Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 55154
Multiples of Six
Students determine if a given number is a multiple of six, both with and without context.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, multiple, skip count, factors
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_MultiplesOfSix_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually, in small groups, or in a whole-group setting. If the task is given in a whole-group setting, the teacher should ask each
student to explain his or her thinking and strategy.
1. The teacher provides the student with the Multiples of Six worksheet and reads the first question to the student.
Is 46 a multiple of six? Why or why not?
2. The teacher then asks the student to consider the next scenario.
If I have some packs of cookies and there are six in each pack. Could there be 53 in all? Why or why not?
TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to correctly determine if a number is a multiple of six.
Examples of Student Work at this Level
The student does not demonstrate an understanding of multiples. For example, the student says that 46 is a multiple of six because it has a six in the ones place or that
you could not have 53 cookies because if there are six in each pack, the total would have to be 46, 56, or 66.
Questions Eliciting Thinking
page 1 of 3 Can you count by sixes? What about threes?
How many cookies are in each pack? How many would be in two packs? What about ten packs?
Instructional Implications
Explain the concept of a multiple and use skip counting to illustrate examples of multiples of numbers. Use a hundred chart to further find examples of multiples. Have the
student circle the multiples of a given number on a hundred chart. As the student becomes more familiar with multiples of given numbers, present the student with
questions about multiples in problems both with and without context.
Provide the student with the opportunity to use objects such as color tiles to build arrays with a given total. This will allow the student to explore the relationship
between a multiple and its factor pairs.
Moving Forward
Misconception/Error
The student uses an inefficient strategy to determine if each given number is a multiple of six.
Examples of Student Work at this Level
The student correctly determines that both 46 and 53 are not multiples of six by counting by ones and circling or highlighting every sixth number.
Questions Eliciting Thinking
Can you count by sixes? What about threes?
Do you think counting by sixes instead of ones would be more efficient? What could you do to count by sixes?
Do you know what five sixes makes (or what 5 x 6 is)? How can that help you?
Instructional Implications
Model the use of skip counting to find and list multiples of a number. Encourage the student to use known multiplication facts to determine if one number is a multiple of
another. Allow the student to observe efficient strategies used by other students.
Almost There
Misconception/Error
The student determines that neither number is a multiple of six but provides an incomplete or unclear justification.
Examples of Student Work at this Level
The student shows work that suggests an understanding of multiples. However, the student:
Provides an explanation that contains incorrect or unclear statements.
Provides an incomplete justification.
Questions Eliciting Thinking
You said that six and eight cannot be multiplied. Is that really true?
Can you explain to me how you determined whether or not 46 (or 53) is a multiple of six? What does this work on your paper mean?
Instructional Implications
Assist the student in correcting any errors in his or her explanation. Model a complete but concise justification for why 46 (or 53) is not a multiple of six. Expose the student
to the written work and explanations of Got It students.
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 uses an understanding of multiplication, skip counting, or multiples to determine if 46 and 53 are multiples of six. For example, the student says that 6 x 7 = 42
and if I add six more to that it will be 48, so 46 cannot be a multiple of six.
page 2 of 3 Questions Eliciting Thinking
What do multiples of six have in common?
Could an odd number be a multiple of six? Why or why not?
Instructional Implications
Encourage the student to begin making generalizations about multiples of given numbers including those that will always be even or those that will be even and odd.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Multiples of Six 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
MAFS.4.OA.2.4:
Description
Investigate factors and multiples.
a. Find all factor pairs for a whole number in the range 1–100.
b. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the
range 1–100 is a multiple of a given one­digit number. c. Determine whether a given whole number in the range 1–100 is prime or composite.
page 3 of 3