Lesson
2 Adding and Subtracting Mixed Numbers:
The LAPS Process
Problem Solving:
Solving Word Problems With Mixed Numbers
Lesson2 SkillsMaintenance
Lesson Planner
Name
Vocabulary Development
Date
SkillsMaintenance
ImproperFractions
LAPS
Activity1
Changetheimproperfractionsintomixednumbers.Usethenumberline,
fractionbars,andcirclestohelpyou.
Improper Fractions, Transformations
1.
13
4
2.
16
5
3.
22
4
31
4
31
5
0
0
1
1
4
2
4
3
4
4
4
2
5
4
6
4
7
4
8
4
3
9
4
10 11
4
4
12 13 14 15
4
4
4
4
Unit 3
Skills Maintenance
Building Number Concepts:
dding and Subtracting Mixed
A
Numbers: The LAPS Process
We begin looking at operations with mixed
numbers. We start with addition and
subtraction. LAPS is the organizer we use
to help students organize their work when
adding and subtracting mixed numbers. LAPS
stands for look, alter, perform, and simplify.
52
4
Transformations
Activity2
Identifythetransformationthatistakingplacebetweeneachpairof
shapes.Circlethecorrectanswer.
1.
Slide or Flip
2.
Slide or Flip
3.
Slide or Flip
4.
Slide or Flip
5.
Slide or Flip
Objective
Students will add and subtract mixed
numbers using a system to help remember
the steps.
Problem Solving:
olving Word Problems With
S
Mixed Numbers
Students are reintroduced to the Scatter
Plots. The Scatter Plots buy an old house that
needs to be renovated. We use this context
for solving word problems involving mixed
numbers.
Objective
Students will solve real-world problems
involving mixed numbers.
Homework
Students use the number lines to convert the
improper fractions to mixed numbers, use
LAPS to add and subtract fractions, and solve
two word problems involving mixed numbers.
In Distributed Practice, students solve a mix of
problems involving operations with fractions.
298 Unit 3 • Lesson 2
Unit3•Lesson2
Skills Maintenance
Improper Fractions, Transformations
(Interactive Text, page 93)
Activity 1
Students convert the improper fraction to its
corresponding mixed number using a number line,
fraction bars, and circles.
Activity 2
Students identify the type of transformation from the
picture shown. They choose from slide or flip.
93
Lesson
2
Adding and Subtracting Mixed Numbers:
The LAPS Process
Problem Solving:
Solving Word Problems With Mixed Numbers
Building Number Concepts:
dding and Subtracting Mixed
A
Numbers: The LAPS Process
How can we remember the steps
for adding and subtracting mixed
numbers?
(Student Text, pages 179–181)
Connect to Prior Knowledge
Discuss the problem 3 15 + 2 3
5 with students.
Ask:
How can we use what we know about adding
fractions to solve this problem?
Adding and Subtracting Mixed Numbers: The LAPS Process
How can we remember the steps for adding
and subtracting mixed numbers?
Let’s look at this addition problem:
Vocabulary
LAPS
31
5
3
+ 25
Solvingproblemswithmixednumbersrequiresmanysteps.Itiseasyto
getconfusedortoforgetastep.Wehaveaword, LAPS , that will help
usrememberthestepsforaddingorsubtractingmixednumbers.
LOOK—Carefully analyze the problem.
Decide what operation should be performed. Is it addition or
subtraction? Make sure the problem is lined up properly.
ALTER—Make any changes necessary to begin solving
the problem.
Find a common denominator and rewrite the problem
if necessary.
PERFORM—Perform the operation.
Add or subtract the fractions. Add or subtract the whole numbers.
SIMPLIFY—Find the GCF of the numerator and the denominator.
Listen for:
Then factor out the answer to find the simplest form.
•The denominators are the same.
•We can add the numerators.
Link to Today’s Concept
Tell students that today we use the LAPS process to help us add and subtract mixed
numbers. Using LAPS helps us stay organized.
Demonstrate
Engagement Strategy: Teacher Modeling
Explain the LAPS process in one of these ways:
: Use the mBook Teacher Edition
for page 179 of the Student Text. ​
Overhead Projector: Reproduce
Student Text, page 179 on a
transparency.
•Show the letters LAPS vertically. ​
L—Look
•For the look step, tell students that we ask,
“Is it addition? Is it subtraction? Is it lined
up properly?” ​
UsingLAPStohelpussolveaproblemislikeswimminglapsinapool.
