Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
5E Lesson Plan Math
Grade Level: 3rd
Lesson Title: Fractions- Equivalency and
Comparisons
Lesson Overview
Subject Area: Math
Unit Number: 11
Lesson Length:
12 Days
This unit bundles student expectations that address representing and explaining
equivalent fractions and comparing fractions. According to the Texas Education
Agency, mathematical process standards including application, tools and
techniques, communication, representations, relationships, and justifications
should be integrated (when applicable) with content knowledge and skills so that
students are prepared to use mathematics in everyday life, society, and the
workplace.
Prior to this unit, in Unit 06, students represented fractions using objects, pictorial
models, and number lines. Students also composed and decomposed fractions as
a sum of unit fractions and solved problems involving partitioning an object or set
of objects using pictorial representations of fractions.
During this unit, students represent equivalent fractions with denominators of 2, 3,
4, 6, and 8 using objects, pictorial models (including strip diagrams and area
models), and number lines. Students explain that two fractions are equivalent if
and only if they are both represented by the same point on the number line or
represent the same portion of a same size whole for an area model. Students
learn the role of the numerator and the role of the denominator. Understandings of
the numerator and denominator assist students when comparing fractions.
Strategies that students begin to develop when comparing fractions include
comparing the size of the numerators when the denominators are the same,
comparing the size of the denominators when the numerators are the same, and
comparing the size of parts and the number of equal sized parts considered when
the numerators and/or denominators are not the same. With extensive exploration,
students develop fractional reasoning skills about the size of a fraction. For
instance, students realize the smaller the number in the denominator, the larger
the size of equal pieces; whereas, the larger the number in the numerator, the
more equal size pieces being considered. A common misunderstanding when
comparing fractions is to compare the numerators of the fractions only with no
consideration of the denominators of the fractions or vice versa. Students develop
an understanding that although a fraction is composed of a number in the
numerator and a number in the denominator, together they represent a single
value. Students also justify the comparison of fractions using symbols, words,
objects, and pictorial models.
After this unit, in Grade 4, students will relate their understanding of fractions that
name tenths and hundredths to decimal numbers and represent both fractions and
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
decimals as distances from zero on a number line. Grade 4 students will also
represent fractions (including those that represent values greater than one) as
sums of unit fractions and decompose fractions into sums of fractions with the
same denominator using concrete and pictorial models.
In Grade 3, representing equivalent fractions and comparing fractions are
identified as STAAR Readiness Standards 3.3F and 3.3H, while explaining
equivalent fractions is identified as STAAR Supporting Standard 3.3G. These
standards are incorporated within the Grade 3 Texas Response to Curriculum
Focal Points (TxRCFP): Understanding fractions as numbers and representing
equivalent fractions and are included in Grade 3 STAAR Reporting Category 1:
Numerical Representations and Relationships. These standards support the
development of the Texas College and Career Readiness Standards (TxCCRS): I.
Numeric Reasoning and IX. Communication and Reasoning.
According to Empson and Levi (2011), teachers play an active role in helping
students understand fraction equivalence by asking probing questions and
choosing number combinations for problems with specific purposes in mind (p.
115). The National Council of Teachers of Mathematics (2009) states that area,
bar, and number line models provide purposeful visual experiences that aid
students in their understanding of equivalent fractions (p. 42-43).
Empson, S. and Levi, L. (2011). Extending children’s mathematics fractions and
decimals. Portsmouth, NH: Heinemann.
National Council of Teachers of Mathematics. (2009). Focus in grade 3: Teaching
with curriculum focal points. Reston, VA: National Council of Teachers of
Mathematics, Inc.
Texas Education Agency & Texas Higher Education Coordinating Board. (2009).
Texas
college
and
career
readiness
standards.
Retrieved
from
http://www.thecb.state.tx.us/collegereadiness/crs.pdf
Texas Education Agency. (2013). Texas response to curriculum focal points for
kindergarten
through
grade
8
mathematics.
Retrieved
from
http://projectsharetexas.org/resource/txrcfp-texas-response-curriculum-focalpoints-k-8-mathematics-revised-2013
Unit Objectives:
Students will be able to represent equivalent fractions with a denominator of 2,3,4,6, and
8 using a variety of objects, pictorial models, and number lines.
Students will be able to use number lines and area models to explain equivalent fractions.
Students will be able to compare two fractions that have the same numerators or
denominators.
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Standards addressed:
TEKS:
3.1A- Apply mathematics to problems arising in everyday life, society, and the workplace.
