Fractions in
Number Stories
Objective To provide experiences with solving number stories
involving fractions.
www.everydaymathonline.com
ePresentations
eToolkit
Algorithms
Practice
EM Facts
Workshop
Game™
Teaching the Lesson
Family
Letters
Assessment
Management
Common
Core State
Standards
Ongoing Learning & Practice
Key Concepts and Skills
Reviewing the Line Plot Routine
• Use pennies, counters, or pictures to solve
fraction number stories. Student Reference Book, pp. 79–81
stick-on notes
Children describe landmarks on a line
plot and compare chances for two
different events.
[Number and Numeration Goal 2]
• Describe solution strategies for solving
fraction number stories. [Number and Numeration Goal 2]
• Use Fraction Cards to compare fractions. [Number and Numeration Goal 6]
• Measure and draw a line segment to
the nearest _14 inch. [Measurement and Reference Frames Goal 1]
Key Activities
The teacher and children make up and solve
number stories involving fractions. Children
practice solving fraction number stories
independently.
Curriculum
Focal Points
Math Boxes 8 8
Math Journal 2, p. 202
Children practice and maintain skills
through Math Box problems.
Differentiation Options
ENRICHMENT
Solving Math Curse Number Stories
Math Curse paper
Children solve and write fraction number
stories based on those found in the book
Math Curse.
EXTRA PRACTICE
Minute Math +
Minute Math®+, pp. 86, 90, 92, and 155
Children solve number stories with fractions.
Home Link 8 8
Math Masters, p. 262
Children practice and maintain skills
through Home Link activities.
Ongoing Assessment:
Informing Instruction See page 689.
Ongoing Assessment:
Recognizing Student Achievement
Use journal page 201. [Number and Numeration Goal 2]
Materials
Math Journal 2, pp. 200 and 201
Home Link 8 7
inch ruler pennies or counters (optional) Fraction Cards (optional) tool-kit clock
(optional) slate
Advance Preparation
Prepare the line plot (pictured on page 692) for Part 2. For the optional Enrichment activity in Part 3,
obtain a copy of the book Math Curse by Jon Scieszka and Lane Smith (Viking, 1995).
Teacher’s Reference Manual, Grades 1– 3 pp. 225–227
688
Unit 8
Fractions
Interactive
Teacher’s
Lesson Guide
Mathematical Practices
SMP1, SMP2, SMP3, SMP4, SMP5, SMP6
Content Standards
Getting Started
3.NF.2, 3.NF.2a, 3.NF.2b, 3.NF.3, 3.NF.3a, 3.NF.3c, 3.NF.3d, 3.MD.4
Mental Math and Reflexes
Math Message
Pose problems like the following as children write the answers
on slates. They may use tool-kit clocks as needed.
Using your ruler, draw a line segment
1 minute = ____ seconds 60
1 hour = ____ minutes 60
1
_
hour = ____ minutes 30
2
inches long on your slate.
that is 1_
4
3
1
_
hour = ____ minutes 20
3
1
_
hour = ____ minutes 5
12
1
_
hour = ____ minutes 10
6
SOL
SOL
SO
SOLVING
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1
-inch
Divide the line segment into _
4
1
-inch segments are there?
segments. How many _
4
Home Link 8 7 Follow-Up
Go over the answer to Problem 5. The
1
_
hour = ____ minutes 15
(or _
)
diagram shows 2 wholes and _
12
3
4
4
2
_
hour = ____ minutes 30
4
3
_
hour = ____ minutes 45
4
1
of a whole. The corresponding mixed number, then, is
(or 2_
). You may want to have children write
2_
12
3
4
1
number models for Problems 1–3. For example:
Problem 1: _
+_
+_
+_
+_
+_
=_
, or 1_
, or 1_
4
4
4
4
4
4
4
4
2
1
1
1
1
1
1
6
1
4
1
4
1
4
1
4
1
4
1
4
2
1
1 Teaching the Lesson
Math Message Follow-Up
WHOLE-CLASS
DISCUSSION
If an overhead projector is available, use it to go over the solution.
Lead children to the conclusion that since there are seven _14 -inch
segments, the line segment is _74 inches long. _74 inches is another
name for 1_34 inches.
Writing and Solving Fraction
Number Stories
SOLVING
3
1
14
Math Message solution
WHOLE-CLASS
ACTIVITY
You and the children make up stories involving fractions of sets.
Children solve the problems in any way they can—using pennies
or counters, drawing pictures or doodles, and so on. You might
want to begin with stories such as the following:
●
0
1
4
Adjusting the Activity
Extend the line segment _14 inch.
Think of the line segment as part of a number
line from 0 to 2. With children, label the points
that are _14 inch apart.
