Integer Rod Operations Multiplying and Dividing. Representing Fractions Using Bars How do we...
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Transcript of Integer Rod Operations Multiplying and Dividing. Representing Fractions Using Bars How do we...
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
Six Steps Required
1. 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 - Continued
3. 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 - Continued
5. Simplify the representation –least number of rods possible
6. Interpret the representation in #5 as a fraction number answer
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
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 1
Problem: ?3 2R W
A. L R
B. 2L 3R G
LC.
GR
LD.
GR
E. G
1F.
3
3 1Problem: ?
5 2L W
A. Y R
B. 2Y 5R E
YC.
EL
YD.
EL
E. E
3F.
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
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