# Equivalent Fractions - Grade 4

Document Sample

```					                                                                                         Grade 4

Texas Essential Knowledge and Skills (TEKS)
4.2A   Number, operation, and quantitative reasoning. The student describes and compares
fractional parts of whole objects or sets of objects. The student is expected to use
concrete objects and pictorial models to generate equivalent fractions.
4.2D   Number, operation, and quantitative reasoning. The student describes and compares
fractional parts of whole objects or sets of objects. The student is expected to relate
decimals to fractions that name tenths and hundredths using concrete objects and pictorial
models.
4.14A Underlying processes and mathematical tools. The student applies Grade 4 mathematics
to solve problems connected to everyday experiences and activities in and outside of
school. The student is expected to identify the mathematics in everyday situations.
4.14C Underlying processes and mathematical tools. The student applies Grade 4 mathematics
to solve problems connected to everyday experiences and activities in and outside of
school. The student is expected to select or develop an appropriate problem-solving plan
or strategy, including drawing a picture, looking for a pattern, systematic guessing and
checking, acting it out, making a table, working a simpler problem, or working
backwards to solve a problem.
4.14D Underlying processes and mathematical tools. The student applies Grade 4 mathematics
to solve problems connected to everyday experiences and activities in and outside of
school. The student is expected to use tools such as real objects, manipulatives, and
technology to solve problems.
4.15A Underlying processes and mathematical tools. The student communicates about Grade 4
mathematics using informal language. The student is expected to explain and record
observations using objects, words, pictures, numbers, and technology.
4.15B Underlying processes and mathematical tools. The student communicates about Grade 4
mathematics using informal language. The student is expected to relate informal language
to mathematical language and symbols.
4.16A Underlying processes and mathematical tools. The student uses logical reasoning. The
student is expected to make generalizations from patterns of sets of examples and
nonexamples.
4.16B Underlying processes and mathematical tools. The student uses logical reasoning. The
student is expected to justify why an answer is reasonable and explain the solution
process.

Mathematics TEKS Connections: Grade 3-5                                                       4-1-1

Materials
• Lasso the Horses Directions transparency (pg. 18)
• Decimal Place Value transparency (pg. 19)
• Lasso the Horses Game Cards (pg. 20) - Copy for each pair of students and cut apart
• Paper Squares (pg. 23) - Cut apart, or use 10-centimeter die-cut squares
• Paper Strips (pg. 23) - Cut apart
• Paper Circles (pg. 24) - Cut apart, or use 4-inch diameter die-cut circles
• Decimal Squares - Tenths Transparency Overlay (pg. 25) - Cut apart
• Decimal Squares - Hundredths Transparency Overlay (pg. 26) - Cut apart
• Decimal Strips - Tenths Transparency Overlay (pg. 27) - Cut apart
• Decimal Strips - Hundredths Transparency Overlay (pg. 27) - Cut apart
• Decimal Circles - Tenths Transparency Overlay (pg. 28) - Cut apart
• Decimal Circles - Hundredths Transparency Overlay (pg. 29) - Cut apart
• Fraction/Decimal Number Line - Copied on 11"×17" paper
• Number Line Decimal Strips - Tenths (pg. 32) - Cut apart
• Number Line Decimal Strips - Hundredths (pg. 33) - Cut apart

For each pair of students:
• Lasso the Horses Game Board (pg. 21)
• Lasso the Horses Game Cards (pg. 20)
• 2 pieces of string about 12 inches long
• 3 sheets of manila paper
• Fraction Problem Set activity page (pg. 22)
• At least 2 each (1 set) of the following (make others available to students as needed):
Paper Squares, Paper Strips, Paper Circles (pg. 23-24)
• 1 each of the following - Decimal Square-Tenths Transparency Overlay, Decimal
Square- Hundredths Transparency Overlay, Decimal Strip - Tenths Transparency
Overlay, Decimal Strip - Hundredths Transparency Overlay, Decimal Circle -
Tenths Transparency Overlay, and Decimal Circle - Hundredths Transparency
Overlay (pg. 25-29)

For each student:
• Lasso the Horses activity page (pg. 34)
• Fraction/Decimal Representations activity pages (pg. 35-37)
• Decimal Place Value activity page (pg. 38)
• Verbal and Visual Word Association activity page (pg. 39)
• Fraction/Decimal Number Line
• Fraction/Decimal Number Line Number Cards (pg. 31)
• Glue
• Scissors
• Performance Assessment activity page (pg. 40)
• Selected Response activity pages (pg. 41-43)

Mathematics TEKS Connections: Grade 3-5                                                  4-1-2

Engage
The Engage portion of the lesson is designed to generate student interest and assess the students’
capacity to visualize fractional parts of sets of objects. This part of the lesson is designed for
pairs of students.

