Download 2.2 Unit Fractions of a Whole

2.2
Unit Fractions of a Whole
?
Essential Question What do the top and bottom numbers of a fraction tell?
Texas Essential
Knowledge and Skills
Number and Operations—3.3.C
Explain that the unit fraction 1/b represents the quantity
formed by one part of a whole that has been partitioned into
b equal parts where b is a non-zero whole number.
What do the top and
bot tom numbers of a
fraction tell ?
Also 3.3.A
MATHEMATICAL PROCESSES
3.1.C Select tools, technology, and techniques
3.1.F Analyze mathematical relationships
Are You Ready?
Access Prior Knowledge
Use the Are You Ready? 2.2 in the
Assessment Guide to assess students’
understanding of the prerequisite skills
for this lesson.
Lesson Opener
Making Connections
Invite students to talk about kites. Ask them the following questions.
Vocabulary
fraction, unit fraction
Go to Multimedia eGlossary at
thinkcentral.com
Have you ever flown a kite? How many kites have you ever seen in the sky at the same
time? What did the most interesting kite you have ever seen look like?
Using the Digital Lesson
You can use the lesson opener to explain to students parts of a whole. Point out, or ask
students to identify, one group of objects in the sky in the lesson opener. Ask students
what objects on the ceiling and walls of the classroom could be grouped together. Point
out to students one group of objects on the ground in the lesson opener. Ask students
what objects on the tables, counters, and floor of the classroom could be grouped
together. Ask students what one kite or one gopher hole represents.
Resources
Learning Task
Direct students’ attention to the group of kites in the sky.
• How many kites does Doc see flying? (4)
• What is the whole in this problem? (the number of kites)
• How would you tell someone that 1 of the kites is blue using the word fourth?
(One fourth of the kites is blue.)
Literacy and Mathematics
You may choose the following activity.
Invite students to draw a picture of the kites. Have them color or label the kites to
show how many are red, blue, and green. Alternately, have students use connecting
cubes to represent the kites in the problem: 1 green, 1 blue, and 2 red.
For the student
For the teacher
Interactive
Student Edition
provides students
with an interactive learning
environment!
Digital Management
Center organizes program
resources by TEKS!
eTeacher
Edition
Math on the Spot
Video Tutor
Online Assessment
System
iTools Virtual
Manipulatives
Soar to Success Math
Online Intervention
Lesson 2.2
43A
Name
Unlock the Problem
2.2
Hands
On
?
How can you use numbers to show a part of a
whole? Solve the problem to find out.
Number and
Operations—3.3.C
Also 3.3.A
MATHEMATICAL PROCESSES
3.1.C, 3.1.F
Unit Fractions of a Whole
Essential Question
What do the top and bottom numbers of a fraction tell?
A fraction is a number that names part of a whole or part of a group.
In a fraction, the top number tells how
many equal parts are being counted.
Example 1
1
_
6
Find part of a whole.
The bottom number tells how many equal
parts are in the whole or in the group.
Read the information with students. Point out that
the “Read” part is in word form and the “Write”
part is in number form.
A unit fraction names 1 equal part of a whole. It has 1 as its top number.
1
_ is a unit fraction.
6
• What does the top number of the unit
fraction 1_6 tell you? the number of pieces of pie that
Luke ate
Example 1 Find part of a whole.
• What does the bottom number tell you? the total
Luke’s family picked strawberries to make a strawberry pie.
They cut the pie into 6 equal pieces. Luke ate 1 piece.
What fraction of the strawberry pie did he eat?
number of equal pieces in the whole pie
Shade 1 of the 6 equal parts.
Example 2
Read: one sixth
Find part of a group.
6
So, Luke ate _
of the strawberry pie.
Example 2 Find part of a group.
Jake has a collection of marbles. What fraction
of his collection is yellow?
There is 1 yellow marble out of a group of 8 marbles.