3.1C- Select tools, including real objects, manipulatives, paper and pencil, and
technology as appropriate, and techniques, including mental math, estimation,
andnumber sense as appropriate, to solve problems.
3.1D- Communicate mathematical ideas, reasoning, and their implications using multiple
representations, including symbols, diagrams, graphs, and language as appropriate.
3.1E- Create and use representations to organize, record, and communicate
mathematical ideas.
3.1F- Analyze mathematical relationships to connect and communicate mathematical
ideas.
3.1G- Display, explain, and justify mathematical ideas and arguments using precise
mathematical language in written or oral communication.
3.3F- Represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety
of objects and pictorial models, including number lines.
Readiness Standard
3.3G- Explain that two fractions are equivalent if and only if they are both represented by
the same point on the number line or represent the same portion of a same size whole for
an area model.
Supporting Standard
3.3H-Compare two fractions having the same numerator or denominator in problems by
reasoning about their sizes and justifying the conclusion using symbols, words, objects,
and pictorial models.
Readiness Standard
ELPS:
ELPS.c.3: The ELL speaks in a variety of modes for a variety of purposes with an
awareness of different language registers (formal/informal) using vocabulary with
increasing fluency and accuracy in language arts and all content areas. ELLs may be at
the beginning, intermediate, advanced, or advanced high stage of English language
acquisition in speaking. In order for the ELL to meet grade-level learning expectations
across the foundation and enrichment curriculum, all instruction delivered in English must
be linguistically accommodated (communicated, sequenced, and scaffolded)
commensurate with the student's level of English language proficiency.
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
ELPS.c.3C: speak using a variety of grammatical structures, sentence lengths, sentence
types, and connecting words with increasing accuracy and ease as more English is
acquired.
ELPS.c.3D: speak using grade-level content area vocabulary in context to internalize
new English words and build academic language proficiency.
ELPS.c.4: The ELL reads a variety of texts for a variety of purposes with an increasing
level of comprehension in all content areas. ELLs may be at the beginning, intermediate,
advanced, or advanced high stage of English language acquisition in reading. In order for
the ELL to meet grade-level learning expectations across the foundation and enrichment
curriculum, all instruction delivered in English must be linguistically accommodated
(communicated, sequenced, and scaffolded) commensurate with the student's level of
English language proficiency. For Kindergarten and Grade 1, certain of these student
expectations apply to text read aloud for students not yet at the stage of decoding written
text.
ELPS.c.4H: read silently with increasing ease and comprehension for longer periods.
ELPS.c.5: The ELL writes in a variety of forms with increasing accuracy to effectively
address a specific purpose and audience in all content areas. ELLs may be at the
beginning, intermediate, advanced, or advanced high stage of English language
acquisition in writing. In order for the ELL to meet grade-level learning expectations
across foundation and enrichment curriculum, all instruction delivered in English must be
linguistically accommodated (communicated, sequenced, and scaffolded) commensurate
with the student's level of English language proficiency. For Kindergarten and Grade 1,
certain of these student expectations do not apply until the student has reached the stage
of generating original written text using a standard writing system.
ELPS.c.5B: write using newly acquired basic vocabulary and content-based grade-level
vocabulary.
ELPS.c.5F: write using a variety of grade-appropriate sentence lengths, patterns, and
connecting words to combine phrases, clauses, and sentences in increasingly accurate
ways as more English is acquired.
ELPS.c.5G: narrate, describe, and explain with increasing specificity and detail to fulfill
content area writing needs as more English is acquired.
Misconceptions:
 Some students may think of equivalency and comparison of fractions as
strictly a numerical consideration rather than realizing equivalency and
comparison of fractions is only valid when referring to the same size whole.
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Underdeveloped Concepts:
 Some students may struggle recording the denominator as the number of
parts in the whole regardless of the number of parts being considered in the
numerator.
 Some students may continue to struggle with the inverse relationship
between the number of fractional pieces in a whole (the denominator) and
the size of each piece.
Vocabulary:
 Denominator – the part of a fraction written below the fraction bar that tells
the total number of equal parts in a whole or set
 Equivalent fractions – fractions that have the same value
 Fraction – a number in the form where a and b are whole numbers and b
is not equal to zero. A fraction can be used to name part of an object or part
of a set of objects.
 Numerator – the part of a fraction written above the fraction bar that tells
the number of fractional parts specified or being considered
Related Vocabulary:
• Compare
• Equal (=)
• Equal sized parts
List of Materials:










Dry Erase Marker (1 per student)
White Board
Index Cards (1 per student)
Pencil
Math Journal
Chart Paper
YouTube Video: Equivalent Fractions
Construction paper
Scissors
Glue
5
• Fractional part
• Fraction bar
• Greater than (>)
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade





Stapler
Two-sided Counters (1 bag per student, 8 counters per bag)
Envision Math 2.0 Lesson 11-11 (optional)
All Handouts
Brainpop
Video:
Equivalent
Fractions
or
YouTube
Video:
https://www.youtube.com/watch?v=IKYvbR9yTGQ
Read Aloud: Lunch with Cat and Dog By Rozanne Lanczak Williams
(available as an eBook)
Sentence Strips
Crayons
LearnZillion Video: Recognize Equivalent Fractions Using Area Models and
Generate Equivalent Fractions Using Area Models
Play-Doh (2 containers per group of students)
Object to cut Play-Doh (i.e. ruler, or protractor) (1 per student)
Fraction Bars
Fraction Circles or Fraction Circles Black line Master
Index Cards









INSTRUCTIONAL SEQUENCE
Phase 1: Engage the Learner
Introducing Equivalent Fractions
Day 1:
Objective: Students will understand the meaning of equivalent fractions and that
equivalent fractions can be shown using different types of models.
Materials:
 Chart Paper
 Math Journals
 YouTube Video: Equivalent Fractions
 Construction paper for foldable
 Scissors
 Glue
 Stapler
Activity:
Begin by showing the YouTube Video: Equivalent Fractions. As students are watching
the video stop at key points to reinforce concepts that are being introduced.
Remind students that in the past we have learned about fractions and how to represent
them using pictorial models. We will now be using those same models to show fractions
that are equal.
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
To introduce vocabulary and concepts that will be covered in this unit make the following
anchor chart and have students copy it into their math journals.
In addition to the anchor chart students will also need to add definitions for the following
words to their math journal:
• Compare
• Equal (=)
• Equal sized parts
• Fractional part
• Fraction bar
• Greater than (>)
Students will now make the following Equivalent Fractions Flap Book. To make the
foldable use construction paper and have students label each flap in the order shown
below.
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
On the inside of each flap have students write the fraction equivalency for each bar.
Students will be able to refer back to this foldable throughout the unit as a way to better
understand equivalent fractions.
After students have completed the foldable ask students the following questions:

𝟏
2 3 4
What fractions are equivalent to 𝟐? How can you tell? 4, 6, 8,
1
5
tell because each fraction is the same size as the 2 fraction bar.

𝟑
What fractions are equivalent to 𝟒? How can you tell?
because the fraction bars are the same size.
, and
10
𝟔
9
𝟖
12
, and
6
. I can
12
. I know this
Repeat these same questions for other fractions on the foldable.

What’s the teacher doing?
Show
YouTube
Video:
Equivalent Fractions to the
class.

What are the students doing?
Watch YouTube video with the class.

Create anchor chart with the
class, and define important
vocabulary.

Copy anchor chart and math vocabulary
words into math journal

Demonstrate how to create
Equivalent
Fractions
Flap
Book ask guiding questions as
students are creating the book.

Create the Equivalent Fractions Flap
Book, and answer questions as the flap
book is being created.
Phase 2: Explore the Concept
8
Understand Equivalent Fractions using
Fraction Bars and Pictorial Models
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Day 2 and 3:
Objective: Students will use fraction bars and other concrete models to understand
equivalent fractions.
Materials:
 Two-sided Counters (1 bag per student, 8 counters per bag)
 Dry Erase Markers (1 per student)
 White Boards (1 per student)
 Fraction Bars or Fraction Bar Black line Master
 Handout: Equivalent Fractions Using Pictorial Models
 Envision Math 2.0 Lesson 11-11
 Brainpop
Video:
Equivalent
Fractions
or
YouTube
https://www.youtube.com/watch?v=IKYvbR9yTGQ
Video:
Activity:
Begin by playing Brainpop Video: Equivalent Fractions or YouTube Video:
https://www.youtube.com/watch?v=IKYvbR9yTGQ
Distribute fraction bars to students. Give students time to explore making equal fractions
with the fraction bars. After students have had enough time to explore using the fraction
bars, have them take out one of the bars labeled one-half. Explain to students that to
make an equivalent fraction we need to find pieces with the same denominator, put them
together and see if they equal the same size as the one-half fraction bar. Tell students to
take out two fraction bars labeled one-fourth, put them together and lay them directly
under the fraction bar labeled one-half.
Ask Students:
 How many one-fourth pieces do you need to equal the one-half piece? I need
to pieces labeled one-fourth to equal one-half.
 What equivalent fraction does this model represent? This model represents
1 2
= .
2 4
Now tell students to use their fraction bars to find another fraction that equals one-half.
Remind students that the pieces they are using to match one-half must have the same
denominator.
Ask Students:


What other fractions did you find that are also equal to one-half? Three-sixths
and four-eighths.
How do you know these fractions are equal? When you put the fraction bars
together they are the same size as one-half.
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Students will now take out three one-fourth pieces and lay them next to each other with
sides touching.
Ask Students:
 What fraction do these three pieces represent? Three-fourths.
Have students use their fraction bars to find a fraction that is equal to three-fourths. When
students are finished, their model should look something like this:


What fraction is equal to three-fourths? Six-eighths is equal to three-fourths.
How do you know? The two fractions are equal because they show the same
amount of the whole.
Finally students will take out four pieces labeled as one-sixth and put them together sides
touching.
Ask Students:
 What fraction do these pieces represent? These pieces represent the fraction
four-sixths.
Students will need to work on their own using their fraction bars to find a fraction that is
equal to four-sixths. When students finish their model should look like this:

What fraction is equivalent to four-sixths? How do you know? Two-thirds is
equivalent to four sixths because they represent the same part of a whole.
Now that students have shown they understand how to make equal fractions using
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
fraction bars they will complete Lesson 11-11 Independent Practice from their Envision
Math textbooks on their own. If you do not have access to Envision then use the
Handout: Equivalent Fractions Using Pictorial Models.
Day 3:
Today students will use counters to show equivalent fractions. Distribute one bag of
counters, a dry erase marker, and a white board to each student. If there isn’t enough
counters for each student to have their own bag then group students together in pairs.
Tell students to take out all of their counters and lay them on their desk yellow side up in
two rows of four. Let them know that all of the counters together represent the whole.
Ask Students:
 How many counters are in your bag? There are 8 counters in my bag.
Because there are eight counters our denominator is eight. Have students draw the
fraction symbol on their dry erase boards, and put an eight as the denominator. Students
will take the top row and flip the counters to the other side (red.)
Ask Students:
 You have eight counters total. How many of them are red? There are four red
counters.
4
 What fraction of your counters are red? 8.
Tell students to add a numerator of four to their white boards. They will then draw an
equal sign and a fraction symbol on the other side. Explain to students that we are going
4
to use our counters to find a fraction equivalent to 8. Tell students to use their dry erase
markers to circle the top row of counters and then the bottom.
Ask students:
 How many total groups are circled? 2
 How many groups contain red counters? 1
 What fraction does this model represent? One-half.
Students will write the fraction one-half on the other side of the equal sign on their white
boards. Ask students to explain on their white boards why four-eighths is equal to onehalf. This is an example of what their picture and explanation could look like when they’re
finished.
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Now have students take away two counters. They should have a total of six counters to
represent their whole. Students will lay the six counters on their desk in two rows of three
yellow side up. Tell students to flip the two counters in the first column to the red side.
Have students write the fraction of counters that are red on their white board. When
students are finished they will hold up their white boards to show what fraction is being
2
represented. The correct answer is 6. They will use their counters to demonstrate a
2
fraction that is equal to 6. Ask students: How can you group your counters together to
make an equal fraction? Give students a few minutes to think about this and use their
counters to make an equal fraction. Students will need to show the equivalent fraction on
their white boards, and explain how the two fractions are equal. When most students are
done have them hold up their white boards to show that they understand.
Ask Students:


What fraction is equivalent to two-sixths? One-third.
Why are those two fractions equal? They both show the same amount of a
whole.
Continue practicing using a few more sets of equivalent fractions. Once students
understand what they’re expected to do, have them work independently to use their
counters and create their own sets of equal fractions. They will need to explain on their
white boards why their fractions are equal.
What’s the teacher doing?

Teacher will play the Brainpop
Video: Equivalent Fractions or
YouTube Video:
https://www.youtube.com/watc
h?v=IKYvbR9yTGQ. The
teacher will stop at key points to
ask questions as either video is
12
What are the student’s doing?

Students will watch the video on
Equivalent fractions, and answer
questions that the teacher asks.
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
playing.

Teacher will model how to show
equivalent fractions using fraction
bars.

Students will work on their own or with a
partner to represent equivalent fractions
using fraction bars.

Teacher will monitor students as
they complete the handout.

Students will complete Handout:
Equivalent Fractions Using Pictorial
Models on their own.

Teacher will model how to show
equivalent fractions using twosided counters.

Students will show how to model
equivalent fractions using counters.

Teacher will monitor students as
they create their own examples
of equivalent fractions using
counters.

Students will create their own examples
of equivalent fractions using counters.
Phase 2: Explore the Concept
Equivalent Fractions Using a Fraction
Circle
Day 4:
Objective: Students will use a fraction pizza as a way to represent equivalent fractions.
Materials:
 Teacher Resource: Pizza Problem
 Handout: Pizza Placemat (1 per group)
 Handout: Pizza Fractions #1 (1 per group)
 Handout: Pizza Fractions #2 (1 per group)
 Handout: Pizza Fractions #3 (1 per group)
 Handout: Pizza Fractions #4 (1 per group)
 Handout: Pizza Fractions #5 (1 per group)
 Handout: Equivalent Fractions (1 per student)
 Scissors
 Read Aloud: Lunch with Cat and Dog By Rozanne Lanczak Williams
(available as an eBook)
Activity:
Divide students into groups of five. Display the Teacher Resource: Pizza Problem for
the class to see. Give students time to read and think about the problem on their own,
and then share their thoughts with their group. Students should figure out that it depends
on which pizza slices each person takes. It’s possible that 4 pieces of pizza might be the
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
same amount as 3 pieces if the 4 pieces are smaller. This pizza is not cut into equal
pieces.
Read Lunch with Cat and Dog By Rozanne Lanczak Williams aloud. This funny story
shows the importance of equal shares.
Ask Students:

Why were both cat and dog satisfied at the end of the story? Answers vary.
Have students think about their answer, then pair with a partner to discuss it. Then, call
on several students to share their ideas with the class.
Give each group Handout: Pizza Fractions #1-5, Handout: Pizza Placemat, and the
Handout: Equivalent Fractions. Each group will place the Pizza Fraction Placemat in
the middle of their group. Then have each student choose a pizza to decorate for the
activity. They can decorate their pizzas with their favorite toppings. When students are
finished decorating they will take turns telling their group about the pizza they decorated.
As they are sharing make sure students aren’t just talking about the decorations on their
pizzas, but also about how many pieces are in their pie and what fraction of the pie 1, 2,
3, etc. pieces represent.
Students will now carefully cut apart their pizzas on the lines. Have them write the fraction
on the back of each piece, along with their group number. Refer to the Handout:
Equivalent Fractions. Explain to students that they are going to use their Handout:
Pizza Placemat and the pieces they cut out to solve each problem. Use the first problem
as an example.
Ask students:

What do you notice about the first problem? The first problem is showing
equivalent fractions with a denominator of four and eight.
Since the first problem shows the fraction one-fourth, have students take out a piece
labeled as one-fourth and put it on their pizza placemat. The equivalent fraction has a
denominator of eight, so have students take out enough eighths and put them on their
placemat to equal one-fourth. Everyone in the team should record the answer on their
own worksheet.
Ask Students:


𝟐
1
How many eighths equals one-fourth? 𝟖 equals 4.
How do you know? I know two-eighths equals one-fourth because when you put
those pieces on the pizza placemat the pieces are of equal size.
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
After the students have solved a few problems using the pizza pieces, challenge them to
try to figure out the answer before they add the pizza pieces to their placemats. At this
point they should use the pizza pieces to check their answers rather than to solve the
problem.
Students will turn in their Handout: Equivalent Fractions for a grade.
What’s the teacher doing?
What are the students doing?

Display Teacher Resource:
Pizza Problem and discuss it
with students.

Think about and respond
question being asked.

Read Lunch with Cat and Dog By
Rozanne
Lanczak
Williams
aloud.

Listen as the story is being read.

Give each students group a set
of handouts.

Give students time to decorate
their fraction pizzas.

Decorate fraction pizzas

Show students how to use their
pizza fraction pieces to answer
the questions on the Handout:
Equivalent Fractions.

Follow
along
as
the
teacher
demonstrates how to use the fraction
pieces to answer the questions on the
Handout: Equivalent Fractions.

Ask students questions about the
equivalent fractions that they
find.

Answer questions about
fractions that they find.
Phase 2: Explore the Concept
to
equivalent
Equivalent Fractions on a Number Line
Day 5:
Objective: Students will be able to represent equivalent fractions on a number line.
Materials:
 YouTube Video: Equivalent Fractions on a Number Line
 Handout: Equivalent Fractions on a Number Line Chart (1 per student)
 Scissors
 Glue
 Math Journals
15
the
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade




Sentence Strips (4 per student. one pair that is the same length. One pair
that are different lengths)
A Second Pair of Sentence Strips (2 per student)
Handout: Finding Equivalent Fractions on a Number Line
Five crayons per student (red, orange, yellow, green, blue)
Activity:
Begin by showing the YouTube Video: Equivalent Fractions on a Number Line. Make
sure to stop at key points to discuss what is happening in the video.
After the video, give each the Handout: Equivalent Fractions on a Number Line Chart.
Students will need to trim the chart and glue it into their math journals. Students will need
to label either end of each of their number lines with a zero or a one.
The first number line will be left blank to show it as the whole. On the second number line
have students draw a tick mark directly between zero and one. This mark will be labeled
as one-half. Next students will split the third number line into three equal parts and label
each third. Students will then split the fourth number line into four equal parts and label
each fourth. Continue the same routine for sixths and eighths.
Once all number lines have been labeled students will use their red crayon to highlight
one-half and all fractions equal to one-half. With an orange crayon students will highlight
one-third and two-sixths to show they are equal. Students will use a yellow crayon to
highlight two-thirds and four-sixths to show they are equal. They will then use a green
crayon to highlight one-fourth and two-sixths to show they are equal. Finally students will
use a blue crayon to highlight three-fourths and six-eighths to show they are equal.
Distribute a set of four sentence strips to each student. In each student’s set will be one
pair of sentence strips that are the same size and one pair of sentence strips of different
sizes.
Tell students to pick out two sentence strips that are the same size and draw a number
line on each strip labeling either side with a zero or a one. Students should label both of
their number lines as follows in the top picture:
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Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Have students place the number line split into six equal parts directly below the number
line split into three equal parts.
Ask Students:
 Looking at these two number lines, can you find any fractions that are
equal? If so, what are they? Yes, looking at these number lines I can tell that
one-third equals two-sixths and two-thirds equals four-sixths.
Explain to students that because these number lines are the same length, the fractions
are equal.

