Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 44675
Three-Fourths on the Number Line
Students are asked to scale a number line from zero to one so that they can find the location of three-fourths.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, number line, scale, fraction, interval
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ThreeFourthsOnTheNumberLine_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 provides the student with the attached Three-Fourths on the Number Line worksheet and reads the prompt to the student to ensure understanding.
2. The teacher should ask the student to explain how he or she located
.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand a fraction as a number that can be located on the number line.
Examples of Student Work at this Level
The student scales the number line with whole numbers and locates
at three or at four.
Questions Eliciting Thinking
Is
more than one or less than one? Between what two whole numbers should
Do you think
be located?
is closer to zero or closer to one?
page 1 of 3 Instructional Implications
Provide direct instruction on representing fractions on a number line. Begin with unit fractions (i.e., fractions of the form
interval from zero to one into b equal parts. Then, emphasize that the fraction
from zero to
is
). Show the student how to partition the
is located at the right endpoint of the first partition because the length of the interval
units long. Give the student additional opportunities to scale the interval from zero to one on a number line in order to locate given unit fractions.
When the student is ready, introduce non-unit fractions.
Moving Forward
Misconception/Error
The student attempts to scale the number line and tries to locate
but makes significant errors.
Examples of Student Work at this Level
The student divides the interval from zero to one into unequal lengths.
The student divides the interval from zero to one into a number of parts other than four (or a multiple of four) and cannot locate
correctly.
Questions Eliciting Thinking
If your number line were a ruler, what would have to be true of the parts you just drew? Do you think you could divide the interval from zero to one into equal parts?
If you divided the interval from zero to one into halves, how many parts would result? What if you divided the interval into fourths? How many parts did you divide the
interval into? Is that really fourths?
Instructional Implications
Relate representing fractions on a number line to measuring with a ruler scaled only to fourths. Guide the student to observe that unit intervals on the ruler are partitioned
into equal lengths. Assist the student in naming fractions that correspond to
inch,
inch, and
,
, and
on the ruler. Have the student use the ruler to measure segments that are
inch long.
Give the student more opportunities to scale and locate fractions on the number line. Provide assistance and feedback, as needed.
Almost There
Misconception/Error
The student’s solution contains minor errors that are easily corrected.
Examples of Student Work at this Level
The student labels the arrowheads on the number line with zero and one rather than making notches to mark the locations of these numbers.
The student struggles to divide the interval into equal parts.
Questions Eliciting Thinking
Where is zero located on your number line? Did you make a notch for zero? What about one? Where is it located? Did you make a notch for one?
How did you divide the interval from zero to one into four equal parts? Did you start by dividing it into two equal parts? How might that help you?
Instructional Implications
Aid the student in gaining greater precision in creating number lines. Guide the student to understand that locations of any number on a number line are associated with
specific locations shown by the notches. Assist the student in dividing intervals in fourths or eighths by first dividing the interval into halves and then dividing each interval in
halves again until it yields the desired number of intervals.
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 locates zero and one and then divides the interval from zero to one into four equal parts and correctly locates
explain how he or she located
. In addition, the student is able to clearly
.
Questions Eliciting Thinking
What fraction goes with this location (point to
and
Can you think of a fraction that is equivalent to
?
on the number line)?
Instructional Implications
Introduce the student to the vocabulary of the number line: scale, coordinates (the number associated with a particular location on the number line), points (used to mark
a particular location on the number line), and point names (generally upper case letters). Give the student the coordinates of points, such as point A has coordinate
,
and ask the student to graph point A (i.e., put a point on the number line marking the location of point A along with the letter A to show the name of the graphed
page 2 of 3 point). Also ask the student to identify the coordinates of graphed points.
Have the student graph mixed numbers on a number line.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Three-Fourths on the Number Line worksheet
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
Description
Understand a fraction as a number on the number line; represent fractions on a number line diagram.
a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning
it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the
number 1/b on the number line.
b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the
resulting interval has size a/b and that its endpoint locates the number a/b on the number line.
Remarks/Examples:
Example of Opportunities for In-Depth Focus
MAFS.3.NF.1.2:
Developing an understanding of fractions as numbers is essential for future work with the number system. It is
critical that students at this grade are able to place fractions on a number line diagram and understand them as a
related component of their ever- expanding number system.
Fluency Expectations or Examples of Culminating Standards
Students fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of
operations, and/or the relationship between addition and subtraction. 3.NBT.1.2 a relatively small and incremental
expectation.
page 3 of 3