HUNDRED BOARD BOOK Table of Contents Introduction...iv Connections to Common Core Standards...v 1. Marching Forward 1 to 100... 2 2. Marching Backward 100 to 1... 4 3. Find the Three Lakes... 6 4. Don t Fall in the Lake!... 8 5. Arrow Paths... 10 6. Hit the Road... 12 7. Backtrack... 14 8. Returning Home... 16 9. On the Diagonal... 18 10. Making Moves... 20 11. Express Train... 22 12. Multiple Paths... 24 13. Zero Moves... 26 14. Place-Value Paths... 28 15. Nicknames... 30 16. Combining Arrows... 32 17. Mental Math... 34 18. Round Up (or Down)... 36 19. Digit Description... 38 20. Quarters... 40 21. Commuting... 42 22. Sliding Sums... 44 23. Associative Property of Addition... 46 24. Missing SUMthing... 48 25. Connecting Addition and Subtraction... 50 26. Moving Left... 52 27. Something s Missing... 54 28. Does This Add Up?... 56 29. Does This Add Up Too?... 58 30. A, B, or C?... 60 Didax www.didax.com 31. Groups of Three... 62 32. Multiple Addition... 64 33. Doing Double... 66 34. Multiplication Switch... 68 35. Dividing Evenly... 70 36. Leftovers... 72 37. Remainders?... 74 38. In the Bag... 76 39. Tiles Off... 78 40. Multiple Patterns... 80 41. Thirteen Threes... 82 42. Multiple Sevens... 84 43. Eight at a Time... 86 44. Hundred Board Dash... 88 45. Common Multiples... 90 46. Prime Time... 92 47. Finding Primes... 94 48. Prime Factorization... 96 49. Pattern Primer... 98 50. Counting Back... 100 51. Create a Pattern... 102 52. What s My Rule?... 104 53. Pattern Puzzles... 106 54. Sticker Selections... 108 55. Increasing and Decreasing... 110 56. Hit or Miss... 112 57. Clue Me In... 114 58. Un(der)cover... 116 59. Bingo Cover-Up... 118 60. Uncover Bingo... 120 Appendix: Hundred Boards... 121 Hundred Board Book iii
34 Teacher s Corner Multiplication Switch Mathematics Content Standard: 4.OA Operations and Algebraic Thinking Generate and analyze patterns. Mathematical Practices Focus: 7. Look for and make use of structure. Activity for 1 or small group 34 1. Take out your Hundred Board and a marker. 2. Use the Commutative Property of Multiplication to change the order of the numbers (factors). For example: 15 3 = 3 15 3. Change the order of the numbers (factors) in these mathematical sentences (equations): 12 4 = 4 x 12 3 x 20 20 3 = Use the Commutative Property of Multiplication to change the order of the numbers in each equation. Use repeated addition to find the solution on your Hundred Board. (The first one has been started for you.) A. 12 3 = 3 12 = 12 + 12 + 12 = B. 28 3 = C. 19 4 = D. 13 4 = E. 23 4 = F. 13 6 = G. 11 6 = H. 19 5 = I. 17 5 = J. 15 6 = Multiplication Switch 36 3 x 28 = 28 + 28 + 28 = 84 4 x 19 = 19 + 19 + 19 + 19 = 76 4 x 13 = 13 + 13 + 13 + 13 = 52 4 x 23 = 23 + 23 + 23 + 23 = 92 6 x 13 = 13 + 13 + 13 + 13 + 13 + 13 = 78 6 x 11 = 11 + 11 + 11 + 11 + 11 + 11 = 66 5 x 19 = 19 + 19 + 19 + 19 + 19 = 95 5 x 17 = 17 + 17 + 17 + 17 + 17 = 85 6 x 15 = 15 + 15 + 15 + 15 + 15 + 15 = 90 Materials (per student): Hundred Board Marker Multiplication Switch activity sheet Completing the Activity: In this activity, students continue working with multiplication as repeated addition. Start by reviewing the Commutative Property of Addition. Have students solve these examples on their Hundred Boards: 14 + 5 =? 5 + 14 =? 26 + 4 =? 4 + 26 =? Ask them whether the order in which they added the numbers changed the sum. Suggest that, when multiplying, sometimes it is easier to change the order of the numbers in a multiplication sentence before using repeated addition to solve the equation. For example: Didax www.didax.com Hundred Board Book 69 7 2 means 2 + 2 + 2 + 2 + 2 + 2 + 2 = 14. 2 7 means 7 + 7 = 14. Teacher Talk: Ask/say: What is the Commutative Property of Addition? What is the Commutative Property of Multiplication? Explain (7 2) 5 and 7 (2 5) using the Hundred Board. Which of the two calculations is easier, and why? In these three problems, which two factors would you multiply fi rst to fi nd the product without pencil and paper? Why do you say that? 4 3 5 2 9 5 6 3 5 Which properties of multiplication are you using in each example? 68 Hundred Board Book Didax www.didax.com
