Calculator Practice:
Computation with Fractions
Objectives To provide practice adding fractions with unlike
denominators
and using a calculator to solve fraction problems.
d
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Teaching the Lesson
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Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Math Boxes 8 4
• Convert between fractions and mixed
numbers. [Number and Numeration Goal 5]
Math Journal 2, p. 258
Students practice and maintain skills
through Math Box problems.
• Express fractions and mixed numbers in
simplest form. [Number and Numeration Goal 5]
• Compare and order fractions. [Number and Numeration Goal 6]
• Use mental arithmetic, paper-and-pencil
algorithms, and calculators to solve fraction
and mixed-number addition problems. Study Link 8 4
Math Masters, p. 226
Students practice and maintain skills
through Study Link activities.
[Operations and Computation Goal 4]
• Use benchmarks to estimate sums. Curriculum
Focal Points
Interactive
Teacher’s
Lesson Guide
Differentiation Options
READINESS
Charting Common Denominators
Math Masters, p. 227
transparency of Math Masters, p. 227
Students use a flowchart to find common
denominators.
ENRICHMENT
Exploring Equivalent Fractions
Math Masters, p. 228
calculator
Students use calculators to explore
fraction-to-decimal conversions.
[Operations and Computation Goal 6]
EXTRA PRACTICE
Key Activities
Students add fractions with unlike
denominators using estimation and paperand-pencil computation by playing Fraction
Action, Fraction Friction. They use
calculators to perform operations with
fractions and mixed numbers.
5-Minute Math
5-Minute Math™, p. 99
calculator
Students use calculators to add fractions.
Ongoing Assessment:
Recognizing Student Achievement
Use the Math Message. [Number and Numeration Goal 6]
Materials
Math Journal 2, p. 257
Student Reference Book, pp. 260–263
and 312
Study Link 83; Math Masters, p. 459
slate scissors per partnership: eight
3" by 5" index cards cut in half (optional) calculator overhead calculator for
demonstration purposes (optional)
Advance Preparation
For the optional Readiness activity in Part 3, make a transparency of Math Masters, page 227.
Background Information This lesson presents example key sequences for the TI-15 and Casio fx-55 calculators.
If other calculators are used, edit the key sequences as needed.
Teacher’s Reference Manual, Grades 4–6 pp. 29–35, 149–152
636
Unit 8
Fractions and Ratios
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6
Content Standards
Getting Started
5.NF.1, 5.NF.2
Math Message Mental Math and Reflexes
1
1
Have students decide if each expression is > _
,<_
,
2
2
1
or = _.
2
1
4
1
_
+_>_
4
8
2
1
1
1
_
_
+
<_
3
16
2
2
1
1
_
+_=_
8
4
2
1
1
1
_
+_<_
Work with a partner. Take one copy of Math Masters,
page 459. Cut out the cards. Put them in order from least to
11
1
_
greatest. Which fraction is the greatest? _
12 Which is the least? 12
3
1
1
_
-_>_
8
6
2
2
1
1
_
+_=_
5
10
2
3
1
1
_
+_>_
8
4
2
5
4
2
8
3
1
_
-_=_
8
6
Study Link 8 3 Follow-Up
2
7
2
1
_
-_>_
8
9
Have partners compare answers and resolve
differences.
2
1 Teaching the Lesson
Math Message Ongoing Assessment:
Recognizing Student Achievement
Use the Math Message to assess students’ ability to order fractions. Watch
students as they order the cards. Students are making adequate progress if they
1
identify the least, the middle (the benchmark of _
2 ), and the greatest fractions and
correctly place one or two fractions in proximity to these three fractions. Some
students may be able to place all of the fractions in order from least to greatest.
[Number and Numeration Goal 6]
▶ Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
1 on the board. Ask: How can you use the fraction _
1 to help
Write _
2
2
you place the other fractions in order? Sample answer: I can use the
1 to place the other fractions as either greater than
benchmark _
2
1 or less than _
1 . Ask a volunteer to write another fraction from
_
2
2
the cards on the board, placing it in order as if on a number line. If
1 , place it to the left of the fraction. If it is
the fraction is less than _
2
1 , place it to the right of the fraction. For example, a
greater than _
2
2 and write it to the right of _
1.
student might choose _
3
2
1
_
2
_
2
3
Continue having volunteers add fractions to the ordered list one by
one. When the list is complete, ask students to rename the
fractions so they have a common denominator of 12. Have
volunteers write the equivalent names above the original fractions.