1. Display the Lasso the Horses Directions transparency (pg. 18).
2. Distribute the Lasso the Horses Game Boards (pg. 21), Lasso the Horses Game Cards
(pg. 20), Lasso the Horses activity page (pg. 34), and lengths of string to each pair of
students.
3. Prompt the students to shuffle the cards and place them in a stack face down.
4. Prompt the students to determine the player to go first by deciding which student has a
birthday closest to New Year’s Day.
5. Player 1 draws one card from the top of the stack and reads the card aloud.
6. Player 1 uses the length of string to “lasso” the fractional part of the set of horses indicated
on the card.

Example:
Put your
lasso around
1
4
of the
horses.

7. Player 1 then records his or her responses on the Lasso the Horses activity page (pg. 34).
8. Player 2 repeats Steps 5-7.
9. Play continues until each player has drawn 4 cards.
10. Players determine the total number of horses that they lassoed during the course of the game.
11. The player who has lassoed the most horses wins.

Mathematics TEKS Connections: Grade 3-5                                                          4-1-3

Facilitation Questions – Engage Phase
• How can you group the horses to represent the denominator of the fraction on the card
that you drew?
Responses may vary. Possible responses include: The denominator of my fraction is ____
(2, 3, 4, 6, or 12) so I know that my whole group of horses needs to be grouped into____
(2, 3, 4, 6, or 12) equal parts. The denominator of a fraction indicates the number of
parts that a whole is divided into.
Examples:

Denominator = 2

Denominator = 3

Denominator = 4

Denominator = 6

Denominator = 12

Mathematics TEKS Connections: Grade 3-5                                                   4-1-4

Facilitation Questions – Engage Phase
• How did you represent the numerator of the fraction on the card that you drew?
Responses may vary. Possible responses include: The numerator of my fraction is
represented by the number of groups of horses that I lassoed.
Examples:

1                                                       1 group lassoed
equals 6 horses
2

1                                                       1 group lassoed
equals 4 horses
3

1                                                       1 group lassoed
equals 3 horses
4

1                                                       1 group lassoed
equals 2 horses
6

1                                                       1 group lassoed
equals 1 horse
12

Mathematics TEKS Connections: Grade 3-5                                                   4-1-5

Explore
The Explore portion of the lesson provides the student with an opportunity to be actively
involved in the exploration of the mathematical concepts addressed. This part of the lesson is
designed for pairs of students.

1. Distribute the Fraction Problem Set activity page (pg. 22), 3 sheets of manila paper, and
1 set each of the Paper Squares (pg. 23), Paper Strips (pg. 23), and Paper Circles (pg. 24)
to each pair of students.
2. Prompt the students to cut the 3 problems on the Fraction Problem Set activity page
(pg. 21) apart.
3. Prompt the students to fold a Paper Square (pg. 23), Paper Strip (pg. 23), and Paper
Circle (pg. 24) as indicated, and shade part of the model to represent the problem situation.
4. Prompt the students to fold a second Paper Square (pg. 23), Paper Strip (pg. 23), and
Paper Circle (pg. 24) as indicated and shade it to represent a different fraction that is
equivalent to the fraction in the problem.
5. Prompt the students to glue the problem being represented and their paper models to the
sheet of manila paper.
6. Prompt the students to express the relationship between the two fractions and the two models
representing the fractions in words and numbers.
7. Prompt the students to explain their thinking.

Sample presentation:

Facilitation Questions – Explore Phase
• What made you decide to fold the paper the way that you did?
