Showing Equivalent Fractions with Components of SIOP
Name: Danielle Leavitt
Content Area(s): Mathematics
Estimated Time: 1 hr 15 min/or 2 Days
Number of Students: 30
Grade Level(s): 4th
Stage 1- Desired Results
Established Goals: STATE CORE
Standard 1: Students will acquire number sense and perform operations with whole numbers, simple fractions,
and decimals.
Objective 2: Analyze relationships among whole numbers, commonly used fractions, and decimals to
hundredths.
Sub-Objective A: Generate equivalent fractions and simplify fractions using models, pictures, and symbols.
Content Objectives: SIOP-(Write on White Board)
Students will better understand how to show equal (equivalent) fractions by engaging in a hands-on
activity with Pattern Blocks to construct shapes that show equal fractions. Students will be able to use
fraction strips, circle fractions, and Cubes to make equal (equivalent) fractions.
Language Objectives: SIOP-( Write on White Board)
Students will understand how to explain equal (equivalent) fractions through listening, speaking, and
writing equivalent fractional amounts.
Understanding
Students will recognize equivalent
representations of same fractional amount, use
models and equivalent forms to judge the size
of fractions, and recognize and generate
equivalent forms of commonly used fractions.
Objectives
Student will be able to:
1. Identify equal/simple
representations of fractions
using fractional amounts.
(Standard 1)
2. Analyze relationships and
model equal fractions in various
forms.
(Objective 2)
3. Interpret, produce and
simplify missing equivalent
fractions using manipulatives.
(Sub-Objective A)
Essential Questions
What are Equivalent Fractions?
What is the relationship between the
numerator and the denominator of a fraction?
What are different ways to show equivalent
fractions?
Stage 2-Assessment Evidence
Contextual Factors
3-Students need extra time
and scaffolding to complete
tasks
3-Students have a hard time
keeping on task-due to
distractions.
1-Student has physical
limitations, but is able to
process information, but
extra time is needed.
4-Students show gifted
qualities
Ability Levels: Class has a
closely related range of
academic skills/abilities
from low, moderate, and
high.
Assessments
Students will:
1. Identify equal representations of
simple fractions using Pattern
Blocks as fractional amounts to
construct shapes to show equal
fractions.
2. Analyze relationships and model
equal fractions using Counting
Cubes to show equal representations
three different ways (pictures,
simplified fractions, and equivalent
fractions).
3.Interpret, produce and simplify
missing equivalent fractions using
fractions strips and rainbow
Fraction Circles.
Stage 3-Learning Plan
Procedures
Building Background:
Experiences: Relate students’ understanding of
equal fractions to sharing a sliced apple, orange,
sandwich, pizza, any object etc. with a friend(s)
family member.
Time
Supplementary
Materials
Accommodations/
Differentiation/ SIOP
Fun Attitude
and Loud
Voice!
Students will reinforce their
knowledge and understanding
of equal fractions through past
learning experiences and
review of key vocabulary.
.
Past Learning: Students previously learned how
to find a fraction of a set, compare and find
equivalent shares. Now it is time to deepen their
understanding of how to apply and show their
knowledge of equal fractions through using
manipulatives that represent fractional shares.
Students will also learn how to use a Fraction
Strip to visually see a more concrete way of how
equivalent fractions are the same.
Key Vocabulary: Students will continue their
knowledge of understanding the words
equivalent, denominator, and numerator
through the use of hearing, speaking, and writing
these words.
What are Equivalent Fractions?
I will write the word Equivalent on the board and
ask the students what word it similar to it. ASK:
What does this word mean to generate various
ideas of the word equal and write/ show equal
numbers.
What is the relationship between the numerator
and the denominator of a fraction?
I will review their understanding of the parts of a
fraction-the numerator and denominators
meaning by using the visual previously taught.
1. Students will Identify equal representations of
simple fractions using Pattern Blocks as
fractional amounts to construct shapes to show
equal fractions. Using the Pattern Block
Worksheet students will first give the fraction
name for each kind of block used to cover the
outlined shape. (one-half or 1/2; one-fourth or
1/4) Meaningful Activity-Listening & Speaking
Reinforce how to say each fraction by having
students say the name of each after me and
writing the fraction and block down on paper.
White
Board/Marker
Paper Visuals
of Fractional
Charts
Previously used visuals will
help students retain and
reiterate their knowledge of
key vocabulary and add to the
understanding of those
students who are becoming
more familiar with key terms.
Pattern
Blocks
Students will work in pairs to
complete tasks A-D, but will
use their own Pattern Blocks
and Patter Block Worksheet.
Students will gain from
partner’s insight and have peer
support throughout activity
10
Min.
20
Min.
Pattern Block
Worksheet
Using visuals, such as Pattern
Blocks will support students in
their goal of understanding
how to identify equal
representations of simple
fractions.
A. Students will show how to cover the shapes
with all one type of Pattern Block.
B. Meaningful Activity-Writing.
How much of the shape is covered by: write
fractional answer by each.
One Yellow block
One Red block
One Blue block
One Green block
C. What are different ways to show equivalent
fractions? What are four different ways to cover onehalf of the shape?
Write students responses on board. Have student
volunteers write fractional pairs on board and relate
them to being "equal" Possible answers 2/4, 3/6, and
6/12. Use transparency to show meaning. Make sure
students are using fractions as they describe the
answers.
D. In outlined shape-students will find different ways
to cover the shape; each time using blocks of only one
color. Writing the fractions that describe how different
kinds of blocks covered one-fourth (1/4) of the shape.