Ask: Is the order correct? How do you know? The order is correct if
the numerators for the twelfths are in order from least to greatest.
The complete order not counting repeats:
2
_
3
_
4
_
6
_
8
_
9
_
10
_
12
12
12
12
12
12
12
1
_
_1
_1
_1
5
_
_1
7
_
_2
_3
_5
11
_
12
6
4
3
12
2
12
3
4
6
12
Lesson 8 4
637
Student Page
▶ Introducing Fraction Action,
Games
Fraction Action, Fraction Friction
Materials 䊐 1 Fraction Action, Fraction Friction Card
Deck (Math Masters, p. 459)
䊐 1 or more calculators
Players
2 or 3
Skill
Estimating sums of fractions
Object of the game To collect a set of fraction cards with
a sum as close as possible to 2, without going over 2.
Directions
1. Shuffle the deck and place it number-side down on
the table between the players.
2. Players take turns.
♦ On each player’s first turn, he or she takes a card
from the top of the pile and places it number-side
up on the table.
♦ On each of the player’s following turns, he or she
announces one of the following:
Fraction Action, Fraction
Friction Card Deck
1
2
1
3
2
3
1
4
3
4
1
6
1
6
5
6
1
12
1
12
5
12
5
12
7
12
7
12
11
12
11
12
“Action” This means that the player wants an additional
card. The player believes that the sum of the fraction cards
he or she already has is not close enough to 2 to win the
hand. The player thinks that another card will bring the
sum of the fractions closer to 2, without going over 2.
“Friction” This means that the player does not want an
additional card. The player believes that the sum of the
fraction cards he or she already has is close enough to 2 to
win the hand. The player thinks there is a good chance that
taking another card will make the sum of the fractions
greater than 2.
Fraction Friction
(Student Reference Book, p. 312;
Math Masters, p. 459)
Refer students to the fraction cards from the Math Message or the
display on the board, and ask the following questions:
●
What common denominator might you use to find the sum of all
the fourths and all the sixths? 12, 24, and so on . . .
●
What common denominator might you use to find the sum of all
the thirds and all the sixths? 6, 12, and so on . . .
●
What common denominator might you use to find the sum of all
the thirds, fourths, and sixths? 12, 24, and so on . . .
●
What is the least common denominator for all the fractions on
the cards? 12
Once a player says “Friction,” he or she cannot say
“Action” on any turn after that.
3. Play continues until all players have announced “Friction”
or have a set of cards whose sum is greater than 2. The
player whose sum is closest to 2 without going over 2 is
the winner of that round. Players may check each other’s
sums on their calculators.
4. Reshuffle the cards and begin again. The winner of the
game is the first player to win 5 rounds.
Go over the rules for Fraction Action, Fraction Friction on
Student Reference Book, page 312 with the class. Play a few
practice rounds against the class before partners play the game
on their own. Remind students to compare the fractions with
benchmarks to help them estimate the sums.
Student Reference Book, p. 312
Adjusting the Activity
Have students make their own set
of Fraction Action, Fraction Friction cards.
They should make up two fractions for each
of the following denominators: 3, 4, 5, 6,
8, 9, 10, and 12. Each fraction should be
1
less than _
2 , when possible. (With thirds and
fourths, this will not be possible.) Using the
3 in. by 5 in. cards, they will have a total
of 16 cards, each with a different fraction.
Encourage students to make estimates of
their sums as they play.
AUDITORY
KINESTHETIC
TACTILE
WHOLE-CLASS
ACTIVITY
VISUAL
Science Link In physics, friction is a force that resists
relative motion. Compare pulling a heavy box across a rough
concrete floor versus pulling it across smooth ice. The greater
resistance to motion on the concrete is due to greater friction.
In the game, a player might call Friction! to ask for resistance to
motion if the player does not wish to move any further toward 2.
