Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 60823
Adding and Subtracting Mixed Numbers
Students are given pairs of mixed numbers to either add or subtract.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, like denominators, equivalent fractions, subtraction, addition, mixed numbers, regrouping
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_AddingAndSubtractingMixedNumbers_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 Adding and Subtracting Mixed Numbers worksheet and asks the student to determine the sum or difference in each of the
four problems.
2. Provide ample time to determine the sum or difference in each of the problems.
Note: The student does not need to write the product in simplified form (or lowest terms). "There is no mathematical reason why fractions must be written in simplified
form, although it may be convenient to do so in some cases."
TASK RUBRIC
Getting Started
Misconception/Error
The student does not know how to add and subtract fractions with like denominators.
Examples of Student Work at this Level
The student adds numerators to numerators and denominators to denominators in each of the first two problems and determines the sums to be
last two problems, the student subtracts numerators from numerators and denominators from denominators and determines the differences to be
and
and
. In the
.
page 1 of 4 Questions Eliciting Thinking
If you have
of a cookie and I give you another
of a cookie, how much cookie will you have? Will you have
of a cookie?
How is a fraction different than a whole number?
How do you add (subtract) fractions with like denominators?
What is a mixed number? How can it be represented?
Instructional Implications
Provide direct instruction on the meaning of the numerator and denominator of a fraction. The student should understand that the denominator refers to the number of
equal parts into which the whole has been divided and the numerator refers to a certain number of these parts. Guide the student to interpret the denominator as a unit
of measure so that a fraction such as
represents three units; the unit just happens to be a fourth. Consequently, it does not make sense to add or subtract fractions
with different denominators. However, if the denominators are the same, it does make sense to add or subtract the numerators. Explain that a problem such as
can be thought of as adding 4 tenths to 3 tenths which results in 7 tenths commonly written as
+
. Again, emphasize that the denominator is like a unit of measure.
Provide instruction on the meaning of mixed numbers and their relationship to improper fractions. Explain to the student that the fraction portion of a mixed number is
conventionally written so that it is less than one. Model regrouping strategies to convert mixed numbers to improper fractions and improper fractions to mixed numbers.
Show the student that mixed numbers can be written as improper fractions in order to add or subtract them. Encourage the student to use this strategy as an alternative
to regrouping.
Model for the student how to subtract fractions using fraction tiles, manipulatives, and visual models. Give the student additional practice opportunities to model addition and
subtraction of fractions and mixed numbers with manipulatives making sure to include problems that require use of regrouping strategies to compute the sum or difference.
Pair the student with a partner to model addition and subtraction problems using manipulatives.
Moving Forward
Misconception/Error
The student does not have an effective strategy to add and subtract mixed numbers when regrouping is necessary to complete the problem.
Examples of Student Work at this Level
The student correctly determines the sum and difference in the first and third problems but makes errors in the second and fourth problems. The student says that
=
and is unable to convert the fraction to a mixed number such as
or
. When subtracting
, the student says the answer is
+
. Considering
the whole number and the fraction independent of each other, the student subtracts the smaller whole number or fraction from the larger one in each case.
Questions Eliciting Thinking
What do you know about the fraction
Can you change
? Does this fraction equal more than one whole?
so that the fraction portion of the number is less than one?
What is the relationship between a mixed number and an improper fraction?
Instructional Implications
Provide instruction on the meaning of mixed numbers and their relationship to improper fractions. Explain to the student that the fraction portion of a mixed number is
conventionally written so that it is less than one. Model regrouping strategies to convert mixed numbers to improper fractions and improper fractions to mixed numbers.
Show the student that mixed numbers can be regrouped into improper fractions in order to add or subtract them. Encourage the student to use this strategy as an
alternative to regrouping within the mixed number. Then provide additional problems in which the student must use regrouping strategies to compute sums or differences.
Pair the student with a partner to model addition and subtraction problems using manipulatives.
Almost There
Misconception/Error
The student makes a minor computation error converting between mixed numbers and improper fractions.
Examples of Student Work at this Level
The student has an effective strategy for adding and subtracting mixed numbers but makes a minor error when converting between mixed numbers and improper fractions.
The error most likely occurs when the student tries to convert
. The student understands that the mixed number
must be converted and understands the steps
page 2 of 4 to change the mixed number, but makes an error.
Questions Eliciting Thinking
Good mathematicians always check their work. Can you examine your work to see if you completed all of the problems correctly?
Instructional Implications
Provide feedback on errors and allow the student to revise incorrect work. Encourage the student to always check his or her work.
Provide the student with created samples of student work that contain errors. Challenge the student to find the errors and correct them.
Consider using the MFAS tasks Anna Marie and the Pizza (4.NF.2.3) and Fraction Word Problems (4.NF.2.3).
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 adds or subtracts each pair of mixed numbers getting the following answers:
1.
2.
or
3.
or
4.
or
Questions Eliciting Thinking
Another student added
+
and said the answer is
. Should we leave the answer this way? Why or why not?
Why do fractions need to have the same denominator in order to add or subtract them?
If I ate
of a pizza and you ate
of a pizza, how much of the whole pizza did we eat? How can you add or subtract fractions with unlike denominators?
Instructional Implications
Have the student create word problems that require adding and subtracting mixed numbers. Give the student specific addition or subtraction problems to use or allow the
student to make up his or her own problems.
Provide opportunities for the student to explore adding and subtracting fractions with unlike denominators. Begin with fractions such as
divide the rectangle into half. Then cut one-half into fourths. Shade in
equation
+
=
and
and
. Draw a rectangle and
and ask the student how much of the rectangle is shaded. Relate this exercise to the
.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Adding and Subtracting Mixed Numbers 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
page 3 of 4 Access Privileges: Public
License: CPALMS License - no distribution - non commercial
Related Standards
Name
MAFS.4.NF.2.3:
Description
Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each
decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8
+ 1/8 + 1/8 ; 3/8 = 1/8 + 2/8 ; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent
fraction, and/or by using properties of operations and the relationship between addition and subtraction.
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like
denominators, e.g., by using visual fraction models and equations to represent the problem.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
This standard represents an important step in the multi-grade progression for addition and subtraction of fractions.
Students extend their prior understanding of addition and subtraction to add and subtract fractions with like
denominators by thinking of adding or subtracting so many unit fractions.
page 4 of 4