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Lesson 7�10 621
Advance Preparation
Teacher’s Reference Manual, Grades 4–6 pp. 143–147
Key Concepts and Skills• Given a fractional part of a region, name
the ONE.
[Number and Numeration Goal 2]
• Given a fractional part of a collection,
name the ONE.
[Number and Numeration Goal 2]
• Identify a hexagon, trapezoid, and
rhombus.
[Geometry Goal 2]
Key ActivitiesStudents use pattern blocks and counters to
find the ONE for given fractions, and they
solve “What is the ONE?” problems.
MaterialsMath Journal 2, pp. 208 and 209
Study Link 7� 9
pattern blocks � beans, pennies, or other
counters � slate � Geometry Template �
overhead pattern blocks (optional)
Playing Fraction Top-ItStudent Reference Book, p. 247
Math Masters, p. 506
Fraction Cards (Math Journal 2,
Activity Sheets 5 and 6)
Students practice comparing fractions.
Ongoing Assessment: Recognizing Student Achievement Use Math Masters, page 506. [Number and Numeration Goal 6]
Plotting Insect DataMath Journal 2, pp. 209A and 209B
Students plot insect lengths on a
line plot.
Math Boxes 7�10Math Journal 2, p. 210
Students practice and maintain skills
through Math Box problems.
Study Link 7�10Math Masters, p. 231
Students practice and maintain skills
through Study Link activities.
ENRICHMENTPlaying Getting to OneStudent Reference Book, p. 248
calculator
Students apply their proportional reasoning
skills and their understanding of the concept
of ONE.
ENRICHMENTFinding the ONEMath Masters, p. 232
Students determine how a candy bar
was divided.
Teaching the Lesson Ongoing Learning & Practice
132
4
Differentiation Options
The ONE for FractionsObjective To guide students as they find the whole, or the ONE,
for given fractions.f
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eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
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622 Unit 7 Fractions and Their Uses; Chance and Probability
NOTE The blocks that make up the ONE
can often be arranged in several ways.
Investigating various arrangements is worth-
while, but in this lesson, it does not matter
how the blocks in the ONE are arranged.
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
Discuss students’ answers. For Problem 2, have volunteers describe or show how they solved the problem.
Tell students that in this lesson they will use pattern blocks and counters as tools to help them find the ONE.
� Using Pattern Blocks to WHOLE-CLASS ACTIVITY
Find the ONEPose problems like those below in which a part is given and students are to find the whole, or the ONE. Display one or two pattern blocks on the overhead projector, and tell what fraction is represented by this block or pair of blocks. Then direct students to use their pattern blocks to show the ONE. Discuss solutions. Suggestions:
● If is 1 _ 2 , then what is the ONE? 1 wide rhombus or equivalent
● If is 3 _ 4 , then what is the ONE? 2 wide rhombuses or equivalent
● If is 2 _ 3 , then what is the ONE? 3 trapezoids or equivalent
● If is 1 _ 3 , then what is the ONE? 6 squares
● If is 1 _ 2 , then what is the ONE? 4 wide rhombuses
Getting Started
Math MessageSolve Problems 1 and 2 at the top of journal page 208.
Study Link 7�9 Follow-UpHave students share how they know the fractions in Problems 3 and 4 are equivalent. Encourage students to use a model to explain.
Mental Math and Reflexes Write fractions with denominators of 10 or 100 on the board, and have students write the equivalent decimals on their slates. Then write decimals on the board, and have students write the equivalent fractions or mixed numbers on their slates. Do not insist that the fractions be in simplest form. Suggestions:
34
_ 100
0.34
80 _
100 0.80, or 0.8
0.6 6
_ 10
0.3 3
_ 10
132
_ 100
1.32
206
_ 100
2.06
1.99 199
_ 100
or 1 99
_ 100
65.79 6,579
_ 100
, or 65 79
_ 100
5
_ 100
0.05
9 _
100 0.09
0.03 3
_ 100
0.065 65
_ 1,000
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Adjusting the Activity
What Is the ONE?LESSON
7�10
Date Time
Math Message
1. If the triangle below is �13
�, then what is the whole—the ONE? Draw it on the grid.
2. If �14
� of Mrs. Chin’s class is 8 students, then
how many students does she have altogether? students
Use your Geometry Template to draw the answers for Problems 3–6.
3. If is �12
�, then what is the ONE? 4. If is �14
�, then what is the ONE?
5. If is �23
�, then what is the ONE? 6. If is �25
�, then what is the ONE?
