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Integer Rod Operations. Adding, Subtracting, Multiplying, and Dividing. Six Steps Required. Represent the fraction with the smallest and least number of rods possible Race the denominators to a tie. This will ALWAYS take 3 rows – the new common denominator is at the bottom. - PowerPoint PPT Presentation
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Integer Rod Operations
Adding, Subtracting, Multiplying, and Dividing
Six Steps Required1. Represent the fraction with
the smallest and least number of rods possible
2. Race the denominators to a tie. This will ALWAYS take 3 rows – the new common denominator is at the bottom
Six Steps Required - Continued3. Represent the fraction using
the “race” as a guide using the common denominator rod and the least number of rods possible for the numerator
4. Do the operation
Six Steps Required - Continued5. Simplify the representation –
least number of rods possible6. Interpret the representation
in #5 as a fraction number answer
Do the Operation: Addition Use one common
denominator bar Place both numerators (in
order, from left to right) directly above the common denominator
Total of 2 rows
Simplify the Representation: Addition Use one common
denominator bar Represent all with the least
number of rods possible Total of 2 rows
Addition – Semi-Concrete1 2 ?2 3
76
A.B.
C.
D.E.F.
A.B.
C.D.E.F.
2 4 ?3 5
2215
Addition – Semi-Concrete1 2 ?2 3
76
W
G
R
P
R L
R R RL L
L
L
G
G
PG
GK
A.
B.
C.D.E.F.
A.
B.
C.D.E.F.
2 4 ?3 5
2215
Y
YE R
E E R
E YE R
Y
EE Y
PY
Y YL L
E YL
EE
E
RL
L L
Adding – Semi-Abstract1 2Problem: ?2 3W RA. R L
B. 3R 2L GL PC. G GL PD. GKE. G
7F. 6
2 4Problem: ?3 5R PA. L Y
B. 5L 3Y EYE ERC. EY EYE ERD. EYEERE. EY
22F. 15
Do the Operation: Subtraction Use one common denominator bar Place the minuend (the sum) directly
above the common denominator Place the subtrahend (addend) directly
above the minuend (the sum) Use dashed lines to indicate the
difference (missing addend) next to the subtrahend
Total of 3 rows
Simplify the Representation: Subtraction Use one common denominator bar Place the difference (missing
addend) directly above the common denominator bar
Represent all with the least number of rods possible
Total of 2 rows
Subtraction – Semi-Concrete2 1 ?3 2
16
A.
B.C.D.E.F.
A.
B.
C.D.
E.F.
4 1 ?5 2
310
Subtraction – Semi-Concrete2 1 ?3 2
16
A.
B.C.D.E.F.
A.
B.
C.D.E.F.
4 1 ?5 2
310
W
W
W
G
G
L
L
G
G
P
G
R
P
RL
R R RL L
W
Y
NY L
R
E
E
R R R R R
NE
PY
Y Y
E
E
L
Subtraction – Semi-Abstract2 1Problem: ?3 2R WA. L R
B. 2L 3R GP LC. G GP LD. G
WE. G1F. 6
4 1Problem: ?5 2P WA. Y R
B. 2Y 5R EN YC. E E
N YD. ELE. E
3F. 10
Race Representation: Multiplication Use one common denominator
bar The numerator will represent the SECOND factor only
Do NOT represent the first factor
Do the Operation: Multiplication Use one common denominator bar Place the numerator of the second
factor directly above the common denominator
Look at the first factor in the problem Treat the numerator of the second factor
as the denominator of the first factor Place a bar above it that represents the
numerator for the first factor Total of 3 rows
Simplify the Representation: Multiplication Use one original common
denominator bar Place the top bar from the step
above directly above the common denominator bar
Represent all with the least number of rods possible
Total of 2 rows
Multiplication – Semi-Concrete2 1 ?3 2
13
A.
B.
C.D.
E.F.
A.B.
C.D.
E.F.
3 1 ?5 2
310
Multiplication – Semi-Concrete2 1 ?3 2
13
A.B.
C.D.
E.F.
A.
B.
C.D.E.F.
3 1 ?5 2
310
WRRL
R R RL L
G
G
R
G
G
L
L
R
W
E
E
L
LY
Y Y
R
E
E
R R R R R
Y
YL
Multiplication – Semi-Abstract2 1Problem: ?3 2R WA. L R
B. 2L 3R GLC. G
RLD. G
RE. G1F. 3
3 1Problem: ?5 2L WA. Y R
B. 2Y 5R EYC. E
LYD. E
LE. E3F. 10
Do the Operation: Division Use one common denominator bar Place the divisor (the factor) directly
above the common denominator Place the dividend (the product)
directly above the divisor (the factor)
Total of 3 rows
Simplify the Representation: Division Use the divisor (the factor) as the
new common denominator Place the dividend (the product)
directly above the divisor (the factor)
Represent all with the least number of rods possible
Total of 2 rows
Division – Semi-Concrete1 2 ?2 3
34
A.B.
C.D.
E.F.
A.
B.
C.D.E.F.
3 1 ?4 5
154
Division – Semi-Concrete1 2 ?2 3
34
A.B.
C.D.
E.F.
A.
B.
C.D.E.F.
3 1 ?4 5
154
W R
P
P
P
G
G G
R L
R R RL L
L
G
L
L
W
P
EY P
PY
LP Y
P P P
E
E
Y Y
E
EE
E
P PY Y
E
E E
E
Y
Division – Semi-Abstract1 2Problem: ?2 3
W RA. R LB. 3R 2L G
L PC. G GL PD. G GLE. P3F. 4
3 1Problem: ?4 5L WA. P Y
B. 5P 4Y 2EEY PC. 2E 2EEY PD. 2E 2EEYE. P15F. 4
Representing Fractions Using Bars How do we represent fractions using integer
bars? Part to whole Whole changes as necessary to make equivalents
A train is two rods put together – ALL trains must have at least one E in them
We will ALWAYS use the least number of bars possible to make a representation
Do NOT draw more lines on representations than necessary
