Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Number, Operation, and Quantitative Reasoning
Activity:
Conversion Creations: From Mixed Numbers to Improper Fractions
TEKS:
(5.2) Number, operation, and quantitative reasoning. The student
uses fractions in problem-solving situations.
The student is expected to:
(B) generate a mixed number equivalent to a given improper
fraction or generate an improper fraction equivalent to a given
mixed number;
(C) compare two fractional quantities in problem-solving situations
using a variety of methods, including common denominators;
(5.14) Underlying processes and mathematical tools. The student
applies Grade 5 mathematics to solve problems connected to everyday
experiences and activities in and outside of school
The student is expected to:
(A) identify the mathematics in everyday situations;
(D) use tools such as real objects, manipulatives, and technology to
solve problems.
(5.15) Underlying processes and mathematical tools. The student
communicates about Grade 5 mathematics using informal language.
The student is expected to:
(A) explain and record observations using objects, words, pictures,
numbers, and technology; and
(B) relate informal language to mathematical language and
symbols.
(5.16) Underlying processes and mathematical tools. The student
uses logical reasoning.
The student is expected to:
(A) make generalizations from patterns or sets of examples and
nonexamples; and
(B) justify why an answer is reasonable and explain the solution
process.
Note: Portions of this lesson address TEKS at other grade levels as well;
however, the intent of the lesson fits most appropriately at the grade level
indicated.
Overview:
Students will have the opportunity to review the meaning of mixed and
improper fractions through the use of concrete and pictorial models.
Then, they will use those models to create or invent procedures for
generating improper fractions from mixed numbers and mixed numbers
from improper fractions.
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 1
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Prerequisites:
Students will have had the opportunity to model fraction quantities greater
than one using concrete objects and pictorial models (4.2B) and locate
and name points on a number line using whole numbers and fractions
(4.10). Likewise, students should have prior experience representing
fractions with length, area, and set models.
Materials:
Manipulatives that can be used to represent length, area, and set models
for fractions, such as the following:
Pattern blocks
Fraction bars
Fraction circles
Color tiles
Geoboard and geobands
Two-color counters
Colored post-it dots
Play money
Adding machine tape
Cuisenaire rods
Measuring tapes
Meter sticks
Yard sticks
Rulers
Student number lines
Measuring cups, spoons
Liter cups
Poster or chart paper with crayons or markers, and/or blank overhead
transparencies with vis-à-vis pens
Modeling Mixed Numbers Recording Sheet – Handouts/Transparencies
1a and 1b
Improper Fractions to Mixed Numbers Recording Sheet –
Handouts/Transparencies 2a and 2b
Fraction Fakeout – Handouts/Transparencies 3a through 3k
Mixing It Up Directions, Playing Cards, Recording Sheet –
Handouts/Transparencies 4a, 4b, 4c, and 4d
Mixing It Up Example Problem – Handout/Transparency 5
Check for Understanding Mixed Numbers and Improper Fractions –
Handouts/Transparencies 6a, 6b, and 6c
Check for Understanding Mixed Numbers and Improper Fractions Answer
Key – Answer Keys 7a, 7b, and 7c
Fraction Calculators
Computer(s) with Internet Connection
Grouping:
Individual, pairs, and whole group
Time:
2-3 periods, teacher discretion
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 2
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Lesson:
1.
Procedures
Modeling Mixed Numbers:
Place a variety of the listed manipulatives on
each table. Be sure to include manipulatives
which can be used to represent length, area,
and set models for fractions and mixed
numbers.
Begin the lesson by asking students to use
any of the materials on their table to
independently construct or draw a model of
one and three-fourths.
Students should be prepared to share their
models with the class.
Notes
This introductory activity can serve
as a formative assessment as well
as an instructional activity.
If some students have difficulty
getting started, prompt with
questions such as the following:
• What could you use to draw
and label a line that is
1 3 inches long?
4
• If I use this as my whole (pick
one manipulative), how could
3
you model 1 ?
4
• How could you draw a picture
3
to show 1 cups of sugar?
4
• If 4 counters make one whole,
how could you model 1 whole
3
and
more?
4
See Van de Walle (2006) for more
information on the types of fraction
models used in this lesson:
1) length (or measurement)
models;
2) area (or region) models; and
3) set models.
