UNIT TITLE: Module 3 Multi-Digit Multiplication and Division Grade: 4th Time: 9 weeks

Transcription

1 Common Core Standards: MAFS.4.OA.1.3, MAFS.4.OA.1.2, MAFS.4.OA.1.3, MAFS.4.OA.2.4, MAFS.4.NBT.2.4, MAFS.4.NBT.2.6, MAFS.4.MD.1.3 Mathematical Practice: Mp.2, MP.4, MP.5, MP.8 CCSS Unpacked Know (Level 2) Understand (Level 2 & 3) Be able to do (Level 3 & 4) Vocabulary & Terms: Multiplication Perimeter Area Factor Product Quotient Dividend Divisor Rectangular array Division Distributive property Expanded form Communicative property Associative property Multiple Formulas Prime Composite Divisibility Area model Remainder Operation Interpret Number Bond (Fact Family) Partial Product Known: Variable Equation Standard algorithm Fluently multiple and divide within 100. Interpret a multiplication equation as a comparison. Representing verbal statements of multiplicative comparisons as equations. List all factors for pairs for a whole number in the range of Explain how multiplication and division are related with inverse operations. Identify fact families and how they relate. Understand the difference between prime and composite number. Understand the difference between perimeter and area. Know how that they always multiply and divide before adding or subtracting. Estimate and explain reasonableness. Draw models to represent the equation. Illustrate and explain the equations using rectangular arrays and/or models for multi-digit multiplication and/or division. Multiply or divide to solve word problems involving multiplicative comparisons using drawings and equations with a variable. Solve multi step word problems posed with whole number and having whole-number answers using the four operations, including problems in which remainders must be interpreted. Represent these problems using equations with a variable. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range is a multiple of a given one-digit number. Determine whether a given whole number in the range is prime or composite. Multiply a whole number of up to four digits by a one-digit whole number and multiply two twodigit numbers, using strategies based on place value and the properties of operations. Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors, using strategies based on place value, the properties of operations and/or the relationship between multiplication and division. Apply the area and perimeter formulas for rectangles in real world and mathematical CCSS Mathematics Unit 1

2 Compute Length Width Equivalent Estimate Place value Multi-digit Equations Reasonableness Comparison Tape diagram Distance Fluency Assessments Vocabulary Assessments Unit Goal: I can... Assessments Sprints Exit Tickets Mid-Chapter Checks Quizzes for each topic (A,B,C,D, E, F, G, H) problems. Assessments Quizzes containing multi-step word problems Mid-Module Assessment using Understand criteria End of Module Assessment multiply or divide to solve word problems using strategies based on place value with a model, tape diagrams or array. determine whether a given whole number is prime or composite, or is a multiple of a given number. use strategies to find whole number quotients with remainders and interpret the remainder. 4 In everyday situations, I will develop a strategy to complete a multi-step word problems using combined operations. 3 I can... multiply or divide to solve word problems using strategies based on place value with a model, tape diagrams or array. determine whether a given whole number is prime or composite, or is a multiple of a given number. use strategies to find whole number quotients with remainders and interpret the remainder. CCSS Mathematics Unit 2

3 2 I can... Fluently multiply and divide within 100. Interpret a multiplication equation as a comparison. Representing verbal statements of multiplicative comparisons as equations. List all factors for pairs for a whole number in the range of Explain how multiplication and division are related with inverse operations. Identify fact families and how they relate. Understand the difference between prime and composite number. Understand the difference between perimeter and area. Know how that they always multiply and divide before adding or subtracting. Estimate and explain reasonableness of an answer. Draw models to represent multiplication and division equations with a variable. Illustrate and explain the equations using rectangular arrays and/or models for multi-digit multiplication and/or division 1 With help, I can... Fluently multiply and divide within 100. Interpret a multiplication equation as a comparison. Representing verbal statements of multiplicative comparisons as equations. List all factors for pairs for a whole number in the range of Explain how multiplication and division are related with inverse operations. Identify fact families and how they relate. Understand the difference between prime and composite number. Understand the difference between perimeter and area. Know how that they always multiply and divide before adding or subtracting. Estimate and explain reasonableness of an answer. Draw models to represent multiplication and division equations with a variable. CCSS Mathematics Unit 3

4 Illustrate and explain the equations using rectangular arrays and/or models for multi-digit multiplication and/or division Major Unit Objectives I can complete multiplicative comparison word problems. I can multiply by 10, 100 and 1,000. I can complete multiplication of up to four digits by single-digit numbers. I can solve multi-step word problems using multiplication. I can divide using tens and ones with successive remainders. I can reason with divisibility. I can compute division of thousands, hundreds, tens and ones. I can multiply two-digit numbers by two-digit numbers. Models/Tools: Area model, place value chart, grid paper, number disks, base ten blocks, arrays, tape diagrams, partial product models through area, number bonds (fact families), anchor charts, exit slips etc. CCSS Mathematics Unit 4