32
55
Math Journal 2, p. 208
Student Page
Lesson 7�10 623
What is the ONE? continuedLESSON
7�10
Date Time
55
Solve. If you wish, draw pictures at the bottom of the page to help you
solve the problems.
7. If is �13
�, then what is the ONE? counters
8. If is �14
�, then what is the ONE? counters
9. If 10 counters are �25
�, then what is the ONE? counters
10. If 12 counters are �34
�, then what is the ONE? counters
11. If �1
5� of the cookies that Mrs. Jackson baked is 12,
then how many cookies did she bake in all? cookies
12. In Mr. Mendez’s class, �34
� of the students take music
lessons. That is, 15 students take music lessons.
How many students are in Mr. Mendez’s class? students
13. Explain how you solved Problem 12.
�1250� is an equivalent fraction to �
34
�.
So, the whole is 4 � 5, which is 20 students.
that each fractional part is equal to 5 students.
Sample answer: I divided 15 by 3, which told me
20
60
16
25
16
15
Math Journal 2, p. 209
Student Page
Adjusting the Activity
� Using Counters to Find the ONE WHOLE-CLASS ACTIVITY
Pose more problems in which part of a collection of objects is given and students are to find the ONE. Display beans, pennies, or other counters on the overhead projector. Tell and write what fraction is represented. Ask students to use their slates to write the number of counters in the ONE. Suggestions:
● If is 1 _ 2 , then what is the ONE? 6 counters
● If is 1 _ 3 , then what is the ONE? 9 counters
● If is 2 _ 5 , then what is the ONE? 10 counters
● If is 2 _ 3 , then what is the ONE? 6 counters
● If is 1 _ 4 , then what is the ONE? 8 counters
Draw boxes around counters to create a visual representation
of the problems.
Example 1:
12
ONE
If 3 counters is 1
_ 2 , then what is the ONE?
Example 2:
15
15
ONE
If 4 counters is 2
_ 5 , then what is the ONE?
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 � V I S U A L
� Solving “What Is the ONE?” PARTNER ACTIVITY
Problems(Math Journal 2, pp. 208 and 209)
Students solve problems in which a fractional part is given, and students identify the ONE.
Have students use pattern blocks and counters to model the problems.
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 � V I S U A L
ELL
PROBLEMBBBBBBBBBBOOOOOOOOOOOBBBBBBBBBBBBBBBBBBBBBBBBBBBBB MMMMMEEEBLEBLBLELBLLLLBLEBLEBLEBLEBLEBLEBLEBLEEEMMMMMMMMMMMMMOOOOOOOOOOOBBBBBBLBLBLBLBLBLBLLLLPROPROPROPROPROPROPROPROPROPRPROPPRPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPROROROOROROROROOPPPPPP MMMMMMMMMMMMMMMMMMMMMMMEEEEEEEEEEEEEEEELELEEEEEEEEEEELLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRRRRRPROBLEMSOLVING
BBBBBBBBBBBBBBBBBBBB EEELEMMMMMMMOOOOOOOOOBBBLBLBLBLBLBROOOOROROROROROROROROROO LELELELEEEEEELEEMMMMMMMMMMMMLEMLLLLLLLLLLLLLLLLLLLLLRRRRRRRRRRRGGGLLLLLLLLLLLLLVINVINVINVINNNVINVINVINNVINVINVINVINVINV GGGGGGGGGGGOLOOOLOOOLOLOO VINVINVVLLLLLLLLLVINVINVINVINVINVINVINVINVINVINVINVINNGGGGGGGGGGGOOOLOLOLOLOLOLOOO VVLLLLLLLLLLVVVVVVVVOSOSOOSOSOSOSOSOSOSOOSOSOSOSOSOOOOOSOSOSOSOSSOOSOSOSOSOSOSOSOSOSOSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS VVVVVVVVVVVVVVVVVVVVVVLLLLLLVVVVVVVLLLVVVVVVVLLLLLLLLVVVVVLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLLSSSSSSSSSSSSSSSSSSSSSS GGGGGGGGGGGGGGGGGOOOOOOOOOOOOOOOOOOO GGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGGNNNNNNNNNNNNNNNNNNNNNNNNNNIIIIIIIIIIIIIIIIIIISOLVING
ELL
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Date Time
Insect Data continuedLESSON
7�10
Use the line plot on journal page 209A to answer the questions. Write a number model
to summarize each problem.
1. a. What is the maximum insect length? 1
3
_ 4 in. The minimum?