Encourage creativity & Exploration
(Check for understanding by observing performance
of task and give Feedback)
2. Creating Equivalent Fractions-Analyze
relationships and model equal fractions using
Counting Cubes to show equal representations three
different ways (pictures, simplified fractions, and
equivalent fractions).
Students will be shown Count Cubes that will
represent a different ways to show the word "equal".
Students will be asked to show the equivalent fraction
using Counting Cubes to help them visually see how
to shade in "half" of the blocks on worksheet pg. 70.
(DAY TWO or EXTENSION)
3. Finding Equivalent Fractions-Interpret, produce
and simplify missing equivalent fractions using
fractions strips and rainbow
Fraction Circles.
Students will write the missing number to make
equivalent fractions using the Fraction Strips and
Fraction Circles for pg. 69.
Teacher to demonstrate both visuals and how to use
them to find the other equivalent fraction.
(Spot check verbal understanding and performance)
Counting
Cubes
15
Min.
Student
Workbook
Pg. 70
Fraction
Circles
15
Min.
Student
Workbook
Pg. 69
(student
workbook
page includes
Fraction
Strips)
Transparency
of Fraction
Strips
Students will continue to work
in pairs to accomplish task of
modeling equal
representations of three
different ways to understand
equal fractional shares.
Students will use Counting
Cubes for hands-on experience
in creating and analyzing a
pictorial presentation of
simple fractions and their
equivalents.
Students will work
individually and as pairs to
complete worksheet pg 69.
Students will complete first
three on their own, next five in
a pair (just to check answers),
and the rest of the six
equivalent fraction on their
own to allow me to check for
their personal understanding.
Review/Assessment:
Review of Key Vocabulary: Use the words
Equivalent, Denominator, and Numerator throughout
lesson for students understanding and listening.
Ask Students, to define each term and have students
vote thumbs up for yes-or thumbs down for no.
Comprehensive Review of Key Content Concepts:
Students will be asked why we should learn how to
work with and solve problems using equivalent
fractions?
Ticket Out: What have they learned from this lesson
and how can they connect it to their personal lives?
Discuss/share with shoulder partner and then turn in.
Feedback:
Teacher will check for understanding and provide
feedback throughout each section of the lesson, while
students work, and especially through Pattern Block
Fraction activity as to make sure students have solid
understanding of concept before we move on.
Assessment of Student Comprehension and
Learning:
Students worksheets pages 69-70 are my formal
assessment of their understanding of key content
concepts.
During feedback and working the crowd I will review
and assess students work and understanding by:
Asking questions during Pattern Block
Activity and spot checking for correct use
of key vocabulary words and
mathematical language. (Individual/group
response-Verbal Summative Assessment)
Teacher will engage herself in listening to
student conversations during partner work
and provide any scaffolding assistance.
(Individual/group response-Verbal
Summative Assessment)
Teacher will review students understanding of
content objectives through asking questions
and reviewing pages 69-70 of students work.
(Formative Assessment-Correct with Growing
With Math Teacher Handbook)
5 Min.
5 Min.
Two different types of visuals
will help students internalize
and familiarize with both or
one way of finding equivalent
fractions.
QUICK WORKERS
For the four gifted students (or
others) who complete work
quicker, have them prepare a
real-life problem where using
equivalent fractions would be
applicable. Share amongst
themselves while
others/partners/groups finish.
Plans for involving parents or families:
Students will discuss with parent(s) what equivalent fractions are and describe to them what the denominator
and numerator of a fraction represent. Students will also be able to show parent(s) an equivalent fraction by
explaining their Pattern Block Fraction worksheet that they take home.
Reflection:
Whew! This lesson had a lot going on, but overall I felt that it went well except for a few weaknesses.
Weaknesses:
One of which was the fact that THERE WAS almost too much to cover in such a short time. I could
have taken 2 solid hours or an extra day to effectively teach this concept and have students really
discover equal fractions within the activities. Because I had to rush some students, I felt that they didn't
get all of what was so quickly taught. I added to my lesson plan (depending on the timing of lesson and
if there are other events going on the week) to extend this lesson to two days or closer to an hour and
thirty minutes-with interventions to follow the next day.
Another weakness that I failed to address was having higher-order thinking games, problems, brain
teasers, or anything of the sort for those students who completed their work ahead of schedule. I know
to have additional experiences for them, but putting this lesson together I completely spaced it. So I
added to the lesson plan to have these students create a question or problem that related to real-life
application using equivalent fractions and share with their partner or group. (I could also share the
problems with the class for a "brain booster" at the beginning of the next math lesson for retention and
application).
Strengths:
I know that a strong area of the lesson plan was the various experiences with the manipulatives
involving equivalent fractions, such as: counting cubes, pattern blocks, fraction strips, and fraction
circles. Even though there was a lot of activity, there were many opportunities for students to gain an
understanding of equivalent fractions.
Another strong component of this lesson plan was the implementation of Sheltered Instruction (SIOP).
I don't have any ESL students in my classroom, but SIOP is great for mainstream students as well. The
students were not only aware of the content objective, but also the language objective, which I believe
is essential when dealing with mathematical terms. Math has a language of its own and if students are
not aware of the proper pronunciation and meaning of these words through personal experiences of
listening, speaking, and writing, then they will not be able to deepen their understanding of a certain
concept.
I felt that most of my students were with it and had a better understanding of the concept. During the
summative, formative, verbal-individual/group activities and assessments. Students were giving correct
answers and were engaged in discovery of how equality is represented in fractions.
Now that I have a better understanding of how to better this lesson plan I would like to re-teach it and
see if the little tweaks will make a difference and hopefully slow the activities down enough for
students to gain a solid understanding of equivalent fractions.