Transcript Subtraction Using Manipulatives & Algorithms for Whole

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
312
-147
165
R → L; NO emphasis on place value (place value is not
explicit in this method)
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Video: Subtraction Alternate Algorithms
• Video Link to Alternate Algorithm explanations.
• The following 4 slides show each of the different
algorithms discussed in the video.
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
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)
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.
European Method
14
74
3
-26
48
10 is given to both numbers. 10 was given
to the 4 to make it 14.
10 was given to the 20 to make it 30.
• Practice using these each of the four algorithms
presented with the problem:
757 – 538
Solutions are on the following slides
Integer Subtraction
757
- 538
-1
+ 20
200
219
Expanded Notation
40 17
700 + 50 + 7
- (500 + 30 + 8)
200 + 10 + 9
Left to Right
17
757
- 538
229
219
European Method
17
757
4
- 538
219
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: Subtraction Using Manipulatives
• Video link
• Complete the problems from the handout
“Subtraction Using Manipulatives”
• The following 4 slides have the solutions to those
problems
Subtraction Using Manipulatives
1. 83 - 47
Draw 1st number, take away 2nd number
36
2. 1012 – 112 =
draw 1st number, take away 2nd number
102
3.
2113 – 1123 =
draw 1st number, take away 2nd number
223
4. 4135 - 2345 =
draw 1st number, take away 2nd number
1245
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
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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”