What do you think would happen if we had number lines of different
lengths? Answers may vary.
Next, students will take the two sentence strips that are different sizes. They will label the
shorter one with thirds, and the longer sentence strip with sixths. When students are done
their strips should look like the ones in the bottom picture.
17
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Ask Students:

Even though these number lines are not the same length are the fractions
still equal? No, because the number lines are different lengths the fractions are
not equivalent.
Now that students understand know how to find equivalent fractions on a number line,
and that the number lines have to be the same length for the fractions to be equal, they
will come up with their own set of equivalent fractions and demonstrate both of those
fractions on another set of sentence strip number lines. On the back of one of those
sentence strips they will write an explanation of why those fractions are equal. When all
students are finished they can share with the class to check for understanding.
What’s the teacher doing?

Show
YouTube
Video:
Equivalent Fractions on a
Number Line and discuss the
video with the class

Distribute
the
Handout:
Equivalent Fractions on a
Number Line Chart to students.

Guide students through labeling
and coloring their chart. Tell
students to trim chart and glue it
18
What are the students doing?

Listen and participate in discussion
about the video.

Fill-in chart and glue it in math journal.
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade

in their math journals.

Model equivalent fractions on a
number line using sentence
strips.

Monitor students as they create
their own equivalent fractions
using sentence strips.
Phase 2: Explore the Concept

Follow
along
as
the
teacher
demonstrates equivalent fractions on a
number line.

Use sentence strips to create and
explain equivalent fractions on a
number line.
Equivalency using an area model
Day 6:
Objective: Students will use area models to show equivalent fractions.
Materials:
 White Boards
 Dry Erase Markers
 Chart Paper (1 piece for every 2 students)
 LearnZillion Video: Recognize Equivalent Fractions Using Area Models and
Generate Equivalent Fractions Using Area Models
Activity:
Begin by showing students the LearnZillion videos: Recognize Equivalent Fractions
Using Area Models and Generate Equivalent Fractions Using Area Models. As the
videos are playing stop a key points to ask guiding questions about what they’re seeing.
Distribute a white board and dry erase marker to each student. Explain to them that we
are going to be demonstrating how to show equivalent fractions using area models.
Have students draw two equal circles. Explain to students that if their circles are not
equal then their fractions will not be equivalent. Tell students to color in one-half of the
first circle with their dry erase marker.
Ask students:


How can we use the second area model to show a fraction equivalent to onehalf? We can split the fraction circle in half, and then split each half into two equal
parts. Next we will shade in the same amount as the first circle.
What fraction is equivalent to one-half? Two-fourths.
When students are finished, their model should look like the top picture.
19
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Next have students erase their white boards and draw two equal rectangles. Students will
need to split the first rectangle into four equal parts and shade in three of the four parts.
Tell students to think of a way they can show an equivalent fraction using the second
rectangle. Then have students share their method with the person sitting next to them.
Students will now use the method they came up with to show an equivalent fraction to
three-fourths.
Ask students:
 What did you do to the second area model to show a fraction equivalent to
three-fourths? I drew four equal parts and then split each part in half. I then
shaded in the same amount of the rectangle as in the first model.
 When looking at your second area what fraction is equivalent to threefourths? Six-eighths is equivalent to three-fourths.
Make sure you tell students that different shapes can be used to make area models as
long as the shapes are equal and can be split into equal parts.
Divide students into groups Each group will be given a piece of chart paper and three
fractions. Students will be challenged to draw area models on their chart paper to show
equivalent fractions. When students are finished they can share their posters with the
class.
What’s the teacher doing?

Show students the LearnZillion
videos: Recognize Equivalent
Fractions Using Area Models
and
Generate
Equivalent
Fractions Using Area Models.
Lead a discussion about what
20
What are the students doing?

Listen and participate in discussion
about what they learned from the
videos.
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
students learned from the videos.

Model how to use area models to
show equivalent fractions.

Follow along as the teacher models how
to use area models to solve equivalent
fractions.

Monitor students as they use
area models to equivalent
fractions on chart paper.

Use chart paper to show equivalent
fractions using area models.
Phase 3: Explain the Concept
Equivalent Fractions Frayer Model
Day 7:
Objective: Students will create a frayer model explaining how to show equivalent
fractions in many different forms.
Materials:
 Construction Paper
 Math Journal
 Pencil
Activity:
Students will create a frayer model to show equivalent fractions in many different forms.
Distribute a piece of construction paper to each student and show them how to fold it into
a frayer model. Give each student a fraction and have them write it in the center diamond.
Students will use their notes in their math journal to find a fraction that is equal to the one
you gave them. In the top left box they will show how the fractions are equal by drawing
fraction circles. In the top right box students will do the same with fraction bars. In the
bottom left box they will show how the fractions are equal by drawing equivalent number
lines. In the bottom right box they will draw counters to show equivalent fractions. When
students are finished they can color and share their frayer models with the class.
What’s the teacher doing?
What are the students doing?

