Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 44677
Generating Equivalent Fractions
Students are given a familiar fraction and asked to generate an equivalent fraction justifying their reasoning.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, fraction, number line, distance, equivalent, model
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_GeneratingEquivalentFractions_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with a small group, or with the whole class.
1. The teacher should provide the student with the Generating Equivalent Fractions worksheet or a dry erase board and marker.
2. The teacher should say, “Look at the fraction . Can you think of another fraction that is equivalent to
?"
3. Next, the teacher should ask, “Can you use a model to show me why those two fractions are equivalent? You can use any of these materials or use the space on this
worksheet to show how you know the two fractions are equivalent.”
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to generate an equivalent fraction for
.
Examples of Student Work at this Level
The student may understand the meaning of
however, the student guesses a fraction that is equivalent or does not know how to generate an equivalent fraction.
Questions Eliciting Thinking
page 1 of 3 What do you know about the fraction
? What does the four in the denominator mean? What does the one in the numerator mean?
Can you think of another way to represent
Can you draw a picture to show
? Can you use these fraction bars to show me?
? Can you draw another picture that shows eighths? How many eighths would need to be shaded in to show
?
Instructional Implications
Use an area model to show that
is equivalent to
point as
. Also use a number line model to show that
is located at the same
.
Provide clear instruction to the student on the meaning of the word equivalent, telling the student that equivalent means, “equal, or the same value as.” Next, using the
available manipulatives, show the student how different fractions can represent the same amount beginning with those fractions that are equivalent to
.
Moving Forward
Misconception/Error
The student needs much prompting to find a fraction equivalent to
.
Examples of Student Work at this Level
The student initially does not know an equivalent fraction. However, after working with the fraction bars or another manipulative, he or she is able to determine that
is equivalent to
.
Questions Eliciting Thinking
I see that you are showing that both of these fraction bars are the same length. What does that mean?
In both pictures,
is the same as
. What does that mean? Can you say more about how you know they are equal?
What does the numerator mean? The denominator?
Instructional Implications
Encourage the student to use what he or she has learned from this task to generate other equivalent fractions. Consider beginning with
.
As the student finds other pairs of equivalent fractions, encourage him or her to justify both orally and in writing why the pairs are equivalent. Have the student begin by
formulating an oral justification. Then, have the student transition to a written justification.
Almost There
Misconception/Error
The student struggles to use a manipulative or model to explain why the fraction he or she generated is equivalent to
.
Examples of Student Work at this Level
The student states that
(or another equivalent fraction) is equivalent to
and begins to use a model or manipulative to prove
the fractions are equivalent. However, the student’s response is lacking clarity or is not fully accurate.
Questions Eliciting Thinking
Can you say more about how you know they are equal?
Can you use the number line to explain how these two fractions are equivalent?
When both of your pictures have the same amount shaded, what does that say about the two fractions?
I noticed that both two and eight are greater than one and four, so how can both fractions be equal?
Instructional Implications
Encourage the student to use representations that are clear to him or her. The teacher may guide the student to develop an area model first. After the student becomes
proficient using area models to represent equivalent fractions, the teacher should introduce representing equivalent fractions on the number line.
As the student finds other pairs of equivalent fractions, encourage him or her to justify both orally and in writing why the pairs are equivalent. Have the student begin by
formulating an oral justification. Then, have the student transition to a written justification.
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 generates a fraction equivalent to
and is able to use a model or manipulative to explain how he or she knows that the two fractions are equivalent.
page 2 of 3 Questions Eliciting Thinking
Think about the fraction
. Can you list some other fractions that are equivalent to it?
What do you notice about the fractions
and
? Do you see a relationship between the numerators? Do you see a relationship
between the denominators? Do you think that will always work when finding equivalent fractions?
How much larger is the numerator than the denominator in the fraction
? What about the numerator and denominator in
?
Do you notice a relationship?
Instructional Implications
Provide additional examples of fractions that are equivalent to
, and encourage the student to look for patterns in the relationship between the numerators and the
denominators. Encourage the student to notice that the numerators and denominators change proportionally when they are equivalent. Once the student sees this
relationship, encourage him or her to explain it.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Generating Equivalent Fractions worksheet or dry erase board and marker
A variety of fraction manipulatives including fraction bars, fraction circles, and number lines.
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.3.NF.1.3:
Description
Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.
a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line.
b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are
equivalent, e.g., by using a visual fraction model.
c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples:
Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line
diagram.
d. Compare two fractions with the same numerator or the same denominator by reasoning about their size.
Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of
comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
page 3 of 3