Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 42699
Adding Odd Numbers
Students are asked to consider what type of number results when adding two odd numbers and when adding three odd numbers.
Subject(s): Mathematics
Grade Level(s): 3
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, odd, even, addition, sum, generalization
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_AddingOddNumbers_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task should be implemented individually or with a small group.
1. The teacher shows the student the equations on the Adding Odd Numbers worksheet and reads the prompt aloud.
2. The teacher should prompt the student to think about the general notion of what happens when adding two odd numbers and then adding three odd numbers.
3. The teacher should ask:
Are the addends in the first equation even or odd? What about the sum, is it even or odd?
Are the addends in the second equation even or odd? What about the sum, is it even or odd?
When you add two odd numbers, it results in an even sum, and when you add three odd numbers it results in an odd sum. Why does that happen? Can you list
other examples? Will it always work?
TASK RUBRIC
Getting Started
Misconception/Error
The student cannot justify why the sum of two odd numbers is an even number.
Examples of Student Work at this Level
The student knows that the addends in each of the given equations are odd, and that the sums are even and odd respectively. However, the student is unable to explain
page 1 of 3 why the sum of two odd numbers is an even number.
Questions Eliciting Thinking
What happens when we add two even numbers? Why is that?
What happens when we add two odd numbers? Why is that?
Can you tell me what it means for a number to be odd? Can you show me an example with these cubes?
Instructional Implications
Encourage the student to view even numbers as those numbers that can be divided into two equal amounts. Then, allow the student to use counters to model and
investigate what happens when two even numbers are added.
Encourage the student to view odd numbers as those numbers that can be divided into two equal amounts plus one. Then, allow the student to use counters to model
and investigate what happens when two odd numbers are added. Encourage the student to use what he or she knows about adding two even numbers to determine
what happens when two odd numbers are added.
Moving Forward
Misconception/Error
The student cannot determine why the sum of three odd numbers is an odd number.
Examples of Student Work at this Level
The student knows that the addends in each of the given equations are odd, and that the sums are even and odd respectively. The student also can explain why the sum
of two odd numbers is an even number. However, the student is unable to explain why the sum of three odd numbers is an odd number.
Questions Eliciting Thinking
Can you show me three odd numbers with these cubes? What happens when we put those three numbers together? What happens with the leftovers?
Will that always work? Can you show me more examples?
Instructional Implications
Encourage the student to view odd numbers as those numbers that can be divided into two equal amounts plus one (or one more than an even number). Then, allow the
student to use counters to model and investigate what happens when two odd numbers are added. Encourage the student to use what he or she knows about adding
two even numbers to determine what happens when two odd numbers are added.
Allow the student to generate many examples of adding two odd numbers and three odd numbers, and begin to express the regularity seen in these examples.
Have the student use counters to investigate what happens when an even number and an odd number are added. Then, encourage the student to use reasoning to
determine the result of adding three odd numbers. For example, when adding three odd numbers, the sum of the first two odd numbers will be even (since the sum of
two odds is always odd). Then, when adding this even number to the third odd number, the sum will be odd (since the sum of an even and an odd is always odd).
Consider implementing MFAS task Adding Odds and Evens (3.OA.4.9).
Almost There
Misconception/Error
The student is reluctant to generalize the two statements about adding odd numbers.
Examples of Student Work at this Level
The student determines that the sum of two odd numbers is an even number, and that the sum of three odd numbers is an odd number. The student can also generate
some additional examples. However, he or she is not sure if these statements are always true.
Questions Eliciting Thinking
Can you show me three odd numbers with these cubes? What happens when we put those three numbers together? What happens with the leftovers?
Do you know what the sum of two even numbers is? How about the sum of an even number and an odd number? Will that always work? Can you show me more
examples?
Instructional Implications
Guide the student to generalize what happens in each of the three basic cases: (1) adding two even numbers, (2) adding two odd numbers, and (3) adding an even and
an odd number. Consider implementing MFAS task Adding Odds and Evens (3.OA.4.9).
Encourage the student to use reasoning to determine the result of adding three odd numbers. For example, when adding three odd numbers, the sum of the first two odd
page 2 of 3 numbers will be even (since the sum of two odds is always even). Then, when adding this even number to the third odd number, the sum will be odd (since the sum of an
even and an odd is always odd).
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 explains that when adding two odd numbers the “leftover ones” in each number can be combined making two, and an even number plus two will always be an
even number. In addition, the student explains that when adding three odd numbers there will be “three leftovers” so the result will be odd.
Questions Eliciting Thinking
Can you think of another way to prove that this will always work?
What do you know about multiplying odd numbers? Will the same hold true as it does for addition?
Instructional Implications
Guide the student to generalize what happens in each of the three basic cases: (1) adding two even numbers, (2) adding two odd numbers, and (3) adding an even and
an odd number. Allow the student to generalize the result in each case in writing. For example, a student could write, "The sum of two even numbers always an even
number."
Encourage the student to use reasoning to determine the result of adding three odd numbers. For example, when adding three odd numbers, the sum of the first two odd
numbers will be even (since the sum of two odds is always odd). Then, when adding this even number to the third odd number, the sum will be odd (since the sum of an
even and an odd is always odd). Pose other possibilities to the student such as adding two even numbers and an odd number. Challenge the student to use reasoning to
determine the result.
Encourage the student to explore what happens when multiplying odd numbers by odd numbers. Then, explore multiplying odd by even numbers. Have the student
generalize this rule as well.
Consider using the MFAS task Multiplying Odd Numbers (3.OA.4.9).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Adding Odd Numbers worksheet
Cubes, and/or counters
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.OA.4.9:
Description
Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using
properties of operations. For example, observe that 4 times a number is always even, and explain why 4 times a
number can be decomposed into two equal addends.
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