Responses may vary. Possible responses include: If I fold the paper once and make sure
that the corners and edges match, I know that the 2 parts created by the fold will be
1
equivalent. One of those parts represents of the whole sheet of paper. If I fold the
2
paper twice, the 4 parts that are created are equivalent and 2 of those parts represents
2
of the whole sheet of paper.
4

Mathematics TEKS Connections: Grade 3-5                                                      4-1-6

Facilitation Questions – Explore Phase
• How did you describe the relationship between the two paper models?
Responses may vary. Possible responses include: One of the pieces of paper is divided
into 2 equal parts. The other piece of paper is divided into 4 equal parts. The second
piece of paper that I folded has twice the number of equal parts as the first piece of
paper I folded.
• How does the number of parts that you divided your paper model into represent the
problem situation?
Responses may vary. Possible responses include: I folded my paper strip to create
5 equal parts. Four of those parts represent the portion of the race that Elias completed
before having to stop. The whole paper strip represents the length of the entire race.

Mathematics TEKS Connections: Grade 3-5                                                      4-1-7

Explain
The Explain portion of the lesson is directed by the teacher to allow the students to formalize
their understanding of the TEKS addressed in the lesson.

1. Explain to the students that fractional parts can be expressed using another notation.
2. Prompt the students to imagine the Paper Squares, Paper Strips, and Paper Circles
(pg. 25-29) models that they created in the Explore phase of the lesson divided into 10 equal
parts.
3. Prompt the students to imagine the Paper Squares, Paper Strips, and Paper Circles
(pg. 25-29) models that they created in the Explore phase of the lesson divided into 100 equal
parts.

Facilitation Questions – Explain Phase
• How would you describe the parts of your model if it were divided into 10 equal parts?
100 equal parts?
Responses may vary. Possible responses include: The pieces would be smaller and there
would be more pieces.
• How would that affect the denominator of your fraction?
Responses may vary. Possible responses include: The denominator would be 10 if the
model were divided into 10 equal parts. The denominator would be 100 if the model
were divided into 100 equal parts.

4. Distribute one Decimal Square-Tenths, Decimal Square- Hundredths, Decimal Strip -
Tenths, Decimal Strip - Hundredths, Decimal Circle - Tenths, and Decimal Circle -
Hundredths Transparency Overlay (pg. 25-29) and the Fraction/Decimal
Representations activity pages (pg. 35-37) to each pair of students.
5. Prompt the students to examine the transparency overlays and determine which
spaces/regions represent tenths and which spaces/regions represent hundredths.
6. Prompt the students to place the appropriate overlay on top of their folded paper models to
simulate dividing the model into tenths/hundredths.
7. Prompt the student to shade the same amount on the Fraction/Decimal Representations
activity pages (pg. 35-37) as on the Paper Square, Paper Strip, and Paper Circle models.
8. Prompt the students to describe the part shaded as a fraction with a denominator of 10 or 100
and record it on the Fraction/Decimal Representations activity pages (pg. 35-37).

Facilitation Questions – Explain Phase
• Were you able to represent all of your models with a fraction with a denominator of
10 or 100?
1
Responses may vary. Possible responses include: Yes. is equivalent to 5 tenths/
2
2                                              4
50 hundredths,      is equivalent to 2 tenths/20 hundredths, and is equivalent to
10                                              5
8 tenths/80 hundredths.

Mathematics TEKS Connections: Grade 3-5                                                       4-1-8

9. Explain to the students that all numbers can be written using place value, including numbers
less than 1.
10. Explain to the students that we can use a decimal to separate the whole number places from
the places that represent a number less than 1. Whole number places are to the left of the
decimal and numbers less than 1 are to the right of the decimal.
11. Display the Decimal Place Value transparency (pg. 19) on overhead.

5
12. Explain to the students that     can be expressed 0.5. Explain to the students that the place
10
just to the right of the decimal is the tenths place. We say 0.5 “five tenths” the same way we
say it in fraction notation.
Sample:

50
13. Explain to students that       can be expressed 0.50. Explain to the students that the place that
100
is 2 places to the right of the decimal is the hundredths place. We say “50 hundredths” the
same way we say it in fraction notation.