By calling Action! the player asks to resume moving toward 2.
Students play Fraction Action, Fraction Friction. Circulate
and assist.
▶ Exploring Fraction-Operation
WHOLE-CLASS
ACTIVITY
Keys on a Calculator
(Student Reference Book, pp. 260–263)
Students can use scientific calculators to perform operations with
fractions and mixed numbers. Students explored these calculator
operations in Lessons 5-4 and 5-5.
If you have a calculator for the overhead, have volunteers use it to
demonstrate how to enter the following fractions and mixed
numbers: Sample answers for TI-15 and Casio fx-55:
5 5 n 8 d , or 5
● _
8
8
●
●
638
Unit 8
Fractions and Ratios
2 73 Unit 2 n 5 d , or 73
73_
5
45 45 n 7 d , or 45
_
7
7
2
5
Student Page
Use these same numbers to have other volunteers demonstrate
how to convert between fractions and mixed numbers:
Sample answers for TI-15 and Casio fx-55:
, or
Calculators
The keys to convert between mixed numbers and improper
fractions are similar on all fraction calculators.
45
Convert 7 to a mixed number with your
calculator. Then change it back.
Write the following problems on the board or a transparency for
students to solve using their calculators:
Sample answers for TI-15 and Casio fx-55:
5 3_
9
45 66_
34
60
1 +_
1 , or 2_
2 -_
4 +_
14 5, or _
● 2_
● 73_
● _
2
8
8
8
5
7
35
12
3
Pressing
is not
optional in this key
sequence.
12
Have the class mirror the volunteers as they explain the key
sequences used for their solutions. Discuss any difficulties or
interesting occurrences students encountered.
Ask: What are some of the important steps to remember when
working with a calculator? Expect these types of responses:
Clear between operations.
Both
and
fraction notation.
toggle between mixed number and improper
Simplifying Fractions
Ordinarily, calculators do not simplify fractions on their own.
The steps for simplifying fractions are similar for many
calculators, but the order of the steps varies. Approaches for
two calculators are shown on the next three pages depending on
the keys you have on your calculator. Read the approaches for
the calculator having keys most like yours.
Check that the fix function is off or set appropriately.
Pay attention to the display as you press keys.
or
key on their calculators.
Ask students to locate the
Have them explore how to use this key and what it does. Then
ask them to report what they found. Refer students to Student
Reference Book, pages 260–263. As a class, read the section on
simplifying fractions, and do the examples together.
▶ Entering Fractions on a Calculator
Pressing
is
optional in this
key sequence.
Student Reference Book, p. 260
PARTNER
ACTIVITY
(Math Journal 2, p. 257)
Have students complete the journal page. Circulate and assist.
2 Ongoing Learning & Practice
Student Page
Date
▶ Math Boxes 8 4
INDEPENDENT
ACTIVITY
(Math Journal 2, p. 258)
Exploring Fraction-Operation Keys
8 4
䉬
Some calculators let you enter, rename, and perform operations with fractions.
Sample answers provided for 2 calculators:
1.
Draw the key on your calculator that you would use to do each of the functions.
Function of Key
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 8-2. The skill in Problem 6
previews Unit 9 content.
Writing/Reasoning Have students write a response to
the following: Explain how you found the answer to
Problem 1b. Include the strategies and the reasoning that
you used. Answers vary.
Time
LESSON
Key
, or
Unit , or
n
, or
d , or
, or
, or
Give the answer to an entered operation or function.
Enter the whole number part of a mixed number.
Enter the numerator of a fraction.
Enter the denominator of a fraction.
Convert between fractions greater than 1 and mixed numbers.
Simplify a fraction.
Use your calculator to solve.
112458
2
2
2. 5 6 9
5
2
7
92,197
16
3
7 2
8
6 241
1
7
4 3 冢冣
10 2332
4.
26,342 6.
In any row, column, or diagonal of this puzzle,
there are groups of fractions with a sum of 1.
Find as many as you can, and write the number
sentences on another piece of paper. The first
one has been done for you.