AUDITORY
KINESTHETIC
TACTILE
VISUAL
Andy bought 24 stamps for his stamp collection. _34 of the stamps
were from the United States. How many stamps were from the
United States? 18 stamps
Possible solution strategy: Take 24 coins or counters and divide
them into 4 equal sets. Each set consists of 6 counters and is
1
_
of the total, so _14 of 24 = 6. Three sets consist of 18 counters and
4
are _34 of the total, so _34 of 24 = 18.
0
1
4
2
4
3
4
1
2
3
1 14 14 14 2
Extending the line segment
Ongoing Assessment: Informing Instruction
Watch for children who are having difficulty solving problems with fractions of
sets. Remind them that the denominator (the bottom number in a fraction) tells
the total number of equal groups, and the numerator (the top number in a
fraction) tells the number of equal groups being considered. Children count the
objects in the number of groups given by the numerator to solve the problem.
Have children use manipulatives to act out each problem.
Lesson 8 8
689
●
Ruthann read 12 books in the last 4 months. Three were
3
nonfiction. What fraction of the books were nonfiction? _
or _14
12
of the books On average, how many books did she read per
month? 3 books
Possible solution strategy: Three out of 12 books is equivalent
3
to _
of the total. Take 12 counters and divide them into 4 sets
12
of 3. Each set is _14 of the total. To find the average number read
per month, divide 12 by 4.
●
Kiko has done _35 of the math problems. What fraction of the
math problems does she still have to do? _25 of the problems
Possible solution strategy: Suppose Kiko has 5 problems to
solve. She solved _35 of the problems—3 problems. This leaves
2 problems still to be solved. Two out of 5 problems is _25 of the
problems.
●
Which would you rather have— _23 of a can of lemonade or _56 of a
can of lemonade? Assuming you like lemonade, _56 of a can
Possible solution strategy: Use Fraction Cards to compare the
fractions, or reason as follows: _23 is equivalent to _46 , which is less
than _56 . Therefore, _56 is more than _23 .
●
Jim has $8. If he shares his money equally with 8 people, each
person gets $8 ÷ 8 = $__88 = $1; if he shares it equally with 4
people, each person gets $8 ÷ 4 = $__84 = $2. If Jim doesn’t share
his money, how much money does he have? $8 Write a fraction
to show how much money Jim has. $__81
Possible solution strategy: The denominator names the
number of people among whom Jim’s $8 is divided. Since the
money was not divided or shared with anyone but Jim, the
denominator is 1. Since there are $8, 8 is the number in the
numerator. $__81 = $8 ÷ 1 = $8
●
Possible solution strategy: The denominator tells how many
parts the whole is divided into. For __13 , the whole is divided into
3 parts and __13 is one of those parts. For __31 , the whole is divided
into 1 part and there are 3 wholes. __31 = 3 × __11 = 3 So, __31 is more
than __13 .
Adjusting the Activity
Make up additional fraction number
stories as appropriate before children solve
problems independently. Use similar number
stories in future Minute Math+ sessions.
AUDITORY
690
KINESTHETIC
Unit 8 Fractions
TACTILE
VISUAL
3 __
Which is the larger fraction, __13 or __
?3
1 1
●
It took Nathan 1_14 hours to do his homework. How many
minutes did he spend on homework? 75 minutes
Possible solution strategy: 1 hour = 60 minutes, _14 hour = _14 of
60 minutes, or 15 minutes. Therefore, 1_14 hours = 60 minutes
+ 15 minutes = 75 minutes.
●
Tamekka had 20 books to put into her bookcase. She put _12 of
the books on the top shelf and _12 of the remaining books on the
second shelf. How many books did she still need to put into the
bookcase? 5 books What fraction of the total number of books is
that? _14 of the total
Possible solution strategy: _12 of 20 = 10, so she put 10 books on
the top shelf, which left 10 books to be shelved. She put _12 of the
remaining 10 books on the second shelf—that’s 5 books. She
put a total of 10 books + 5 books, or 15 books, into the bookcase
which left 5 books to be shelved.
After working through a few examples, ask volunteers to make up
stories for the class to solve.
Solving Fraction Stories
PARTNER
ACTIVITY
(Math Journal 2, pp. 200 and 201)
PROBLEM
PR
PRO
P
RO
R
OBL
BLE
B
LE
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LEM
EM
SO
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SOLVING
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NOTE For practice with adding
Children work with a partner or independently to complete
journal pages 200 and 201.
Ongoing Assessment:
Recognizing Student Achievement
and subtracting fractions, go to
www.everydaymathonline.com.
Journal page 201
Problems
10–13
Use journal page 201, Problems 10–13 to assess children’s progress toward
solving problems involving fractional parts of a collection. Children are making
adequate progress if they are able to successfully complete Problems 10–13.
Some children may successfully complete Problems 14–16.
