1. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Grade 4 – Module 3 – Second Half

2. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Session Objectives Examination of the development of mathematical understanding across the second half of the module with a focus on the Concept Development within the lessons. Introduction to mathematical models and instructional strategies to support implementation of A Story of Units.

3. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

4. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Curriculum Overview of A Story of Units

5. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module Overview – First Half Scan over the Topic Titles and lessons for Topics A-D. Form a general understanding of where the first half of the module begins and where it ends.

6. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Module Overview – Second Half Scan over the Topic Titles and lessons for Topics E-H. Form a general understanding of where the second half of the module begins and where it ends.

7. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

8. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic E: Division of Tens and Ones with Successive Remainders Read Topic Opener E. What types of models will be used? What Standard is addressed? What is the content of the Topic?

9. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Divide with Remainders Fluency T:How many groups of ___ are in ___? T:Prove it by counting by ____. T: Show and say how many groups. T:How many left? Lesson 14, Fluency 12÷3 13÷3 15÷5 17÷5 20÷4 23÷4 50÷5 55÷5

10. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Divide a 2-digit number by a 1-digit number with a remainder using an array and a tape diagram Lesson 14, Problem 3 13 ÷ 6

11. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Debrief: Solve a division problem using an array and the area model.  What does the quotient represent in the area model?  When does the area model present a challenge in representing division problems?  How is the whole represented in the area model?  The quotient represents a side length. The remainder consists of square units. Why? Lesson 15, Application Problem, Problem 2 and Debrief

12. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Division of tens and ones 6 ÷ 3 Lesson 16, Problems 1 and 2 36 ÷ 3

13. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Divide 2-digit numbers by 1-digit numbers, regrouping in the tens 3 ones ÷ 2 Lesson 17, Problem 1 3 tens ÷ 2

14. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Find whole number quotients and remainders 86 ÷ 5 Lesson 18, Problem 2

15. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Solve division problems using area models 48 ÷ 4 Decompose whole to part. Lesson 20

16. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Solve division problems using area models 96÷ 4 Compose part to whole. Lesson 20

17. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Division area models with remainders Lesson 21, Problem 1 Solve for 37÷2

18. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic F: Reasoning with Divisibility Read Topic Opener F. Why is this Topic placed between multiplication and division in the module?

19. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Use division and the associative property to test for factors Can 54 be divided evenly by 3? 2? Do we need to divide to determine if 5 is a factor of 54? Is 6 a factor of 54? If 54 = 6 × 9, then is 54 = (2 × 3) × 9 true? Use the associative property to show both 2 and 3 are factors of 42. Lesson 23

20. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Multiples Use division and the associative property to determine whether a whole number is a multiple of another number (Lesson 24). Explore properties of prime and composite numbers to 100 by using multiples (Lesson 25). Lesson 24 & 25

21. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic G: Division of Thousands, Hundreds, Tens and Ones Read Topic Opener G. Why is division of larger dividends separated in this module?

22. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Lesson 26: Divide multiples of 10, 100 and 1,000 by single-digit numbers. Take 5 minutes to read through the entire lesson. Highlight 2 “ah-has” to share at your table. Complete the Problem Set. Consider today’s lesson only has a 45 minute period. What will you do to keep the balance of rigor and honor the objective? Share solutions and strategies. Lesson 26

23. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Decompose a remainder in the hundreds place to solve a division problem. 783 ÷ 3 Lesson 27, Problem 2

24. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Represent numerically four-digit dividend division with divisors of 2, 3, 4, and 5, decomposing a remainder up to three times. 4,325 ÷ 3 Lesson 29, Problem 2

25. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Solve division problems with a zero in the dividend or quotient. 804 ÷ 44,218 ÷ 3 Lesson 30, Problem 1 and 2

26. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Interpret division word problems as either number of groups unknown or group size unknown. Two hundred thirty-two people are driving to a conference. If each car holds 4 people, including the driver, how many cars will be needed? Lesson 31, Problem 3

27. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Division word problems with larger divisors of 6, 7, 8, and 9. Mr. Hughes has 155 meters of volleyball netting. How many nets can he make if each court requires 9 meters of netting? Lesson 32, Problem 3

28. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Connect the area model to division. Use decomposition for 1,344 ÷ 4 Lesson 33, Problem 1

29. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Topic H: Multiplication of Two-Digit by Two-Digit Numbers Read Topic Opener H. How have the students prepared for this type of multiplication? How are the students prepared to use the area model?

30. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Fluency: Draw a Unit Fraction T:Draw a quadrilateral with 4 equal sides and 4 right angles. T:Name it. S: Square. T:Partition it into 3 equal parts. Shade in 1 part. T:Write the name of the shaded portion of the square. Students write ⅓. Lesson 34, Fluency Repeat with: Rhombus into fourths Rectangle into fifths Rectangle into eighths

31. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Application Problem Lesson 34, Application Problem Mr. Goggins planted 10 rows of beans, 10 rows of squash, 10 rows of tomatoes, and 10 rows of cucumbers in his garden. He put 22 plants in each row. Draw an area model, label each part and then write an expression that represents the total number of plants in his garden.

32. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Find the product of 60 and 34 using an area model. Lesson 35, Problem 2 60 430 3 4 x 6 0 60×30 6 tens×3 tens 18 hundreds 1,800 60×4 6 tens×4 24 tens 240 +1, 8 0 0 2, 0 4 0

33. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Find the product of 23 and 31 using an area model. Lesson 36, Problem 2 3 130 3 1 x 2 3 3×30 9 tens 3×1 3 ones 3 + 6 0 0 7 1 3 20×30 6 hundreds 20×1 2 tens 20 9 0 2 0 23×31=(3×1) + (3×30) + (20×1) + (20×30)

34. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units 4 partial product  2 partial products Draw an area model and solve for 26 × 35. Lesson 37 Problem 1

35. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Solve 2-digit by 2-digit multiplication using the algorithm. Lesson 38, Problem 1

36. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Regrouping. Work with a partner to solve: 29 × 62 46 × 63 Lesson 32, Problems 2 and 3

37. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Agenda

38. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Complete the End-of-Module Assessment. Now with all of the mathematical knowledge and understanding of the models, complete the assessment. You may work alone or with your table to discuss challenges or successes. How did Module 1 and 2 prepare you for Module 3?

39. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Biggest Takeaway Turn and Talk: I am ready to… I still want to know more about… I am better prepared to… My students will…

40. © 2012 Common Core, Inc. All rights reserved. commoncore.org NYS COMMON CORE MATHEMATICS CURRICULUM A Story of Units Key Points Number disks and area models are used heavily throughout the module to support the algorithms. The multiplication and division algorithms are not expected fluencies in Grade 4. Unit language and place value understanding drives the experience of the algorithms. Keep a balance of rigor by addressing each component of a lesson. Honor and respect the objectives. Find a balance between success and mastery.