2
6
1
6
3
6
1
4
2
5
5
6
2
4
2
8
2
10
2
8
2
4
1
2
There are 18 possible number
sentences, including the example.
3
6
1
4
1
6
1
4
2
3
3
4
Example:
Number Sentence
1
6
4
8
1
4
1
4
1
6
1
4
1
3
2
4
2
10
2
6
2
3
1
3
5
12
1
4
1
5
3
6
1
4
3
8
2
6
2
8
1
6
3.
1
4
5.
ⴱ 14 1
Math Journal 2, p. 257
Lesson 8 4
639
Student Page
Date
▶ Study Link 8 4
Time
LESSON
8 4
Add.
1.
2.
1
a. 4
1
b. 4
3
4
7
8
1
2
5
8
6
4
1
c. 6,
6
3
1
d. 2
1
e. 6
1
2
or 1
5
6
1
3
4
6,
or
16.8 , 33.6
6.25 , 3.125
3.4, 10.2, 30.6, 91.8 , 275.4
1.5, 7.5, 37.5, 187.5 , 937.5
16 , 25
1, 4, 9,
a.
2.1, 4.2, 8.4,
b.
50, 25, 12.5,
c.
d.
2
3
(Math Masters, p. 226)
Use the patterns to fill in the
missing numbers.
e.
68
4.
More than 10 hours
3 34 6 12 10 14,
Explain.
which is more than
10 hours.
Make each sentence true by
inserting parentheses.
(
100 15 10 ⴱ 4
b.
4 24 / 4 2
(
3 Differentiation Options
)
)
a.
8 (24 / 4) 2
(10 4 / 2)ⴱ 3 24
e. (10 4)/(2 ⴱ 3) 1
c.
d.
Solve.
Solution
m
a. 10
56
b. 64
k
c. 48
4
d. 30
2
e. 18
45
50
7
n
3
8
12
p
a
180
6.
m9
n8
k 18
p 90
a 20
▶ Charting Common
Circle the congruent angles.
a.
b.
c.
d.
SMALL-GROUP
ACTIVITY
READINESS
222
71
5.
1 and
Home Connection Students compare fractions to _
2
solve a fraction addition puzzle.
230
3
Max worked for 3 hours on Monday and
4
1
6 hours on Tuesday. Did he work more
2
or less than 10 hours?
3.
INDEPENDENT
ACTIVITY
Math Boxes
䉬
15–30 Min
Denominators
(Math Masters, p. 227)
108 109
155
Math Journal 2, p. 258
To explore fraction addition using a common-denominator
strategy, have students use a flowchart to find common
denominators before solving fraction addition problems.
Explain that students can use a flowchart to show the steps and
decisions used to find common denominators. Use the prepared
transparency, and demonstrate how to read the flowchart on the
Math Masters page.
Example:
7 +_
5 in the START circle.
Step 1 Write _
24
6
Step 2 Point to the first triangle and ask: Do the fractions have a
common denominator? No
Step 3 Follow the No side of the triangle.
Step 4 Point to the second triangle and ask: Is one denominator a
factor of the other? Yes. 6 is a factor of 24.
Study Link Master
Name
Date
STUDY LINK
More Fraction Problems
84
䉬
1.
Time
3
4
Circle all the fractions below that are greater than .
4
5
13
20
1
2
9
12
18
25
155
200
66 – 68
7
11
Rewrite each expression by renaming the fractions with a common denominator.
1
1
1
Then decide whether the sum or difference is greater than , less than , or equal to .
2
2
2
Circle your answer.
2
1
7
10
7
70
20
70
1
2
1
2
1
2
5
1
4
6
10
12
3
12
1
2
1
2
1
2
18
2 18
4. 20
5 20
8
20
1
2
1
2
1
2
9
12
4
12
1
2
1
2
1
2
2. 3. 3
1
3
4
5. 15
Procedure: Select three different numbers from this list: 1, 2, 3, 4, 5, 6.
䉬 Write a different number in the circle.
䉬 Write a third number in the hexagon.
6
1
5
6
Sample answer:
41
6
Example:
2
4
3
2
8
2
4
Practice
7.
3 2.564 9.
16 5.438 0.436
10.562
8.
