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Topic
Fractions
Parallel number lines with unit fractions and their
multiples
Understanding relative size of fractions on a
number line
Procedure
Construction of paper fraction strips (Folding Fractions)
1. Distribute four lengths (4" x 1") of colored paper
to each student. Guide the folding and recording of
each fraction fold and corresponding number line
according to the instructions on the activity page:
Folding Fractions.
Learning Goals
• To order fractions on a number line, such as a ruler
• To experience addition and subtraction of fractions
on a number line
• To connect fractions and linear measurement
Application of Slide Rulers
1. Distribute one Slide Ruler B to each student. Ask
them how the Slide Ruler is like the paper strips
they just folded. Inform them that they will now use
the Slide Rulers to add and subtract fractions.
2. Take the students through the instructions to Slide
Ruler Fractions.
5
3
To add two fractions, such as 8 + 16 , find the
5
first fraction, , on Ruler A. Then align 0 on Ruler
8
B with 5 mark on Ruler A. Then slide (your finger)
8
to the right along Ruler B to the mark of the second
fraction, 3 . Read the answer (13 ) directly above
16
16
on Ruler A.
7
3
To subtract two fractions, such as 8 – 4 . Align
0 of Ruler B with the minuend, the larger number
( 7 ) on Ruler A. Find the subtrahend ( 3 ) on Ruler B
8
4
and slide it to the left until 3 on Ruler B is aligned
4
7
with on A. Read the difference on Ruler A directly
8
above the 0 on Ruler B.
Guiding Document
NCTM Standards 2000*
• Develop understanding of fractions as parts of unit
wholes, as parts of collections, as locations on
number lines, and as division of whole numbers
• Use visual models, benchmarks, and equivalent
forms to add and subtract commonly used fractions
and decimals
• Compare and order fractions, decimals, and percents
efficiently and find their approximate locations on
a number line
Materials
Colored paper strips
Scissors
Standard ruler
Discussion
1. What fractions are represented on the Slide Ruler?
[halves, fourths, eighths, sixteenths]
2. How does folding strips of paper help you understand the meaning of half, fourth, and eighth?
[Folding a strip of paper into two equal parts models
dividing a line segment in half. Similarly, folding into
four equal parts models fourths, and eight equal
parts models eighths.]
3. When partitioning a line segment into equal parts
such as halves, fourths, eighths and sixteenths, how
could these parts be distinguished if they cannot be
labeled symbolically? [The lines that par tition the
line segment could be of different lengths. (Notice
on a standard ruler that the mark for one half is
longer than the marks for fourths, etc.)]
4. Explain how a move or slide to the right models
the addition process. [When lengths are added they
are placed end to end thus increasing the total
measure.]
Background Information
The model for exploring fractions in this lesson is a
measured model where lengths are compared. Lines
are drawn and subdivided or physical models such as
paper strips are compared on the basis of length.
Connections can be made to linear measure:
fractions to inches and fractional parts.
Management
1. Prior to the lesson, cut colored paper into lengths
of 4" x 1". Each student will need four strips.
2. Duplicate one Slide Ruler B for each student.
3. It may be beneficial to make transparencies of the
Slide Ruler so that the process of addition and subtraction may be demonstrated to the students.
1
© 2005 AIMS Education Foundation
5. Explain how a move or slide to the left is a model
for subtraction. [Moving or sliding to the left models
covering part of the length and naming what is
leftover. Another model is simply comparing the
two lengths by matching one set of end points.
Evaluation
1. Using two standard rulers, have students apply the
slide ruler technique to add these lengths.
5
3
2
4 + 8 + 16
Ask them to explain how they solved the problem.
Direct the students to make up a problem for your
partner to try. Have students explain their thinking.
Evidence of Learning
1. Look to see if students are able to apply or transfer their understanding of fraction slide rulers to
standard rulers and linear measurement.
*
Reprinted with permission from Principles and Standards for
School Mathematics, 2000 by the National Council of Teachers
of Mathematics. All rights reserved.
2
© 2005 AIMS Education Foundation
Key Question
How can we use our
rulers to add and
subtract fractions?
Learning Goals
• order fractions on a number line,
• experience addition and
subtraction of fractions on
a number line, and
• connect fractions and
linear measurement.
