Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 61538
Adding Five Tenths
Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to
another fraction with a denominator of 100.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, denominators, equivalent fractions, adding fractions
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_AddingFiveTenths_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 attached Adding Five Tenths worksheet.
2. The teacher says, “Look at the fraction . Can you rewrite
3. Provide adequate time for the student to rewrite
as an equivalent fraction with a denominator of 100?”
.
4. The teacher then says, “Use your thinking from above to help you determine the sum of and
.”
5. After the student determines the sum, the teacher should ask the student to explain his or her thinking.
TASK RUBRIC
Getting Started
Misconception/Error
The student cannot correctly rewrite
as an equivalent fraction with a denominator of 100.
page 1 of 3 Examples of Student Work at this Level
The student says that
is equivalent to
or
.
Questions Eliciting Thinking
What does the word equivalent mean?
Do you know how to find fractions that are equivalent to a given fraction?
How can you create a fraction that is equivalent to
Is
equivalent to
Is
? What would you need to do to both the numerator and denominator?
? How do you know?
of a pizza the same as
of a pizza?
Can we add fractions that are not divided into the same size pieces?
Instructional Implications
Using fraction grids, model for the student how to rewrite a fraction with a denominator of 10 as a fraction with a denominator of 100. After modeling with fraction grids,
show the student that a fraction can be written in an equivalent form by multiplying both the numerator and denominator by the same value. Use fraction grids to model
the relationship between
and
. Relate the model to the numerical procedure for rewriting fractions in an equivalent form. Provide the student with additional
opportunities to add a pair of fractions in which one has a denominator of 10 and the other has a denominator of 100 such as
the student converts
to
+
. The teacher should observe if
.
Provide opportunities for the student to practice rewriting fractions in an equivalent form using the denominators 10, 100, and 1000.
Consider using an MFAS task for 4.NF.1.2, which assesses the student’s understanding of equivalent fractions.
Making Progress
Misconception/Error
The student does not recognize the need to rewrite
as
before adding it to
.
Examples of Student Work at this Level
The student rewrites
as
proportionally and adds
The student rewrites
but says the sum of
to
as
and
is
. In the context of an addition problem, the student forgets to adjust the numerator
.
but does not recognize the need to rewrite
denominators to denominators and says the sum is
as
when adding
to
. He or she adds numerators to numerators and
.
Questions Eliciting Thinking
What must be true of two fractions before they can be added?
Why must fractions have like denominators in order to add them?
How could you use the work you did in the first part to help you find the sum of the fractions in the second part?
If I had
of a pizza and added
seem reasonable? Is
of a pizza and just added the numerators and denominators, what would the sum be? That is right, the sum would be
less than or more than
. Does that
?
Instructional Implications
Explain the rationale for rewriting fractions with common denominators by referencing the meaning of the numerator and denominator. For example, when adding
to
, explain to the student that the denominator, “a tenth,” is like a unit of measure; it describes the number of equal parts into which the whole has been divided. The
numerator of each fraction indicates the number of tenths so
means there are five of these units called “tenths.” However, means there are 31 of these units
page 2 of 3 called “hundredths.” Since the units, tenths and hundredths, are different, the fractions cannot be added as written. Use fraction grids to model for the student rewriting as
. Then guide the student to add
to
emphasizing that the fractions can now be added since their denominators are the same.
Provide the student with a problem in context and help the student reason about the denominators and the need for rewriting fractions so that they have the same
denominator. For example, present the student with a problem such as: Mario has
of a medium cheese pizza and
much pizza does Mario have left from the party? In this example, if the student adds
. Help the student understand that this is not reasonable because
+
is also equivalent to
of a medium pepperoni pizza left from a party. How
by adding across the numerators and denominators, the sum of
so the sum of
and
cannot be less than
is less than
.
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 is able to correctly rewrite
as
. When asked to fund the sum of
and
, the student converts
to
and says the sum is
.
Questions Eliciting Thinking
What fraction with a denominator of 10 is equivalent to
How could you determine the sum of
and
?
? What do you think you would need to do?
Instructional Implications
Provide opportunities for the student to solve addition and subtraction word problems that involve unit fractions with unlike denominators. Guide the student through the
process of finding a common denominator and rewriting each fraction with that denominator in order to add or subtract.
Challenge the student to extend his or her understanding of equivalent fractions by solving the following equations:
– +x=
;
– = x;
+x=
;
= x. Encourage the student to write out each step of work.
Consider using the MFAS task Hundredths and Tenths (4.NF.3.5).
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Five Tenths 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.NF.3.5:
Description
Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add
two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100
= 34/100.
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