3 _ 8 in.
b. What is the range of the data set? 1
3
_ 8 in. Number model: 1
3
_ 4 –
3
_ 8 = 1
3
_ 8
2. a. What is the median of the data set? 7 _ 8 in.
b. How much longer is the median length than the minimum length? 4
_ 8 , or
1
_ 2 in.
Number model: 7
_ 8 –
3
_ 8 =
1
_ 2
3. a. What is the mode of the data set? 7 _ 8 in.
b. How much longer is the maximum length than the mode length? 7 _ 8 in.
Number model: 1 3
_ 4 –
7
_ 8 =
7
_ 8
4. Two insects have the maximum length. What is the difference
in length between these insects and the next-longest insects? 1
_ 4 in.
Number model: 1
3
_ 4 – 1 1 _
2 = 1
_ 4
5. There are three insects in Veronica’s collection that are from 1 _ 2 inch to
3
_ 4 inch long.
If these three insects were placed end to end, how long would the line of insects be?
in. Number model: 5
_ 8 +
5
_ 8 +
3
_ 4 = 2
6. How long would the line of insects be if all the
insects less than 1 _ 2 inch long were placed end to end?
in.
Number model: 3
_ 8 +
3
_ 8 =
3
_ 4 in.
7. Make up and solve your own problem about the insect data.
Answers vary.
Number model:
Sample number models are given.
16
__ 8 , or 2
6 _ 8 , or 3 _
4
185-218_EMCS_S_MJ2_G4_U07_576426.indd 209B 3/24/11 9:28 AM
Math Journal 2, p. 209B
Student Page
624 Unit 7 Fractions and Their Uses; Chance and Probability
Adjusting the Activity
Date Time
Insect DataLESSON
7�10
Veronica collected 15 insects for a science project. She measured the length of each
insect to the nearest 1 _ 8 inch. Her measurements are shown in the table below.
InsectLength
(to the nearest 1
_ 8 inch)
InsectLength
(to the nearest 1
_ 8 inch)
Darner dragonfly 1 1 _ 2 Red legged grasshopper 1 1
_ 8
Boreal firefly 3
_ 8 American cockroach 1 1 _ 2
Yellow bumblebee 3
_ 4 June beetle 5
_ 8
Damselfly 1 1 _ 4 Paper wasp 7
_ 8
Ground beetle 7 _ 8 Field cricket 7
_ 8
Green lacewing 1 Indian meal moth 3
_ 8
Lady bug 5
_ 8 Katydid 1 3
_ 4
Carolina mantid 1 3 _ 4
Plot the insect lengths on the line plot below. Then use the completed plot to answer
the questions on the next page.
Length (inches)
Insect Lengths
Nu
mb
er
of
Inse
cts
1 11
81
1
41
3
81
1
21
5
81
3
4
3
8
1
2
5
8
3
4
7
8
XX
XX
X XXX
X X X XX
XX
185-218_EMCS_S_MJ2_G4_U07_576426.indd 209A 3/24/11 9:28 AM
Math Journal 2, p. 209A
Student Page
2 Ongoing Learning & Practice
� Playing Fraction Top-It PARTNER ACTIVITY
(Student Reference Book, p. 247; Math Masters, p. 506)
Students play Fraction Top-It to practice comparing fractions.
Have students play with the shaded side of the cards up. Or have
students play in groups of four and order the fractions. Players score 4 points for
the largest fraction and 2 points for the smallest fraction. The player with the
most points at the end of the game is the winner.
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 � V I S U A L
Ongoing Assessment: Recognizing Student Achievement
Math Masters
Page 506 �
Use Math Masters, page 506 to assess students’ ability to compare fractions.
Students are making adequate progress if they are able to determine which
fraction is larger, with or without referring to the shaded sides of the cards, and
write a number model to illustrate the comparison. Some students may be able
to compare fractions using only the numerical representations.
[Number and Numeration Goal 6]
� Plotting Insect Data INDEPENDENTACTIVITY
(Math Journal 2, pp. 209A and 209B)
Students plot insect lengths in fractions of an inch on a line plot. Then they use the line plot to solve fraction and mixed-number addition and subtraction problems.
� Math Boxes 7�10 INDEPENDENTACTIVITY
(Math Journal 2, p. 210)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 7-12. The skill in Problem 6 previews Unit 8 content.
Writing/Reasoning Have students write a response to the following: Describe two different ways to check your answer for Problem 5. Sample answer: I could divide to check the multiplication. 8,432 / 68 = 124 and 8,432 / 124 = 68. I could also make a ballpark estimate. 70 ∗ 120 = (70 ∗ 100) + (70 ∗ 20) = 7,000 + 1,400 = 8,400. The ballpark estimate 8,400 is close to the product 8,432.