Bothrequirealotofwork.HereweuseLAPStorememberhowtowork
with mixed numbers.
Unit 3 • Lesson 2
179
179
A—ALTER
•For the alter step, explain that we ask, “Is there
a common denominator? If not, how can we find
one?” We rewrite the problem using numbers
that have common denominators. ​
P—Perform
•Explain that the perform step means to perform
the operation. Add or subtract the fractions. Add
or subtract the whole numbers. ​
S—Simplify
•Mention that the simplify step should be familiar
to students at this point because we already
know how to simplify the answers to problems.
The answers need to be in simplest form. ​
Unit 3 • Lesson 2 299
Lesson 2
Lesson 2
Steps for Using LAPS to Add Mixed Numbers
How can we remember the steps
for adding and subtracting mixed
numbers? (continued)
L—LOOK at the problem carefully.
• Make sure that the numbers are lined up correctly.
• Decide if addition or subtraction is supposed to be
performed.
A—ALTER the problem if necessary.
Altermeanschange.Sometimesweneedtochangesomething 3 1
5
aboutaproblembeforewesolveit.Whenaddingor
3
subtractingfractions,thedenominatorsneedtobethesame. + 2 5
Inthisproblem,thedenominatorsarethesame,sowedon’thaveto
alter the fractions.
P—PERFORM the operation.
Nowwearereadytoadd.Webeginbyaddingthe
fractional parts of the two numbers.
Next, we add the whole numbers.
Listen for:
3 4
add the fractions 51 + 5
= 5 . We add the
whole numbers 3 + 2 = 5. The answer is 5 54 .
S—Simplify
•We have to simplify the fraction portion of
the mixed number to its lowest terms.
In this case, 45 is already reduced, so 5 54 is
our answer.
300 Unit 3 • Lesson 2
31
5
31
5
3
+ 25
4
5
3
+ 25
54
5
S—SIMPLIFY the answer.
We have the answer we want because the answer is a mixed number
in its simplest form. So, for this problem, we do not need to do anything
in this step.
L—Look
•We look at the problem to see if the numbers
are lined up. We look at the problem to see
what the operation is. In this problem, it’s
addition.
p—perform
•Now we can perform the addition. We
3
+ 25
Inthisproblem,thefractionsandwholenumbersarelinedupcorrectly,
and we need to add.
Demonstrate
•Have students turn to page 180 of the
Student Text, where we demonstrate an
addition problem using the LAPS strategy.
Ask students to describe each of the steps
in the LAPS strategy as you go through the
example together.
a—alter
•We see if we need common denominators. In
this problem, the fractions already have the
same denominator. We do not need to alter
anything.
31
5
180
180
Remember from the
last unit that simplest
form means there are
no common factors
that can be pulled out
of the numerator
and denominator.
Unit 3 • Lesson 2
•Be sure students look carefully at each step.
Some of the steps do not apply, but it is
important to go through the process each time
to build the good habits that LAPS provides for
students.
Lesson 2
Steps for Using LAPS to Subtract Mixed Numbers
Explain
Have students turn to page 181 of the Student
Text. Explain that we can also use LAPS to help
us remember the steps for subtracting mixed
numbers.
Demonstrate
•Demonstrate how to solve the subtraction
1
problem 5 2
3 − 1 3 using LAPS. Again, walk
through the process with students, step
by step.
L—LOOK
•Remind students to ask themselves, “Is the
problem lined up properly? Is it addition? Is
it subtraction?”
A—ALTER
•Point out that in this case, we do not need to
alter the problem because the denominators
are the same. However, students should
remember to include this step as a check.
P—PERFORM
•Walk through the subtraction in the perform
step, first subtracting the fractional parts
and then the whole numbers.
S—SIMPLIFY
•Point out that the answer is already in its
simplest form, but again, students should
include the simplify step as a check.
Check for Understanding
Engagement Strategy: Think, Think
Ask students the following questions. Tell them
that you will call on one of them to answer a
question after you ask it. Tell them to listen for
their names. After each question, allow time
for students to think of the answer. Then call
on a student.
L—LOOK at the problem carefully.
• Make sure the numbers are lined up correctly.
• Decide if addition or subtraction is supposed to be
performed.
52
3
− 11
3
Inthisproblem,thefractionsandwholenumbersarelinedupcorrectly,
and we need to subtract.
A—ALTER the problem if necessary.