5 Instruction Based on Engage NY supplemented by Go Math!, recorded on Marzano lesson plan template. Standards Topics and Objectives Days 4.OA.1 4.OA.2 4.MD.3 4.OA.3 4.NBT.5 4.OA.1 4.OA.2 4.NBT.1 A Multiplicative Comparison Word Problems Lesson 1: Lesson 2: Lesson 3: Investigate and use the formulas for area and perimeter of rectangles. Solve multiplicative comparison word problems by applying the area and perimeter formulas. B Multiplication by 10, 100, and 1,000 Lesson 4: Demonstrate understanding of area and perimeter formulas by solving multistep real world problems. Interpret and represent patterns when multiplying by 10, 100, and 1,000 in arrays and numerically. Lesson 5: Multiply multiples of 10, 100, and 1,000 by single digits, recognizing patterns. Lesson 6: Multiply two-digit multiples of 10 by two-digit multiples of 10 with the area model. 3 3 Strategies Addressing Content (how will you help students): DQ2 Process: direct instruction, concept development scaffolding, incorporate prior knowledge, turn and talk, Elaborate: word problems that ask to explain why, homework, Record: problem set, homework Reflect: tracking progress, exit tickets DQ3 ID Similarities & differences: multiplication and division relationships, Examine errors: student debrief discussion and review, exit slips Practice: problem set, homework DQ4 Engage in complex tasks: apply knowledge on assessments and class discussion, student debrief discussions 4.NBT.5 4.OA.2 4.NBT.1 C Multiplication of up to Four Digits by Single-Digit Numbers Lesson 7: Use place value disks to represent twodigit by one-digit multiplication. 5 Lesson 8: Extend the use of place value disks to represent three- and four-digit by one- CCSS Mathematics Unit 5

6 digit multiplication. Lessons 9 10: Multiply three- and four-digit numbers by one-digit numbers applying the standard algorithm. Lesson 11: Connect the area model and the partial products method to the standard algorithm. 4.OA.1 4.OA.2 4.OA.3 4.NBT.5 D Multiplication Word Problems Lesson 12: Lesson 13: Solve two-step word problems, including multiplicative comparison. Use multiplication, addition, or subtraction to solve multi-step word problems. 2 Mid-Module Assessment: Topics A D (review 1 day, assessment ½ day, return ½ day) 2 CCSS Mathematics Unit 6

7 4.NBT.6 4.OA.3 E Division of Tens and Ones with Successive Remainders Lesson 14 Solve division word problems with remainders. 8 Lesson 15: Understand and solve division problems with a remainder using the array and area models. Lesson 16: Lesson 17: Lesson 18: Lesson 19: Lesson 20: Lesson 21: Understand and solve two-digit dividend division problems with a remainder in the ones place by using number disks. Represent and solve division problems requiring decomposing a remainder in the tens. Find whole number quotients and remainders. Explain remainders by using place value understanding and models. Solve division problems without remainders using the area model. Solve division problems with remainders using the area model. 4.OA.4 F Reasoning with Divisibility Lesson 22: Find factor pairs for numbers to 100 and use understanding of factors to define prime and composite. 4 Lesson 23: Lesson 24: Use division and the associative property to test for factors and observe patterns. Determine whether a whole number is a CCSS Mathematics Unit 7

8 multiple of another number. Lesson 25: Explore properties of prime and composite numbers to 100 by using multiples. 4.OA.3 4.NBT.6 4.NBT.1 G Division of Thousands, Hundreds, Tens, and Ones Lesson 26: Divide multiples of 10, 100, and 1,000 by single-digit numbers. 8 Lesson 27: Lesson 28: Lesson 29: Lesson 30: Represent and solve division problems with up to a three-digit dividend numerically and with number disks requiring decomposing a remainder in the hundreds place. Represent and solve three-digit dividend division with divisors of 2, 3, 4, and 5 numerically. Represent numerically four-digit dividend division with divisors of 2, 3, 4, and 5, decomposing a remainder up to three times. Solve division problems with a zero in the dividend or with a zero in the quotient. Lesson 31: Interpret division word problems as either number of groups unknown or group size unknown. Lesson 32: Lesson 33: Interpret and find whole number quotients and remainders to solve onestep division word problems with larger divisors of 6, 7, 8, and 9. Explain the connection of the area CCSS Mathematics Unit 8

9 model of division to the long division algorithm for three- and four-digit dividends. 4.NBT.5 4.OA.3 4.MD.3 H Multiplication of Two-Digit by Two-Digit Numbers Lesson 34: Multiply two-digit multiples of 10 by two-digit numbers using a place value chart. 5 Lesson 35: Lesson 36: Multiply two-digit multiples of 10 by two-digit numbers using the area model. Multiply two-digit by two-digit numbers using four partial products. Lessons 37 38: Transition from four partial products to the standard algorithm for two-digit by two-digit multiplication. End-of-Module Assessment: Topics A H (review 1 day, assessment ½ day, return ½ day, remediation or further application 1 day) 3 Total Number of Instructional Days 43 Content: How will you vary what students will learn and the materials that represent the content? - Re-teaching or remediating Go Math! Lessons Process: How will you vary activities through which students make sense of key ideas using essential skills? -Differentiated centers, triple I, Go Math!, small group instruction, math games, grab and go, ALEX, Soar to Success, Think Central, Product: How will you vary the way students demonstrate and extend what they understand and can do as a result of a span of learning? - Building on foundational skills and scaffolding instruction to students eventually applying their knowledge CCSS Mathematics Unit 9

10 Leaning Environment: How will you vary the classroom conditions that set the climate, expectations for learning, and physical conditions? - Teaching Learning Goals and Scales Expectations, Tracking progress, - Routines! - Established partnerships. - Differentiated peer groups and peer tutoring CCSS Mathematics Unit 10