2.
Call on several students to share their
models with the class. Collect drawings of
the various models on a chart, on the board,
or on a transparency.
After the sharing session, you will
have a collection of
3
representations for 1 . Look to
4
see if length, area, and set models
have been shared. If any of these
models are missing, ask questions
to assist students in constructing
them.
3.
Have students examine the collection for
similarities and differences.
If needed, prompt students by
asking questions such as the
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 3
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Procedures
Notes
following:
• How are the models the same?
• How are the models different?
• Which models are represented
with some type of line? With
some area or region? With
sets of items?
• Where is the number 1
represented in each model?
3
• Where is the fraction
4
represented in each model?
• Why are the 4th’s in this model
bigger than the 4th’s in this
one?
Students need to see that each
model includes one whole as well
as an additional fractional part.
The size of the fractional parts is
determined by the size of the
whole. The whole may or may not
be subdivided into parts. Students
may remark or describe how each
7
model also represents . Do not
4
interject or elaborate on this
comment (improper fraction) at
this point.
4.
3
is an example of a mixed
4
3
number. Numbers like 1 are called mixed
4
numbers because they are a mixture of a
whole number plus a fraction. Show and tell
students how this mixed number is written
3
and read ( 1 , one and three-fourths).
4
Explain that 1
Van de Walle (2004) emphasizes
that fractional quantities should
always be written with the
horizontal division bar and not a
slanting line. This reinforces the
concept of denominator as divisor.
Using several of the models on the posters,
3
3
illustrate and verbalize how 1 is 1 + .
4
4
Ask students to relate where they have seen
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 4
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Procedures
or heard mixed numbers used in everyday
life.
5.
Ask students to work with a partner to
choose or generate a mixed number and
create at least two different models for that
mixed number. They should create a poster
by drawing their models on chart paper.
They should not write the mixed number on
their poster.
6.
Give one or two pairs of students the
opportunity to show their posters to the
class.
Notes
Students will have seen various
models for a mixed number after
completing procedures 1-4 above.
Their new posters should reflect a
variety of representations for their
chosen mixed number. The more
diverse the models, the better the
understanding.
For each poster shared, ask the class the
following:
• What mixed number is represented by
the models?
• How do we write and read this mixed
number?
• Does this model represent a length
model? Area model? Set model?
When the correct mixed numbers have been
identified by the class, have the student pairs
record the mixed number (in symbolic and
word form) on their posters.
7.
Display the remaining posters around the
room and number the posters so that they
can be matched to the numbers on Modeling
Mixed Numbers Recording Sheet –
Handouts/Transparencies 1a and 1b.
This recording sheet, as well as
the posters, can serve as a
formative assessment.
Ask students to record the mixed number (in
symbolic and word form) for each poster on
the recording sheet. Include the posters that
have already been shared.
8.
Converting Mixed Numbers to Improper
Fractions:
Adapted from Van de Walle
(2004).
Choose and focus on any one of the models
For students who are unable to
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 5
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Procedures
(length, area, or set) on the posters.
Notes
comprehend the task or cannot
proceed after sufficient wait time,
Example: A pair of students uses adding
have them count out 8th’s (using
an appropriate manipulative such
5
machine tape to model 2 .
as 8th’s of a fraction circle) until
8
8
they get to . Have them write
8
Ask students to find a single fraction that
names the same amount. They can use the this fraction and tell you how many
same manipulative, a different one, a
8
drawing, or any other method as long as they circles 8 represents. (1 circle).
can explain and model their results.
8
is a single fraction which
Say:
8
names the same amount as 1.
Now see if you can find a single
fraction to name the same amount
⎛ 16 ⎞
as 2. ⎜ ⎟
⎝ 8 ⎠
Finally, can you find a single
fraction to name the same amount
⎛ 21⎞
5
as 2 ? ⎜ ⎟
8
⎝8⎠
9.
Have students share their methods for
⎛ 21⎞
arriving at the new fraction ⎜ ⎟ .
⎝8⎠
Ask:
What does the denominator (8) tell us?
(It tells us what fractional part we are
counting – eighths.)
What does the numerator (21) tell us?
(It tells us how many eighths we have.)
