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 91 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  178776Information 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 notationThe exercise 2981 + 306 + 247 = ? would be

expanded as:1000 100 10 2000 + 900 + 80 + 1

300 + 0 + 6 + 200 + 40 + 7

3000 + 500 + 30 + 4MUST 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

178776Information 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 AlgorithmsSolve: 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 10100

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 ManipulativesFor more practice or for use in your

classroom:•http://nlvm.usu.edu/en/nav/frames_asid_15

4_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