Overview. Essential Questions. Grade 4 Mathematics, Quarter 2, Unit 2.1 Multiplying Multi-Digit Whole Numbers

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1 Multiplying Multi-Digit Whole Numbers Overview Number of instruction days: 5 7 (1 day = 90 minutes) Content to Be Learned Use strategies based on place value and properties of operations to multiply a whole number of up to four digits by a one-digit whole number. Use strategies based on place value and properties of operations to multiply 2 two-digit whole numbers. Solve multi-step word problems involving whole numbers and having whole number answers. Represent problems using an equation with a letter standing for an unknown quantity. Estimate and use mental computation to assess the reasonableness of answers. Mathematical Practices to Be Integrated 1 Make sense of problems and persevere in solving them. Represent multiplication problems with arrays and area models to help conceptualize and solve them. Assess the reasonableness of answers using estimation strategies, including rounding and mental computation. 7 Look for and make use of structure. Make sense of decomposing a number when using the area model to multiply. Use equations to accurately represent multidigit multiplication calculations. Essential Questions How can you explain multiplication using equations, area models, and/or rectangular arrays? What are some strategies for solving multidigit multiplication problems? How can you represent and solve for the unknown in word problems? How can you use place value when multiplying 2 two-digit numbers? How can you assess whether your answer is reasonable? Providence Public Schools D-29

2 Multiplying Multi-Digit Whole Numbers (5 7 days) Standards Common Core State Standards for Mathematical Content Number and Operations in Base Ten 2 2 Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000, NBT Use place value understanding and properties of operations to perform multi-digit arithmetic. 4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models. Operations and Algebraic Thinking 4.OA Use the four operations with whole numbers to solve problems. 4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number answers using the four operations, including problems in which remainders must be interpreted. 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. Common Core State Standards for Mathematical Practice 1 Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, Does this make sense? They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. 7 Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 8 equals the well remembered , in preparation for learning about the distributive property. In the expression x 2 + 9x + 14, older students can see the 14 as 2 7 and the 9 as They recognize the D-30 Providence Public Schools

3 Multiplying Multi-Digit Whole Numbers (5 7 days) Grade 4 Mathematics, Quarter 2, Unit 2.1 significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 3(x y) 2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Clarifying the Standards Prior Learning In Grade 2 students worked with equal groups of objects to gain a foundation for multiplication. They used addition to find the total number of objects arranged in rectangular arrays of up to five rows and five columns. They wrote equations to express the total as a sum of equal addends. In Grade 3 students multiplied and divided within 100 fluently. By the end of Grade 3, students knew from memory all the products of 2 one-digit numbers. In the PARCC framework, multiplication is a major focus in Grade 3. Current Learning In Grade 4 students multiply a whole number of up to four digits by a one-digit number. They also multiply 2 two-digit numbers. They illustrate and explain multiplication calculations using equations, arrays, and/or area models. Operations with whole numbers, including multiplication, are a major focus in fourth grade. Students develop fluency with efficient procedures for multiplying whole numbers. They use understanding of place value and properties of operations to solve problems involving multiplication. Students use mental computation and estimation to assess the reasonableness of their answers. Future Learning In Grade 5, performing operations with multi-digit whole numbers is a major focus. Students will extend their previous understandings of multiplication to multiply a fraction of a whole number by a fraction. They also will fluently multiply multi-digit whole numbers using the standard algorithm, and they will multiply decimals to the hundreds place. Additional Findings In Grades 3-5, students should focus on the meanings of and relationship between multiplication and division. It is important that students understand what each number in a multiplication or division expression represents. (Principles and Standards for School Mathematics, p. 151) Providence Public Schools D-31

4 Multiplying Multi-Digit Whole Numbers (5 7 days) Assessment When constructing an end-of-unit assessment, be aware that the assessment should measure your students understanding of the big ideas indicated within the standards. The CCSS for Mathematical Content and the CCSS for Mathematical Practice should be considered when designing assessments. Standards-based mathematics assessment items should vary in difficulty, content, and type. The assessment should comprise a mix of items, which could include multiple choice items, short and extended response items, and performance-based tasks. When creating your assessment, you should be mindful when an item could be differentiated to address the needs of students in your class. The mathematical concepts below are not a prioritized list of assessment items, and your assessment is not limited to these concepts. However, care should be given to assess the skills the students have developed within this unit. The assessment should provide you with credible evidence as to your students attainment of the mathematics within the unit. Multiply a whole number of up to four digits by a one-digit whole number. Multiply two two-digit whole numbers. Illustrate and explain calculations using equations, rectangular arrays, and/or area models. Solve multi-step word problems involving whole numbers. Represent problems using an equation with a letter standing for an unknown quantity. Estimate and use mental computation to assess the reasonableness of answers. Learning Objectives Instruction Students will be able to: Use strategies based on place value and properties of operations to multiply a whole number of up to four digits by a one-digit whole number. Use strategies based on place value and properties of operations to multiply two two-digit whole numbers. Illustrate and explain calculations using equations, rectangular arrays, and/or area models. Solve multi-step word problems involving whole numbers and having whole number answers. Represent problems using an equation with a letter standing for an unknown quantity. Estimate and use mental computation to assess the reasonableness of answers. Demonstrate understanding of the concepts and skills in this unit. Resources envision Math Grade 4, Pearson Education, Inc., 2009 Topic 5, Multiplying 1-Digit Numbers, Teacher Edition D-32 Providence Public Schools