One student’s method might be
folding each of the 2 whole strips
of adding machine tape into
eighths, then, labeling and
counting the total number of
eighths,
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
or adding
10.
Explain to students that this type of fraction
is called an improper fraction. The
numerator is larger than the denominator.
Sometimes they are described as “top
heavy.”
8 8 5 21
+ + =
.
8 8 8 8
A classroom teacher related the
following analogy that she uses
with her students when
introducing improper fractions.
She gives her students the
analogy of trying to eat spaghetti
with our fingers. It is “improper to
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 6
Mathematics TEKS Refinement 2006 – K-5
Procedures
11.
Repeat the task above several times with
different mixed numbers from other posters.
Have students share and verbalize their
procedure for generating an improper
fraction.
12.
Have students contrast the use of improper
fractions with that of mixed numbers. Ask
students which form they see most often
used in everyday life. Share and discuss
real life situations in which improper fractions
are utilized.
Tarleton State University
Notes
do so,” but it still “gets the job
done” because we are able to eat
and fill our empty stomachs.
In our everyday lives, we express
quantities more often as mixed
numbers, even when the initial
situation may utilize an improper
fraction.
Example:
1
yard of cloth for
2
each wall hanging she is making.
If she is making 7 wall hangings,
how many yards of cloth should
7
1
she purchase? ( or 3 yards)
2
2
Jean needs
In middle school, students will
begin to compute with fractions. It
is often easier to compute with
improper fractions than with the
corresponding mixed numbers.
13.
Finally, ask students to work with a partner to
determine a method for changing any mixed
number to an improper fraction without the
use of manipulatives. They should be able
to develop and express a generalization or
rule that makes sense to them.
Van de Walle (2004) states, “there
is absolutely no reason ever to
provide a rule” for “converting
mixed numbers to common
fractions and the reverse.”
In support of students developing
Student words might sound like the following: their own procedures for
conversion, see “Reflecting on
• Divide the wholes into the same type of
Learning Fractions without
fractional parts as the fraction, and then
count how many of those parts you have Understanding,” (2003). NCTM
On-Math e-resources
altogether.
http://my.nctm.org/eresources/vie
• Find the number of fractional parts in
w_article.asp?article_id=6430&pa
each whole, and then add those to the
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 7
Mathematics TEKS Refinement 2006 – K-5
•
14.
Procedures
numerator of the fraction to get the total
number of parts.
Multiply the whole number by the
fractional part we are counting (the
denominator), then combine that number
of fractional parts with the parts in the
fraction (numerator), and that tells how
many parts there are in all.
Tarleton State University
Notes
ge=1
Or, see the IMAP version below:
http://www.sci.sdsu.edu/CRMSE/I
MAP/pubs/Reflections_on_Fractio
ns.pdf
Have students share and demonstrate their
rules for the class. Compare the various
methods and draw attention to the
similarities.
Allow students to publish their rules in a
class book. Let them illustrate their page
and provide ideas for the cover. Keep the
class book on the shelf for them to read and
refer to throughout the year.
15.
Converting Improper Fractions to Mixed
Numbers:
Prepare baggies with sets of identical
fractional parts. Include a card on which the
relationship of the part to the whole is
identified.
Students are to write the single fraction
represented by the parts, and then change
that single fraction into a mixed number that
names the same amount.
Rotate the baggies among the students.
Number the baggies so that students can
record their results for each one on a
recording sheet. See Improper Fractions to
Mixed Numbers Recording Sheet –
Handouts/Transparencies 2a and 2b.
16.
Discuss and verify or check student results.
17.
Ask students to work with a partner to
determine a method for changing any
improper fraction to a mixed number without
the use of manipulatives. Once again, they
Prepare enough baggies for each
student or each pair of students to
have one.
Examples might include:
• 14 rhombi from a pattern block
set with a card labeled “thirds.”
• 24 red Cuisenaire rods with a
card labeled “fifths.”
• 33 base ten unit cubes with a
card labeled “tenths.”
• 12 two-colored counters with a
card that shows a set of 3
equals “one-third.”
Students will likely “work
backwards” or reverse the
procedures suggested in #13
above. For instance, they may
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 8
Mathematics TEKS Refinement 2006 – K-5
Procedures
should be able to develop and express a
generalization or rule that makes sense to
them.
