Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 61465
Decomposing Three-Fifths
Students are asked to use a visual fraction model to decompose three-fifths in two different ways.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, fraction, unit fraction, decompose, model, addition, visual fraction model
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DecomposingThreeFifths_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task may be implemented individually or in small groups.
1. The teacher provides the student with the Decomposing Three-Fifths worksheet and reads the following aloud to the student:
Use a visual fraction model to show one way to decompose
decomposed
. Make sure to label each fraction part in the model and write an equation to show how you
.
2. If the student successfully decomposes
using a visual fraction model and records an equation, the teacher then asks the student to decompose
in a different way
using a visual fraction model.
Note: It is important that one of the decompositions uses unit fractions only (e.g.,
and
=
=
, the teacher should ask the student to show a way to decompose
) as this is required by the standard. If the student only writes
=
using only unit fractions (fractions with a non-zero whole number as the
denominator and one as the numerator).
TASK RUBRIC
Getting Started
Misconception/Error
page 1 of 4 The student cannot create a visual fraction model to represent a decomposition of
.
Examples of Student Work at this Level
The student attempts to create a visual fraction model to represent a decomposition of
, but even with prompting is unable to accurately draw a decomposition.
The student attempts to split each fifth into smaller parts and even after prompting and examples, the student is unable to accurately decompose
.
Questions Eliciting Thinking
Can you make a model to show
? Where is one of the fifths?
Can you label each fifth?
How many fifths did you need to make
?
You can decompose the number four into three plus one, two plus two, or one plus one plus one plus one. How can you decompose the number three?
Can you break this rectangle into fifths? Can you shade
of the rectangle? What does the three in
represent?
Instructional Implications
Provide instruction for the student on how to model the decomposition of fractions in a variety of ways (e.g., using area models, linear models, set models, and equations).
Encourage the student to initially decompose non-unit fraction into unit fractions (e.g.,
using unit fractions (e.g.,
). Then model another way to decompose the given fraction
). Ask the student to label each of the unit fractions in the model and then record the decomposition with an equation.
Provide additional opportunities for the student to decompose non-unit fractions and mixed numbers in more than one way and record the decompositions with an
equation.
Use an area model or fraction tiles to illustrate the meaning of the numerator and denominator in a given fraction.
Moving Forward
Misconception/Error
The student is unable to decompose
in two different ways.
Examples of Student Work at this Level
The student correctly models one decomposition of
is unable to decompose
using a visual fraction model. He or she may struggle to label the parts or write an equation to match. The student
a second way using a visual fraction model.
Questions Eliciting Thinking
Can you decompose three in more than one way?
What other ways could you show
If you had a piece that represented
?
, how many more fifths would you need to make
How many one fifths do you need to make
?
?
Instructional Implications
Model another way to decompose the given fraction using unit fractions. If the student did not decompose
, model this decomposition. If so, show the student a second way to decompose
into the sum of three unit fractions e.g.,
using unit fractions (e.g.,
). Ask the student to
label each of the unit fractions in the model and then record the decomposition with an equation.
Provide additional opportunities for the student to decompose non-unit fractions and mixed numbers in more than one way and record the decompositions with an
equation.
Provide the student with different colored counters and ask the student to arrange the counters in different ways. Encourage the student to notice that no matter how
the counters are arranged, the total number of counters does not change. Next, provide the student with fifths fraction tiles and ask the student to arrange the tiles in
different ways while noticing that the total number of fifths does not change.
Almost There
Misconception/Error
The student struggles to label the fractional parts of the decomposition or write an equation to represent the decomposition.
page 2 of 4 Examples of Student Work at this Level
The student correctly creates two visual fraction models to show two different decompositions of
. However, he or she is unable to label the parts or write an equation
in one or both of the decompositions.
Questions Eliciting Thinking
What two fractions did you put together to make
? How can you show that with an equation?
What fraction does this piece represent (point to an unlabeled part of the model)?
Instructional Implications
Encourage the student to label each of the parts in the model and then demonstrate how to write an equation to represent the model. Note: In effort to not perpetuate
a misconception about the equal sign, it is important for the teacher to model this by writing
. For example,
first in the equation, as this is what the student hears when decomposing
. Provide additional opportunities for the student to decompose non-unit fractions and mixed numbers in more than one way and
record the decompositions with an equation.
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
Examples of Student Work at this Level
The student correctly creates two visual fraction models to show two different decompositions of
. The student also labels each part and writes an equation to model
the decompositions.
Questions Eliciting Thinking
Can you draw a visual fraction model to show
Can you find a fraction equivalent to
?
and decompose it using a model?
Instructional Implications
Remind the student that fractions with different denominators can be equivalent and challenge the student to decompose
using a unit fraction other than
.
Challenge the student to create visual fraction models that show the decomposition of a whole number into fractional parts. Ask the student to write an equation (or
several related equations) that correspond to the model. See the example shown in the image below.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Decomposing Three-Fifths worksheet
page 3 of 4 SOURCE AND ACCESS INFORMATION
Contributed by: MFAS FCRSTEM
Name of Author/Source: MFAS FCRSTEM
District/Organization of Contributor(s): Okaloosa
Is this Resource freely Available? Yes
Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.4.NF.2.3:
Description
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each
decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8
+ 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent
fraction, and/or by using properties of operations and the relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like
denominators, e.g., by using visual fraction models and equations to represent the problem.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
This standard represents an important step in the multi-grade progression for addition and subtraction of fractions.
Students extend their prior understanding of addition and subtraction to add and subtract fractions with like
denominators by thinking of adding or subtracting so many unit fractions.
page 4 of 4