Use the fifths circle and a blank circle
to display fractions in fifths.
1
Start with a blank circle. Think of
it as the face of a clock, with the
cut in the 12 o’clock position.
2
Insert the fraction circle
into the blank circle.
3
Arrange the circles so they
overlap, interlock, and align
with a marked line. This
setting shows the fraction ⅗.
4
Hold the blank circle in a fixed
position and rotate the fraction
circle clockwise to the next
position to display ⅘.
5
Hold the blank circle in a fixed
position and rotate the fraction
circle counterclockwise two
positions to display ⅖.
©DIDAX
Table of Contents
Introduction .............................................................................................................4
Teacher N otes ............................................................................................................5
How to Use Your Fraction Circles ...........................................................................6
1. Reading Fractions .......................8
7. Mixed Numbers .......................32
TeacherN otes..............................................8
Worksheets ............................................9–10
Answers ..................................................... 11
TeacherN otes........................................32
Worksheets ......................................33–34
Answers .................................................35
2. Changing Fractions ...................12
8. Adding Like Fractions............36
TeacherN otes............................................12
Worksheets ..........................................13–14
Answers .....................................................15
TeacherN otes........................................36
Worksheets ......................................37–38
Answers .................................................39
3. Parts of a Whole ........................16
9. Adding Unlike Fraction .........40
TeacherN otes............................................16
Worksheets ..........................................17–18
Answers .....................................................19
TeacherN otes........................................40
Worksheets ......................................41–42
Answers .................................................43
4. Equivalent Fractions.................20
10. Subtracting Fractions ........... 44
TeacherN otes............................................20
Worksheets ..........................................21–22
Answers .....................................................23
5. Comparing Fractions ............... 24
TeacherN otes............................................24
Worksheets ..........................................25–26
Answers .....................................................27
6. Ordering Fractions ....................28
TeacherN otes............................................28
Worksheets ..........................................29–30
Answers .....................................................31
TeacherN otes........................................44
Worksheets ......................................45–46
Answers .................................................47
11. Decimals ..................................48
TeacherN otes........................................48
Worksheets ......................................49–50
Answers .................................................51
12. Probability ..............................52
TeacherN otes........................................52
Worksheets ......................................53–54
Answers .................................................55
T ransparencies ...............................56
Interlocking Fraction Circles
3
Teacher Notes
The classroom activities in Interlocking Fraction Circles cover the following topics:
•
•
•
•
•
•
•
•
Reading and changing fractions
Finding equivalent fractions
Comparing and ordering fractions
Using mixed numbers
Adding like and unlike fractions
Subtracting fractions
Representing decimals
Finding probabilities
This book includes:
•
•
•
•
Suggested notes for teaching each lesson
Two student worksheet masters per lesson
An answer key plus a suggested extension for each lesson
Accompanying transparencies for each lesson
There are two transparencies for each lesson:
• The first, in color, models the specific activity with examples, shows appropriate
fraction circle settings, and poses an additional related question.
• The second contains five follow-up, hands-on practice questions for students to
answer using the fraction circles.
Worksheet problems can be completed with or without use of the fraction circles,
depending on grade and ability level.
All students should have their own personal set of interlocking fraction circles.
However, many activities lend themselves to students working in teams with multiple
sets of fraction circles. The hands-on practice questions can make good cooperative
learning experiences, but they can be done individually as well.
To assess their understanding, have students display selected fraction circle answers by
holding them up so you, as the teacher, can quickly see and measure their overall performance. This can be an effective way to determine student progress.
Use the set of larger fraction circles when demonstrating to the class. Occasionally,
encourage students to explain their own thinking and answers to the entire class, using
these same larger fraction circles.
Interlocking Fraction Circles
5
How to Use Your Fraction Circles
Use the fifths circle and a blank circle to display fractions in fifths.
1.
2.
6
Start with a blank circle. Think of it as the face of
a clock, with the cut in the 12 o’clock position.
Insert the fraction circle into
the blank circle.
Interlocking Fraction Circles
3.
4.
Arrange the circles so they overlap, interlock, and
align with a marked line. This setting shows the
fraction 3/5.
Hold the blank circle in a fixed position
and rotate the fraction circle clockwise to
the next position to display 4/5.
5.
Hold the blank circle in a fixed position and
rotate the fraction circle counterclockwise
two positions to display 2/5.
Interlocking Fraction Circles
7
Reading Fractions
Content
Activity
The thirds circle divides the whole of 1
into 3 equal parts. Insert and interlock it
in a white circle and turn it clockwise to
display the fraction one-third.
Insert and interlock a fifths circle in a
white circle. Turn it clockwise to display
the fraction two-fifths.
1
3
3
3
three-thirds
1
1 of 3 equal parts
2
5
5
5
In the fraction two-fifths, the 2 is the
numerator and the 5 is the denominator.
2
5
five-fifths
numerator
denominator
Example
Show five-eighths.
Choose the blue eighths circle for the denominator.
Count off 5 parts for the numerator.
Practice
Use fraction circles.
Show nine-tenths as 9 out of 10 equal parts.
Show the fraction seven-twelfths.
Answers
For nine-tenths –
Choose the tenths circle for the denominator.
Count off 9 parts for the numerator.
2 of 5 equal parts
5
8
five-eighths
9
10
7
12
For seven-twelfths –
Choose the twelfths circle for the denominator.
Count off 7 parts for the numerator.
Notes
In this warm-up activity, students get to explore
their fraction circles. Have them focus on the
equal subdivisions, viewing them as equal parts
of the whole, where the whole is always 1.
