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648 Unit 8 Fractions
Naming Partswith Fractions
Objective To guide children as they use fractions to name a of b
equal parts.e
Advance Preparation
Teacher’s Reference Manual, Grades 1–3 pp. 59–62
Key Concepts and Skills• Use manipulatives to solve problems
involving fractional parts of collections.
[Number and Numeration Goal 2]
• Identify equivalent halves and fourths
of a shaded region.
[Number and Numeration Goal 5]
• Use shaded regions to compare fractions.
[Number and Numeration Goal 6]
• Use equal sharing to solve fractional
part-of-a-collection problems.
[Operations and Computation Goal 6]
Key ActivitiesChildren review basic fraction concepts
and notation. They name fractional parts
of regions and sets of objects.
Ongoing Assessment: Informing Instruction See pages 650
and 651.
Ongoing Assessment: Recognizing Student Achievement Use journal page 180. [Number and Numeration Goal 2]
Key Vocabularyequal � whole (the ONE) � denominator �
numerator � unit fraction
MaterialsMath Journal 2, pp. 180 and 181
slate � 25 pennies or counters
Practicing with Fact Triangles×, ÷ Fact Triangles
Children practice multiplication and
division facts with Fact Triangles.
Math Boxes 8�1Math Journal 2, p. 182
Children practice and maintain skills
through Math Box problems.
Home Link 8�1Math Masters, p. 237
Children practice and maintain skills
through Home Link activities.
READINESS
Exploring FractionsMath Masters, p. 238
counters � ruler or straightedge
Children explore the concept of a fraction
of a set.
ENRICHMENTSolving Fraction PuzzlesMath Masters, p. 239
centimeter cubes
Children solve Fraction Puzzles to create
the whole when a part is given.
ELL SUPPORT
Building a Math Word BankDifferentiation Handbook, p. 132
Children add the terms numerator and
denominator to their Math Word Banks.
Teaching the Lesson Ongoing Learning & Practice Differentiation Options
�������
eToolkitePresentations Interactive Teacher’s
Lesson Guide
Algorithms Practice
EM FactsWorkshop Game™
AssessmentManagement
Family Letters
CurriculumFocal Points
Common Core State Standards
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180
Date Time
Fraction ReviewLESSON
8�1
Math Message1. Draw an X through 2
_ 3 of the circles.
Label each picture with one of the following numbers: 0, 0–4,
1–4,
1–2,
2–4, or
3–4.
2. 3. 4. 5.
4–4 or 1
0 or 0—4
1
_ 4
3
_ 4
1 _ 2 or
2
_ 4
Each whole figure represents ONE.
Write a fraction that names each region inside the figure.
6. 7. 8.
9. 10. 11.
1212
14
14
14
14
13
13
13
12
12
14 1
4
12
12 1
414
34
14
14
1414
18
18
� � �
�
Each whole figure represents ONE. Write a fraction that names each
region inside the figure.
12. 13.
Try This
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Math Journal 2, p. 180
Student Page
Lesson 8�1 649
NOTE To extend fraction review, have
children compare the fractions in
Problems 2– 5, Math Journal 2, page 180.
Interactive whiteboard-ready
ePresentations are available at
www.everydaymathonline.com to
help you teach the lesson.
1 Teaching the Lesson
� Math Message Follow-Up WHOLE-CLASSDISCUSSION
(Math Journal 2, p. 180)
Go over the answers to the Math Message problems while reviewing the use of fractions to express parts of wholes. Be sure to include the following points in the discussion:
� Fraction notation is one way to express equal parts of any whole. (Decimal notation is another way.)
� Fractions are not meaningful unless they refer to a part of a particular whole (the ONE). Throughout this unit, consistently ask children to identify the ONE in problem situations. For example, 1 __ 4 of a large pizza is not the same as 1 __ 4 of a small pizza.
� A fraction has two parts. The denominator names the number of equal parts into which the whole (the ONE) has been divided. The numerator names the number of those equal parts being used or considered.
3 numerator
7 denominator
� A fraction with the same numerator and denominator names all the parts of the whole (the ONE). For example, 3 __ 3 , 4 __ 4 , and 5 __ 5 are all equivalent names for 1.
� A fraction with 1 in the numerator is called a unit fraction. 1 __ 4 , 1 __ 8 , and 1 __ 25 are examples of unit fractions.
