Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 56852
Five Tenths
Students are asked to consider how much larger five is than five tenths.
Subject(s): Mathematics
Grade Level(s): 5
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, place value, tenths place, base ten
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_FiveTenths_Worksheet.docx
FORMATIVE ASSESSMENT TASK
Instructions for Implementing the Task
Note: This task may be implemented individually or in small groups.
1. The teacher provides the student with the Five Tenths worksheet, points to each number and asks, “How are these two numbers related?”
2. If the student does not state that five is ten times as large as five tenths, then the teacher asks, “How many times larger is five than five tenths?” or “How many five
tenths do you need to make five?”
3. If necessary, the teacher may ask probing questions such as, “How much would you have if you had two groups of five tenths? What about four groups of five tenths?
Does that help you to know how many five tenths you would need to make five?”
TASK RUBRIC
Getting Started
Misconception/Error
The student can only use additive reasoning to compare the two numbers.
Examples of Student Work at this Level
The student says that both numbers have a five and one is a decimal. After prompting, the student can explain that five is greater than five tenths and attempts to
subtract 0.5 from 5 to determine how many times larger it is.
Questions Eliciting Thinking
page 1 of 3 Which is greater, five or five tenths?
What does this decimal point mean?
Do you know what two groups of five tenths would equal?
Instructional Implications
Provide the student with clear instruction on the meaning of the decimal point and how it relates to whole numbers. Encourage the student to read numbers such as 0.5
as “five tenths” rather than “zero­point­five.”
Encourage the student to compare whole numbers using multiplicative reasoning. For example, ask the student to tell how many times larger 60 is than six. Then move to
comparing 600 and six using multiplicative reasoning.
Using base ten blocks, allow the student to consider the ten rod as one whole. Ask the student to consider how much each individual cube would represent. If the student
is able to say that it is one tenth, expose the student to the decimal fraction notation (0.1). Then ask the student to compare how many one tenths it would take to
make the whole (10).
Consider using the MFAS task Family Vacations (4.NBT.1.1).
Moving Forward
Misconception/Error
The student incorrectly compares the two decimals despite teacher prompting.
Examples of Student Work at this Level
The student is able to answer some of the teacher’s questions correctly but is unable, even with prompting, to determine that five is ten times as large as five tenths.
The student is able to talk about how the two numbers are different and alike, but answers that five tenths are needed to make five.
Questions Eliciting Thinking
How much would you have if you had two groups of five tenths? What about four groups of five tenths? Does this help you to determine how many five tenths you would
need to make five?
How many tenths would you need to make one whole? Can that help you compare five tenths to five ones?
Instructional Implications
Using base ten blocks, allow the student to consider the ten rod as one whole. Ask the student to consider how much each individual cube would represent. If the student
is able to say that it is one tenth, expose the student to the decimal fraction notation (0.1). Then ask the student to compare how many one tenths it would take to
make the whole (10).
Almost There
Misconception/Error
The student is only able to correctly compare the two decimals with teacher prompting.
Examples of Student Work at this Level
The student needs prompting to determine that five is ten times as large as five tenths. However, after prompting, the student seems to understand the multiplicative
relationship between the two numbers.
Questions Eliciting Thinking
How many groups of five tenths would you need to make one whole?
How many tenths would you need to make one whole? Can that help you compare five tenths to five ones?
Instructional Implications
Encourage the student to talk about how one tenth compares to one, and guide him or her in making the transition to five tenths and five ones.
Use base ten blocks to model why five is ten times as large as five tenths. This can be done by using five ten rods and comparing them to five individual cubes. First, the
teacher must establish that the one whole is now represented by one ten rod so the ten individual cubes would represent a tenth. On this basis, the student can see that
five wholes (five ten rods) are ten times as large as five tenths (five individual cubes).
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 explains how the two numbers are related and also states that five is ten times as large as five tenths because you would need to multiply five tenths
by ten to get five.
page 2 of 3 Questions Eliciting Thinking
What about six tenths and six? How do those compare? How much larger is six than six tenths?
How about five hundredths and five ones? How much larger is five than five hundredths?
Can you use cubes to model five ones and five hundredths?
Instructional Implications
Encourage the student to explore the relationship between digits in the tenths place and digits in the ones place.
Extend the student’s thinking by introducing the relationships between hundredths and ones, using base ten blocks. To model hundredths and ones, establish that the
hundred block is one and the individual blocks are each one hundredth of one. Use models to challenge the student to compare pairs of numbers such as 5 and 0.05.
Challenge the student to compare decimals that are one hundred or one thousand times as large (e.g., 0.6 and 0.006).
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.5.NBT.1.1:
Description
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place
to its right and 1/10 of what it represents in the place to its left.
Remarks/Examples:
Examples of Opportunities for In-Depth Focus
The extension of the place value system from whole numbers to decimals is a major intellectual accomplishment
involving understanding and skill with base-ten units and fractions.
page 3 of 3