18.
Tarleton State University
Notes
describe a procedure whereby
they group the parts into wholes
and then record any leftovers as a
fraction.
Have students share and demonstrate their
rules for the class. Compare the various
methods and draw attention to the
similarities.
Again, allow students to publish their rules in
the class book.
19.
20.
Optional: Students can work in groups of 3-4
to play Fraction Fakeout. (See Fraction
Fakeout – Handouts/Transparencies 3a
through 3k.)
This game provides students the
opportunity to match mixed
numbers and improper fractions
with various pictorial
representations.
Laminate and cut out as many decks of
cards as needed.
Fraction Fakeout is played like the
card game, “Old Maid.” The goal
is to make the greatest number of
sets/ books (mixed or whole
number, improper fraction, and
pictorial representation).
Have participants play Mixing It Up. (See
Mixing It Up Directions, Playing Cards, and
Recording Sheet – Handouts/Transparencies
4a, 4b, 4c, and 4d.)
This is a game to encourage
practice of changing a mixed
number to an improper fraction
and vice versa.
Before the game is started, use Mixing It Up
Example Problem (Handout/Transparency 5)
to model the following problem:
In addition to using the game to
give students practice in
converting between mixed
numbers and improper fractions,
you could use the scenarios to
explore division and interpreting
the remainder within a given
context (5.3 C).
Terel needed to buy 32 ice cream
sandwiches. He can only buy the ice cream
sandwiches in packages of 6. Exactly how
many boxes does Terel need to buy?
32
First demonstrate 6 using manipulatives.
Then demonstrate what this number would
look like as a mixed number.
Sample Demonstration:
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 9
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Procedures
Using pattern blocks designate that the
yellow hexagon is the whole. Next take out
32 green triangular pieces. This represents
32
6 . Now group the triangular pieces into
wholes. You should now have 5 whole with
2
6 left over.
Notes
Let the participants work for 10 minutes
playing Mix It Up.
21.
Calculator Activities:
Students can use a fraction calculator to
practice conversions from mixed numbers to
improper fractions and the reverse.
Have students input a given mixed number
and use the rule they have developed to
mentally calculate the improper fraction.
They can use the conversion key to check
their results. Do the same with improper
fractions.
22.
Give students a targeted mixed number such
1
as 3 . Have students program their TI-15
5
calculator to count by 5th’s until they reach
what they believe is the correct number of
⎛ 16 ⎞
5th’s ⎜ ⎟ equal to the targeted number.
⎝ 5 ⎠
Adapted from Van de Walle
(2006).
The TI-12 Explorer, TI-15, and
Casio fx55 are all fraction
calculators which can be utilized
for this activity.
You will need to program the
calculators so they will not simplify
fractions automatically.
The TI-15 has the capability of
storing fractions as “constants” in
one or two operation keys. When
you use these keys, the counter
on the left shows how many times
you have used the fraction, while
the total appears on the right of
the display.
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 10
Mathematics TEKS Refinement 2006 – K-5
Procedures
They can use the conversion key to check
their answer.
You may wish to provide fraction
manipulatives for students who need
concrete or visual support.
Tarleton State University
Notes
Example: Enter › + 1 
5 ¥ ›. Count by pressing ›,
›, ›, etc. until you reach the
desired total of 5th’s. Use the
conversion key ¦ to change
the improper fraction to a mixed
number or vice versa.
Be sure you are in manual mode
and have the calculator set to
fraction, not mixed number, mode.
23.
Computer Activities:
Students can complete the activities on each
of the sites listed below and print out a report
of their results.
http://www.visualfractions.com/identify.htm
Select the third bullet “Identify Mixed
Numbers with Lines,” or “Identify Mixed
Numbers with Circles.”
http://www.visualfractions.com/rename.htm
Select the first bullet “Mixed Numbers to
Fractions with Lines,” or “Mixed Numbers to
Fractions with Circles.”
24.
This applet allows students to explore circle,
rectangular, and set models for fractions by
adjusting the numerators and denominators.
http://my.nctm.org/eresources/repository/207
1/applet/FractionPie/index.html
The first link allows students to
identify mixed numbers from line
and circle models of fractional
parts. The second link allows
students to rename mixed
numbers as improper fractions.