Mental Math and ReflexesPose problems like the following. Children write their answers on slates and share their strategies. Encourage children to write number models to show their strategies.
A fin whale weighs about 50 tons. About how much do 6 fin whales weigh? 6 × 50 T = 300 T
1 ton = 2,000 pounds. About how much does 1 fin whale weigh in pounds? 50 × 2,000 lb = 100,000 lb
A 9-year-old’s heart beats about 90 times per minute. About how many times does it beat per hour? 60 × 90 beats = 5,400 beats About how many times does it beat in 10 hours? 54,000 beats
Getting Started
Math MessageTurn to page 180 in your journal. Do Problems 1–5 only.
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650 Unit 8 Fractions
NOTE The numerator of a fraction can be 0;
for example, 0
_ 1 ,
0
_ 2 , and
0
_ 3 are names for no
parts of the whole, or 0. The denominator of a
fraction cannot be 0. Because the reason for
this is beyond the grasp of most third graders,
do not mention this unless someone makes
up a fraction with 0 in the denominator. You
might also enter a fraction such as 3
_ 0 into a
calculator to see what the display shows.
Some calculators will display an error
message when the = key is pressed. Others
will not allow 0 to be entered.
Adjusting the Activity
Have one child divide a slate in half and shade one half, and another child divide
another slate into 4 equal parts and shade 2 fourths. Then compare the shaded parts.
Explain that 1
_ 2 and
2
_ 4 are equivalent fractions.
AUDITORY � KINESTHETIC � TACTILE � VISUAL
ELL
� Any whole number can be named as a fraction with 1 in the denominator. For example, a fraction name for 6 is 6 _ 1 . The numerator 6 tells how many copies you have of the unit fraction with the denominator 1:
6 _ 1 = 6 × 1 _
1
= 1 _ 1 + 1 _
1 + 1 _
1 + 1 _
1 + 1 _
1 + 1 _
1
= 1 + 1 + 1 + 1 + 1 + 1
= 6
Ongoing Assessment: Informing Instruction
Watch for children who have difficulty remembering which part of a fraction is the
numerator and which part is the denominator. Explain that they might remember
the numerator by thinking that the word has a u for up and denominator has a d
for down.
As you continue to discuss fractions with children, emphasize the importance of equal parts and consistently ask them to identify the ONE in problem situations.
� Reviewing Fractions as Names WHOLE-CLASS ACTIVITY
for Parts of RegionsWhen a slate is divided into equal parts, each part can be expressed as a fraction. The slate’s drawing surface is the ONE. Lead the class in activities such as the following:
● Divide the slate into 2 equal parts. First shade one part, and then the other. What is equal to the two halves? The whole slate, or the ONE How would you write this as a fraction? 2 _ 2
● Divide the slate into 3 equal parts. What fraction of the slate is each part? 1 _ 3 of the slate Divide it into 6 equal parts. What is each part called? 1 _ 6 of the slate Share your strategies for shading 1 _ 6 of the slate. Use one line to divide the thirds in half. Or add three more parts by dividing each third with a line.
● Divide the slate into 4 equal parts. Shade 3 of the 4 parts. What fractional part of the slate have you shaded? 3 _ 4 of the slate What fractional part is not shaded? 1 _ 4 of the slate
● Which is larger, 1 _ 2 or 1 _ 4 of the slate? 1 _ 2 Why? With the fraction 1 _ 2 , the slate is divided into fewer equal parts so each of those parts is larger. Which is smaller, 1 _ 2 or 2 _ 4 ? Neither; they’re equal. Why? The same amount is shaded.
● Divide the slate into 6 equal parts. Shade 0 sixths. How much of the slate is shaded? Nothing is shaded. How would you write that as a fraction? 0 _ 6
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Adjusting the Activity
Date Time
Fraction Review continuedLESSON
8�1
14. a. Show 1–4 of a set of8 counters. Howmany counters is that?
15. a. Show 1–3 of a set of12 counters. Howmany counters is that?
16. a. Show 1–5 of a set of 15 counters. Howmany counters is that?
18. Show 2–3 of a set of 18 counters. Howmany counters?
b. Show 2–4 of the set. Howmany counters?
b. Show 2–3 of the set. Howmany counters?
b. Show 4–5 of the set. Howmany counters?
