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Subtraction Using Manipulatives & Algorithms for Whole-Number Subtraction

Subtraction Using Manipulatives & Algorithms for Whole-Number Subtraction. 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

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Subtraction Using Manipulatives & Algorithms for Whole-Number Subtraction

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

  2. Algorithms for Subtraction algorithm – a systematic procedure used to accomplish an operation Standard algorithm 2 10 12 312 - 1 4 7 1 6 5 R → L; NO emphasis on place value (place value is not explicit in this method)

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

  4. 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

  5. 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)

  6. Left to Right 42,437 - 15,928 37,519 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.

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

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

  9. Integer Subtraction 757 - 538 -1 + 20 200 219

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

  11. Left to Right 757 - 538 229 219 17

  12. European Method 757 - 538 219 17 4

  13. 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

  14. Video: Subtraction Using Manipulatives • Video link

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

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

  17. 2. 1012 – 112 =draw 1st number, take away 2nd number 102

  18. 3. 2113 – 1123 =draw 1st number, take away 2nd number 223

  19. 4. 4135- 2345 =draw 1st number, take away 2nd number 1245

  20. 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.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”

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