NOTE: Students are able to
access an explanation of the
correct answer before submitting
their own answer. In addition, the
bottom part of the page (scroll
down) offers a rule for converting
an improper fraction to a mixed
number. Therefore, it is
recommended for use only as an
extension beyond the lesson.
Although this site includes topics
beyond the scope of 5th grade
TEKS (percents), it presents a
variety of ways to examine
patterns and relationships which
would enhance 5th graders’
understanding of fractions and
decimals. The following article
elaborates on how the applet can
be utilized in the classroom to
promote understanding of these
relationships among rational
numbers.
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 11
Mathematics TEKS Refinement 2006 – K-5
Procedures
Tarleton State University
Notes
http://my.nctm.org/eresources/vie
w_media.asp?article_id=2071
Homework:
Ask students to find examples of mixed numbers and improper
fractions in everyday life. Students could create a collage or poster to
present their findings.
Assessment:
See Check for Understanding Mixed Numbers and Improper Fractions
– Handouts/Transparencies 6a, 6b, and 6c.
Resources:
Integrating Mathematics and Pedagogy (IMAP). (2002)
http://www.sci.sdsu.edu/CRMSE/IMAP/pubs/Reflections_on_Fractions.pdf
National Council of Teachers of Mathematics. (ON-Math, Fall 2002)
http://my.nctm.org/eresources/view_media.asp?article_id=2071
National Council of Teachers of Mathematics. (ON-Math, Fall 2002)
http://my.nctm.org/eresources/repository/2071/applet/FractionPie/index.html
National Council of Teachers of Mathematics. (ON-Math, Winter 2003)
http://my.nctm.org/eresources/view_article.asp?article_id=6430&page=1
Rand, R. E. (2006). Visual Fractions. Available online:
http://www.visualfractions.com/identify.htm
http://www.visualfractions.com/rename.htm
Reys, R. E., Lindquist, M. M., Lambdin, D. V., Smith, N. L., Suydam,
M. N. (2004). Helping children learn mathematics. Hoboken: John
Wiley and Sons, Inc.
Van de Walle, J. A. (2004). Elementary and middle school
mathematics: Teaching developmentally. Boston: Pearson
Education, Inc.
Van de Walle, J. A. & Lovin, L. H. (2006). Teaching Student-Centered
Mathematics: Grades 3-5. Boston: Pearson Education, Inc.
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 12
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Modeling Mixed Numbers
Recording Sheet
Poster
Number
Example
Mixed
Number
Mixed Number in Word
Form
3
4
one and three-fourths
1
1
2
3
4
5
6
7
Handout/Transparency 1a
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 13
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Modeling Mixed Numbers
Recording Sheet
Poster
Number
Mixed
Number
Mixed Number in Word
Form
8
9
10
11
12
13
14
15
Handout/Transparency 1b
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 14
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Improper Fractions to Mixed Numbers
Recording Sheet
Bag
Number
Common
Fraction
Example
21
8
Mixed Number
2
5
8
1
2
3
4
5
6
7
Handout/Transparency 2a
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 15
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Improper Fractions to Mixed Numbers
Recording Sheet
Bag
Number
Common
Fraction
Mixed Number
8
9
10
11
12
13
14
15
Handout/Transparency 2b
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 16
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Fraction Fakeout
(Similar to the game Old Maid)
This game can be played by 3 or 4 players. The deck
contains 72 cards (24 triples consisting of 1 mixed or
whole number, its corresponding improper fraction, and a
graphic representation) and two FAKE FRACTION cards.
Each group of 3 or 4 students will play with half of the
deck (36 cards made up of 12 triples) and one of the
FAKE FRACTION cards. The object of the game is to
make the most “books” with the three matching cards and
not be caught with the FAKE FRACTION card.
Rules: The dealer deals out all cards to the players even
though some will have more cards than others. The
players examine their cards and lay down any matching
pairs or triples (books) they have. Players must verify
each others’ matches. Each player’s pairs are placed face
up until he is able to make a book. When a player
completes a book, he turns it face down in front of him.