[Number and Numeration Goal 2]
Student Page
Date
Student Page
Time
LESSON
Date
Fraction Number Stories
8 8
䉬
8 8
䉬
Solve these number stories. Use pennies, counters, or draw
pictures to help you.
1.
There are 8 apples in the package.
Glenn did not eat any. What fraction
of the package did Glenn eat?
Anik bought a dozen eggs at the
supermarket. When he got home, he
1
found that ᎏᎏ of the eggs were cracked.
6
How many eggs were cracked?
4.
I had 2 whole cookies. I gave you ᎏᎏ
4
of 1 cookie. How many cookies did I
have left?
3.
2
2
ᎏᎏ
3
Chante used of a package of
ribbon to wrap presents. Did she use
3
more or less than ᎏᎏ of the package?
5.
There are 10 quarters. You have 3.
I have 2. What fraction of the
quarters do you have?
1ᎏ34ᎏ
6.
3
ᎏᎏ
10
2
ᎏᎏ
10
or
7.
or
cookies
1
ᎏᎏ
3
1
Neither;
1ᎏ12ᎏ
⫽
1ᎏ24ᎏ
Math Journal 2, p. 200
夹
夹
10. 6
ᎏᎏ
12
12. ᎏ3ᎏ
12
夹
夹
14. 3
ᎏᎏ
4
1
ᎏᎏ
2
Dorothy walks 1ᎏᎏ miles to school.
2 2
Jaime walks 1ᎏᎏ miles to school.
4
Who walks the longer distance?
8.
Sample answers:
7
ᎏᎏ
12
1
One day, Edwin read ᎏᎏ of a book.
3
1
The next day, he read another ᎏᎏ of
3
the book. What fraction of the book
had he read after 2 days?
What fraction of the quarters do
we have together?
5
ᎏᎏ
10
Draw eggs in each carton to show the fraction.
Example:
What fraction of the book did he
have left to read?
1
ᎏᎏ
5
continued
Sample answer: Jerome gave 2 new pens to
his little sister. If the package had 10 pens in
it, what fraction of the pens did he keep for
8
himself? ᎏ10ᎏ of the pens
eggs
2
ᎏᎏ
3
What fraction of the quarters do
I have?
Fraction Number Stories
Write a fraction story. Ask your partner to solve it.
1
4
less
9.
2.
0
ᎏᎏ
8
Time
LESSON
Twelve children shared
2 medium-size pizzas equally.
What fraction of 1 whole pizza
did each child eat?
ᎏ1ᎏ
6
or
ᎏ2ᎏ
12
1
16. Julie drank ᎏᎏ of a glass of juice.
4
Draw an empty glass.
Shade in the glass to show how much
juice is left. Write the fraction.
11. ᎏ4ᎏ
12
13. ᎏ1ᎏ
2
15. 1
ᎏᎏ
3
3
–
4
of the
glass of
juice is left.
Math Journal 2, p. 201
Lesson 8 8
691
2 Ongoing Learning & Practice
Reviewing the Line Plot
WHOLE-CLASS
ACTIVITY
Routine
(Student Reference Book, pp. 79–81)
Use pages 79–81 in the Student Reference Book to review data
landmarks. On the board, prepare a line plot with stick-on notes
using this data: 42, 42, 43, 45, 45, 46, 46, 46, 46, 47, 47, 48, 48, 48,
48, 48, 50, 51, 53. To provide a context for children, suggest
that the line plot shows the arm span measures in inches of a
class of third graders.
Number
of
Children
42 43 44 45 46 47 48 49 50 51 52 53
Number of Inches
Line plot of 3rd grade arm spans
Ask children to identify the maximum arm span 53 inches, the
minimum arm span 42 inches, the mode 48 inches, and the range
11 inches from the line-plot data. Next, ask children to think of
another way to find the median without removing the stick-on
notes from the line plot. If no one suggests it, have volunteers
cross out the first and last stick-on note from each end of the line
plot over and over until one remains—this is the median arm
span. 47 inches
Number
of
Children
42 43 44 45 46 47 48 49 50 51 52 53
Number of Inches
The median arm span is 47 inches.
Have children imagine that you will put all the stick-on notes in a
container and draw one out at random without looking. To
practice comparing chances for two different events, pose the
following:
●
692
Unit 8 Fractions
Compare the chance of drawing a note that says 42 with the
chance of getting a note that says 50. There is a greater chance
of drawing 42 than 50. Explain how you figured it out. There
are two 42s and only one 50.
Student Page
●
Compare the chances of drawing 42 and 47. The chances are
equal because there are two 42s and two 47s.
Date
●
䉬
2
3.
Draw two ways to show ᎏᎏ
Compare the chances of drawing 46 and 48. There is a greater
chance of drawing 48 because there are five 48s and four 46s.