Sample:

14. Prompt the students to write the fractions from their problems in decimal notation on the
Fraction/Decimal Representations activity page (pg. 35-37).
15. Prompt the students to record the decimals from the Fraction/Decimal Representations
activity page (pg. 35-37) on the Decimal Place Value activity page (pg 38).
16. Distribute the Verbal and Visual Word Association activity page (pg. 39).
17. Prompt the students to complete the Verbal and Visual Word Association activity page
(pg. 39).

Mathematics TEKS Connections: Grade 3-5                                                         4-1-9

Sample:
Vocabulary Term                Visual Representation

Equivalent Fractions

7                70
10               100
Definition                      Example

Fractions that represent the same part to
whole relationship.

4 2 1
= =
8 4 2

Mathematics TEKS Connections: Grade 3-5                                 4-1-10

Elaborate
The Elaborate portion of the lesson provides an opportunity for the student to apply the concepts
of the TEKS within a new situation. In this lesson, students will generate fractions, express the
fraction in decimal notation, and place the fractions and decimals on a number line to verify
equivalency. This part of the lesson is designed for groups of three to four students.

1. Distribute a Fraction/Decimal Number Line to each student.

Teacher Note: An 8.5” × 11” black line master of the number line is included. The number line
should be printed on an 11” × 17” sheet of paper to allow students more room to work.

2. Distribute one sheet of Fraction/Decimal Number Line Number Cards (pg. 31) to each
student.
3. Prompt the students to cut the Fraction/Decimal Number Line Number Cards (pg. 31)
apart on the lines indicated.
4. Distribute one Number Line Decimal Strip (Tenths) (pg. 32) and one Number Line
Decimal Strip (Hundredths) (pg. 33) to each student.
5. Prompt the students to use their Fraction/Decimal Number Line Decimal Strip (Tenths)
(pg. 32) and Fraction/Decimal Number Line Decimal Strip (Hundredths) (pg. 33) to help
them see the relationships in the positions of the various numbers.

Teacher Note: The size of the Fraction/Decimal Number Line and the Fraction/Decimal Number
Line Strips (Tenths and Hundredths) are different sizes by design to allow students to see the
part-to-whole relationships between different-sized objects. Demonstrate for the students how to
fold the decimal strip into halves, fourths, etc. to determine a relative location on their number
line. The purpose of the activity is to demonstrate that the size of the whole can vary, but the
relationships between fractional parts remain constant.

6. Remind the students that some fractions and/or decimals may be equivalent.
7. Prompt the students to glue their number cards on the number line in the appropriate position.

Sample number line:

Mathematics TEKS Connections: Grade 3-5                                                     4-1-11

Facilitation Questions – Elaborate Phase
• How can we show on a number line that fractions and/or decimals are equivalent?
Responses may vary. Possible responses include: Equivalent fractions and/or decimals
will be in the same position on the number line.
• How can you use your decimal strips to help you find the appropriate location for the
number cards on your number line?
Responses may vary. Possible responses include: When I fold my decimal strip in half,
the fold is at 0.5 on my strip, so 0.5 must go halfway between 0 and 1 on my number
line. One half is equivalent to 0.5.
• What did you notice about the position of the fold when you folded your
Fraction/Decimal Number Line Decimal Strip (Tenths) (pg. 31) to represent fifths?
Responses may vary. Possible responses include: The folds aligned with every second
number on the strip.
• How can you use your Fraction/Decimal Number Line Decimal Strips (Hundredths)
4
(pg. 32) to find another way to express ? Explain your thinking.
5
Responses may vary. Possible responses include: When I fold my Fraction/Decimal
Number Line Decimal Strip (Hundredths) to represent fifths, the fold is on a line.
4                 80
There are 80 segments on the strip before that mark so is equivalent to        or 0.80.
5                100

Mathematics TEKS Connections: Grade 3-5                                                  4-1-12

Evaluate
The Evaluate portion of the lesson provides the student with an opportunity to demonstrate his or
her understanding of TEKS addressed in the lesson.

