2. Subtraction Using Manipulatives & Algorithms for Whole-Number Subtraction

3. Algorithms for Subtraction algorithm – a systematic procedure used to accomplish an operation Standard algorithm 2 10 12 3 1 2 - 1 4 7 1 6 5 R → L; NO emphasis on place value (place value is not explicit in this method)

4. Video: Subtraction Alternate Algorithms Video Link to Alternate Algorithm explanations. The following 4 slides show each of the different algorithms discussed in the video.

5. Integer subtraction 312 − 147 −5 −30 200 165 R to L; NO emphasis on place value (place value is not explicit in this method) Must understand how to add integers

6. Expanded notation 100 200 0 12 300 + 10 + 2 100 + 40 + 7 100 + 60 + 5 MUST interpret this method, so final answer is: 165 R to L; Emphasis on place value (place value IS explicit in this method)

7. Left to Right 42,437 42,437 - 15,928 37,519 37,519 26,509 26,509 One students explanation: 4 – 1 is 3, trouble is coming so the 3 becomes a 2. 12 – 5 = 7, trouble is coming so the 7 becomes a 6. 14 – 9 = 5, trouble is not coming so it stays a 5. 3 – 2 = 1, trouble is coming so the 3 becomes a 2. 17 – 8 = 9.

8. European Method 14 14 74 74-26 48 48 3 10 is given to both numbers. 10 was given to the 4 to make it 14. 10 was given to the 20 to make it 30.

9. Practice using these each of the four algorithms presented with the problem: 757 – 538 Solutions are on the following slides

10. Integer Subtraction 757 - 538 + 20 200 219

11. Expanded Notation 700 + 50 + 7 - (500 + 30 + 8) 200 + 10 + 9 40 17

12. Left to Right 757 - 538 229 219 17

13. European Method 757 - 538 219 4 17

14. base-ten blocks units = centimeter cubes; long = 10 cm x 1 cm x 1cm square prism or 10 units; flat = 10 cm x 10 cm x 1 cm rectangular prism, 10 longs, or 100 units

15. Video: Subtraction Using Manipulatives Video link

16. Complete the problems from the handout “Subtraction Using Manipulatives” The following 4 slides have the solutions to those problems

17. Subtraction Using Manipulatives 1. 83 - 47 Draw 1 st number, take away 2 nd number 36

18. 2. 101 2 – 11 2 = draw 1 st number, take away 2 nd number 10 2

19. 3. 211 3 – 112 3 = draw 1 st number, take away 2 nd number 22 3

20. 4. 413 5 - 234 5 = draw 1 st number, take away 2 nd number 124 5

21. National Library of Virtual Manipulatives For more practice or for use in your classroom: http://nlvm.usu.edu/en/nav/frames_asid_154_ g_2_t_1.html?from=topic_t_1.htmlhttp://nlvm.usu.edu/en/nav/frames_asid_154_ g_2_t_1.html?from=topic_t_1.html ▫Base Block Addition  Click on Create problem  Change base  Drag blocks from top bar to create your problem  Once created, drag blocks to regroup them so that you will have enough to “take away”