Decideifthedenominatorsneedtochange.
52
3
Thedenominatorsarethesame,sowedonotneedtochange
anythingbeforewesubtractthesetwonumbers.
P—PERFORM the operation.
Now we do the subtraction.
Firstwesubtractthefractionalparts.
Then we subtract the whole numbers.
− 11
3
52
3
52
3
− 11
3
1
3
− 11
3
41
3
S—SIMPLIFY the answer.
We have the answer we want because the answer is a mixed number in
itssimplestform.So,forthisproblem,wedonotneedtodoanythingin
this step.
Unit 3 • Lesson 2
181
181
Ask:
What do the letters in LAPS stand for? (look,
alter, perform, and simplify)
What do we do in the look step? (We look at the
operation and look to see if the numbers are lined
up correctly.)
What do we do in the alter step? (We look to see if
we need to find a common denominator.)
What do we do in the perform step? (We do the
addition or subtraction.)
What do we do in the simplify step? (We put the
answer in simplest form.)
Unit 3 • Lesson 2 301
Lesson 2
Lesson 2
How do we check our answer using
fraction bars?
How do we check our answer using
fraction bars?
Let’scheckouranswerfromthesubtractionproblemusingfractionbars
toseeifwegetthesameansweraswedidusingLAPS.
Example 1
(Student Text, page 182)
1
1
Use fraction bars to check that 5 2
3 − 13 = 43 .
Westartbyshowing5 2
3 usingfractionbars.Weshade5wholefraction
Demonstrate
•Have students turn to Example 1 on page
182 of the Student Text. It is a demonstration
of subtraction using fraction bars.
bars and 2
3 of another.
Next, we take away, or subtract, 1 1
3.
•Explain to students that fraction bars
provide us with a way to check our answers
to see if they are correct. In this example,
1
we look again at the problem 5 2
3 − 13 .
•Start by showing 5 23 using fraction bars.
Then we remove the parts that we put an X on. We have 4 whole
1
fraction bars and 1
3 of another fraction bar left. This represents 4 3 .
Make sure students see how the six fraction
bars represent 5 2
3 and why we need six
The answer we found using the fraction bars is 4 13 .
fraction bars to demonstrate this number.
It’sthesameanswer.
•Show students how we use Xs to cross out
Apply Skills
Reinforce Understanding
Turn to Interactive Text,
page94.
Use the mBook Study Guide
to review lesson concepts.
11
3 . We cross out one whole fraction bar. We
cross out one part, or 1
3 , of another of the
fraction bars.
•Be sure students see that there are four
whole fraction bars left and 1
3 of another
fraction bar. The answer is 4 13 . This is the
same answer we got using LAPS.
•Explain to students that we look at fractions
with unlike denominators in the next
lesson, but we first practice using the LAPS
strategy with easier problems. Our goal is
to think about an organized strategy, LAPS,
for solving complex, multistep problems.
Check for Understanding
Engagement Strategy: Think Tank
Distribute strips of paper to the students, and
write the problem 4 19 + 6 19 Q10 92 R on the board.
Have students solve the problem, reminding
them to use LAPS to help them. Tell students
302 Unit 3 • Lesson 2
The answer we found using LAPS was 4 13 .
182
182
52
3
1
− 13
41
3
Unit 3 • Lesson 2
to write their names and answers on the strips of
paper. When students finish, collect the papers in a
container. Draw out an answer to read aloud. If it is
correct, congratulate the student. If it is incorrect,
have a student volunteer give the correct answer.
Review the solutions with the class. If there is time,
check the answer with fraction bars.
Reinforce Understanding
If you feel students need more practice before
moving to the independent practice, try these
additional problems:
2 1
10 3
8 − 5 8 Q5 8 R
2
5
83
7 + 7 7 Q15 7 R
1
1
15 2
3 − 7 3 Q8 3 R
Lesson2 ApplySkills
Name
Apply Skills
Date
ApplySkills
AddingandSubtractingMixedNumbers:TheLAPSProcess
(Interactive Text, page 94)
Activity1
Shadethefirstnumber,thenuseXstosubtractthesecondnumber.
Have students turn to page 94 in the Interactive
Text, which provides students an opportunity to
practice LAPS.
1.
33
4
− 11
4
22
4
Activity 1
Activity2
UseLAPStosolvethemixednumberproblems.Completeeachstepintheboxes.
Students use fraction bars to solve a subtraction
problem involving fractions.