ELL
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STUDY LINK
7�10 What Is the ONE?
44
Name Date Time
For Problems 1 and 2, use your Geometry Template or sketch the shapes.
1. Suppose is 1
_ 4 . Draw each of the following:
Example: 3
_ 4 a. 1 b. 1
1
_ 2 c. 2
2. Suppose is 2
_ 3 . Draw each of the following:
a. 1
_ 3 b. 1 c.
4
_ 3 d. 2
Use counters to solve the following problems.
3. If 14 counters are 1
_ 2 , then what is the ONE?
28 counters
4. If 9 counters are 1
_ 3 , then what is the ONE?
27 counters
5. If 12 counters are 2
_ 5 , then what is the ONE? 30 counters
6. If 16 counters are 4
_ 9 , then what is the ONE? 36 counters
7. 3
_ 4 = 1
_ 4 +
1
_ 2 8.
1
_ 3 +
1
_ 6 =
3
_ 6 , or 1
_ 2
9. 3
_ 4 -
1
_ 4 =
2
_ 4 , or 1
_ 2 10. 3
_ 6 , or 1
_ 2 = 5
_ 6 -
1
_ 3
Practice
203-246_EMCS_B_MM_G4_U07_576965.indd 231 1/25/11 9:58 AM
Math Masters, p. 231
Study Link Master
Lesson 7�10 625
in out
55 0.846... When 55 is divided by the ONE, the result is a
decimal close to one. The ONE must be greater
than 55.
70 1.076... When 70 is divided by the ONE, the result is
greater than 1. The ONE must be less than 70.
65 1 When 65 is divided by the ONE, the result is 1.
The ONE must be 65.
LESSON
7�10
Name Date Time
A Whole Candy Bar
Two friends cut a large candy bar into equal pieces. Harriet ate 1
_ 4 of the pieces.
Nisha ate 1
_ 2 of the remaining pieces. Six pieces were left over.
1. How many pieces was the candy bar originally divided into? pieces
2. Explain how you got your answer. Include a drawing and number models
as part of your explanation.
Sample answer: I shaded 1 _ 4 of a
bar for Harriet. Then I divided the
remaining 3 _ 4 into 12 pieces because
6 is 1 _ 2 of 12. If 3 _ 4 = 12, then 4 _ 4 = 16.
16
Harriet Nisha
Sample answer:
203-246_EMCS_B_MM_G4_U07_576965.indd 232 1/25/11 9:58 AM
Math Masters, page 232
Math Boxes LESSON
7�10
Date Time
1. Name the shaded area as a fraction and
a decimal.
a. fraction:
27
___ 100
b. decimal:
0.27
31518 19
3. Write 6 fractions equivalent to 14
_
16
.
27 61
4. Divide. Use a paper-and-pencil algorithm.
723
_
14
= 51 R9, or 51 9 __ 14
53 54
6. Compare.
a. 1 day is 12 times as long as 2 hours.
b. 6 years is 18 times as long as
4 months.
c. 3 gallons is 6 times as much as
8 cups.
d. 8 cm is 40 times as long as 2 mm.
e. 1 meter is 50 times as
long as 2 cm.
5. Multiply. Use a paper-and-pencil algorithm.
8,432 = 68 ∗ 124
22 2317949–51
Sample answers
7 _ 8 28
__
32
21
__ 24 70
__
80
35
__ 40 168
___
192
2. Which number sentence is true? Fill in the
circle next to the best answer.
A 5 _ 6 < 1 _
6
B 4 _ 10
> 4 _ 5
C 1 _ 7 > 1 _
100
D 2 _ 12
= 3 _ 6
185-218_EMCS_S_MJ2_G4_U07_576426.indd 210 1/27/11 10:51 AM
Math Journal 2, p. 210
Student Page
ENRICHMENT INDEPENDENTACTIVITY
� Finding the ONE 15–30 Min
(Math Masters, p. 232)
To apply students’ understanding of the concept of the ONE, have them determine how a candy bar was divided.
� Study Link 7�10 INDEPENDENTACTIVITY
(Math Masters, p. 231)
Home Connection Students solve “What is the ONE?” problems.
3 Differentiation Options
ENRICHMENT PARTNER ACTIVITY
� Playing Getting to One 5–15 Min
(Student Reference Book, p. 248)
To apply students’ proportional reasoning skills and their understanding of the concept of the ONE, have them play Getting to One. Ask students to use a “What’s My Rule?” table to organize their guesses and explain their thinking. For example:
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