The dealer begins the game. The dealer must offer his
cards spread face down to the player on his left who
selects a card without seeing it and adds it to his hand. If
that player can make a pair or triple, he declares a match
and lays the cards down appropriately. The player who
just selected a card then offers his hand to the next player
on his left. The process continues.
Handout/Transparency 3a
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 17
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
When a player completes his books and has no more
cards, he is “safe.” The turn passes to the next player.
Eventually, all of the cards will be matched except for the
player holding the FAKE FRACTION card. The holder of
that card loses and gets no points for the books he has
made. The other players score 5 points for each book
they have made.
The game can be played multiple times and students can
keep a running tally of their scores. Rotating decks
among groups will give students the opportunity to work
with different numbers and representations.
Handout/Transparency 3b
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 18
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3c
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 19
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3d
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 20
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3e
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 21
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3f
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 22
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3g
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 23
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3h
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 24
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3i
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 25
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3j
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 26
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Handout/Transparency 3k
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 27
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Mixing It Up Directions
Materials Needed:
Mixing It Up Playing Cards
Counters
Fraction bars
Fraction squares
Cuisenaire rods
Pattern blocks
Grid paper
Recording sheet
Pencil
Procedures:
1. Divide students into groups of 4.
2. Have a set of Mixing It Up Playing Cards for each group.
3. Each person takes a turn drawing a card. The player has the option
of building with a manipulative of his or her choice, drawing pictures,
or using other methods to represent the improper fraction or mixed
number indicated.
4. If the number is an improper fraction, the participant must explain
how it can be written as a mixed number and vice versa. All
participants write the improper fraction and the mixed number on the
recording sheet.
5. Play continues until all cards have been selected and discussed.
Handout/Transparency 4a
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 28
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Mixing It Up Playing Cards
Donna is buying cupcakes for
Molly’s birthday party.
Seventeen children RSVP to the
party. Donna wants to order just
enough cupcakes so that each
child will have one.
How many dozen cupcakes does
Donna need to order from the
bakery?
Represent this amount as a
mixed number and as an
improper fraction.
Sun-Yung is helping in her
grandmother’s kitchen. There are
seven extra pounds of sugar in a
canister.
Her grandmother asked her to
divide the sugar evenly into
separate bags so that she could
deliver them to her neighbors,
Mrs. Chang, Mrs. Chung, Mrs.
Cibrario, and Mrs. Dickerman.
How many pounds of sugar will
each neighbor receive?
Represent this amount as a
mixed number and as an
improper fraction.
Dorcas went shopping with her
mother. She had to buy enough
pizza for 12 people. If each pizza
is cut into 8 pieces, she will need
to buy 2 pizzas for everyone to
get at least one piece.
Jarvis took 5 packages of
chewing gum to the pitcher’s
mound. There are six sticks of
gum in each package.
In the first inning, Jarvis chewed
3 sticks of gum.
Exactly how many pieces of pizza
Exactly how many packages of
will each person receive?
gum does he have left?
Represent this amount as a
Represent this amount as a
mixed number and as an
mixed number and as an
improper fraction.
improper fraction.
Handout/Transparency 4b
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 29
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Valentina is cutting up bananas
for pudding.
Bethany went to the store to buy
tortilla chips.
She has 10 bananas to be
divided evenly among 3 bowls of
pudding.
There were 3 brands of chips.
1
The first brand weighed 7 and 2
ounces.
Exactly how many bananas will
go in each bowl?
Represent this amount as a
mixed number and as an
improper fraction.
Represent this amount as a
mixed number and as an
improper fraction.
1 Rahim worked for a local
Fan and Lai-Sang bought 2 and 2 company selling cups of coffee.
dozen cookies to share with their
On Monday morning he sold 20
friends.
cups of coffee.
Represent this amount as a
If each pot holds 12 cups of
mixed number and as an
coffee, exactly how many pots of
improper fraction.
coffee did Rahim sell?
Represent this amount as a
mixed number and as an
improper fraction.
Handout/Transparency 4c
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 30
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Mixing It Up
Recording Sheet
Name
Mixed
Number
Improper
Fraction
Name
Bethany
Jarvis
Donna
Rahim
Dorcas
Sun-Yung
Fan and
Lai Sang
Valentina
Mixed
Number
Improper
Fraction
Handout/Transparency 4d
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 31
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Mixing It Up
Example Problem
Terel needed to buy 32 ice cream sandwiches.