19. Five counters is 1–5 of a set. How manycounters are in thewhole set?
c. Show 3–4 of the set. Howmany counters?
c. Show 3–3 of the set. Howmany counters?
17. Show 3–4 of a set of 20 counters. Howmany counters?
20. Six counters is 1–3 of a set. How manycounters are in thewhole set? 18
15
12
6
25
12
8
4
12
3
4
2
21. Twelve counters is 3–4 of a set. How many counters are in the complete set?
22. Pretend that you have a set of 15 cheese cubes. What is �
12� of that set? Use a fraction
or decimal in your answer.
16 counters
71—2 or 7.5 cheese cubes
You need at least 25 pennies or other counters to help you solve these problems. Share solution strategies with others in your group. Unit
counters
Try This
Math Journal 2, p. 181
Student Page
Lesson 8�1 651
Ongoing Assessment: Informing Instruction
Watch for children who are having difficulty
solving the fractional part-of-a-set number
stories. Have them divide their slates and act
out the problems. For example, to show 3
_ 4 of
a set of 20 counters, have children divide
their slates into 4 sections. They distribute
the 20 counters equally among the sections
and then count to find the total in 3 of the
4 sections.
� Reviewing Fractions as Names WHOLE-CLASS ACTIVITY
for Parts of SetsAsk 5 children to lend their journals to make a set of books. Show the pile of 5 books. The 5 books are the whole set, or the ONE. To support English language learners, discuss the meaning of the word set in this context. Hold up several books, and ask children to name the fractional part of the set.
Ask: What fractional part of the set is 1 book? 1 _ 5 3 books? 3 _ 5 No books? 0 _ 5 5 books? 5 _ 5 , the whole set, or the ONE
Name a fractional part, and ask children to tell you how many books to hold up.
Ask: How many books are 2 _ 5 of the set? 2 books 4 _ 5 of the set? 4 books
Repeat with a set of 9 books.
Ask: How many books are in 8 _ 9 of the set? 8 books How many books are 1 _ 3 of the books? 3 books What fractional part are 6 of the books? 6 _ 9 or 2 _ 3
Continue with similar questions.
Ask children how many books each child would get if 3 children were to
share the 9 books equally. 3 books Each share is 1
_ 3 of the set. Ask: How many
total books would 2 of the children get? 6 books What fraction of books do the
2 children get? 2
_ 3 of the set Have children model this and other situations using
counters.
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
Say that you have a case of juice boxes. Five juice boxes are 1 _ 2 of the case. Ask: How many juice boxes are in the whole case? 10 juice boxes
Say that 4 apples are 1 _ 4 of a bag. How many apples are in the whole bag? 16 apples
Say that 8 girls are 2 __ 3 of a group. How many children are in the group? 12 children
Continue with similar questions.
� Using Fractions to Name Parts INDEPENDENTACTIVITY
of Regions and Sets(Math Journal 2, pp. 180 and 181)
Children work alone or with a partner to complete the journal pages. They can use counters to help solve problems involving fractional parts of sets. Bring the class together to discuss children’s solutions.
ELL
ELL
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652 Unit 8 Fractions
Name Date Time
Fractions All AroundHOME LINK
8�1
Help your child understand the idea of the ONE as well as fractions of objects and sets. Help your child look for objects and pictures that have fractions or decimals printed on them.
Please return this Home Link to school tomorrow.
FamilyNote
22–24
Each square flag below represents the ONE. Write the fractions that nameeach region inside each flag.
1. 2. 3.
Write the fractions.
4. of the buttons have 4 holes.
5. of the buttons have 2 holes.
Look for items around your home that have fractions or decimals on them, suchas recipes, measuring cups, wrenches, package labels, or pictures in newspapers.Ask permission to bring them to school to display in our Fractions Museum.
Solve. Show your work.
6. 275 7. 684 8. 429� 88 � 97 � 237
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�27�
�57�
12
12 1
4
14 1
414
14
34
PracticeUnit
Math Masters, p. 237
Home Link Master
Date Time
5. Shade of the circle.
What fraction is unshaded? 58
38
3. This drawing shows a rectangular prism.
It has faces.
It has edges.
It has vertices.8126
2. Fill in the missing numbers.
4. Complete the number models.
(4 + 3) � 2 �
10 � 6 + (2 + )
� 3 � (9 � 0)
(5 � 5) � 4 � 2127
25
6. 9 cups. 9 ice cubes per cup. Howmany ice cubes in all? Fill in thecircle for the best answer.
