fractions in number stories - everyday math · pdf filemath curse paper children solve and ......
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688 Unit 8 Fractions
Advance PreparationPrepare 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
Key Concepts and Skills• Use pennies, counters, or pictures to solve
fraction number stories.
[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 1
_ 4 inch.
[Measurement and Reference Frames Goal 1]
Key ActivitiesThe teacher and children make up and solve
number stories involving fractions. Children
practice solving fraction number stories
independently.
Ongoing Assessment: Informing Instruction See page 689.
Ongoing Assessment: Recognizing Student Achievement Use journal page 201. [Number and Numeration Goal 2]
MaterialsMath Journal 2, pp. 200 and 201
Home Link 8�7
inch ruler � pennies or counters (optional) �
Fraction Cards (optional) � tool-kit clock
(optional) � slate
Reviewing the Line Plot RoutineStudent Reference Book, pp. 79–81
stick-on notes
Children describe landmarks on a line
plot and compare chances for two
different events.
Math Boxes 8�8Math Journal 2, p. 202
Children practice and maintain skills
through Math Box problems.
Home Link 8�8Math Masters, p. 262
Children practice and maintain skills
through Home Link activities.
ENRICHMENTSolving Math Curse Number StoriesMath 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.
Teaching the Lesson Ongoing Learning & Practice Differentiation Options
Fractions in Number Stories
Objective To provide experiences with solving number stories
involving fractions.
�������
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
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Lesson 8�8 689
14
14
14
14
14
14
14
0 1 341
Math Message solution
0 3412
4114
34
24
14 11 2
Extending the line segment
Adjusting the ActivityExtend the line segment
1
_ 4 inch.
Think of the line segment as part of a number
line from 0 to 2. With children, label the points
that are 1
_ 4 inch apart.
AUDITORY � KINESTHETIC � TACTILE � VISUAL
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
If an overhead projector is available, use it to go over the solution. Lead children to the conclusion that since there are seven 1 _ 4 -inch segments, the line segment is 7 _ 4 inches long. 7 _ 4 inches is another name for 1 3 _ 4 inches.
� Writing and Solving Fraction WHOLE-CLASS ACTIVITY
Number StoriesYou 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:
● Andy bought 24 stamps for his stamp collection. 3 _ 4 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 _ 4 of the total, so 1 _ 4 of 24 = 6. Three sets consist of 18 counters and are 3 _ 4 of the total, so 3 _ 4 of 24 = 18.
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.
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Getting Started
Mental Math and Reflexes Pose problems like the following as children write the answers on slates. They may use tool-kit clocks as needed.
Math Message Using your ruler, draw a line segment
that is 1 3
_ 4 inches long on your slate.
Divide the line segment into 1
_ 4 -inch
segments. How many 1
_ 4 -inch segments are there?
Home Link 8�7 Follow-Up Go over the answer to Problem 5. The
diagram shows 2 wholes and 4
_ 12
(or 1
_ 3 )
of a whole. The corresponding mixed number, then, is
2 4
_ 12
(or 2 1
_ 3 ). You may want to have children write
number models for Problems 1–3. For example:
Problem 1: 1
_ 4 +
1
_ 4 +
1
_ 4 +
1
_ 4 +
1
_ 4 +
1
_ 4 =
6
_ 4 , or 1
2
_ 4 , or 1
1
_ 2
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1 minute = ____ seconds 60
1 hour = ____ minutes 60
1
_ 2 hour = ____ minutes 30
1
_ 4 hour = ____ minutes 15
2
_ 4 hour = ____ minutes 30
3
_ 4 hour = ____ minutes 45
1
_ 3 hour = ____ minutes 20
1
_ 12
hour = ____ minutes 5
1
_ 6 hour = ____ minutes 10
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690 Unit 8 Fractions
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 � KINESTHETIC � TACTILE � VISUAL
● Ruthann read 12 books in the last 4 months. Three were nonfiction. What fraction of the books were nonfiction? 3 _ 12 or 1 _ 4 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 to 3 _ 12 of the total. Take 12 counters and divide them into 4 sets of 3. Each set is 1 _ 4 of the total. To find the average number read per month, divide 12 by 4.