34 Multiplication Switch 1. Take out your Hundred Board and a marker. 2. Use the Commutative Property of Multiplication to change the order of the numbers (factors). For example: 15 3 = 3 15 3. Change the order of the numbers (factors) in these mathematical sentences (equations): 12 4 = 20 3 = Use the Commutative Property of Multiplication to change the order of the numbers in each equation. Use repeated addition to find the solution on your Hundred Board. (The first one has been started for you.) A. 12 3 = 3 12 = 12 + 12 + 12 = B. 28 3 = C. 19 4 = D. 13 4 = E. 23 4 = F. 13 6 = G. 11 6 = H. 19 5 = I. 17 5 = J. 15 6 = Didax www.didax.com Hundred Board Book 69
35 Teacher s Corner Dividing Evenly Mathematics Content Standard: 3.OA Operations and Algebraic Thinking Represent and solve problems involving multiplication and division. (Understand division as repeated subtraction.) Mathematical Practices Focus: 8. Look for and express regularity in repeated reasoning. Activity for 1 or small group Materials (per student): Hundred Board Blank tile or marker Dividing Evenly activity sheet Completing the Activity: In this activity, students explore division as repeated subtraction. Begin by reviewing subtraction on the Hundred Board. Present 5 5 =? Ask: What is the answer? Have students put the tile on 5 and subtract 5. Say: We must go off the board for zero. Next, explain that division can sometimes be thought of as sharing equally. When dividing, we can fi nd the quotient (answer) through repeated subtraction. Teacher Talk: Pose the following problem to students: I have 21 apples and I want to put 7 apples in each bag. How many bags will I need? Didax www.didax.com Hundred Board Book 71 Have students place their tile on 21 on their Hundred Boards, and move the tile to subtract 7 for the fi rst bag. Ask: Which number did you end on? How many apples are left? (14) Have students move their tile to subtract 7 for the second bag. Ask: Which number did you end on this time? How many apples are left? (7) Have students move the tile to subtract 7 for the third bag. Ask: Which number did you end on? (0) Say: Since you ended on zero and have nothing left, you have divided evenly. How many bags did you fi ll? How many 7 s did you subtract? (3) Therefore, we can say 21 7 = 3. 7 was subtracted 3 times: 21 7 7 7 = 0, so 21 7 = 3. Note: As shown above, it may be very useful to use objects when modeling division problems. Have students write their own problems and draw pictures showing how they used repeated subtraction to solve the problems. 70 Hundred Board Book Didax www.didax.com 35 Dividing Evenly 1. Take out your Hundred Board and a blank tile. 2. When we want to share, we can divide. When dividing, we can fi nd the quotient (answer) through repeated subtraction. For example: 20 5 = N, so 20 5 = 15 (1), 15 5 = 10 (2), 10 5 = 5 (3), and 5 5 = 0 (4). We went off the board for zero, which means we have nothing left, so we have divided evenly: 20 5 = 4. Solve these division problems on your Hundred Board using repeated subtraction. Remember, you must go off the board one space to reach zero and divide evenly. (The first one has been done for you.) 24 8 = 16 (1); 16 8 = 8 (2); 8 8 = 0 (3); 24 8 = 3 A. 24 8: 72 18 = 54 (1); 54 18 = 36 (2); 36 18 = 18 (3); 18 18 = 0 (4); 72 18 = 4 B. 72 18: 57 19 = 38 (1); 38 19 = 19 (2); 19 19 = 0 (3); 57 19 = 3 C. 57 19: 30 10 = 20 (1); 20 10 = 10 (2); 10 10 = 0 (3); D. 30 10: 30 10 = 3 85 17 = 68 (1); 68 17 = 51 (2); 51 17 = 34 (3); E. 85 17: 34 17 = 17 (4); 17 17 = 0 (5); 85 17 = 5 65 13 = 52 (1); 52 13 = 39 (2); 39 13 = 26 (3); F. 65 13: 26 13 = 13 (4); 13 13 = 0 (5); 65 13 = 5 45 9 = 36 (1); 36 9 = 27 (2); 27 9 = 18 (3); G. 45 9: 18 9 = 9 (4); 9 9 = 0 (5); 45 9 = 5 82 41 = 41 (1); 41 41 = 0 (2); 82 41 = 2 H. 82 41:
35 Dividing Evenly 1. Take out your Hundred Board and a blank tile. 2. When we want to share, we can divide. When dividing, we can fi nd the quotient (answer) through repeated subtraction. For example: 20 5 = N, so 20 5 = 15 (1), 15 5 = 10 (2), 10 5 = 5 (3), and 5 5 = 0 (4). We went off the board for zero, which means we have nothing left, so we have divided evenly: 20 5 = 4. Solve these division problems on your Hundred Board using repeated subtraction. Remember, you must go off the board one space to reach zero and divide evenly. (The first one has been done for you.) A. 24 8: 24 8 = 16 (1); 16 8 = 8 (2); 8 8 = 0 (3); 24 8 = 3 B. 72 18: C. 57 19: D. 30 10: E. 85 17: F. 65 13: G. 45 9: H. 82 41: Didax www.didax.com Hundred Board Book 71