• What number represents the total number of
marbles to write as the bottom number? 8
• What number represents the total number of
yellow marbles to write as the top number? 1
English Language Learners
Leveled Activities
ELPS
Beginning: Activity 20
1.A.1, 3.G.2, 4.C.3
Intermediate: Activity 3
2.D.2, 2.E.3, 3.F.2
Advanced: Activity 41
4.F.3, 4.F.8
Advanced High: Activity 48
4.F.1, 4.F.2, 4.G.2
thinkcentral.com for the ELL Activity
Guide containing these leveled activities.
Module 2
© Houghton Mifflin Harcourt Publishing Company
Have students look at Jake’s marbles first and guide
them through the text.
• What is the relationship between the number of
yellow marbles and the total number of marbles?
Write: 1_6
1
_
Tell students that they have learned how to find the
fractional part of a whole. Now they will learn how
to describe a fraction of a group.
43
Hands
On
Unlock
Unlock the
the Problem
Problem
number of
yellow marbles → 1
___
total number → 8
of marbles
Read: one eighth or one out of eight
Write: 1_8
1
_
8 of Jake’s collection is yellow.
So, _
ELL Language Support
Module 2 43
Verbal / Linguistic
Small Group
ELPS 1.A.1, 2.E.3
Strategy: Identify Patterns
• Students identify patterns in language to help communicate about
fractions.
• Help students find patterns between cardinal numbers, which tell
about quantity, and unit fractions.
• As students work through problems, prompt them
to identify these patterns: four/fourth; six/sixth;
eight/eighth, etc.
• Point out that these numbers don’t follow the
pattern: two/half, three/third.
Math Talk
Share
Share and
and Show
Show
Mathematical Processes
1
_
3
1. What fraction names the shaded part? _
Explain how you knew
what number to write as
the bottom number of the
fraction in Exercise 1.
Think: 1 out of 3 equal parts is shaded.
Share and Show
The first problem connects to the learning model.
Have students use the MathBoard to explain their
thinking.
I counted the total number of equal
parts in the whole. Since there
Write the number of equal parts in the whole.
are 3 equal parts, I wrote 3 as the
Then write the fraction that names the shaded part. bottom number.
2.
3.
Math Talk
4.
Mathematical Processes
Use Math Talk to reinforce that the denominator
tells how many equal parts there are in the whole.
3 equal parts
_
4 equal parts
_
8 equal parts
_
1
_
3
_
1
_
4
_
8
_
Guide students in completing Exercises 2–4.
1
_
• For which part of the fraction do you write the
number of equal parts? the bottom number in the
Write a fraction to name the yellow part of each group.
5.
fraction
6.
Use the checked exercises for Quick Check.
1
_
1
_
4
_
3
_
7.
3
8.
1
_
4
_
2
1
_
5
_
Quick Check
1
IF
Problem
Problem Solving
Solving
Draw a picture of the whole. Check students’ drawings.
THEN
1
10. _ is
6
Possible drawing:
44
© Houghton Mifflin Harcourt Publishing Company
1
9. _ is
2
a student misses the checked exercises
Differentiate Instruction with
RtI Tier 1 Lesson 8
In Exercises 5–8, students write the fraction that
names part of a group. Remind them to count the
total number of objects in the group for the bottom
number in the fraction.
Problem Solving
Problems 9–10 require students to visualize and
draw a picture of the whole given a part of it. Guide
students to think about how many of the parts shown
make up a whole.
Enrich
Kinesthetic
Individual
Go Deeper
Materials: pattern blocks
• Give students a set of pattern blocks. Explain that the yellow hexagon
represents 1 whole.
• Have students find what fraction of the yellow hexagon is represented
by other blocks. For example, 2 red trapezoids together completely
cover the yellow hexagon. So, a red trapezoid is 1_2 of a yellow hexagon.
whole
one
half
one
third
Go to Go to thinkcentral.com for additional enrichment
activities in the Enrich Activity Guide.
To extend students’ thinking, have them draw more
than one possible whole for Problems 9–10. Then ask
them to draw other pictures showing part of a whole,
exchange with a classmate, and draw a picture of the
whole.
one
sixth
Lesson 2.2
44
Name
Problem
Problem Solving
Solving
Problem Solving
Use the pictures for 11–13.
Students use the pictures in the chart to solve
Problems 11–13. If students have difficulty with
Problem 13, have them find a lunch item that relates
to the fraction 1_4 .
