1. Multiplying and Dividing in the Common Core (grades 3-5) Julia Doverspike, Armando Rodriguez, Maricela Garcia

2. Second Grade Iden'fy numbers (up to 20) as Odd or Even Count by 2s, 5s, 10s, and 100s up to 1000 Show repeated addi'on with objects and numbers up to 5 groups of 5 Third Grade Mul'ply and Divide up to 100 using pictures Understand the rela'onship between mul'plica'on and division Relate area of a shape to mul'pica'on Know from memory mul'pica'on facts up to 9X9=81 Fourth Grade Interpret a mul'plica'on equa'on as a comparison Mul'ply numbers with up to 4--‐digits by a 1--‐digit number or 2--‐digit by 2--‐ digit using drawings and equa'ons Divide numbers up to 4--‐ digit by 1--‐digit using drawings and equa'ons Fi1h Grade Mul'ply mul'--‐digit whole numbers Divide numbers up to 4--‐digit by 2--‐digit using drawings and equa'ons Relate volume of a 3D shape to mul'plica'on Understand place value using Powers of 10 Libby Schwaegler 2015

3. Reasoning with numbers Arrays Kristy Cortright 2015

4. Creating Arrays 3 rows 2 columns 2 + 2 + 2 = 6 Kristy Cortright 2015

5. Area How many different rectangles can I make with an area of 12? Kristy Cortright 2015

6. Area Models Five rows of 3 3 + 3 + 3 + 3 + 3 = 15 5 x 3 = 15 Kristy Cortright 2015

7. Equal Groups Model 2 groups of 4 4 + 4 = 8 2 x 4 = 8 Kristy Cortright 2015

8. Using Manipulatives Modeling Division Kristy Cortright 2015

9. Quotative Division  Uses repeated subtraction  Provides student with a total number and the number of objects in each group  Focus on the question, “How many equal groups can you make?” Kristy Cortright 2015

10. Partitive Division  Provides student with a total number and the number of groups  Focus on the question, “How many objects are in each group so that the groups are equal?” Kristy Cortright 2015

11. Number Line There are 12 cookies on the counter. If you put 3 cookies in each bag, how many bags will you fill? 12 36 9 0 - 3 12 ÷ 3 = 4 Kristy Cortright 2015

12. Tape Diagram There are 12 brownies on the plate. If you are sharing the brownies equally among three bags, how many brownies will go in each bag? ??? = 12 44 4 12 ÷ 3 = 4 Kristy Cortright 2015

13. Array Model If 15 cars are parked 3 in each row, then how many rows will they fill? 3 5 Kristy Cortright 2015

14. For Multiplication Properties of Operations Kristy Cortright 2015

15. Identity Property Kristy Cortright 2015

16. Commutative Property 4 x 5 = 20 5 x 4 = 20 Kristy Cortright 2015

17. Associative Property 3 x 5 x 2 = 30 5 x 2 x 3 = 30 2 x 3 x 5 = 30 Kristy Cortright 2015

18. Distributive Property Decomposing rectangles 8 x 6= (3 x 6) + (5 x 6) Kristy Cortright 2015

19. Multiplication and Division Patterns Doubles(2) Double-Doubles(4) Double-Double-Doubles(8) Halves By 10s and 5s Kristy Cortright 2015

20. Multiplicative Comparison Kristy Cortright 2015

21. Language 18 = 6 x 3 40 is 5 times as much as 8 5 x 8 = 40 18 is 6 times as much as 3 Kristy Cortright 2015

22. Bar Model (Tape Diagram) A tennis ball costs $2. A soccer ball costs six times as much as a tennis ball. How much does the soccer ball cost? 6 x 2 = n Kristy Cortright 2015

23. Try These  Manny has lived in Illinois for 21 years and that is 7 times as many years as Lucas. How many years has Lucas lived in Illinois?  A tree in Ashton’s yard is 15 feet tall. Ashton is 3 feet tall. The tree is how many times as tall as Ashton? Kristy Cortright 2015

24. Place Value Each place value is ten times as much as the previous place value Kristy Cortright 2015

25. Including Prime and Composite Factors and Multiples

26. Rectangles How many different rectangles can I make with an area of 7? How many different rectangles can I make with an area of 12? Composite Prime

27. Number Line Show the multiples of 4 1 234 5 20 16 128 4 0 Factors Multiples

28. Table 16 212 318 424 x 6

29. Multi-digit Multiplication

30. Digi Blocks Kristy Cortright 2015

31. Base Ten Blocks (or Digi-blocks) 321 x 3= 963 Kristy Cortright 2015

32. Base Ten Area Model 31 x 24 X = 744 Kristy Cortright 2015

33. Area Model 24 x 35 = (20 + 4) x (30 + 5) 20 4 305 20120 100600 = 840 Kristy Cortright 2015

34. Partial Products 24 X 36 24 6 x 4 120 6 x 2 tens 120 3 tens x 4 600 3 tens x 2 tens 864 Kristy Cortright 2015

35. Column Method Regroup 44 26 4 2 62 808 44 1 11 Kristy Cortright 2015

36. Multi-digit Division Kristy Cortright 2015

37. Base Ten Blocks (or Digi-blocks) My team earned $175. There are 5 people on my team. We decided to split the money up evenly between the 5 of us. How much money will we each receive? $35 each Kristy Cortright 2015

38. Area Model 966 ÷ 7 9667 HundredsTens Ones 100 966 - 700 266 30 266 - 210 56 8 - 56 0 = 138 Kristy Cortright 2015

39. Partial Quotient 3745 200 - 600 145 40 - 120 25 8 - 24 1 745 ÷ 3 248 remainder 1 Kristy Cortright 2015

40. Interpreting Remainders  Sam wants to hide 40 eggs for his cousins to find. How many dozen eggs must he buy?  Sam buys 2 dozen packages of chocolates for his cousins. Each package has 22 chocolates. He has 9 bowls to hold the chocolates. If he wants to have the same number of chocolates in each bowl, how many chocolates will be in each bowl? Kristy Cortright 2015

41. Base Ten Area Model 231 ÷ 21 X Divisor Quotient Dividend = 11 Kristy Cortright 2015

42. Column Division - introduction 231 ÷ 21 21231 1 210 - 21 1 - 0 Kristy Cortright 2015

43. Column Division (long division) 231 ÷ 21 21231 1 - 21 21 1 - 0 Kristy Cortright 2015

44. Please let us know if you ever need anything! Thank you for spending your time with us Teaching is more than imparting knowledge, It is inspiring change. Learning is more than absorbing facts, It is acquiring understanding. William Arthur Ward Kristy Cortright 2015