Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 56910
Decimals in Expanded Form
Students are asked to write numbers involving decimals in both standard form (as base ten numerals) and expanded form.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, multi-digit whole numbers, base-ten numerals, expanded form
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_DecimalsInExpandedForm_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 says, “I am going to read aloud five numbers. I would like you to write each number as a base­ten numeral (standard form) and then in expanded form on
the paper provided.”
2. The teacher reads aloud the following numbers and provides adequate time for the student to write each number as a base-ten numeral (standard form) and in expanded
form. Repeat the numbers if needed.
A. 7.03 (Read as seven and three hundredths)
B. 305.9 (Read as three hundred five and nine tenths)
C. 67.103 (Read as sixty-seven and one hundred three thousandths)
D. 13.4 (Read as thirteen and four tenths)
E. 2.025 (Read as two and twenty-five thousandths)
3. The teacher says, “I would like you to write the base­ten numeral for the number given in expanded form at the bottom of the paper.”
page 1 of 4 TASK RUBRIC
Getting Started
Misconception/Error
The student is unable to correctly write decimal numbers in standard form.
Examples of Student Work at this Level
The student:
Writes all or most of the numbers as whole numbers.
Correctly writes the whole number part of each number and then writes the decimal part as a whole number after inserting the word “and” (or an equivalent symbol).
Incorrectly combines decimal and fractional notation.
Questions Eliciting Thinking
Can you read this number for me (show the student the numeral 5.13)? Can you tell me the value of each digit?
Can you write the numeral for “three tenths”? Can you write the numeral for “two hundredths”? Can you write the numeral for “five thousandths”? What do you think the
numeral for “three hundred twenty five thousandths” would look like? How about “three hundred two thousandths”?
Can you read to me what you wrote? I’ll repeat the number again; make sure you have the number written exactly as I say it.
I see you wrote a fraction for the number thirteen and four tenths, how could you write the four tenths as a decimal?
Instructional Implications
Assess the student in writing and expanding whole numbers that are read aloud. Consider implementing MFAS tasks aligned to 4.NBT.1.2. Then review how decimal
numbers are written and the place value of decimal digits.
Assist the student in reading and writing decimal numbers. Have the student use a place value mat and emphasize the relationship between the location of each decimal
digit of a number written in standard form (e.g., in 7.03, the three is two places to the right of the decimal point), its actual value (e.g., the three in 7.03 represents
3/100), and how it is read (e.g., 0.03 is read “three­hundredths”).
Provide the student with sets of matching cards. One set of cards should contain base-ten numerals. The other set should contain the corresponding number names. Mix
the cards up and have the student match a base-ten numeral card to the correct number name card.
If the student has difficulty writing decimals in expanded form, model using place value blocks and a place value mat. Provide instruction on how to write decimal numbers in
expanded form using both fractions and decimals [e.g., 7.03 could be written as (7 x 1) + (3 x 1/100) and as 7 + 0.03].
Consider using the MFAS task Writing and Reading Decimals (5.NBT.1.3).
Moving Forward
Misconception/Error
The student is unable to correctly write decimal numbers in expanded form.
Examples of Student Work at this Level
The student writes all or most of the numbers correctly in standard form. However, the student is unable to correctly write the numbers in expanded form.
page 2 of 4 Questions Eliciting Thinking
What is the place value of each digit in 7.03? How can you show “seven ones” and “three hundredths” when writing this number in expanded form?
Can you write 305 in expanded form? How can this help you write 305.9 in expanded form?
How is 67.103 read? Can you write 0.103 as a fraction?
Instructional Implications
Provide feedback to the student concerning any errors made writing the numbers in standard form and assist the student in correcting these errors. Then guide the
student to write each number in expanded form using a place value mat. Emphasize the relationship between the location of each decimal digit of a number written in
standard form (e.g., in 7.03, the three is two places to the right of the decimal point), its actual value (e.g., the three in 7.03 represents 3/100), and how it is read (e.g.,
0.03 is read “three hundredths”).
Provide additional opportunities to write the expanded forms of decimals given in standard form. Be sure to include numbers that contain zero as one or more of the digits.
Almost There
Misconception/Error
The student makes errors but is able to correct with prompting.
Examples of Student Work at this Level
The student writes all or most of the numerals correctly in both standard and expanded form. The student makes one or two errors that he or she is able to later correct
with prompting from the teacher. For example, the student:
Writes 2.25 instead of 2.025 but provides the correct expansion for the written number.
Writes 67.013 instead of 67.103 but provides the correct expansion for the written number.
Writes 36.134 for the given expansion of 360.134.
Questions Eliciting Thinking
You expanded two and twenty-five hundredths correctly but can you go back and look at your base-ten numeral (if the student wrote 2.25)? Check what you wrote as I
read this number again.
Can you review the last problem? Did you write this number correctly in standard form?
Instructional Implications
Provide feedback to the student concerning any errors made and allow the student to revise his or her work. Provide additional opportunities to write decimal numbers in
standard form that are read aloud and to write the expanded forms of decimals given in standard form. Be sure to include numbers that contain zero as one or more of the
digits.
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 writes each number in both standard and expanded form.
1. 7.03 = (7 x 1) + (3 x 1/100)
2. 305.9 = (3 x 100) + (5 x 1) + (9 x 1/10)
3. 67.103 = (6 x 10) + (7 x 1) + (1 x 1/10) + (3 x 1/1000)
page 3 of 4 4. 13.4 = (1 x 10) + (3 x 1) + (4 x 1/10)
5. 2.025 = (2 x 1) + (2 x 1/100) + (5 x 1/1000)
The student writes 360.134 for the number whose expansion is given.
Questions Eliciting Thinking
Can you also write the expanded form for a number like 723.0415?
Instructional Implications
Challenge the student to write numbers with ten thousandths in decimal and fractional expanded form and as base-ten numerals.
Relate the expanded form of a number to verbal descriptions of its component parts (e.g., 4.75 = 4 + 0.7 + 0.05 which corresponds to 4 ones + 7 tenths + 5
thousandths). Then have the student explore other expansions such as 47 tenths + 5 thousandths to determine if they represent the same value.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Decimals in Expanded Form 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.5.NBT.1.3:
Description
Read, write, and compare decimals to thousandths.
a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g.,
347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000).
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols
to record the results of comparisons.
page 4 of 4