10.
3 ⴱ 2.564 3,049 / 15 7.692
203.26
226
Math Masters, p. 226
640
Unit 8
5
6
, or 6
䉬 Add the two fractions.
Fractions and Ratios
24
24
24
8
Have students use the flowchart as they solve the following
problems:
13 + _
8 _
6 , or 1_
21 , 1_
2
● _
Select and place three different numbers so the sum is as large as possible.
䉬 Write the same number in each square.
Step 8 Add the numerators. 7 + 20 = 27
7 +_
20 = _
27 , 1_
3 , or 1_
1
Step 9 Write the solution. _
24
Fraction Puzzle
6.
Step 5 Follow the YES side of the triangle.
5 with a denominator of 24. _
5∗4 =_
20
Step 6 Rename _
6
6∗4
24
Step 7 Follow the line that leads to the next rectangle.
15 15
15
5
●
18 + _
5 _
38 , 1_
7
14 , or 1_
_
●
3 +_
3 _
33 , or 1_
5
_
●
3 +_
13 _
79 , or 1_
7
_
24
4
8
6 24
7 28
18 72
24
12
28
72
Teaching Master
Name
Adjusting the Activity
Date
LESSON
84
Have students list the steps they take as they decide whether to use
the QCD or to find the least common denominator.
A U D I T O R Y
K I N E S T H E T I C
T A C T I L E
START
V I S U A L
No
ENRICHMENT
▶ Exploring Equivalent Fractions
(Math Masters, p. 228)
Time
Charting Common Denominators
SMALL-GROUP
ACTIVITY
15–30 Min
PROBLEM
PRO
P
RO
R
OB
BLE
BL
LE
L
LEM
EM
SO
S
SOLVING
OL
O
LV
LV
VIN
IN
NG
G
No
Find the
least
common
denominator.
To extend students’ understanding of equivalent fractions, have
them explore fraction-to-decimal conversions using a calculator.
3 on their calculators and then locate and
Have students enter _
4
press the key that will convert the display to an equivalent
decimal. On many calculators, this key is labeled F D . Ask: Will
equivalent fractions convert to the same decimal? Explain that in
this exploration students will work to support their responses.
Have each student write a fraction. Make adjustments so there
are no duplicates. Students complete Math Masters, page 228.
They use their fractions to make a list of 10 equivalent fractions,
use their calculators to convert the fractions to decimals, and
summarize their results.
Common
denominator?
Is one
denominator
a factor of the
other denominator?
Yes
Yes
Use
the
QCD.
Rename
both
fractions.
Rename
the
fraction.
Add numerators.
Write the solution
number sentence.
STOP
Math Masters, p. 227
221-253_434_EMCS_B_MM_G5_U08_576973.indd 227
2/22/11 4:08 PM
Discuss students’ summaries. Equivalent fractions name the same
amount. They can also be defined as fractions that have the same
decimal result when their numerators are divided by their
denominators.
EXTRA PRACTICE
▶ 5-Minute Math
SMALL-GROUP
ACTIVITY
5–15 Min
To offer students more experience with using a calculator to add
fractions, see 5-Minute Math, page 99.
Teaching Master
Name
LESSON
84
Date
Time
Exploring Equivalent Fractions
Yes
1.
Do equivalent fractions convert to the same decimal?
2.
Complete the fraction column in the table so there are 10 equivalent fractions.
3.
Use your calculator to convert each fraction to a decimal. Write the display in Sample
the decimal column. (Don’t forget to use a repeat bar, if necessary.)
answers:
Fractions
3
_
4
6
_
8
9
_
12
12
_
16
15
_
20
18
_
24
21
_
28
24
_
32
27
_
36
30
_
40
4.
Decimals
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
0.75
Explain your results. Describe the relationship between the equivalent
fractions and their decimal form.
The equivalent fractions can all be renamed as _34 ,
the simplest form. Converted to a decimal, _34 is equal to
0.75. So all equivalent fractions have the same decimal form.
Math Masters, p. 228
221-253_434_EMCS_B_MM_G5_U08_576973.indd 228
2/22/11 4:08 PM
Lesson 8 4
641