Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 62509
Sums and Differences in Scientific Notation
Students are asked to add and subtract numbers given in scientific notation in real-world contexts.
Subject(s): Mathematics
Grade Level(s): 8
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, scientific notation, exponent, power, base
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_SumsAndDifferencesInScientificNotation_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
This task can be implemented individually, with small groups, or with the whole class.
1. The teacher asks the student to complete the problems on the Sums and Differences in Scientific Notation worksheet.
2. The teacher asks follow-up questions, as needed.
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand that the numbers cannot be added or subtracted in their given forms.
Examples of Student Work at this Level
The student attempts to add or subtract the numbers in scientific notation even though the powers of 10 are not the same. The student adds or subtracts coefficients
and exponents.
1.1 x
8.4 x
as 1.100, 1100, or
.
as 0.84, 840, -840, or -0.084.
page 1 of 3 Questions Eliciting Thinking
How do you add and subtract numbers written in standard notation, for example, 1496 – 72? How would you write this problem if you were preparing to subtract?
If written in standard notation, would the eight (in
) and the one (in
) be in the same place and have the same place value? How could you tell?
Instructional Implications
If needed, provide instruction on converting between standard and scientific notation. Provide opportunities for the student to determine if a number is correctly written in
scientific notation.
Demonstrate that it does not make mathematical sense to add or subtract numbers given in scientific notation by adding or subtracting their coefficients or exponents. Have
the student add 120,000 and 23,000. Then ask the student to convert each to scientific notation. Next show the student that (1.2 x
since 3.5 x
= 3,500,000,000
) + (2.3 x
)
3.5 x
143,000 (the sum of 120,000 and 23,000).
Guide the student to determine when numbers of the form
can be combined (i.e., when the powers of 10 are the same) and how to determine the result. Provide
additional opportunities to add and subtract numbers written in scientific notation.
Moving Forward
Misconception/Error
The student makes errors when converting numbers to a compatible form or combining compatible numbers.
Examples of Student Work at this Level
The student understands that each pair of numbers must be written in a compatible form before combining. However, the student:
Makes errors when converting numbers to standard notation.
Makes an error when converting numbers to a compatible exponential form, for example, writes
as
or
as
.
Does not correctly align decimal points before adding or subtracting.
Rewrites 1.07 x
as 10.7 x
and says the sum of 10.7 x
and 1.5 x
is 12.2 x
+
or 12.2 x
.
Questions Eliciting Thinking
How did you convert this number to standard notation (or to exponential form)?
Can you show me how you added (or subtracted) these two numbers? What must be true of the decimal points?
Your approach to the second problem is very clever, but I think you made an error in adding the two numbers. Can you factor out
before adding? What will you get
then?
Instructional Implications
As needed, review converting between scientific and standard notation.
Remind the student that the decimal points of the two numbers to be added or subtracted must be aligned. Indicate to the student that he or she made an addition or
subtraction error and challenge the student to find and correct the error.
Model for the student how to add (1.07 x
) + (1.5 x
) and (1.5 x
) can be rewritten as (10.7 + 1.5) x
) by first rewriting 1.07 x
as 1.07 x (10 x
) = 10.7 x
. Then show the student that (10.7 x
by applying the Distributive Property. Ask the student to complete the calculation and explain what must be
true of the powers of 10 in order to use this strategy.
Almost There
Misconception/Error
The student makes a minor error.
Examples of Student Work at this Level
The student:
Subtracts another combination of masses (instead of the smallest from the largest) in the first problem but does so correctly.
Correctly adds the two masses given in the second problem but makes an error in rewriting the sum in scientific notation. For example, the student writes the sum as
12.2 x
.
Questions Eliciting Thinking
I think you may have subtracted the wrong values in the first problem. Can you reread the problem and check your work?
Is 12.2 x
written in scientific notation? What part of this expression violates the form of scientific notation?
page 2 of 3 Instructional Implications
Provide feedback to the student regarding any errors made and allow the student to revise his or her work. If needed, provide opportunities for the student to rewrite
numbers of the form a x
in which a < 1 or a 10 in scientific notation. Provide the student with a set of numbers written in the form a x
only some of which are in
scientific notation. Ask the student to identify those that are not in scientific notation and to convert them to scientific notation.
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 and subtracts in each problem, getting answers of 109.916 grams and 1.22 x
kilograms.
Questions Eliciting Thinking
One of the meteorites has a mass of 6.8 x
. What does
equal? What does 6.8 x
equal?
Instructional Implications
If unfamiliar, show the student the following strategy for adding (or subtracting) numbers written in scientific notation: given (a x
) = (a + b) x
) and (b x
) then (a x
) + (b x
(by an application of the Distributive Property). Provide opportunities for the student to rewrite numbers given in scientific notation so they involve
equal powers of 10 and then apply this strategy.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Sums and Differences in Scientific Notation 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.8.EE.1.4:
Description
Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific
notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very
small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been
generated by technology.
page 3 of 3