Chapter 3:Numeration Systems and Whole-Number Computation
3.2Algorithms for Whole-Number Addition and Subtraction
3.2.1.Vocabulary
3.2.1.1.algorithm – a systematic procedure used to accomplish an operation
3.2.1.2.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
Addition
The Standard Algorithm
1122
4 7 3 9 6
7 0 1 9 4
5 8 3 0 7
+ 2 8 7 9
1 78776
R L; NO emphasis on place value (place value is not explicit in this method)
Partial Sum
47396
7019 4
58307
+2879
2 6Sum of ones
2 5 0Sum of tens
1 5 0 0Sum of hundreds
1 7 0 0 0Sum of thousands
1 6 0 0 0 0Sum of ten-thousands
1 7 8 7 7 6
Information in RED is for notes ONLY – Do NOT include as part of algorithm.
R L; Emphasis on place value (place value IS explicit in this method)
Denominate numbers
Using denominate numbers, the addition problem 4567 + 319 + 208 = ? becomes:
1 thousand2 tens
4 thousands 5 hundreds6 tens7 ones
3 hundreds1 ten9 ones
+2 hundreds0 tens 8 ones
5 thousands0 hundreds9 tens4 ones
MUST interpret this method, so final answer is: 5094
R 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 L; Emphasis on place value (place value IS explicit in this method)
Left to right addition
47396
70194
5830 7
+2879
1 6 0 0 0 0Sum of ten thousands
1 7 0 0 0Sum of thousands
1 5 0 0Sum of hundreds
2 5 0Sum of tens
2 6Sum of ones
1 7 8 7 7 6
Information in RED is for notes ONLY – Do NOT include as part of algorithm.
L R; Emphasis on place value (place value IS explicit in this method)
Scratch Addition Method
48971
563 20
123 49
+ 69899
1 65329
8753
MUST interpret this method, so final answer is: 187539
L R; NO emphasis on place value (place value is NOT explicit in this method)
Any column first
48971
56320
12349
+ 69899
2 3 0 0
1 6 0 0 0 0
1 9
2 5 0 0 0
+ 2 2 0
1 8 7 5 3 9
No Order; Emphasis on place value (place value IS explicit in this method)
Low stress addition
The demonstration below shows the addition of 9 + 8 + 9 + 7 + 9.
Side work below in parentheses are for notes only – they are not part of algorithm
9
8
17 (9 + 8 = 17)
9
16 (7 + 9 = 16)
7
13 (6 + 7 = 13)
+9
1_____ (10 from 3 + 9)
2(2 from 3 + 9)
+4 0 (sum the 10s at the left)
4 2
Typically, the 40 is not shown as a part of the partial sum. Rather, the problem would be shown as:
9
8
1 7
9
1 6
7
1 3
+ 9
1_____
4 2
R L; NO emphasis on place value (place value is not explicit in this method)
Just need to know facts for this method.
3.2.2.Subtraction algorithms
3.2.2.1.Begin similar to addition
3.2.2.2.Equal addends algorithm
3.2.2.3.start concrete – use base ten blocks
3.2.2.4.Which of the addition alternate algorithms will work for subtraction?
Subtraction
Standard algorithm
R L; NO emphasis on place value (place value is not explicit in this method)
Denominate numbers
MUST interpret this method, so final answer is: 165
R L; Emphasis on place value (place value IS explicit in this method)
Expanded notation
MUST interpret this method, so final answer is: 165
R L; Emphasis on place value (place value IS explicit in this method)
Left to right subtraction
MUST interpret this method, so final answer is: 165
L R; Emphasis on place value (place value IS explicit in this method)
Scratch method
MUST interpret this method, so final answer is: 165
L R; NO emphasis on place value (place value is NOT explicit in this method)
Any column first
MUST interpret this method, so final answer is: 165
No Order; Emphasis on place value (place value IS explicit in this method)
Integer subtraction
R L; NO emphasis on place value (place value is not explicit in this method)
Must understand how to add integers
3.2.3.Ongoing Assessment p. 178
3.2.3.1.Home work: 1a, 4a, 8a, practice any four of the different algorithms learned in class to do:
209 + 135 + 447
887 + 325
757 – 538
956 – 218