Use the fifths circle and a blank circle to display fractions in fifths.

Start with a blank circle. Think of it as the face of a clock, with the

cut in the 12 o’clock position.

1

Insert the fraction circle into the blank circle.

2

Arrange the circles so they overlap, interlock, and align

with a marked line. This setting shows the fraction ⅗.

3

Hold the blank circle in a fixed position and rotate the fraction

circle clockwise to the next position to display ⅘.

4

Hold the blank circle in a fixed position and rotate the fraction

circle counterclockwise two positions to display ⅖.

5

©DIDAX

Interlocking Fraction Circles 3

1. Reading Fractions .......................8Teacher N otes ..............................................8Worksheets ............................................9–10 Answers ..................................................... 11

2. Changing Fractions ...................12Teacher N otes ............................................12Worksheets ..........................................13–14 Answers .....................................................15

3. Parts of a Whole ........................16Teacher N otes ............................................16Worksheets ..........................................17–18 Answers .....................................................19

4. Equivalent Fractions .................20Teacher N otes ............................................20Worksheets ..........................................21–22 Answers .....................................................23

5. Comparing Fractions ............... 24Teacher N otes ............................................24Worksheets ..........................................25–26 Answers .....................................................27

6. Ordering Fractions ....................28Teacher N otes ............................................28Worksheets ..........................................29–30 Answers .....................................................31

7. Mixed Numbers .......................32Teacher N otes ........................................32Worksheets ......................................33–34 Answers .................................................35

8. Adding Like Fractions ............36Teacher N otes ........................................36Worksheets ......................................37–38 Answers .................................................39

9. Adding Unlike Fraction .........40Teacher N otes ........................................40Worksheets ......................................41–42 Answers .................................................43

10. Subtracting Fractions ........... 44Teacher N otes ........................................44Worksheets ......................................45–46 Answers .................................................47

11. Decimals ..................................48Teacher N otes ........................................48Worksheets ......................................49–50 Answers .................................................51

12. Probability ..............................52Teacher N otes ........................................52Worksheets ......................................53–54 Answers .................................................55

T ransparencies ...............................56

Table of ContentsIntroduction .............................................................................................................4

Teacher N otes ............................................................................................................5

How to Use Your Fraction Circles ...........................................................................6

Interlocking Fraction Circles 5

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 fi rst, in color, models the specifi c activity with examples, shows appropriate • fraction circle settings, and poses an additional related question.The second contains fi ve 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 per-formance. 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.

6 Interlocking Fraction Circles

How to Use Your Fraction Circles

Use the fi fths circle and a blank circle to display fractions in fi fths.

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.

Interlocking Fraction Circles 7

3. Arrange the circles so they overlap, interlock, and align with a marked line. This setting shows the fraction 3/5.

4. Hold the blank circle in a fi xed position and rotate the fraction circle clockwise to the next position to display 4/5.

5. Hold the blank circle in a fi xed position and rotate the fraction circle counterclockwise two positions to display 2/5.

8 Interlocking Fraction Circles

Reading Fractions Activity 1

For nine-tenths – Choose the tenths circle for the denominator. Count off 9 parts for the numerator.

For seven-twelfths – Choose the twelfths circle for the denominator. Count off 7 parts for the numerator.

910

712

Insert and interlock a fifths circle in a white circle. Turn it clockwise to display the fraction two-fifths.

In the fraction two-fifths, the 2 is the numerator and the 5 is the denominator.

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.

Show five-eighths. Choose the blue eighths circle for the denominator. Count off 5 parts for the numerator.

5 2 numerator

denominator

55

33

three-thirds

five-fifths

1 of 3 equal parts

2 of 5 equal parts

five-eighthsUse fraction circles. Show nine-tenths as 9 out of 10 equal parts. Show the fraction seven-twelfths.

13

25

58

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-

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.

Content

Example

Practice

Answers

Notes

Interlocking Fraction Circles 9

three-fourths

3 of 4 equal parts 4 3

1 Reading Fractions Worksheet One

Fill in the missing words and numbers for each fraction circle model.

1. 2.

of equal parts

of equal parts

3. 4.

of equal parts

of equal parts

5. 6.

of equal parts

of equal parts

7. 8.

of equal parts

10 Interlocking Fraction Circles

Choose the correct fraction circle for each fraction. Shade in the needed number of parts, starting at the top.

1 Reading Fractions Worksheet Two

5. 6. 7. 8.

1. 2. 3. 4.512

14

310

12

45

23

38

56

12 5

Interlocking Fraction Circles 11

1 Answers Reading Fractions

Worksheet One

1. three-fourths 3 of 4 2. three-fifths 3 of 5

3. nine-tenths 9 of 10 4. one-half 1 of 2

5. four-sixths 4 of 6 6. five-eighths 5 of 8

7. five-twelfths 5 of 12 8. one-third 1 of 3

4 3

6 4

10 9

12 5

5 3

8 5

2 1

3 1

Worksheet Two

5. 6. 7. 8.

1. 2. 3. 4.

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?

sevenths

Standard1 ActivityGrade 3Number & Operations – Fractions (3.NF) 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

3.NF. 2. Understand a fraction as a number on the number line; represent fractions on a number line diagram.

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

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.

p. 14

3.NF.3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. pp. 20–23

b. Recognize and generate simple equivalent fractions. Explain why the fractions are equivalent. pp. 20–23

c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. pp. 16–19

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.

pp. 20–23, 24–27,28–31

Grade 4Number & Operations – Fractions (4.NF)Extend understanding of fraction equivalence and ordering.

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.

pp. 28–31

Interlocking Fraction CirclesCorrelation to Common Core State Standards

1 Standards for which there is no correlation to the activities in this book are not listed.

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. pp. 36–39, 44–47

b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation.

pp. 32–35

c. Add and subtract mixed numbers with like denominators. pp. 44–47Understand decimal notation for fractions, and compare decimal fractions.4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100. pp. 48–51

4.NF.6. Use decimal notation for fractions with denominators 10 or 100. pp. 48–51

Grade 5Number & Operations – Fractions (5.NF)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.

pp. 40–43

Grade 6Ratios 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