11.
1
_
8
Give students the opportunity to share and discuss
their explanations for Problem 14.
12.
Problem
What fraction of the cookie did Kylie
eat? Write the fraction in numbers
and in words.
1
_
2
Problem 15 is a multi-step problem that requires
students to reason about equal parts and the number
of parts that equal 1 whole.
Kylie’s Lunch
Dylan’s Lunch
sandwich
pizza
cookie
fruit bar
Use Diagrams The missing parts
of the pictures show what Kylie and
Dylan ate for lunch. What fraction of
the pizza did Dylan eat?
one half
Write Math
13.
What’s the Question? The answer is 1_4 .
Possible question: What fraction of the fruit bar did
Dylan eat?
COMMON ERRORS
C
14.
E
Error
Students might count only the unshaded
parts as the denominator.
Example When writing
the fraction that names
the shaded part, students
might write the answer
1
_ instead of 1_ .
5
6
M
Math
on the Spot
Video Tutor
V
Through the Math on the Spot Video Tutor,
students will be guided through an interactive
solving of this type of H.O.T. problem. Use this
video to also help students solve the H.O.T.
problem in the Interactive Student Edition. With
these videos and the H.O.T. problems, students
will build skills needed in the TEXAS assessment.
No; possible explanation: the square is not divided into six
equal parts, so he did not shade _16 .
15.
© Houghton Mifflin Harcourt Publishing Company
Springboard to Learning
Remind students that the bottom number should
tell the total number of equal parts in the whole or
in the group.
Diego drew lines to divide the square into
6 pieces as shown. Then he shaded part of the square.
Diego says he shaded 1_6 of the square. Is he correct?
Explain how you know.
Multi-Step Riley and Chad each have
a granola bar broken into equal pieces. They each eat
one piece, or 1_4 , of their granola bar. How many more
pieces altogether do Riley and Chad need to eat to
finish both granola bars? Draw a picture below to
justify your answer.
6 more pieces
Check students’ drawings.
Possible drawing:
Module 2 • Lesson 2 45
3
RtI Tier 1 Lesson 8
2
1
Enrich 7
Name
Name
Unit Fractions of a Whole
LESSON
8
Enrich 7
1
3.3.C
OBJECTIVE Use a fraction to name one part of a whole that is divided into
equal parts.
Whole Lot of Fractions!
Draw lines and shade each shape to show the fraction.
Math on the Spot videos are in the
Interactive Student Edition and at
thinkcentral.com.
A fraction is a number. It names part of a whole or part of a group.
1
1. __
The top number tells how many equal parts are being counted.
The bottom number tells how many equal parts are in the whole.
A unit fraction names 1 equal part of a whole. It always has 1
as its top number.
Possible answers are shown.
1
2. __
2
4
How much is 1 part of a fruit bar that is cut into 8 equal parts?
Step 1 Use fraction strips. Make a strip showing 8 equal parts, or eighths.
1
3. __
1
4. __
1
5. __
1
6. __
4
8
Step 2 Shade 1 of the parts and name it.
3
© Houghton Mifflin Harcourt Publishing Company
__.
This fraction is called 1
8
1.
So, 1 part of a fruit bar that can be divided into 8 equal parts is __
8
Write the number of equal parts in the whole.
Then write the fraction that names the shaded part.
1.
2.
4
1
__
4
45
Module 2
2
equal parts
Number and Operations
3.
3
1
__
3
equal parts
7.
6
1
__
6
Stretch Your Thinking What unit fraction
of the figure is shaded? Explain your answer.
_1 ;
6
equal parts
possible answer: I can divide the shape
into 6 equal triangles, and 1 out of 6 equal
parts is shaded.
15
Enrich
© Houghton Mifflin Harcourt Publishing Company
E7
Mathematical Processes
Model ¥ Reason ¥ Communicate
Daily
Daily Assessment
Assessment Task
Task
3
Fill in the bubble for the correct answer choice.
16.
17.
Daily Assessment Task
There are 2 red cubes, 3 yellow cubes, and 1 blue cube in
a bag. What fraction of the cubes are blue?
