Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 58671
Are the Fractions Equivalent
Students partition squares to model two fractions and then determine if the fractions are equivalent.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, fraction, equivalent, area model, visual fraction model
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_AreTheFractionsEquivalent_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually or in small groups.
1. The teacher provides the student with the Are the Fractions Equivalent worksheet and a ruler.
2. The teacher says, “I want you to partition the two squares to show the fractions and
. You may use the ruler if you find it helpful.” Note: If the student would
like to use a ruler to partition the squares, the ruler is provided. However, it is not necessary for the student to use the ruler.
3. After the student partitions the two squares, the teacher asks, “Are the two fractions equivalent? Why or why not?”
4. If the student responds by saying that the two fractions are equivalent, the teacher asks, “How can these two models show the same amount even if there are different
numbers in the fractions?”
Note: If the student determines the fractions are equivalent without partitioning the squares, encourage the student to justify his or her reasoning by partitioning the
squares.
TASK RUBRIC
Getting Started
Misconception/Error
The student makes significant mistakes when partitioning the two squares and does not correct despite prompting.
page 1 of 4 Examples of Student Work at this Level
The student initially draws circles in one square and shades five of the six circles. With teacher modeling using the fraction
, the student is able to draw lines to partition
the square. However, the parts are not equal and the student is unable to correct despite prompting.
The student draws unequal parts in both squares. When asked if the parts of the square should be the same size (equal parts), the student says no.
Questions Eliciting Thinking
Is it important that each of the parts in the square be the same size? Why or why not?
How could I draw lines to make six equal parts in each square? What would happen if I draw a line to partition each of the six parts into two parts? How many total parts
are there now?
What does the fraction
mean? What does the five represent? What about the six?
Instructional Implications
Consider using the MFAS Task Different Fourths (2.G.1.3).
Model partitioning a figure into six equal parts. Then model partitioning a figure into 12 equal parts using the same lines drawn to make six equal parts (see image below).
Provide direct instruction on creating same size parts when partitioning shapes to represent fractions.
Provide the student with fraction bars. Provide the student with a fraction such as
the fraction bars to find at least two other fractions that are equivalent to
and have the student use the fraction bars to show
. Then have the student use
.
Moving Forward
Misconception/Error
The student says that the two fractions are not equivalent.
Examples of Student Work at this Level
The student correctly partitions each of the squares but the student is unable to see that
is equivalent to
.
Questions Eliciting Thinking
What do you know about the fraction
?
What does the word equivalent mean?
Can you draw a picture to show
? Can you draw another picture to shows twelfths? How many twelfths would need to be shaded in to show
?
How could I draw lines to make six equal parts in each square? What would happen if I draw a line to partition each of the six parts into two parts? How many total parts
are there now?
Instructional Implications
Use a number line model to show that
is located at the same point as
.
Provide direct instruction to the student on the meaning of the word equivalent, telling the student that equivalent means “equal or the same value as.”
Consider using the MFAS Tasks Generating Equivalent Fractions or Equivalent Fractions (3.NF.1.3).
Almost There
Misconception/Error
The student is unable to describe the relationship between the numerators and denominators of equivalent fractions.
Examples of Student Work at this Level
The student correctly partitions the two squares and says that
is equivalent to
but the student is unable to explain that the size of one equal in the square
page 2 of 4 showing
is twice as large as one part in the square showing
. He or she cannot say that it takes two equal parts in
to equal one part in
even though the
fractions are equivalent.
Questions Eliciting Thinking
Can you draw a picture to show
? Can you draw another picture to show twelfths? How many twelfths would need to be shaded to show
?
What do you know about the denominators in the two numbers? How does that relate to the size of the equal parts in each of the squares?
Instructional Implications
Partition and shade two squares to model the fractions
the student generalize this to the fractions
and
and
. Show the student that one part in the model of
is twice as large as a part in the model of
. Help
because 2 x 5 = 10 (numerator) and 2 x 6 = 12 (denominator).
Encourage the student to share his or her thinking with another student to provide more practice explaining how to show equivalence on a number line or with an area
model.
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 partitions the two squares to model
and
and says that both fractions are equivalent because they both show the same amount. When asked
to explain how the two fractions can be the same amount even though the numbers are different, the student explains that if you multiply 2 x 5 you get 10 and 2 x 6
equals 12. So
equals
, and it takes two parts in
to equal one part in
.
Questions Eliciting Thinking
Are the fractions
and
equivalent? Why or why not?
Instructional Implications
Provide additional pairs of fractions that are equivalent and encourage the student to look for patterns in the relationship between the numerators and the denominators
(e.g.,
and
;
and
).
Consider using the MFAS Task Equivalent Fractions On a Number Line (4.NF.1.1).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Are the Fractions Equivalent worksheet
ruler
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
page 3 of 4 Name
MAFS.4.NF.1.1:
Description
Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to
how the number and size of the parts differ even though the two fractions themselves are the same size. Use this
principle to recognize and generate equivalent fractions.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
Extending fraction equivalence to the general case is necessary to extend arithmetic from whole numbers to
fractions and decimals.
page 4 of 4