1.
4
31
6 + 56
L
Activity 2
The problem is lined up and we are adding.
The problem is set up appropriately because the
denominators are the same.
1
4
5
P 3 +5 =8
6
6
6
A
Students use LAPS to solve one addition and one
subtraction problem.
S No simplification needed.
Be sure to explain to students that even though
we are not using some of the steps from LAPS in
today’s practice, we need to remember all of the
steps eventually when we look at more complex
problems.
Monitor students’ work as they complete the
activities.
85
6
2.
1
93
5 − 45
L
52
5
Problem is lined up and we are subtracting.
Problem is set up appropriately because the
denominators are the same.
3
1
2
P 9 −4 =5
5
5
5
A
S No simplification needed.
94
Unit3•Lesson2
Watch for:
•Can students shade the first fraction
correctly?
•Can students determine the resulting
answer from the fraction bars?
•Can students remember what the LAPS
steps are and what they mean?
•Can students solve the problems using LAPS?
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
Unit 3 • Lesson 2 303
Lesson 2
Problem Solving:
olving Word Problems With Mixed
S
Numbers
Lesson 2
Problem Solving: Solving Word Problems With Mixed Numbers
How do we solve real-world problems with
mixed numbers?
THE SCATTER PLOTS WOULD BE AN UP-AND-COMING
THE SCATTER
PLOTS ARE
AND COMING
ROCKTO
BAND.
GARAGE
BAND EXCEPT
FOR AN
ONEUPTHING:
THEY HAVE
THEY PRACTICE
IN DRUMMER‛S
THEIR DRUMMER‛S
APARTMENT.
PRACTICE
IN THEIR
APARTMENT.
THEY ARE VERY LOUD AND GET
LOTS OF COMPLAINTS FROM ALL
OF THE NEIGHBORS.
KEEP IT DOWN
IN THERE!!
How do we solve real-world problems
with mixed numbers?
(Student Text, page 183)
Explain
Have students look at page 183 of the Student
Text. Introduce the problem-solving theme for
this unit. In today’s lesson, we reintroduce the
Scatter Plots, a fictitious musical band. We
first introduced the Scatter Plots in Level 1 of
TransMath as a context for looking at ways to
display data; reading information from tables
and charts; determining distances on maps as
the band went on tour; and computing, analyzing,
and projecting CD sales and other numeric data
for the band.
SO THE BAND PUT ALL THEIR MONEY TOGETHER AND
BOUGHT AN OLD HOUSE AT THE EDGE OF TOWN. NOW
THEY CAN PRACTICE WITHOUT DISTURBING OTHERS.
BUT THEY CAN‛T JUST PRACTICE AND DREAM OF
MAKING IT BIG. THE OLD HOUSE NEEDS A LOT OF
REPAIRS. IT HAS GRIMY CARPETING, BROKEN PIPES,
AND A RICKETY STAIRCASE.
THE SCATTER PLOTS HAVE A LOT OF REPAIRS TO
MAKE BEFORE THEY CAN REALLY ROCK N‛ ROLL.
Let’shelptheScatterPlotssolveaproblem.
Problem:
A cracked pipe in the bathroom needs to be fixed.
TheScatterPlotsboughtapipethatis3 3
4 feetlong.
The pipe that needs to be fixed is 2 1
4 feetlong.How
much pipe do they need to cut off the new pipe
in order to replace the broken one?
33
4
1
− 24
1
12
4 = 12
1
The Scatter Plots need to cut 1 2
4, or 1 2, feet off of the new pipe in
order to replace the old one.
Problem-Solving Activity
Reinforce Understanding
Turn to Interactive Text,
page95.
Use the mBook Study Guide
to review lesson concepts.
Unit 3 • Lesson 2
In this unit, the Scatter Plots buy an old house
and fix it up to use as their practice studio. This
setting provides a real-world context for word
problems involving mixed-number operations.
An important part of gaining conceptual
understanding of a topic is to be able to connect
it with a familiar context. These word problems
give students some real-world connections for
thinking about mixed-number operations. Be
sure to encourage students to use the LAPS
method to keep their work organized in word
problems as well.
Demonstrate
•Have students read the comic strip to put
the word problem in context. Then read the
word problem at the bottom of the page.
304 Unit 3 • Lesson 2
•Walk through the problem with students,
making sure they understand why we need to
use subtraction for this problem. Have them
recall the LAPS steps as you work through the
problem.