A
1
_
4
C
1
_
6
B
1
_
3
D
1
_
2
2
1
Can students explain what the top and bottom
numbers of a fraction tell?
THEN
IF
Representations Brandon shared a large burrito with
two of his friends. The missing part of the picture shows
what Brandon ate. What fraction of the burrito did
Brandon eat?
NO
•
Soar to Success Math
Warm-Up 5.08, 5.10
YES
•
•
Enrich 7
Homework and Practice
Lesson 2.2
A
18.
1
_
4
B
1
_
3
1
_
2
C
D
1
_
6
TEXAS Test Prep Coach
Multi-Step For an art project, Tonya and Sahil each
have a piece of fabric cut into equal pieces. They each
used one piece, or 1_3 , of their fabric. How many more
pieces altogether do Tonya and Sahil have left to use?
Test Prep Coach helps teachers to identify common
errors that students can make.
A
2
C
4
In the Test Prep exercise, if students selected:
B
6
D
5
A They switched the numerator and the
denominator.
C They miscounted the number of equal parts.
TEXAS Test Prep
Mary shaded part of a rectangle. What
fraction names the part she shaded?
A
3_
1
B
1
_
3
C
1
_
4
D
1
_
2
© Houghton Mifflin Harcourt Publishing Company
19.
46
D They counted the number of unshaded parts
instead of the total number of parts.
?
Essential Question
Write
Math
What do the top and bottom numbers of a fraction
tell? The top number tells how many equal parts are being
counted. The bottom number tells how many equal parts are
in the whole.
Differentiated Centers Kit
Literature
Pizza Parts!
Students read about how to find
equal parts to write fractions.
Activities
Fish for Fractions
Students complete orange
Activity Card 11 by playing a Go
Fish game in which they match
fraction symbols, words, and
pictures.
Lesson 2.2
46
5
Number and Operations—3.3.C
Also 3.3.A
MATHEMATICAL PROCESSES 3.1.C, 3.1.F
Ho mewo rk
and Practice
2.2
Fill in the bubble completely to show your answer.
Unit Fractions of a Whole
7.
Write the number of equal parts in the whole.
Then write the fraction that names the shaded part.
The drawing below shows what
the moon looks like tonight. What
fraction names the shaded part?
2 equal parts
6 equal parts
1
_
1
_
6
2
3.
B
9.
4.
8 equal parts
4 equal parts
1
_
8
1
_
4
Problem
Problem Solving
Solving
© Houghton Mifflin Harcourt Publishing Company
Mike divided a piece of paper into
4 equal parts. He shaded one of the
parts. What fraction of the piece of
paper did Mike shade?
2.
A
Toni’s fruit bar is divided into three
equal pieces. Toni ate one piece.
What fraction of the fruit bar did
Toni eat? Draw a picture to
show your answer.
10.
6.
The missing part of the picture shows
what Kylie ate for lunch. What fraction
of the sandwich did Kylie eat?
2
__
1
1__
3
C
D
1
__
2
1__
6
A
B
1
_
1
_
2
3
Module 2 • Lesson 2
Use the Homework and Practice pages to provide
students with more practice on the concepts and
skills of this lesson.
Module 2
47
48
1
__
2
1__
4
C
D
1
__
8
4
__
1
What is __1 of this rectangle?
3
A
C
B
D
Multi-Step Two brothers each have
a sandwich divided into 4 equal
pieces. Each brother eats one part,
or 1_4 , of his sandwich. How many
parts of the sandwiches are left
altogether?
Check students’ drawings.
Homework and Practice
47-48
8.
11.
Multi-Step Taylor has a yellow
block of cheese and an orange block
of cheese. He cuts each block into
eight equal parts and takes one
part, or 1_8 , of each block. How many
parts of the blocks of cheese are left
altogether?
A
1 part
C
6 parts
A
6 parts
C
8 parts
B
4 parts
D
8 parts
B
14 parts
D
12 parts
© Houghton Mifflin Harcourt Publishing Company
1.
5.
TEXAS Test Prep
Lesson
Lesson Check
Check
Name