1. Provide each student with a Performance Assessment activity page (pg. 40).
2. Upon completion of the activity page, use a rubric to assess student understanding of the
3. Prompt the students to complete the Selected Response activity pages (pg. 41-43).

Performance Assessment
Martel and Juan were having a contest to see who could read 10 books in the least amount of
4
time. After 3 days, Martel said that he was winning the contest because he had read of the
5
books on his list. Juan said that he was winning the contest because he had read 0.8 of the
books on his list. Which boy was correct? Use the models below to find your answer.

Answer: Neither boy was correct. Both boys had read the same portion of the books on their list.

Possible models:
4
5                                    0.8

Mathematics TEKS Connections: Grade 3-5                                                    4-1-13

Selected Response Answer Key and Error Analysis

Question               Correct     Conceptual   Conceptual   Procedural   Procedural
TEKS                                                                      Guess
Number                 Answer        Error        Error         Error       Error
1        4.2A         D              B                       A            C
2        4.2A         A              B          C                                    D
3        4.2D         C              A          B                                    D
4        4.2D         C              A          B                                    D

Mathematics TEKS Connections: Grade 3-5                                                   4-1-14

Fraction/Decimal Representations (Page 1)

1   5                                         1   50
=   = 0. 5                                    =    = 0. 5 0
2 10                                          2 100

Mathematics TEKS Connections: Grade 3-5                                        4-1-15

Fraction/Decimal Representations (Page 2)

4   8
=   = 0. 8
5 10

4   80
=    = 0. 80
5 100

Mathematics TEKS Connections: Grade 3-5                                      4-1-16

Fraction/Decimal Representations (Page 3)

2  2                                          2   20
= = 0. 2                                      =    = 0. 20
10 10                                         10 100

Mathematics TEKS Connections: Grade 3-5                                         4-1-17

Lasso the Horses Directions
Transparency
Each player takes turns doing the
following:
• Draw one card from the pile.
• Write the fraction shown on the
• Use your string to “lasso” that
portion of the horses on the
Lasso the Horses Game Board.
• Record the number of horses

After all cards have been drawn
(4 per player), find the total number of
horses that each player lassoed.

The player that lassoed the greatest
number of horses is the winner.

Mathematics TEKS Connections: Grade 3-5     4-1-18

Decimal Place Value Transparency

Mathematics TEKS Connections: Grade 3-5     4-1-19

Lasso the Horses Game Cards

lasso    lasso    lasso    lasso
around around around around
1                         1         1         1
2                         3         4        12
of the   of the   of the   of the
horses. horses. horses. horses.
lasso    lasso    lasso    lasso
around around around around
1                         2         3         6
6                         3         4         6
of the                     of the        of the    of the
horses.                    horses.       horses.   horses.

Mathematics TEKS Connections: Grades 3-5                     4-1-20

Lasso the Horses Game Board

Mathematics TEKS Connections: Grade 3-5                                   4-1-21

Fraction Problem Set Activity Page
1
Mr. and Mrs. Blackerby paved                 of their backyard with
2
stone tiles.
portion of the yard paved with stone tiles.
• Fold another paper square to represent a different
1
fraction equivalent to .
2

4
Elias was running a race. After completing               of the race,
5
Elias hurt his knee and had to stop.
portion of the race that Elias completed.
• Fold another paper strip to represent a different
4
fraction equivalent to .
5

The fourth grade students at Myers Elementary use a big
2
parachute that is     yellow to play games during P.E.
10
class.
portion of the parachute that is yellow.
• Fold another paper circle to represent a different
2
fraction equivalent to    .