● Kiko has done 3 _ 5 of the math problems. What fraction of the math problems does she still have to do? 2 _ 5 of the problems
Possible solution strategy: Suppose Kiko has 5 problems to solve. She solved 3 _ 5 of the problems—3 problems. This leaves 2 problems still to be solved. Two out of 5 problems is 2 _ 5 of the problems.
● Which would you rather have— 2 _ 3 of a can of lemonade or 5 _ 6 of a can of lemonade? Assuming you like lemonade, 5 _ 6 of a can
Possible solution strategy: Use Fraction Cards to compare the fractions, or reason as follows: 2 _ 3 is equivalent to 4 _ 6 , which is less than 5 _ 6 . Therefore, 5 _ 6 is more than 2 _ 3 .
● Jim has $8. If he shares his money equally with 8 people, each person gets $8 ÷ 8 = $ 8 __ 8 = $1; if he shares it equally with 4 people, each person gets $8 ÷ 4 = $ 8 __ 4 = $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. $ 8 __ 1
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. $ 8 __ 1 = $8 ÷ 1 = $8
● Which is the larger fraction, 1 __ 3 or 3 __ 1 ? 3 __ 1
Possible solution strategy: The denominator tells how many parts the whole is divided into. For 1 __ 3 , the whole is divided into 3 parts and 1 __ 3 is one of those parts. For 3 __ 1 , the whole is divided into 1 part and there are 3 wholes. 3 __ 1 = 3 × 1 __ 1 = 3 So, 3 __ 1 is more than 1 __ 3 .
● It took Nathan 1 1 _ 4 hours to do his homework. How many minutes did he spend on homework? 75 minutes
Possible solution strategy: 1 hour = 60 minutes, 1 _ 4 hour = 1 _ 4 of 60 minutes, or 15 minutes. Therefore, 1 1 _ 4 hours = 60 minutes + 15 minutes = 75 minutes.
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Fraction Number Stories continuedLESSON
8� 8
Date Time
9. Write a fraction story. Ask your partner to solve it.
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
himself? �180� of the pens
Draw eggs in each carton to show the fraction. Sample answers:Example:
�1
7
2�
10.�1
6
2�
11.�1
4
2�
12.�1
3
2�
13.�1
2�
14.�3
4�
15.�1
3�
16. Julie drank �1
4� of a glass of juice.
Draw an empty glass.
Shade in the glass to show how much
juice is left. Write the fraction.
34–
glass of
juice is left.
of the
� �
� �
Math Journal 2, p. 201
Student Page
Lesson 8�8 691
Fraction Number StoriesLESSON
8 � 8
Date Time
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?
3. Chante used �2
3� of a package of
ribbon to wrap presents. Did she use
more or less than �3
4� of the package?
5. There are 10 quarters. You have 3.
I have 2. What fraction of the
quarters do you have?
What fraction of the quarters do
I have?
What fraction of the quarters do
we have together?
7. Dorothy walks 1�1
2� miles to school.
Jaime walks 1�2
4� miles to school.
Who walks the longer distance?
2. Anik bought a dozen eggs at the
supermarket. When he got home, he
found that �1
6� of the eggs were cracked.
How many eggs were cracked?
eggs
4. I had 2 whole cookies. I gave you �1
4�
of 1 cookie. How many cookies did I
have left?
cookies
6. One day, Edwin read �1
3� of a book.
The next day, he read another �1
3� of
the book. What fraction of the book
had he read after 2 days?
What fraction of the book did he
have left to read?
8. Twelve children shared
2 medium-size pizzas equally.
What fraction of 1 whole pizza
did each child eat?
�13
�
�23
�
1�34
�
2
�130�
�08
�
Neither; 1�12
� � 1�24
�
�150� or �
12
�
�120� or �
15
�
less
�16
� or �122�
Math Journal 2, p. 200
Student Page
● Tamekka had 20 books to put into her bookcase. She put 1 _ 2 of the books on the top shelf and 1 _ 2 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? 1 _ 4 of the total
Possible solution strategy: 1 _ 2 of 20 = 10, so she put 10 books on the top shelf, which left 10 books to be shelved. She put 1 _ 2 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)
Children work with a partner or independently to complete journal pages 200 and 201.
