www.em2.edc.org
Eliciting Mathematics Misconceptions
ASSESSMENT
Understanding
Decimals
Comparing Decimals I
The Comparing Decimals 1 assessment is designed to elicit
information about a common misconception that students have
when comparing two decimal numbers:
• Misconception 1 (M1): Using Whole-Number Thinking / A Focus
on “Longer Is Larger”
Although you can access the assessment here at any time, we
strongly recommend that you reference the information below to
learn more about this misconception, including how it appears in
student work, and how to score pre- and post-assessments once
you have given them to students.
»»Contents
Topic Background: Learn about comparing decimals. ...................................................................................................................... 2
Student Misconceptions: Learn about student misconceptions related to the topic. ............................................................... 3
Administering the Pre-Assessment: Learn how to introduce the pre-assessment to your students. .................................... 5
Scoring: Learn about the scoring process by reviewing the Scoring Guide. ................................................................................. 7
Sample Student Responses: Review examples of student responses to assessment items. ...............................................35
Administering the Post-Assessment: Learn how to introduce the post-assessment to your students. .............................39
This research was supported by the IES, U.S. DOE., through Grant 305A110306 to EDC, Inc.
The opinions expressed are those of the authors and do no represent views of the IES. or the U.S. DOE.
Education Development Center, Inc. | EM2 ©2015 All Rights Reserved.
ASSESSMENT
Comparing Decimals I
Topic Background
»»Learn about comparing decimals.
There are multiple research-based misconceptions related to comparing decimals, but this set of diagnostic assessments
focuses on one in particular: overgeneralizing from experiences with whole-number comparisons when comparing the
digits to the right of the decimal point. Because students are accustomed to thinking of a number with more digits as the
larger number, they extend this rule to decimals; they compare the decimal numbers according to how many digits appear
to the right of the decimal point and assume that the decimal number with more digits is larger.
Students typically do not apply this thinking when given numbers with different digits in the ones place, such as comparing
2.36 and 5.1. Instead, they tend to appropriately compare the values of the digits in the ones place, in this case reasoning
that since 5 is greater than 2, 5.1 is greater than 2.36.
Connections to Common Core Standards in Mathematics (CCSS)
The CCSS outline specific understandings that students should be able to meet at each grade level.
At grade 4, students should be able to do the following:
»» 4.NF: Understand decimal notation for fractions, and compare decimal fractions.
»» 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.
»» Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a
length as 0.62 meters; locate 0.62 on a number line diagram.
»» Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only
when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <,
and justify the conclusions, e.g., by using a visual model.
At grade 5, students should be able to do the following:
»» 5.NBT. Understand the place value system.
»» 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.
»» Read, write, and compare decimals to thousandths.
»» 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 × (1/1,000).
»» Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols
to record the results of comparisons.
2 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
Student Misconceptions
»»Learn about student misconceptions related to the topic.
When students are developing the understandings described above (see Topic Background), they can develop flawed
understanding leading to misconceptions about how to compare decimals.
The following common misconception when comparing decimals is targeted in the Comparing Decimals 1 assessments:
»» Misconception 1 (M1): Using Whole-Number Thinking / A Focus on “Longer Is Larger”
Students with this misconception consistently compare decimals by comparing the numbers to the right of the
decimal point as if they were comparing whole numbers (e.g., they consider 0.34 to be greater than 0.8 because
34 is greater than 8). Because they are accustomed to thinking of numbers with more digits as larger numbers,
they overgeneralize from their experiences with whole-number comparisons and extend this rule to decimals.
Access the website to watch a brief video clip for a fuller
description of this misconception.
http://em2.edc.org/portfolio/comparing-decimals-i
To see additional examples of student work illustrating this
misconception, go to the Sample Student Responses tab
on the website, or refer to p. 35 of this document.