A 18 ice cubes
B 81 ice cubes
C 90 ice cubes
D 99 ice cubes
1. Double each amount.
$0.25
$0.50
$0.75
$1.25
$5.00 $10.00$2.50$1.50$1.00$0.50
Math BoxesLESSON
8�1
115 16
22 23 66 67
�, � 700 60
8 5,600 4807 4,900 420
Math Journal 2, p. 182
Student Page
Journal
Page 180�Problems 6–9
Ongoing Assessment:Recognizing Student Achievement
Use journal page 180, Problems 6–9 to assess children’s ability to identify and
write fractions that name regions. Children are making adequate progress if they
are able to successfully complete Problems 6–9. Some children may be able to
complete problems 10 and 11.
[Number and Numeration Goal 2]
2 Ongoing Learning & Practice
� Practicing with Fact Triangles PARTNER ACTIVITY
Partners practice basic facts by flashing ×, ÷ Fact Triangles. Children can keep track of the facts they miss so they can focus on those facts during a second round.
� Math Boxes 8�1 INDEPENDENTACTIVITY
(Math Journal 2, p. 182)
Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-3. The skill in Problem 6 previews Unit 9 content.
� Home Link 8�1 INDEPENDENTACTIVITY
(Math Masters, p. 237)
Home Connection Children use fractions to name parts of objects and sets. They are asked to bring in items with fractions or decimals printed on them for the Fractions Museum.
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LESSON
8�1
Name Date Time
Exploring Fractions
1. Explain how you can tell whether something shows �14�.
For Problems 2 and 3—� Take the number of counters.� Figure out how to show �
14� of
the counters.� Use the rectangles to the right to
make four equal piles of counters.� Draw a picture to record your answer.
2. Take 8 counters. Show �14� of 3. Take 20 counters. Show �
14�
the counters. of 20 counters.
one part is represented, then that shows �14�.
Sample answer: If something has four equal parts and
4. Divide the figure below into four 5. Divide the figure below into fourequal parts. equal parts another way.
Sample answer: Sample
answer:
Is �14� in Problem 4 larger or �
14� in Problem 5 larger? Explain your answer on the
back of your paper.
These show �14�. These do NOT show �
14�.
Math Masters, p. 238
Teaching Master
LESSON
8�1
Name Date Time
Fraction Puzzles
Use centimeter cubes to help you solve the puzzles.
1. The 1st graders are building a little house with centimeter cubes. The drawing shows �
23� of
the floor of their house. Use centimeter cubes to build the whole floor of the house. Then finish the picture.
2. This drawing shows �170� of a line segment. Use centimeter cubes to
figure out how long the line segment is. Figure out how much longerthe line segment should be to make it whole. Use a ruler to draw therest of the whole line segment.
3. Make up a puzzle. Ask a partner to solve it. Answers vary.This drawing shows — of a .
Draw the whole .
Sampleanswer:
Math Masters, p. 239
Teaching Master
Lesson 8�1 653
NOTE Remind children to continue to record
the sunrise, sunset, and length of day in their
journals on pages 279–281. They will also
continue to record the national high and low
temperatures on journal page 175 and then
graph the temperature ranges on journal
pages 176 and 177.
3 Differentiation Options
READINESS PARTNER ACTIVITY
� Exploring Fractions 5–15 Min
(Math Masters, p. 238)
To explore the concept of a fraction of a collection, have children solve the fraction problems on Math Masters, page 238. When children have finished the page, have them discuss how they can find 1 _ 4 of any number. Sample answer: I can divide the number into four equal piles or the area into 4 equal parts. Each pile or part is 1 _ 4 .
ENRICHMENT PARTNER ACTIVITY
� Solving Fraction Puzzles 5–15 Min
(Math Masters, p. 239)
To apply children’s understanding of fractions as parts of wholes, have them solve Fraction Puzzles on Math Masters, page 239.
ELL SUPPORT PARTNER ACTIVITY
� Building a Math Word Bank 5–15 Min
(Differentiation Handbook, p. 132)
To provide language support for fractions, have children use the Word Bank template found on Differentiation Handbook, page 132. Ask children to write the terms numerator and denominator, draw a picture representing each term, and write other related words. See the Differentiation Handbook for more information.
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