Download Story Problems About Comparing

Chapter 8
Lesson
1
-1 -3
10
Story Problems About
Comparing
NCTM Standards 1, 2, 6, 7, 8, 9, 10
Common Core State Standards 2.OA.1, 2.NBT 5, 7
STUDENT OBJECTIVES
Lesson Planner
• n
• n
o choose the appropriate operation in addition and subtraction
T
situations
To solve two-step word problems involving comparisons
(CCRG p. CC 27)
Open Ended Problem Solving / Headline Story
Skills Practice and Review—
Mental Math
(CCRG p. CC 28–CC 30)
Comparing Secret Numbers (CCRG p. CC 28)
Creating and Solving Story Problems (CCRG p. CC 29)
Solving More Story Problems (CCRG p. CC 30)
•CCRG: Activity Master, Writing Your Own
Story Problem
•sticky notes
•counters (optional)
•
LAB Masters, CCRG pp. CC 32–CC 33
(CCRG p. CC 31)
Leveled Problem Solving (CCRG p. CC 31)
Practice Master, CCRG p. CC 34
Intervention Activity (CCRG p. CC 31)
Extension Master, CCRG p. CC 35
Extension Activity (CCRG p. CC 31)
Lesson Notes
Lesson 8.10-3 has been added. Use after Lesson 8.10-2.
About the Lesson
Lesson 8.10-3 is the third in a series of three lessons
on two-step word problems. If you are using this
lesson later in the year, after Chapter 10, you may
want to use three-digit numbers in the classroom part
of the lesson.
About the Mathematics
The comparison model is another way for children to
think about subtraction. To compare two numbers to
find their difference, children can form two separate
groups of counters to represent the numbers. Then
they line up the counters in the two groups, matching
them one-to-one. When no more matches can be
made, the counters left over in the larger number
represent the difference.
CC 26 Common Core Resource Guide
TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 26
In solving word problems involving comparing, the
critical skill is identifying which operation to use. For
example, if you know that Jake has 3 more marbles
than Dana, and then find out that Jake has 15 marbles,
how do you know whether to add or subtract the 3
to find out how many marbles Dana has? Help your
children think about this by asking them to identify
the larger of the two numbers. Jake has more marbles,
so to find out how many Dana has, you will want to
subtract the difference, 3, from Jake’s total.
Chapter 8 • Lesson 10-3
12/21/10 4:06:49 PM
Developing
Mathematical
Language
Vocabulary: compare,
difference, more, less, fewer
While working on word problems,
pair ELL students with fluent
readers. Encourage children to
think carefully about the meaning
of sentences involving comparison
words.
Open-Ended Problem Solving
Share this headline story with your class. Encourage children to think
about all the possible numbers of cars that Jack might have, and to
compare those numbers to the number that Amy and Rory have.
Amy has 23 toy cars. Rory
has 32 toy cars. Jack has
more cars than Amy, but
fewer cars than Rory.
Beginning Count out 13 counters
and hand them to one student.
Then count out 8 counters and
hand them to another student.
Say, write, and read sentences
comparing the counters that the
two children have, “Jon has 5 more
counters than Ali. Ali has 5 fewer
counters than Jon.”
Possible responses:
Jack might have 24 cars. That is 1 more than Amy but 8 fewer than
Rory. He could have 28 toy cars. That is 5 more than Amy and 5
fewer than Rory. He could have anywhere from 24 to 31 toy cars.
Intermediate Have children take
some counters from a pile and
count them. Take 12 counters for
yourself. Say, “I have 12 counters.
Who has more than 12?” and
then, “Who has fewer than 12?”
Help children compare the number
of counters they have to 12.
“I have 15 counters. That is 3 more
than 12.” Write some of their
comparisons on the board.
Advanced Have children take
some counters from a pile and
count them. Then ask children to
compare the number of counters
they have to the number that
others have. “I have 3 more
counters than Jon, but 2 fewer
than Ali.” Write some of these
sentences on the board.
Skills Practice and Review
Mental Math
Write an addition or subtraction problem on the board. Call on a
student for the answer. Explain that you want children to use mental
math to solve the problems. If your children enjoy silent teaching,
you can do this activity silently by handing the chalk to the student
you wish to answer. Start by presenting problems that do not require
regrouping. If children are successful, try some with regrouping in
one place. At the end of the practice, ask children to share their
strategies for solving these problems.