Show students how to fold and
create a frayer model.

Fold construction paper to create a
frayer model.

Give each student a fraction.
Students will work to find an
equivalent fraction.

Find a fraction equivalent to the one
given by the teacher.

Monitor students as they create
their frayer models and show

Create frayer model and demonstrate
how to show equivalent fractions in
21
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
how to model equivalent fractions
in different ways.
Phase 2: Explore the Concept
different ways.
Comparing Fractions Using Pictorial
Models
Day 8 and 9:
Objective: Students will be able to compare fractions with the same numerator or
denominator using symbols, words, objects and pictorial models
Materials:
 Play-Doh (2 containers per group of students)
 Object to cut Play-Doh (i.e. ruler, or protractor) (1 per student)
 Handout: Greater Than, Less Than Equal Cards
 Pencils or dowels for rolling pins (1 per student)
 Dry Erase Marker (1 per group)
 White Boards (1 per group)
 Scissors
 YouTube Video: Comparing Fractions With Like Denominators or Like
Numerators
 Handout: Compare Fractions With the Same Denominator
 Handout: Compare Fractions With the Same Numerator
Activity: Comparing Fractions with the Same Denominator
Begin by showing the YouTube Video: Comparing Fractions With Like Denominators
or Like Numerators.
Explain to students that today we are going to be using Play-Doh to compare fractions
with the same denominator. Divide students into groups of two and give each group two
containers of Play-Doh, dry erase marker, white board, and the Handout: Greater Than,
Less Than Equal Cards. They will need to cutout the greater than, less than, and equal
cards from the handout. Each student will also need a pencil to use as a rolling pin, and a
ruler or protractor to use for cutting. Tell students that each of their containers represents
one whole and that they are going to make fraction pies to cut into fractional parts and
then compare the sizes of the parts.
Have students draw two large rectangles on their white boards with a circle in-between
them (where the greater than, less than, or equal card will go.) Students will roll out and
shape their Play-Doh into a pie (circle.) Tell students to use their rulers to cut their pies
into four equal parts. One student from each group will take two pieces of their pie and
place it into one rectangle on their white boards, and will write the represented fraction
directly below. The other student will only take one piece and place it into the other
rectangle on their white board, and write the represented fraction directly below. Their
fractions should be two-fourths and one-fourth. Students will now place one of their
22
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
comparison symbols in the middle to show which fraction is bigger.
Ask Students:


Which is the bigger fraction? Two-fourths is greater than one-fourth.
How do you know? I know this because when two fractions have the same
denominator I have to compare the numerator. Two is bigger than one so twofourths is bigger than one-fourth.
Tell students that when fractions have the same denominator you compare the
numerators. The fraction with the bigger numerator is the bigger fraction.
Repeat this same process, but with other fractions. Some other fractions to compare
could be two-sixths and five-sixths, seven-eighths and two-eighths, one-sixth and foursixths, and one-third and one-third.
Save the Play-Doh and all tools, as the same activity will be used for Day 9.
Once students have grasped this concept they can complete the Handout: Compare
Fractions With the Same Denominator independently.
Day 9: Comparing Fractions with the Same Numerator
Students will be completing the same activity today, but instead will be comparing
fractions with the same numerator.
Tell students to get with their same partner from yesterday. Students will need the same
tools to complete today’s activity. Again have students draw to large rectangles on their
white board with a circle in the middle for the comparison symbol.
Tell students to use a pencil to roll their Play-Doh out into a flattened circle. Have one
student from each group use their ruler to cut their circle into six equal parts, and the
other student cut their circle into three equal parts. Tell each student to take two pieces
out of their fraction circle and place them in the rectangles on their white board. They
need to write the fraction that each circle represents directly below their Play-Doh. They
will need to place a greater than, less than, or equal to sign in the circle between their
pictures to show which fraction is greater.
Ask students:
 Which fractions were you asked to show? Two-sixths and two-thirds.
 Looking at your model how do the two fractions compare? Two-sixths is less
than two-thirds, or two-thirds is greater than two-sixths.
Make sure to tell students that when comparing fractions with different denominators that
the bigger the denominator the smaller the fraction.
23
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
Repeat this same process with the fractions two-thirds and two-fourths, four-eighths and
four-eighths, five-sixths and five-eighths, one-eighth and one-half, and one-fourth and
one-third.
When you are sure that students understand the concept of comparing fractions with the
same numerator have them complete the Handout: Compare Fractions With the Same
Numerator independently for a grade.
What’s the teacher doing?