183
183
Lesson2 Problem-SolvingActivity
Name
Problem-Solving Activity
Problem-SolvingActivity
SolvingWordProblemsWithMixedNumbers
(Interactive Text, page 95)
BeforetheScatterPlotscanmovethingstothesecondfloor
ofthehouse,theyneedtofixthestaircase.Thiswillrequire
accuratemeasurement.HelptheScatterPlotsbysolvingthe
fourproblems.
Have students turn to page 95 in the Interactive
Text, which provides them an opportunity to
solve word problems using mixed numbers.
1.
Students solve word problems about the Scatter
Plots’ new house. Monitor students’ work as they
complete this activity.
The step at the bottom of the staircase is broken.
The Scatter Plots have a board 4 5
8 feet long. The board
only nee to be 3 3
8 feet long. How much of the board
needs to be cut off?
Unit 3
Date
4 5 − 3 3 = 1 2 feet
8
8
8
2.
There is a hole in the floor at the top of the staircase.
Two boards are needed to cover the hole. Each board is
11
3 feet wide. How wide is the hole in the floor?
1 1 + 1 1 = 2 2 feet
3
3
3
Watch for:
•Can students remember the LAPS steps for
3.
keeping their work organized?
Another part of the floor needs to be replaced. It can be done with
5
two boards. The first board is 3 16
feet long and the second board
9
is 4 16
feet long. How long is the part of the floor that needs to be
replaced?
•Can students identify the operation in each
3 5 + 4 9 = 7 14 feet
16
16
16
word problem and set up the problem?
4.
•Can students solve the problem and come
up with the correct answer?
One railing on the staircase is cracked. The only board the band
members have to fix the problem is 5 7
8 feet long. The new railing
should be 5 1
8 feet long. How much will have to be cut off to make
the board fit?
5 7 − 5 1 = 6 feet
8
8 8
Once students complete the activity, discuss the
answers together in class.
ReinforceUnderstanding
Use the mBook Study Guide to review lesson concepts.
Unit3•Lesson2
95
Reinforce Understanding
Remind students that they can review
lesson concepts by accessing the
online mBook Study Guide.
Unit 3 • Lesson 2 305
Lesson 2
Lesson 2
Homework
Activity 1
Convert the improper fractions to mixed numbers.
0
1
Homework
1.
Go over the instructions on page 184 of the
Student Text for each part of the homework.
7
5
0
3
3.
Students use the number lines to convert the
improper fractions to mixed numbers.
2
5
1
3
2
3
3
3
1
4
2
4
3
4
0
2. 11
Activity 1
1
5
3
5
5
5
4
3
5
3
5
4
1
0
2
6
5
7
5
8
5
6
3
7
3
8
3
6
4
7
4
2
0
9
4
4
5
10
5
11
5
9
3
10
3
11
3
9
4
10
4
11
4
3
1
0
9
5
2
4
4
8
4
21
4
Activity 2
2
1
1. 2 4 + 3 4
3.
10 79
− 8 29
53
4
25
9
2
1
16 45
− 10 15
2. 5 8 + 2 8
4.
73
8
63
5
Activity 3
Students use LAPS to add and subtract fractions.
Solve the word problems involving addition and subtraction of mixed
numbers. Use LAPS to organize your work.
1. TherearenocurtainsinthelivingroomofthehousethattheScatterPlots
bought.Thebandmembersmeasurethewindowsandfindoutthatthey
are 3 13 feet tall. They want the curtains to be another 1 13 feet below
thewindows.Howlongdothecurtainshavetobe?
Activity 3
Students use LAPS to solve two word problems
involving mixed numbers.
2. Thefencearoundthefrontofthehouseisfallingapartontwosides.The
fence is 6 18 yardsalongthedrivewayand8 68 yards in front of the house.
Howlongisthispartofthefence?
Activity 4 • Distributed Practice
Activity 4 • Distributed Practice
Solve.
Students solve problems involving operations
with fractions for ongoing practice of these skills.
1
2
5
8
2
3
1. 3 + 9
4.
184
184
Unit 3 • Lesson 2
32
3
Use LAPS to add and subtract the fractions. Label each step.
Activity 2
306 12
5
−
5
9
− 1
24
Unit 3 • Lesson 2
4
1
6
8
1
8
2. 7 − 7
5.
÷
3
7
6
3.
1
9
· 24
1
18
4 2 feet
3
14 7 yards
8