Ongoing Assessment: Recognizing Student Achievement
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]
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NOTE For practice with adding
and subtracting fractions, go to
www.everydaymathonline.com.
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692 Unit 8 Fractions
Number
of
Children
Number
of
Children
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.
42 43 44 45 46 47 48 49 50 51 52 53Number 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
42 43 44 45 46 47 48 49 50 51 52 53Number 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:
● 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.
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5. Show two ways a team can score
37 points in a football game.
3. Use simple drawings to show all of
the possible ways you can take
2 blocks from the bag.
Date Time
2. 6 feet � yards
feet � 18 inches
1�1
3� yards � feet
1�1
2� yards � inches54
4
2
6. 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: $6.25
1. Draw two ways to show �3
2
.�
Math BoxesLESSON
8 � 8
22–24 246
Sample answers:1�
12
�
4. Tara frosted �4
5� of the cupcakes.
What fraction of the cupcakes
is not frosted?
Did she frost more or less than �1
2�
of the cupcakes?
If there were 20 cupcakes in all,
how many did she frost?
16 cupcakes
more
�15
�
3 1 2 22 3 1 1
Write a number model:
16 17
(3 � 7) � 6 � (2 � 3) �
(2 � 2) � 37; (2 � 7) �
(3 � 6) � 3 � 2 � 37
Sample answer:7 6 3 2
points points points points
Math Journal 2, p. 202
Student Page
Name Date Time
Fraction Number StoriesHOME LINK
8�8
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.
Please return this Home Link to school tomorrow.
Family Note
22–24
Solve these fraction stories. Use pennies, counters, or pictures to help.
1. Elizabeth bought a dozen eggs. She dropped her bag on the
way home, and 2
_ 3 of the eggs broke. How many eggs broke? 8 eggs
2. Katie mowed 3
_ 4 of the lawn before lunch. What
fraction of the lawn did she have to finish after lunch? 1
_ 4 of the lawn
3. Donnie lives 1 mile from school. One day he walked 1
_ 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 miles
4. Sheridan made 4 trays of cookies. She took 2 trays to school for her
classmates. She took 3
_ 4 of a tray of cookies to her
teacher. How many trays of cookies did Sheridan have left? 1
1
_ 4 trays
5. Jackson needed 2 pints of milk for his recipe. If he had one gallon of milk
in the refrigerator, how much did he use?
(Hint: 1 gallon = 4 quarts, and 1 quart = 2 pints) 1
_ 4 gallon
Write these problems on the back of this page. Solve and
show your work.
6. 2,083 + 4,678 =
7. 6,714 - 3,806 =
8. 4,762 + 4,762 = 9,524
2,908
6,761
PracticeUnit
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Math Masters, p. 262
Home Link Master
Lesson 8�8 693
● Compare the chances of drawing 42 and 47. The chances are equal because there are two 42s and two 47s.
● 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 INDEPENDENTACTIVITY
(Math Journal 2, p. 202)
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.
Writing/Reasoning Have children draw or write an answer to the following: In Problem 4, is 1 __ 5 more or less
than 1 _ 2 ? Use >, <, or = to compare the two fractions. 1 __ 2 > 1 __ 5 or 1 __ 5 < 1 __ 2 How do you know? Sample answer: 1 __ 5 is less than 1 _ 2 because 1 of 5 equal parts is less than 1 of 2 equal parts.
� Home Link 8�8 INDEPENDENTACTIVITY
(Math Masters, p. 262)
Home Connection Children solve fraction number stories like those in the lesson. They solve multidigit addition and subtraction problems.
3 Differentiation Options
ENRICHMENT SMALL-GROUP ACTIVITY
� Solving Math Curse 15–30 Min
Number StoriesTo 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.
EXTRA PRACTICE SMALL-GROUP ACTIVITY
� Minute Math+ 5–15 Min
To offer children more experience with fractions, see the following pages in Minute Math+: pp. 86, 90, 92, and 155.
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