Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 44672
Five-Eighths on the Number Line
Students are asked to locate five-eighths on a number line that has been anchored by zero and one, but that has not yet been scaled.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, number line, fraction, interval
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_FiveEighthsOnTheNumberLine_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 Five-Eighths on the Number Line worksheet and reads the prompt to the student to ensure understanding.
2. If the student correctly scales the number line and locates
, the teacher should point to the interval from zero to
and ask the student, “What is the length of this
interval (or this part of the number line)?”
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 attempts to extend and scale the number line beyond one but is unable to locate
The student does not scale the number line and places
.
without using any mathematical rationale.
Questions Eliciting Thinking
Let’s focus on the part of the number line between zero and one. Can you put a notch on the number line that divides this interval into two equal parts? Do you know
page 1 of 3 what fraction goes with this notch?
Now let’s focus on the part of the number line between zero and half . Can you put a notch on the number line that divides this interval into two equal parts? Do you know
what fraction goes with this notch?
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 begins making notches working from left to right without regard to equal spacing. After making five notches, the student labels the last notch as
.
The student begins making notches working from left to right without considering how to divide the interval into eighths. After making five notches, the student labels the
last notch as
.
Questions Eliciting Thinking
If you divided the interval from zero to one into halves, how many parts would you have? What if you divided the interval into fourths? So, how many parts would result if
you divide the interval into eighths?
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?
How did you locate
on your number line? Did you count notches or intervals?
Instructional Implications
Model how to divide the interval from zero to one into halves, fourths, and then eighths. Emphasize the importance of scaling the number line before locating the fraction.
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
segments that are
inch,
inch, and
inch,
inch, and
inch on the ruler. Have the student use the ruler to measure
inch long.
Almost There
Misconception/Error
The student correctly locates
on the number line but does not understand that the resulting interval has a length of
.
Examples of Student Work at this Level
The student divides the interval from zero to one into eight equal parts and correctly locates
interval from zero to
. The student is confused by the question concerning the length of the
.
Questions Eliciting Thinking
If this number line were a ruler and the interval from zero to one is one inch long, how long would the interval from zero to
be?
Instructional Implications
Relate the number line to a ruler. Give the student a number line scaled from zero to one in eighths and ask the student to measure a variety of fractional lengths
Got It
Misconception/Error
The student provides complete and correct responses to all components of the task.
page 2 of 3 Examples of Student Work at this Level
The student divides the interval from zero to one into eight equal parts and correctly locates
. In addition, the student recognizes that the interval from zero to
is
of a unit long.
Questions Eliciting Thinking
What fraction goes with this location (point to
Can you think of a fraction that is equivalent to
,
, and
? 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 a coordinate of
,
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 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:
Five-Eighths 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