Common Core Resource Guide CC 27
TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 27
12/21/10 4:06:49 PM
whole class
15
MIN
NCTM Standards 1, 2, 6, 7, 8, 9, 10
CCSS 2.OA.1, 2.NBT.5, 7
Comparing Secret Numbers
Purpose To explore problems involving comparing
Introduce Without letting your children see what numbers you are writing, write
three two-digit numbers on the board such as 28, 37, and 41. Cover each number with a
sticky note. Label the sticky notes A, B, and C. Tell your class that these are your secret
numbers.
Give the following clues to the secret numbers:
• A is 9 less than B
As you are working with the
class, look for children who
are having trouble choosing
an operation to solve
comparing problems. During
the second activity, you may
be able to work more closely
with these children and help
them understand how to
make the correct choices.
• C is 13 more than A
• B is 4 less than C
Work with your class to rephrase each of the three clues, until you have this list:
• A is 9 less than B; B is 9 more than A
• C is 13 more than A; A is 13 less than C
• B is 4 less than C; C is 4 more than B
Problem Is there anything else we can figure out? Let children work on this for a
bit. Hopefully, they will come up with more than one solution. Possible solutions include
A 5 5, B 5 14, C 5 18; A 5 68, B 5 77, C 5 81. As a class, decide that you don’t have
enough information to figure out the numbers. Reveal any one of the three numbers, for
example, show that B = 37. Have children figure out what the other two are.
Talk Math
I know that B is 4 less than C. Should I add or subtract 4 from B to find
C? Possible answer: C has to be greater than B, so you should add 4 to
get 41.
Once you know all three numbers, what questions could you ask about
them? Possible answer: We could ask for the sum of the three numbers.
We could ask which one is the greatest.
Write a word problem using your numbers. Let children help you decide about what
objects will be counted in the problem and the names you will use. Here is a sample
problem for these numbers:
Jesse has 13 more marbles than Sophie. Sophie has 4 fewer marbles than Dale. Dale has
37 marbles. How many marbles does Jesse have?
Help children see that they can solve this problem with only two comparing sentences.
Children should already realize that they have to reveal at least one number for the
problem to be solvable. Discuss how you would solve this problem if you didn’t already
know the secret numbers.
CC 28 Common Core Resource Guide
TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 28
Chapter 8 • Lesson 10-3
12/21/10 4:06:49 PM
Creating and Solving Story Problems
pairs
Materials
Purpose To write and solve two-step word problems involving comparing
• For each child: AM:
Writing Your Own Story
Problem
Introduce Tell children that you want them to write their own comparing problems.
Give each student a copy of Activity Master: Writing Your Own Story Problem. Go
through the instructions for the page with the class.
Name
Date
6Xi^k^inBVhiZgM
6Xi^k^inBVhiZg
NCTM Standards 1, 2, 6, 7, 8, 9, 10
CCSS 2.0A 1, 2.NBT 5, 7
Writing Your Own Story Problem
Master: Writing Your Own Story Problem, each student
writes a comparison story problem. When the word
problem is complete, children should fold the top edge of
the paper down to the dotted line on the activity master
to hide the solution. You may need to demonstrate how to
fold the paper.
Next, children exchange papers with a partner and solve
the problem they get on a separate piece of paper. They
can check their work by unfolding the paper to see the
solution.
Choose 3 secret numbers.
A
B
Which secret number will you tell?
Write a question you can ask about your numbers.
After you write your story,
fold the top edge of your paper
down to the dotted line to cover
the answers.
Write a story problem about your numbers.
88(+ 8dbbdc8dgZGZhdjgXZ<j^YZ
Activity Master: Writing Your
Own Story Problem
Talk Math
Concept Alert
How do you know whether to add or subtract? Possible answer: I just
think about which number is supposed to be greater. If the number I
want to find is less than the number I know, I subtract. If the number I
want to find is greater than the number I know, I add.
Share Ask children to share any strategies they have developed for solving these
problems. Children may also want to share problems they thought were funny
or especially tricky. You can keep this collection of story problems for children to
use for practice. Since the solutions are included, children will be able to practice
independently.
Chapter 8 • Lesson 10-3
C
Write some sentences comparing the numbers.
