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Algorithms for Whole-Number Addition & Addition Using Manipulatives

Algorithms for Whole-Number Addition & Addition Using Manipulatives. Algorithms for Whole-Number Addition. The Standard Addition Algorithm 1 1 2 2 4 7 3 9 6 7 0 1 9 4 5 8 3 0 7 + 2 8 7 9 1 7 8 7 7 6.

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Algorithms for Whole-Number Addition & Addition Using Manipulatives

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

  2. Algorithms for Whole-Number Addition The Standard Addition Algorithm 1 1 2 2 4 7 3 9 6 7 0 1 9 4 5 8 3 0 7 + 2 8 7 9 1 7 8 7 7 6 • algorithm – a systematic procedure used to accomplish an operation R → L; NO emphasis on place value (place value is not explicit in this method)

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

  4. Partial Sums 47396 70194 58307 + 2879 26 Sum of ones 250Sum of tens 1500 Sum of hundreds 17000Sum of thousands 160000Sum of ten-thousands   178776 Information in RED is for notes ONLY – Do NOT include as part of algorithm. R to L; Emphasis on place value (place value IS explicit in this method)

  5. Expanded notation The exercise 2981 + 306 + 247 = ? would be expanded as: 1000 100 10 2000 + 900 + 80 + 1 300 + 0 + 6 + 200 + 40 + 7 3000 + 500 + 30 + 4 MUST interpret this method, so final answer is: 3534 R to L; Emphasis on place value (place value IS explicit in this method)

  6. Left to right addition 47396 70194 58307 + 2879 160000 Sum of ten thousands 17000 Sum of thousands 1500 Sum of hundreds 250 Sum of tens 26Sum of ones 178776 Information in RED is for notes ONLY – Do NOT include as part of algorithm. L to R; Emphasis on place value (place value IS explicit in this method)

  7. Addition Algorithms Solve: 432 + 685 and 278 + 832 using each of the algorithms below: Partial Sum Left-to Right Expanded Notation Solutions are on the following slides

  8. Partial Sums 432 278 + 685+ 832 7 10 110 100 + 1000+ 1000 1117 1110

  9. Left to Right 432 278 + 685+ 832 1000 1000 110 100 + 7 +10 1117 1110

  10. Expanded Notation 1000 100 100 10 1000 400 + 30 + 2 200 + 70 + 8 + 600 + 80 + 5 + 800 + 30 + 2 1000 + 100 + 10 + 7 1000 + 100 + 10 + 0 = 1117 = 1110

  11. 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

  12. Video: Addition Using Manipulatives • Video using manipulatives

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

  14. 34 + 87 121

  15. 1012 + 112 10002

  16. 2123 + 1123 11013

  17. 2134 + 1334 10124

  18. 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, group blocks together by the base number you chose and move to appropriate place value to solve

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