Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 45673
Measuring our Pencils – Part One
Students are asked to measure their pencils to the nearest quarter inch.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, measure, length, inch, half-inch, quarter-inch
Resource Collection: MFAS Formative Assessments
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task should be implemented individually.
1. The teacher gives the student a ruler scaled in quarter inches and asks the student to measure the length of his or her pencil to the nearest quarter of an inch.
2. If the student correctly measures his or her pencil and the length actually rounds to a half-inch or whole number of inches, the teacher should present the student with a
prepared pencil to verify that the student can measure and round to the nearest quarter of an inch.
3. The teacher should observe the student as he or she measures. Student measurement data can be collected and used in making a line plot when implementing MFAS
task Measuring Our Pencils – Part Two.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not line up his or her pencil with the zero point on the ruler.
Examples of Student Work at this Level
The student lines up the end of his or her pencil at the edge of the ruler rather than at the zero point.
The student lines up the end of his or her pencil with the “one” on the ruler.
page 1 of 3 Questions Eliciting Thinking
Can you show me where you placed the ruler to begin your measurement? Why did you place it there?
Where does the ruler actually begin? Can you find “zero” on the ruler?
Instructional Implications
Have the student write “0” at the appropriate location on his or her ruler. Provide direct instruction on using a ruler to measure length. Guide the student to understand
that length is measured using linear units such as inches and centimeters and is given as the number of these units that span the length with no gaps or overlaps. Emphasize
the importance of beginning the measurement at the zero point on the measuring tool.
Give the student frequent opportunities to measure lengths of both line segments and actual objects to the nearest whole, half, and quarter unit. Provide feedback.
Moving Forward
Misconception/Error
The student is only able to measure lengths to the nearest whole inch.
Examples of Student Work at this Level
The student rounds the measurement to the nearest whole inch when the measure more accurately rounds to one-fourth, one-half, or three-fourths of an inch.
The student correctly measures the length of his or her pencil which when rounded to the nearest quarter inch, rounds to a whole inch. When asked to measure the
length of the prepared pencil, the student is unable to measure its length to the nearest half or quarter inch.
The student rounds to the nearest “n and one­fourth inch” (e.g., the student thinks that rounding to the nearest quarter of an inch means that the measure must be a
number such as 5
, 6
, 7
).
Questions Eliciting Thinking
Can you count by fourths? Start with one-fourth and give it a try. One-half is the same as how many fourths? One whole is the same as how many fourths?
Let’s look at the ruler. What number goes with this mark (point to the notch that corresponds to one­fourth)? What number goes with this mark (point to the notch that
corresponds to one-half)? What number goes with this mark (point to the notch that corresponds to three-fourths)? What number goes with this mark (point to the notch
that corresponds to one)?
Can you show me how you measured your pencil? Which mark on your ruler is the end of your pencil closest to? What number goes with that mark?
Instructional Implications
Give the student a number line scaled from zero to six. Model scaling and labeling the interval from zero to one by fourths. Ask the student to scale and label the remaining
intervals by fourths. Then, point to a location on the number line, and ask the student which notch is nearest this location. Finally, ask the student what number
corresponds to the notch. Repeat as needed.
Provide the student more opportunities to measure lengths of segments and objects to the nearest quarter of an inch using a ruler scaled to fourths. Provide feedback as
needed.
Almost There
Misconception/Error
The student is only able to measure to the nearest half inch.
Examples of Student Work at this Level
The student rounds the measurement to the nearest half inch when the measure more accurately rounds to
or
inch.
The student correctly measures the length of his or her pencil which when rounded to the nearest quarter inch, rounds to a half inch. When asked to measure the length
of the prepared pencil, the student is unable to measure its length to the nearest half.
The student rounds to the nearest “n and one­fourth inch” or “n and three­fourth inch” (e.g., the student thinks that rounding to the nearest quarter of an inch means
that the measure must be a number such as 5
, 6
, 7
… or 5
, 6
, 7
).
Questions Eliciting Thinking
Can you count by fourths? Start with one-fourth and give it a try. One-half is the same as how many fourths? One whole is the same as how many fourths?
Let’s look at the ruler. What number goes with this mark (point to the notch that corresponds to one­fourth)? What number goes with this mark (point to the notch that
corresponds to one-half)? What number goes with this mark (point to the notch that corresponds to three-fourths)? What number goes with this mark (point to the notch
that corresponds to one)?
Can you show me how you measured your pencil? Which mark on your ruler is the end of your pencil closest to? What number goes with that mark?
Instructional Implications
page 2 of 3 Give the student a number line scaled from zero to six by halves. Model scaling and labeling the interval from zero to one by fourths emphasizing that two-fourths is the
same as one-half. Ask the student to scale and label the remaining intervals by fourths. Then, point to a location on the number line, and ask the student which notch is
nearest this location. Finally, ask the student what number corresponds to the notch. Repeat as needed.
Provide the student more opportunities to measure lengths of segments and objects to the nearest quarter of an inch using a ruler scaled to fourths. Provide feedback as
needed.
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 measures the length of his or her pencil and rounds to the nearest quarter inch.
The student correctly measures the length of his or her pencil which rounds to a whole or half inch. When asked to measure the length of the prepared pencil, the student
correctly measures its length and rounds to the nearest quarter inch.
Questions Eliciting Thinking
Suppose I make a notch midway between zero and one-fourth. Do you know what number corresponds to this notch?
Do you know what the notches between whole numbers on a centimeter ruler represent? Can you count the number of intervals there are between zero and one on this
ruler (hand the student a centimeter ruler)? Can you measure your pencil in centimeters to the nearest tenth?
Instructional Implications
Give the student a conventional ruler scaled to eighths or sixteenths. Ask the student to locate the notches that correspond to one-fourth, one-half, and three-fourths.
Then, ask the student to measure the lengths of objects to the nearest fourth. Introduce the student to eighths and ask the student to measure lengths of objects to
the nearest eighth of an inch.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
A ruler scaled to quarter inches.
A pencil whose length measures
inch more than a whole number of inches (e.g., 7
inch).
A centimeter ruler (for follow up with Level 4 students).
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.MD.2.4:
Description
Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the
data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or
quarters.
page 3 of 3