© School Specialty
Task Write your own story problem. Using Activity
'%
B>C
As children are working,
check to see that they are
writing problems with enough
information to be solvable. For
example, if they don’t include
a comparison sentence that
mentions one of the numbers,
it may not be possible to find
that number later.
Common Core Resource Guide CC 29
individuals
Solving More Story Problems LAB Masters,
20
CCRG pp. CC 32–CC 33
MIN
Purpose To write comparison sentences and to solve two-step word problems
NCTM Standards 1, 2, 6, 7, 8, 9, 10
CCSS 2.OA 1, 2.NBT 5, 7
involving comparisonsPurpose To solve two-step word problems involving putting together
and taking apart
Lesson Activity Book Master, CCRG p. CC 32
Chapter 8
Lesson
Name
Lesson Activity Book Master, CCRG p. CC 33
Answer each question. Show your work.
Date/Time
10-3 Story Problems About
Comparing
NCTM Standards 1, 2, 6, 7, 8, 9, 10
Common Core State Standards 2.OA 1, 2.NBT 5, 7
4. Bevfound23plasticbottles.
Tomfound9fewerplastic
bottles.Thetwochildren
recycledallthebottlesthey
found.Howmanybottlesdid
theyrecycle?
Sample work is shown.
Evan has 22 baseball cards.
Drew has 41 more cards than Evan.
Evan
37
1. Circle the name of the person who has more
baseball cards.
2. How many baseball cards does Drew have?
Show your work.
Possible response: Drew has 63 cards.
Drew has 41 more cards than Evan, so Drew has
22 + 41 = 63 cards.
2
moreflowers
© School Specialty
© School Specialty
Answer your question. Show your work.
Kerry
Jo
Eric
HowmanyflowersdidKyleplant?
15
7 + 8 = 15
HowmanymoreflowersdidMaya
plant? 13
Possible solutions are shown.
6. F
indthreedifferentsolutions
tothisproblem.
Possible response: How many baseball cards do
Evan and Drew have in all?
Evan and Drew have 85 cards altogether.
22 + 63 = 85 cards
Howmanybottlesdidthey
recycle? 37 bottles
9 + 4 = 13
Challenge
3. Write another question about the baseball cards.
14
23 – 9 = 14
23 + 14 = 37
bottles
5. Kyleplanted7rosesand8
tulips.Mayaplanted9roses
and4tulips.Howmanymore
flowersdidKyleplantthan
Maya?
Drew
Sample work is shown.
HowmanybottlesdidTomfind?
Kerryhas21moreraisins
thanJo.Erichas12fewer
raisinsthanKerry.Howmany
raisinsdoeseachhave?
Solution 1
Solution 2
Solution 3
31
10
19
41
20
29
51
30
39
NOTE: Your child is learning to solve story problems involving comparisons. Play a game where you and
your child guess numbers from clues, such as, “My number is 18 more than 53.”
CC 32 Common Core Resource Guide
TMG2CCRG_CH08_L10-3_LAB_p32-p33.indd 32
Common Core Resource Guide
CC 33
12/21/10 1:19:12TMG2CCRG_CH08_L10-3_LAB_p32-p33.indd
PM
33
12/21/10 1:19:12 PM
Teaching Notes for LAB Master,
CCRG Page CC 32
Teaching Notes for LAB Master,
CCRG Page CC 33
Problem 1 guides children to make sense of what they are
reading by having them identify the person with the greater
number of baseball cards. Then, they answer one question
about the problem and write another question that could be
answered from the information in the problem.
Encourage children to start each problem by looking for a
number they know or can find. Then they should look for a
number compared to the number they know.
Ongoing Assessment Children who are not sure
what operation to use may need more help with interpreting
comparison statements. Children who have difficulty finding a
place to start may need more help with logical reasoning and
reading comprehension.
Challenge Problem In this problem, children are not
given any of the numbers they are looking for. They will have
to choose a value for one of the numbers, and then figure
out the other two from that value. Encourage children to
investigate the solutions they find and look for patterns.
Reflect and Summarize the Lesson
There are 12 bicycles in the rack. 7 are blue. The rest of the bicycles in the rack are red.
How many more blue bicycles than red bicycles are in the rack?
Possible answer: I know that there are 12 bicycles and that 7 of them are blue. That means that 5
bicycles are red. That means that there are 2 more blue bicycles than red bicycles.
