate examples of the commutative and identity properties of addition. Measurement and Data 3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets. 3.5.a Compare data and interpret quantities represented on tables and different types of graphs (line plots, pictographs, and bar graphs), make predictions, and solve problems based on the information. (DOK 3) 5.a. Basic, Proficient, Adv. Test 1: Question(s)- 16, 18, 31, 49, 52 Test 2: Question(s)- 17, 18, 36, 50, 51 Test 3: Question(s)- 16, 21, 30, 37, 53 I CAN: 3.MD.3. Answer questions about a graph to analyze and interpret data. 3.MD.3. Collect and organize data to create a graph. 3.MD.3. Create a scaled bar graph to represent data. 3.MD.3. Create a scaled picture graph to represent data. 3.MD.3. Explain the data on a graph. 3.MD.3. Read and analyze a horizontal and vertical scaled bar graph. 3.MD.3. Read and analyze a scaled picture graph. 3.MD.3. Use a bar graph to solve 1-step “how many more” and “how many less” questions. 3.MD.3. Use a bar graph to solve 2-step “how many more” and “how many less” questions. 3.MD.3. Use a key to solve word problems for a picture graph. 3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and 3.5.a 5.a. Basic, Proficient, Adv. Compare data and interpret Test 1: Question(s)- 16, quantities represented on tables and 18, 31, 49, 52 The MMFR does not specify that students measure to the nearest 5 fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units—whole numbers, halves, or quarters. different types of graphs (line plots, pictographs, and bar graphs), make predictions, and solve problems based on the information. (DOK 3) Test 2: Question(s)- 17, 18, 36, 50, 51 Test 3: Question(s)- 16, 21, 30, 37, 53 January 2013 1/4 of an inch until grade 4.4.a. By grade 4, the framework specifies that students measure to the nearest 1/8 of an inch. I CAN: 3.MD.4. Collect and organize data to create a line plot. 3.MD.4. Create a line plot using given measurement data. No CCSS I CAN: --Analyze and predict the number of different combinations of two or more objects. --Model the number of different combinations of two or more objects. --Relate the combinations to multiplication. 3.5.b. Analyze, predict, and model the number of different combinations of two or more objects, and relate to multiplication. (DOK 2) Working with equal groups to gain foundations for multiplication is found at the 2nd grade of the CCSS. 6
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