Compare the chances of drawing 48 or a number larger than
48. There is a greater chance of drawing 48 because there are
five 48s and only three numbers larger than 48.
Math Boxes 8 8
Math Boxes
8 8
1.
●
Time
LESSON
2.
6 feet ⫽
Sample answers:
1
3
1
1ᎏᎏ
2
4
54
feet
inches
246
22–24
3.
Use simple drawings to show all of
the possible ways you can take
2 blocks from the bag.
4.
4
Tara frosted ᎏᎏ of the cupcakes.
5
What fraction of the cupcakes
1
ᎏᎏ
5
is not frosted?
Did she frost more or less than ᎏᎏ
2
of the cupcakes?
more
INDEPENDENT
ACTIVITY
If there were 20 cupcakes in all,
how many did she frost?
16 cupcakes
5.
Show two ways a team can score
37 points in a football game.
6.
Sample answer:
7
points
6
points
3
points
2
points
3
2
1
3
2
1
2
1
Use your calculator. Pretend the
division key is broken. Solve this
problem.
Will, Wes, Sam, and Ameer want
to share $25 equally. How much
money will each person get?
Answer:
Write a number model:
Writing/Reasoning Have children draw or write an
answer to the following: In Problem 4, is __15 more or less
than _12 ? Use >, <, or = to compare the two fractions. __12 > __15 or __15 < __12
How do you know? Sample answer: __15 is less than _12 because 1 of 5
equal parts is less than 1 of 2 equal parts.
(Math Masters, p. 262)
yards ⫽
1
Mixed Practice Math Boxes in this lesson are paired with
Math Boxes in Lesson 8-6. The skill in Problem 6
previews Unit 9 content.
yards
feet ⫽ 18 inches
1ᎏᎏ yards ⫽
(Math Journal 2, p. 202)
Home Link 8 8
2
1
1ᎏ2ᎏ
(3 ⫻ 7) ⫹ 6 ⫹ (2 ⫻ 3) ⫹
(2 ⫻ 2) ⫽ 37; (2 ⫻ 7) ⫹
(3 ⫻ 6) ⫹ 3 ⫹ 2 ⫽ 37
$6.25
16 17
Math Journal 2, p. 202
INDEPENDENT
ACTIVITY
PROBLEM
PR
PRO
P
RO
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OBL
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LEM
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SO
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SOLVING
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Home Connection Children solve fraction number stories
like those in the lesson. They solve multidigit addition and
subtraction problems.
3 Differentiation Options
Home Link Master
Name
HOME LINK
88
ENRICHMENT
Solving Math Curse
SMALL-GROUP
ACTIVITY
15–30 Min
Number Stories
Family
Note
Date
Time
Fraction Number Stories
In class we have been solving many kinds of fraction number stories. If some of these Home
Link problems seem difficult, encourage your child to model them with pennies or draw
pictures to help solve them.
22–24
Please return this Home Link to school tomorrow.
Solve these fraction stories. Use pennies, counters, or pictures to help.
1. Elizabeth bought a dozen eggs. She dropped her bag on the
To apply children’s understanding of fraction concepts, read
Math Curse and identify and solve the fraction problems in the
story. Have children write their own fraction number stories based
on daily activities, like those in Math Curse. The class can then
discuss and solve these stories. Consider assembling the stories
into a class book.
8
2
way home, and _3 of the eggs broke. How many eggs broke?
eggs
3
_
1
2. Katie mowed 4 of the lawn before lunch. What
fraction of the lawn did she have to finish after lunch? 4 of the lawn
_
1
_
3. Donnie lives 1 mile from school. One day he walked 2 of the way to school
when he remembered he had to return home to get a book.
When he finally made it to school, how far did he walk in all?
2
classmates. She took _4 of a tray of cookies to her
teacher. How many trays of cookies did Sheridan have left?
3
1 _14
EXTRA PRACTICE
Minute Math+
in the refrigerator, how much did he use?
(Hint: 1 gallon = 4 quarts, and 1 quart = 2 pints)
_1
4
gallon
To offer children more experience with fractions, see the following
pages in Minute Math+: pp. 86, 90, 92, and 155.
Unit
Write these problems on the back of this page. Solve and
show your work.
6. 2,083 + 4,678 =
5–15 Min
trays
5. Jackson needed 2 pints of milk for his recipe. If he had one gallon of milk
Practice
SMALL-GROUP
ACTIVITY
miles
4. Sheridan made 4 trays of cookies. She took 2 trays to school for her
7. 6,714 - 3,806 =
8. 4,762 + 4,762 =
6,761
2,908
9,524
Math Masters, p. 262
EM3MM_G3_U08_237-266.indd 262
1/18/11 1:04 PM
Lesson 8 8
693