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ASSESSMENT
Comparing Decimals I
»»Student Misconceptions
Resources
The Common Core Standards Writing Team (2011). Progressions for the Common Core State Standards in Mathematics (draft):
3–5, Number and Operations—Fractions. Retrieved from http://ime.math.arizona.edu/progressions/#products
The Common Core Standards Writing Team (2011). Progressions for the Common Core State Standards in Mathematics (draft):
K–5, Number and Operations in Base Ten. Retrieved from http://ime.math.arizona.edu/progressions/#products
Irwin, K. (1996). Making sense of decimals. In J. Mulligan & M. Mitchelmore (Eds.), Children’s Number Learning (pp. 243–
257). Adelaide, Australia: MERGA & AAMT.
Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing Effective
Fractions Instruction for Kindergarten Through 8th Grade: A Practice Guide (NCEE #2010-4039). Washington, DC: National
Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
Steinle, V., & Stacey, K. (2004). Persistence of Decimal Misconceptions and Readiness to Move to Expertise. In M. Johnsen
Hoines & A. Berit Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of
Mathematics Education—PME 28, 4(1), 225–232. Bergen, Norway: Bergen University College.
4 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
Administering the Pre-Assessment
»»Learn how to introduce the pre-assessment to your students.
About This Assessment
These EM2 diagnostic, formative pre- and post-assessments are composed
of items with specific attributes associated with student conceptions that are
specific to comparing decimals. Each item within any EM2 assessment includes
a selected response (multiple choice) and an explanation component. Each
item has three response choices: Greater than (>), Less than (<), and Equivalent
(=). The symbol is provided with the text to provide broader accessibility.
Pre-Assessment [Student Version]
See Appendix A for the student
version of the Pre-Assessment.
Comparing Decimals I Pre Assessment Name_________________________ Date__________ Class___________
Compare the two decimals provided. Select the choice that shows the relationship between the two decimals.
1)
Explain your thinking.
Greater than (>)
0.352 Less t han ( <) 0.476 Equivalent (=)
The learning target for the Comparing Decimals 1 assessment is as follows:
Explain your thinking.
2)
The learner will accurately compare decimals to identify which is larger and
which is smaller.
Greater than (>)
12.86 Less t han ( <) 12.659 Equivalent (=)
Explain your thinking.
3)
Greater than (>)
0.788 Less than ( <) 0.88 Equivalent (=)
Prior to Giving the Pre-Assessment
Copyright © 2015, Education Development Center, Inc. All rights reserved.
• Arrange for 15 minutes of class time to complete the administration
process, including discussing instructions and student work time. Since
the pre-assessment is designed to elicit misconceptions before instruction, you do not need to do any special review
of this topic before administering the assessment. (See the “Student Misconceptions” tab for information and a
video that describes this misconception. You can also refer to p. 3–4 of this document.)
Administering the Pre-Assessment
• Inform students about the assessment by reading the following:
Today you will complete a short individual activity, which is designed to help me understand how you think
about comparing decimals.
• Distribute the assessment and read the following:
The activity includes five problems. For each problem, choose your answer by completely filling in the circle to
show which answer you think is correct. Because the goal of the activity is to learn more about how you think
about comparing decimals, it’s important for you to include some kind of explanation in the space provided.
This can be a picture, words, a combination of pictures and words, or something else that shows how you
chose your answer.
You will have about 15 minutes to complete all the problems. When you are finished please place the paper on
your desk and quietly [read, work on ____] until everyone is finished.
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ASSESSMENT
Comparing Decimals I
»»Administering the Pre-Assessment
• Monitor the students as they work on the assessment, making sure that they understand the directions. Although
this is not a strictly timed assessment, it is designed to be completed within a 15-minute timeframe. Students may
have more time if needed. When a few minutes remain, say:
You have a few minutes left to finish the activity. Please use this time to make sure that all of your answers
are as complete as possible. When you are done, please place the paper face down on your desk. Thank you
for working on this activity today.
• Collect the assessments.
After Administering the Pre-Assessment
Use the analysis process (found in the Scoring Guide PDF document under the Scoring Process section and found on
p. 7 of this document) to analyze whether your students have this misconception:
»» Misconception 1 (M1): Using Whole-Number Thinking / A Focus on “Longer Is Larger”
6 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
Scoring
»»Learn about the scoring process by reviewing the Scoring Guide.