CC 30 Common Core Resource Guide
TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 30
Chapter 8 • Lesson 10-3
12/21/10 4:06:50 PM
Leveled Problem Solving
Sami found 16 golf balls at the park. Mark found 7 fewer golf balls than Sami.
Basic Level
How many golf balls did Mark
find? Mark found 9 golf balls.
On Level
Kofi found 12 more than Mark.
How many golf balls did Kofi
find? Kofi found 21 golf balls.
Practice Master, CCRG p. CC 34
Name
Extension Master, CCRG p. CC 35
Practice
Lesson
Lesson10-3
34
Date
Above Level
Rona found three fewer golf balls
than Sami and Mark put together.
How many did Rona find? Mark
found 9. Together Sami and Mark
found 25. That means that Rona
found 23 golf balls.
Name
Extension
Lesson 10-3
Date
Solving Story Problems with Comparing
Stories with Many Steps
Solve the problem.
Solve the problem.
Sample work is shown.
1. Anna ate 26 carrot sticks. Anna ate
13 more carrot sticks than Bret. Bret
ate 18 fewer carrot sticks than Dana.
Carly ate 15 fewer carrot sticks than
Dana. Eliot ate 10 more carrot sticks
than Carly.
Show your work.
Sample work is shown.
1. Emma buys 3 shirts at one store and
2 shirts at another store.
She buys 1 more shirt than Gail did.
How many shirts does Gail buy?
Gail buys
4
shirts.
Show your work.
Emma buys:
3 1 2 5 5 shirts
Gail buys:
5 2 1 5 4 shirts
Who else ate the same number of
carrot sticks as Anna?
Eliot
2. Julio reads 9 books this summer.
Kate reads 3 fewer books than
Julio.
Together, how many books do they
read?
Together they read
15
books.
ate the same number of
carrot sticks as Anna.
Show your work.
Julio:
9 books
2. Five friends were jumping rope.
Anna jumped 48 jumps. Anna
jumped 31 fewer jumps than Dana.
Bret jumped 32 fewer jumps than
Carly. Eliot jumped 8 more jumps
than Carly. Dana jumped 23 more
jumps than Bret.
Kate:
9 2 3 5 6 books
Together:
9 1 6 5 15 books
Wes has
3
more marbles.
Wes:
8 1 8 5 13 marbles
© School Specialty
How many more marbles does Wes
have than Luc?
Show your work.
© School Specialty
3. Wes has 5 marbles in his hand and
8 marbles in his pocket.
Luc has 10 marbles.
Bret ate 26 2 13 5 13.
Dana ate 13 1 18 5 31.
Carly ate 31 2 15 5 16.
Eliot ate 16 1 10 5 26.
Eliot ate the same number
as Anna.
Show your work.
Anna jumped 48 jumps.
Dana jumped
48 1 31 5 79 jumps.
How many jumps did Eliot jump?
Bret jumped
79 2 23 5 56 jumps.
96
Carly jumped
56 1 32 5 88 jumps.
Eliot jumped
jumps.
Eliot jumped 88 1 8 5 96
jumps.
Luc:
10 marbles
CC 34 Common Core Resource Guide
TMG2CCRG_CH08_L10-3_Practice_p34.indd 34
Anna ate 26 carrot sticks.
Common Core Resource Guide
12/21/10 2:13:22 PM
Intervention Activity
TMG2CCRG_CH08_L10-3_Extension_p35.indd 35
CC 35
12/20/10 6:07:20 PM
Extension Activity
Number Match
Stories About Comparing Give children index cards. Have them make several pairs
of cards: one with a number, such as 9, and the other
with a comparison clue to the number, such as “4 less
than 13,” or, “5 more than 4.” Check their pairs of cards.
Then have them play a memory game with the cards.
Children lay out all the cards face down, and then turn
two cards face up. If the cards match they get to take
the pair and go again. If they don’t match, they turn both
cards face down again.
Challenge children to write comparison word problems
using three-digit numbers. If you like, you can make extra
copies of Activity Master: Writing Your Own Problems for
children to use. Give children access to base-ten blocks
to support both writing and solving the problems.
