Algorithms for Whole-Number Addition & Addition Using Manipulatives

Algorithms for Whole-Number Addition algorithm – a systematic procedure used to accomplish an operation R → L; NO emphasis on place value (place value is not explicit in this method) 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

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

Partial Sums 47396 70194 58307 + 2879 26 Sum of ones 250 Sum of tens 1500 Sum of hundreds 17000 Sum of thousands 160000 Sum 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)

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)

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 26 Sum 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)

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

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

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

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

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

Video: Addition Using Manipulatives Video using manipulatives

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

34 + 87 121

1012 + 112 10002

2123 + 1123 11013

2134 + 1334 10124

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