3
© 2005 AIMS Education Foundation
Fold each strip as directed. Label each fraction part.
Attach the paper strip directly above the number line. Label the fractions on the number
line between 0 and 1.
ce.
ts.
Fold on
tion par
c
a
r
f
e
h
t
Record number line.
e
h
t
Label
0
1
å
0
1
Fold twice.
Record previous fractions first.
Record the new fraction parts.
Label the number line.
Fold three times.
Record previous fractions first.
Record the new fraction parts.
Label the number line.
0
1
Fold four times.
Record the previous fractions first.
0
Record new fraction parts.
1
4
© 2005 AIMS Education Foundation
5
3
5
5
8
+ 11
16
5
13
0
1 1
16 8
3
16
1
4
5
16
3
8
7
16
1
2
9 5 11
16 8 16
3
4
13 7 15
16 8 16
1
1 1
16 8
3
16
1
4
along Ruler B to the mark of the second fraction, 16 . Read the answer ( 16 )
directly above on Ruler A.
7 3
3. To subtract two fractions, such as 8 – 4 . Align 0 of Ruler B with the minuend,
7
the larger number ( ) on Ruler A. Find the subtrahend on Slide Ruler B and
8 3
7
slide it to the left until on Ruler B is aligned with on A. Read the difference
4
8
on Ruler A directly above the 0 on Ruler B.
3
2. To add two fractions, such as 8 + 16 , find the first fraction, 8 , on Ruler A. Then
5
align 0 on Ruler B with 8 mark on Ruler A. Then slide your finger to the right
1. Cut out Slide Ruler B.
7
16
+ 3
4
5
16
3
8
7
16
15
16
1
–
4
3
4
+ 5
16
1
2
9 5 11
16 8 16
3
4
5
8
– 3
16
13
16
+ 3
8
2
7
8
– 3
4
13 7 15
16 8 16
Try these problems and record your answers.
Slide Ruler A
© 2005 AIMS Education Foundation
3
8
– 3
16
6
0
0
0
0
0
1 1
16 8
1 1
16 8
1 1
16 8
1 1
16 8
1 1
16 8
1
4
5
16
5
16
1
3 4 5
16
16
3
16
3
16
3
8
3
8
3
8
3
8
1
3 4 5
16
16
1
4
3
8
1
3 4 5
16
16
7
16
7
16
7
16
7
16
7
16
1
2
1
2
1
2
1
2
1
2
9 5 11
16 8 16
9 5 11
16 8 16
9 5 11
16 8 16
9 5 11
16 8 16
9 5 11
16 8 16
3
4
3
4
3
4
3
4
3
4
13 7 15
16 8 16
13 7 15
16 8 16
13 7 15
16 8 16
13 7 15
16 8 16
13 7 15
16 8 16
1
1
1
1
1
1 1
16 8
1 1
16 8
1 1
16 8
1 1
16 8
1 1
16 8
1
4
5
16
5
16
1
3 4 5
16
16
3
16
3
16
1
4
1
3 4 5
16
16
1
3 4 5
16
16
3
8
3
8
3
8
3
8
3
8
7
16
7
16
7
16
7
16
7
16
1
2
1
2
1
2
1
2
1
2
9 5 11
16 8 16
9 5 11
16 8 16
9 5 11
16 8 16
9 5 11
16 8 16
9 5 11
16 8 16
3
4
3
4
3
4
3
4
3
4
13 7 15
16 8 16
13 7 15
16 8 16
13 7 15
16 8 16
13 7 15
16 8 16
13 7 15
16 8 16
2
2
2
2
2
Slide Ruler B
© 2005 AIMS Education Foundation
Connecting Learning
1. What fractions are represented
on the Slide Ruler?
2. How does folding strips of paper
help you understand the meaning of half, fourth, and eighth?
3. When partitioning a line segment into
equal parts such as halves, fourths,
eighths and sixteenths, how could
these parts be distinguished if they
cannot be labeled symbolically?
4. Explain how a move or slide to the
right models the addition process.
5. Explain how a move or slide to the
left is a model for subtraction.
7
© 2005 AIMS Education Foundation