5 Multiplying Multi-Digit Whole Numbers (5 7 days) Grade 4 Mathematics, Quarter 2, Unit 2.1 Also see Section I, Supplemental Materials Lesson 5.6A, Connecting the Expanded and Standard Algorithms Lesson 5.8A, Multiplying 3- and 4-Digit by 1-Digit Numbers Topic 7, Multiplying 2-Digit Numbers, Teacher Edition Also see Section I, Supplemental Materials Lesson 7.4A, Arrays and an Extended Algorithm Teacher Resource Masters Student Edition Investigations in Numbers, Data, and Space, Grade 4, Pearson Education, Inc., 2008 Implementing Investigations in Grade 4- Implementation Guide Unit 3, Multiple Towers and Division Stories, Teacher Edition Investigation 2: Adding It Up Unit 8, How Many Packages? How Many Groups?, Teacher Edition Investigation 1: Multiplication with 2-Digit Numbers Investigation 2: Strategies for Multiplication Also see Section I, Supplemental Materials Session 2.4A, Multiplying by 4-Digit by 1-Digit Numbers Teacher Resources Binder Pearson Online Success Net - Implementing Investigations Site - Exam View Assessment Suite Note: The district resources may contain content that goes beyond the standards addressed in this unit. See the Planning for Effective Instructional Design and Delivery and Assessment sections for ample resources to refer to when planning your unit and individual lessons. Materials Calculators, colored chalk, centimeter grid paper, quarter-inch grid paper, tape, place-value blocks, array cards, connecting cubes Instructional Considerations Key Vocabulary compatible numbers factor product Providence Public Schools D-33

6 Multiplying Multi-Digit Whole Numbers (5 7 days) Planning for Effective Instructional Design and Delivery There is an abundance of resources for this unit. Be sure that you are able to use the parts of the resources that will achieve the standards. Carefully look at the Supplemental lessons found in Section I. These lessons were created with the CCSS in mind. This is a major focus in grade 4 and prepares the students for the algorithm in grade 5. Developing flexibility in breaking numbers apart gives students a better understanding of the importance of place value and the distributive property in multi-digit multiplication. Students use base ten blocks, area models, partitioning, compensation strategies, etc. when multiplying whole numbers and use words and diagrams to explain their thinking. They use the terms factor and product when communicating their reasoning. Multiple strategies enable students to develop fluency with multiplication and transfer that understanding to division. Students will use the standard algorithm in grade 5. When planning for this unit, refer to the Operations and Algebraic Thinking Progression, page 23. Here you will find a table with examples of multiplication and division situations. In envision Lesson 5-1 (TE, page 96B), use cues, questions, and advance organizers to activate prior knowledge about multiplication facts and patterns. Ask inferential and analytic questions such as, What are some things that come in groups of tens and hundreds? Why is it easier to count in groups of tens or hundreds? This strategy can help students connect their prior knowledge to new knowledge. In envision Lesson 7-3 (page 146B), use cues, questions and advance organizers to activate prior knowledge. Ask students inferential questions such as, Why do humans like things arranged in columns or rows? What kinds of things do you see neatly arranged in rows and columns, or in arrays? [Egg cartons, six-pack of soda, theater seating, etc.] Why do we like patterns? Incorporate Ten Minute Math Activities, the Problem of the Day, and the Daily Spiral Review that are aligned to The Common Core State Standards for Mathematics. EnVision Center Activities and Investigations Activities offer additional practice for student learning and support small group differentiated instruction. Use teacher created common tasks as formative assessments to monitor student progress and understanding of critical content and essential questions. Use data from formal and informal assessments to guide your instruction and planning. For planning considerations, read through the teacher editions for suggestions about scaffolding techniques, using additional examples, and differentiated instruction as suggested by the envision and Investigations resources, particularly the Algebra Connections and Teacher Notes section. D-34 Providence Public Schools

7 Multiplying Multi-Digit Whole Numbers (5 7 days) Grade 4 Mathematics, Quarter 2, Unit 2.1 Notes Providence Public Schools D-35

8 Multiplying Multi-Digit Whole Numbers (5 7 days) D-36 Providence Public Schools