He can only buy the ice cream sandwiches in
packages of 6.
Exactly how many boxes does Terel need to
buy?
32
First demonstrate 6 using manipulatives.
Then, demonstrate what this number would
look like as a mixed number.
Handout/Transparency 5
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 32
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Check for Understanding
Mixed Numbers and Improper Fractions
Change the following mixed numbers to improper
fractions.
1. 3 7 =
8
3
4
=
2
5
=
2.
6
3.
1
Change the following improper fractions to mixed
numbers.
4. 13 =
6
5.
22
7
=
6.
11
2
=
Use the symbols <, >, and = to compare the following
numbers.
7.
8
3
3
1
3
8.
22
7
3
1
7
9.
11
2
6
1
2
Handout/Transparency 6a
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 33
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
10. How many fourths are in 5 wholes?
11. Mrs. Lara, the art teacher, has
4
3
4
yards of ribbon.
She needs to cut it so that each student will have
1
4
yard for the craft project. How many fourths of a yard
will Mrs. Lara be able to cut?
12. Riley is making a cake for the cake walk. She needs
1
1
cup measuring
2 cups of flour, but she only has a
2
2
cup. How many half cups should she measure?
Handout/Transparency 6b
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 34
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
13. The new bakery cuts its square pans of brownies into
ninths. How many pieces (ninths) can be cut from 2 4
9
pans of brownies?
14. The Draper family bought 2 medium pizzas. Scott ate
6
of a pizza. Steven ate 4 of a pizza, and Stephanie
8
ate
8
3
8
of a pizza. How many eighths did they eat?
15. What mixed number expresses the same amount of
pizza that the Drapers ate?
Handout/Transparency 6c
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 35
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
Check for Understanding
Mixed Numbers and Improper Fractions
Answer Key
Change the following mixed numbers to improper
fractions.
1. 3 7 = 31
8
8
3
4
=
27
4
2
5
=
7
5
2.
6
3.
1
Change the following improper fractions to mixed
numbers.
4. 13 = 2 1
6
6
5.
22
7
=
3
6.
11
2
=
5
1
7
1
2
Use the symbols <, >, and = to compare the following
numbers.
7.
8.
9.
8
3
22
7
11
2
<
=
<
3
1
3
3
1
7
6
1
2
Answer Key 7a
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 36
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
10. How many fourths are in 5 wholes?
⎛ 20 ⎞
There are twenty fourths ⎜ ⎟ in 5 wholes.
⎝ 4 ⎠
11. Mrs. Lara, the art teacher, has
4
3
4
yards of ribbon.
She needs to cut it so that each student will have
1
4
yard for the craft project. How many fourths of a yard
will Mrs. Lara be able to cut?
⎛ 19 ⎞
Mrs. Lara will be able to cut nineteen fourths ⎜ ⎟ of a yard.
⎝ 4⎠
12. Riley is making a cake for the cake walk. She
needs 2 1 cups of flour, but she only has a 1 cup
2
2
measuring cup. How many half cups should she
measure?
⎛5⎞
Riley should measure five half-cups ⎜ ⎟ .
⎝2⎠
Answer Key 7b
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 37
Mathematics TEKS Refinement 2006 – K-5
Tarleton State University
13. The new bakery cuts its square pans of brownies
into ninths. How many pieces (ninths) can be cut
from 2 4 pans of brownies?
9
4
⎛ 22 ⎞
Twenty-two ninths ⎜ ⎟ can be cut from 2 pans of brownies.
9
⎝ 9 ⎠
14. The Draper family bought 2 medium pizzas. Scott
ate 6 of a pizza. Steven ate 4 of a pizza, and
8
8
Stephanie ate
3
8
of a pizza. How many eighths did
they eat?
⎛ 13 ⎞
They ate thirteen eighths ⎜ ⎟ of the pizza.
⎝ 8 ⎠
15. What mixed number expresses the same amount
of pizza that the Drapers ate?
1
5
8
Answer Key 7c
Number, Operation, and Quantitative Reasoning
Conversion Creations: From Mixed Numbers to Improper Fractions
Grade 5
Page 38