10

Mathematics TEKS Connections: Grades 3-5                              4-1-22

Paper Squares and Paper Strips

Mathematics TEKS Connections: Grades 3-5                4-1-23

Paper Circles

Mathematics TEKS Connections: Grades 3-5                 4-1-24

Decimal Squares – Tenths Transparency Overlays

Mathematics TEKS Connections: Grades 3-5          4-1-25

Decimal Squares – Hundredths Transparency Overlays

Mathematics TEKS Connections: Grades 3-5           4-1-26

Decimal Strips - Tenths Transparency Overlays
Decimal Strips - Hundredths Transparency Overlays

Mathematics TEKS Connections: Grades 3-5         4-1-27

Decimal Circle -Tenths Transparency Overlays

Mathematics TEKS Connections: Grades 3-5              4-1-28

Decimal Circle - Hundredths Transparency Overlays

Mathematics TEKS Connections: Grades 3-5          4-1-29
(duplicate on 11” × 17” paper)

Mathematics TEKS Connections: Grades 3-5                        4-1-30

Fraction/Decimal Number Line Number Cards

1                1   3     2
2                4   4     4
1                2   3     4
5                5   5     5

0.5 0.50 0.25 0.75

0.1             0.2     0.3   0.4

0.6             0.7     0.8   0.9

Mathematics TEKS Connections: Grades 3-5                     4-1-31

Number Line
Decimal Strips – Tenths

Mathematics TEKS Connections: Grades 3-5                 4-1-32

Number Line
Decimal Strips – Hundredths

Mathematics TEKS Connections: Grades 3-5                 4-1-33

Lasso the Horses Activity Page

I lassoed         of the horses.             I lassoed      of the horses.

Group the dots to represent the               Group the dots to represent the
denominator of the fraction.                  denominator of the fraction.

Represent the fraction using the dot array.   Represent the fraction using the dot array.

Number of horses lassoed ___________          Number of horses lassoed ___________

I lassoed         of the horses.             I lassoed      of the horses.

Group the dots to represent the               Group the dots to represent the
denominator of the fraction.                  denominator of the fraction.

Represent the fraction using the dot array.   Represent the fraction using the dot array.

Number of horses lassoed ___________          Number of horses lassoed ___________

Total number of horses lassoed                   _____________

Mathematics TEKS Connections: Grades 3-5                                               4-1-34

Fraction/Decimal Representations (Page 1)

1                                             1
=  = 0.                                       =   = 0.
2 10                                          2 100

Mathematics TEKS Connections: Grades 3-5                                    4-1-35

Fraction/Decimal Representations (Page 2)

4
=  = 0.
5 10

4
=   = 0.
5 100

Mathematics TEKS Connections: Grades 3-5                                    4-1-36

Fraction/Decimal Representations (Page 3)

2                                          2
=  =0.                                     =   =0.
10 10                                      10 100

Mathematics TEKS Connections: Grades 3-5                                    4-1-37

Decimal Place Value Activity Page

Mathematics TEKS Connections: Grades 3-5                  4-1-38

Verbal and Visual Word Association Activity Page

Vocabulary Term             Visual Representation

Equivalent
Fractions

Definition                   Example

Mathematics TEKS Connections: Grades 3-5                             4-1-39

Performance Assessment
Martel and Juan were having a contest to see who could read 10 books in
the least amount of time. After 3 days, Martel said that he was winning the
4
contest because he had read       of the books on his list. Juan said that he
5
was winning the contest because he had read 0.8 of the books on his list.
Which boy was correct? Use the models below to find your answer.

Mathematics TEKS Connections: Grades 3-5                                  4-1-40

Selected Response
2
1. Which fraction model shows a shaded portion that is equivalent to     ?
3

A

B

C

D

Mathematics TEKS Connections: Grades 3-5                              4-1-41

2.   Which two fractions could            3.   After dinner, Mrs. Rodolfo
be used to describe the                                 3
noticed that of the
shaded portion of the model                             5
shown below?                              lasagna that she had
Which model shows an
3
equivalent to ?
5

A
2      4
A       and
5     10

2      6
B       and
3     10
B
3      6
C       and
5     10

2     2
D       and
5     6
C

D

Mathematics TEKS Connections: Grades 3-5                                 4-1-42

4.    Beverly was spreading fertilizer on her lawn. By 10:00 A.M Beverly had
3
spread fertilizer on   of her lawn.
4
Beverly’s Lawn

3
Which model below shows an amount shaded that is equivalent to       ?
4

A                                          C

B                                          D

Mathematics TEKS Connections: Grades 3-5                                4-1-43