Chapter 8 • Lesson 10-3
TMG2CCRG_CH08_L10-3_TG_p26-p31.indd 31
Common Core Resource Guide CC 31
12/21/10 4:06:50 PM
Chapter 8
Lesson
Name
Date/Time
10-3 Story Problems About
Comparing
NCTM Standards 1, 2, 6, 7, 8, 9, 10
Common Core State Standards 2.OA 1, 2.NBT 5, 7
Evan has 22 baseball cards.
Drew has 41 more cards than Evan.
1. Circle the name of the person who has more
baseball cards.
Evan
Drew
2. How many baseball cards does Drew have?
Show your work.
3. Write another question about the baseball cards.
© School Specialty
Answer your question. Show your work.
NOTE: Your child is learning to solve story problems involving comparisons. Play a game where you and
your child guess numbers from clues, such as, “My number is 18 more than 53.”
CC 32 Common Core Resource Guide
TMG2CCRG_CH08_L10-3_LAB_p32-p33.indd 32
12/21/10 1:18:54 PM
Answer each question. Show your work.
4. Bev found 23 plastic bottles.
Tom found 9 fewer plastic
bottles. The two children
recycled all the bottles they
found. How many bottles did
they recycle?
How many bottles did they
recycle?
bottles
bottles
5. Kyle planted 7 roses and 8
tulips. Maya planted 9 roses
and 4 tulips. How many more
flowers did Kyle plant than
Maya?
How many bottles did Tom find?
How many flowers did Kyle plant?
How many more flowers did Maya
plant?
more flowers
Challenge
6. F
ind three different solutions
to this problem.
© School Specialty
Solution 1
Kerry has 21 more raisins
than Jo. Eric has 12 fewer
raisins than Kerry. How many
raisins does each have?
Solution 2
Solution 3
Kerry
Jo
Eric
Common Core Resource Guide CC 33
TMG2CCRG_CH08_L10-3_LAB_p32-p33.indd 33
12/21/10 1:18:55 PM
Name
Date
Practice
Lesson
Lesson10-3
34
Solving Story Problems with Comparing
Solve the problem.
1. Emma buys 3 shirts at one store and
2 shirts at another store.
She buys 1 more shirt than Gail did.
Show your work.
How many shirts does Gail buy?
Gail buys
shirts.
2. Julio reads 9 books this summer.
Kate reads 3 fewer books than
Julio.
Show your work.
Together, how many books do they
read?
books.
3. Wes has 5 marbles in his hand and
8 marbles in his pocket.
Luc has 10 marbles.
How many more marbles does Wes
have than Luc?
Wes has
Show your work.
© School Specialty
Together they read
more marbles.
CC 34 Common Core Resource Guide
TMG2CCRG_CH08_L10-3_Practice_p34.indd 34
12/21/10 2:13:33 PM
Name
Date
Extension
Lesson 10-3
Stories with Many Steps
Solve the problem.
1. Anna ate 26 carrot sticks. Anna ate
13 more carrot sticks than Bret. Bret
ate 18 fewer carrot sticks than Dana.
Carly ate 15 fewer carrot sticks than
Dana. Eliot ate 10 more carrot sticks
than Carly.
Show your work.
Who else ate the same number of
carrot sticks as Anna?
ate the same number of
carrot sticks as Anna.
2. F
ive friends were jumping rope.
Anna jumped 48 jumps. Anna
jumped 31 fewer jumps than Dana.
Bret jumped 32 fewer jumps than
Carly. Eliot jumped 8 more jumps
than Carly. Dana jumped 23 more
jumps than Bret.
Show your work.
© School Specialty
How many jumps did Eliot jump?
Eliot jumped
jumps.
Common Core Resource Guide CC 35
TMG2CCRG_CH08_L10-3_Extension_p35.indd 35
12/21/10 2:27:55 PM
Name
Date
Activity
ActivityMaster
MasterX
Writing Your Own Story Problem
Choose 3 secret numbers.
A
B
C
Write some sentences comparing the numbers.
Which secret number will you tell?
Write a question you can ask about your numbers.
After you write your story,
fold the top edge of your paper
down to the dotted line to cover
the answers.
CC 36 Common Core Resource Guide
© School Specialty
Write a story problem about your numbers.
Common Core Resource Guide CC 37
TMG2CCRG_CH08_L10-3_TN_p37.indd 37
12/21/10 4:07:50 PM