Begin by showing the YouTube
Video: Comparing Fractions
With Like Denominators or
Like Numerators. Discuss with
students what they learned from
the video.

Divide students into groups and
distribute all necessary supplies.


What are the students doing?

Listen to and discuss the video the
teacher has shown.
Guide students through using
Play-Doh
to
show
equal
fractions.

Work with partner to show equal
fractions using Play-Doh.
Students will complete the
Handout: Compare Fractions
With the Same Denominator
and
Handout:
Compare
Fractions With the Same
Numerator

Complete handouts independently
Phase 3 and Phase 4: Explain The
Concept and Elaborate on the
Concept
Day 10 and 11:
Compare fractions in real world problem
situations
Objective: Students will compare fractions in real world problem situations.
Students will create their own fraction comparison word problems and will trade with other
students to solve.
Materials:
 Fraction Bars
 Fraction Circles or Fraction Circles Black line Master
 Dry Erase Marker (1 per student)
 White Board
24
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade



Index Cards (1 per student)
Pencil
Math Journal
Activity:
Give each student a white board, dry erase marker, and either fraction bars or fraction
circles. If using the black line masters students can cut out their fraction bars or fraction
circles and use them to help them solve each problem. Present the following word
problem to the class:
Tell students to use their manipulatives to show four equal sized pieces and eight equal
sized pieces. Students will need to take two pieces from each model and compare the
size. Students will then write a comparison sentence on their white boards. When
students are finished they can hold up their white boards to check for understanding.
Ask Students:
 What two fractions were you comparing in this word problem? Two-fourths
and two-eighths.
 What comparison did you make? Two-fourths is greater than two-eighths.
 How do you know this is true? Even though both fractions have the same
numerator, two-fourths is greater than two-eighths because each fourth piece is
larger than each eighth piece.
 Which cake had the most eaten? The chocolate cake
Display the following problem for students to see:
Each day, the keepers at the zoo feed an elephant the same amount of hay. On
𝟐
𝟐
Monday the elephant ate 𝟔 of his food. On Wednesday, the elephant ate 𝟑 of his
food. Use comparison symbols to compare the fractions, and tell which day the
elephant ate more hay.
Students will work on their own to solve this problem. When they’re finished have all
students hold up their white board to show their comparison sentence.
Ask students:
25
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade


On which day did the elephant eat more of his food? Wednesday
How did you know this? I can tell this by looking at my fraction bars. Two-thirds
is larger than two-sixths so two-thirds is greater than two-sixths.
To close this lesson discuss with students where they might see fractions in real life, and
how comparing fractions can be important in everyday situations.
Day 11: Elaborate
Students will work independently to create their own comparison fraction word problems
and write them on index cards. The word problem will be placed around the room.
Students will walk around the room and solve each problem by drawing a picture and
writing their comparison sentence in their math journals.
What’s the teacher doing?
What are the students doing?

Teacher will guide students
through using manipulatives to
compare fractions in real-world
problem situations.

Use manipulatives to solve example
problems.

Teacher will monitor students as
they create and solve the own
word
problems
comparing
fractions.

Create their own real-life problem
situation involving comparing fractions.
Students will then solve each others
word problems.
Phase 5: Evaluate the Concept
Performance Assessment
Day 12:
Mathematics Grade 3 Unit 11 PA 01
Analyze the problem situations and tasks described
below. Organize and record your work for each task.
Using precise mathematical language, justify and explain
each solution process.
1) For each fraction model:
• Name the fractions represented by the model.
• Create a model that represents an equivalent fraction.
• Use symbols and words to explain the relationship
between the models.
a)
What fractional value does the shaded portion
represent?
26
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
b)
What fractional value does the non-shaded portion
represent?
c)
What fractional value does the black bar represent?
2) For each pair of fraction models:
• Name the fraction represented by the shaded part of
each model in the pair.
• Determine if the fractions represented by the shaded
parts of each model in the pair are equivalent.
Explain why or why not.
a)
b)
c)
3) For each problem situation:
• Create a model to represent the problem.
• Use the model, symbols, and words to explain and
justify your solution.
a) Janie and Hilary both baked the same size pan of
brownies to sell at a charity bake sale. Janie cut her pan
of brownies into 8 equal sized pieces and sold 5 pieces.
Hilary cut her pan of brownies into 6 equal sized pieces
and also sold 5 pieces. Which girl sold the greater
amount of their pan of brownies?
b) Gilbert and Arthur are reading the same book. Gilbert
has read of the book and Arthur has read of the
book. Which boy has more of the book left to read?
Standard(s): 3.1A , 3.1C , 3.1D , 3.1E , 3.1F , 3.1G
, 3.3F , 3.3G , 3.3H
27
Unit 11- Fractions- Equivalency and Comparisons
3rd Grade
What’s the teacher doing?
 Teacher will monitor students as
they complete the performance
assessment.
28

What are the students doing?
Students will complete the performance
assessment.