Establish a common procedure for using the
interlocking circles to display fractions. Start
with a blank circle. Think of it as the face of a
clock, oriented so the cut is in the 12 o’clock
position. Insert the fraction circle, from the right,
into the blank circle so the two circles overlap
and interlock. Keep the blank circle fixed at the
12 o’clock position and rotate the fraction circle.
As you rotate the fraction circle clockwise, from
one position to the next, it displays fractions of
increasing value. As you rotate it in a counter-
8
clockwise fashion, from one position to the
next, it displays fractions of decreasing value.
With this single fraction circle, interlocked
and rotated step-by-step, an entire family of
fractions from 0 to 1 can be displayed. Change
the fraction circle to another of the eight choices
and display a different family of fractions.
For assessment purposes, display some settings
and have the students verbally identify the
fractions represented. Then name some fractions
and have students display them using their own
interlocking fraction circles. Emphasize that the
denominator of the fraction determines which
fraction circle to use.
Interlocking Fraction Circles
1
Reading Fractions
Worksheet One
Fill in the missing words and numbers for each fraction circle model.
1.
2.
three-fourths
3 of 4 equal parts
3.
3
4
of
equal parts
of
equal parts
of
equal parts
of
equal parts
4.
of
equal parts
5.
6.
of
equal parts
7.
8.
of
equal parts
Interlocking Fraction Circles
9
1
Reading Fractions
Worksheet Two
Choose the correct fraction circle for each fraction. Shade in the needed number of
parts, starting at the top.
1. 5
2. 3
3. 1
4. 3
5. 5
6. 2
7. 1
8. 4
12
6
8
3
4
2
10
5
5
12
10
Interlocking Fraction Circles
1
Answers
Reading Fractions
Worksheet One
1.
three-fourths 3 of 4
3
4
2.
three-fifths
3 of 5
3
5
3.
nine-tenths
9 of 10
9
10
4.
one-half
1 of 2
1
2
5.
four-sixths
4 of 6
4
6
6.
five-eighths
5 of 8
5
8
7.
five-twelfths
5 of 12
5
12
8.
one-third
1 of 3
1
3
Worksheet Two
1.
2.
3.
4.
5.
6.
7.
8.
Extension
A fraction circle is marked in seven equal parts.
Can it be used to model a fraction with a denominator of 7?
What about a numerator of 7?
Can it be used to model a fraction with a numerator of 3?
What about a denominator of 3?
Interlocking Fraction Circles
sevenths
11
Interlocking Fraction Circles
Correlation to Common Core State Standards
Standard 1
Grade 3
Number & Operations – Fractions (3.NF)
Activity
Develop understanding of fractions as numbers.
3.NF.1. Understand a fraction 1/b as the quantity formed by 1 part when
a whole is partitioned into b equal parts; understand a fraction a/b as the
quantity formed by a parts of size 1/b.
pp. 8–11, 12–15
a. Represent a fraction 1/b on a number line diagram by defining the
interval from 0 to 1 as the whole and partitioning it into b equal parts.
Recognize that each part has size 1/b and that the endpoint of the part
based at 0 locates the number 1/b on the number line.
p. 14
3.NF. 2. Understand a fraction as a number on the number line; represent
fractions on a number line diagram.
b. Represent a fraction a/b on a number line diagram by marking off a
lengths 1/b from 0. Recognize that the resulting interval has size a/b
and that its endpoint locates the number a/b on the number line.
3.NF.3. Explain equivalence of fractions in special cases, and compare
fractions by reasoning about their size.
p. 14
a. Understand two fractions as equivalent (equal) if they are the same size,
or the same point on a number line.
pp. 20–23
c. Express whole numbers as fractions, and recognize fractions that are
equivalent to whole numbers.
pp. 16–19
b. Recognize and generate simple equivalent fractions. Explain why the
fractions are equivalent.
d. Compare two fractions with the same numerator or the same
denominator by reasoning about their size. Recognize that comparisons
are valid only when the two fractions refer to the same whole. Record
the results of comparisons with the symbols >, =, or <, and justify the
conclusions.
Grade 4
Number & Operations – Fractions (4.NF)
pp. 20–23
pp. 20–23, 24–27,28–
31
Extend understanding of fraction equivalence and ordering.
1
4.NF.2. Compare two fractions with different numerators and different
denominators, e.g., by creating common denominators or numerators,
or by comparing to a benchmark fraction such as 1/2. Recognize that
comparisons are valid only when the two fractions refer to the same whole.
Record the results of comparisons with symbols >, =, or <, and justify the
conclusions, e.g., by using a visual fraction model.
Standards for which there is no correlation to the activities in this book are not listed.
pp. 28–31
Build fractions from unit fractions by applying and extending previous understandings of
operations on whole numbers.
4.NF.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and
separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same
denominator in more than one way, recording each decomposition by an
equation.
c. Add and subtract mixed numbers with like denominators.
pp. 36–39, 44–47
pp. 32–35
pp. 44–47
Understand decimal notation for fractions, and compare decimal fractions.
4.NF.5. Express a fraction with denominator 10 as an equivalent fraction
with denominator 100.
4.NF.6. Use decimal notation for fractions with denominators 10 or 100.
Grade 5
Number & Operations – Fractions (5.NF)
pp. 48–51
pp. 48–51
Use equivalent fractions as a strategy to add and subtract fractions.
5.NF.1. Add and subtract fractions with unlike denominators (including
mixed numbers) by replacing given fractions with equivalent fractions in
such a way as to produce an equivalent sum or difference of fractions with
like denominators.
Grade 6
pp. 40–43
Ratios and Proportional Relationships (6.RP)
Understand ratio concepts and use ratio reasoning to solve problems.
6.RP.1 Understand the concept of a ratio and use ratio language to describe
a ratio relationship between two quantities.
pp. 52–55