The Comparing Decimals 1 assessment is composed of five items with specific attributes associated with a misconception
that is directly related to comparing decimals. We encourage you to carefully read the Scoring Guide to understand these
specific attributes and to find information about analyzing your students’ responses.
How to Use This Guide
This Scoring Guide is intended for use with both the pre-assessment and the post-assessment for Comparing Decimals 1.
To use this guide, we recommend following these steps:
• Read the Misconception Description below, and be sure you understand what the misconception is. You may want
to view the video found under the “Student Misconceptions” tab. Numerous examples of student work illustrating
this misconception are included in this guide, but you may also want to refer to the additional examples of student
work found under the “Sample Student Responses” tab and found on p. 35 of this document.
• Familiarize yourself with the five assessment items and what they assess.
• Consider completing the optional scoring practice items and checking your scoring against the answer key.
• Score your students’ work using the Pre-/Post-Assessment Analysis Process described below.
• Refer to the various examples found here and under the “Sample Student Responses” tab for guidance when you are
unsure about the scoring.
Misconception Description
There are multiple research-based misconceptions related to comparing decimals, but this set of diagnostic assessments
focuses on one in particular: overgeneralizing from experiences with whole-number comparisons when comparing the
digits to the right of the decimal point. Because students are accustomed to thinking of a number with more digits as the
larger number, they extend this rule to decimals; they compare the decimal numbers according to how many digits appear
to the right of the decimal point and assume that “longer is larger.”
Students typically do not apply this thinking when given numbers with different digits in the ones place, such as comparing
2.36 and 5.1. Instead, they tend to appropriately compare the values of the digits in the ones place, in this case reasoning
that since 5 is greater than 2, 5.1 is greater than 2.36.
7 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
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Comparing Decimals I
»»Scoring
The EM2 Comparing Decimals 1 assessments have designated this misconception in the following way:
»» Misconception 1 (M1): Using Whole-Number Thinking / A Focus on “Longer Is Larger”
Students with this misconception consistently compare decimals by comparing the numbers to the right of
the decimal point as if they were comparing whole numbers (e.g., they consider 0.34 to be greater than 0.8
because 34 is greater than 8). Because they are accustomed to thinking of numbers with more digits as larger
numbers, they over-generalize from their experiences with whole-number comparisons and extend this rule to
decimals.
Resources
The Common Core Standards Writing Team (2011). Progressions for the Common Core State Standards in Mathematics (draft):
3–5 Number and Operations—Fractions. Retrieved from http://ime.math.arizona.edu/progressions/#products
The Common Core Standards Writing Team (2011). Progressions for the Common Core State Standards in Mathematics (draft):
K–5, Number and Operations in Base Ten. Retrieved from http://ime.math.arizona.edu/progressions/#products
Irwin, K. (1996). Making sense of decimals. In J. Mulligan & M. Mitchelmore (Eds.), Children’s Number Learning (pp. 243–
257). Adelaide, Australia: MERGA & AAMT.
Siegler, R., Carpenter, T., Fennell, F., Geary, D., Lewis, J., Okamoto, Y., Thompson, L., & Wray, J. (2010). Developing Effective
Fractions Instruction for Kindergarten Through 8th Grade: A Practice Guide (NCEE #2010-4039). Washington, DC: National
Center for Education Evaluation and Regional Assistance, Institute of Education Sciences, U.S. Department of Education.
Steinle, V., & Stacey, K. (2004). Persistence of Decimal Misconceptions and Readiness to Move to Expertise. In M. Johnsen
Hoines & A. Berit Fuglestad (Eds.), Proceedings of the 28th Conference of the International Group for the Psychology of
Mathematics Education—PME 28, 4(1), 225–232. Bergen, Norway: Bergen University College.
8 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
PRE-ASSESSMENT
Pre-Assessment Items
The pre-assessment is composed of five items with specific attributes associated with comparing decimals. Each item
may elicit information about students’ understanding of place value when comparing decimals.
Item
Understandings and Misconceptions
• NOTE: This is considered a “baseline” item; it is included in the assessment to confirm that students
understand the basic concept of reading decimal numbers. A lack of understanding of this concept
would invalidate the rest of the diagnostic assessment, so this item is a “double check” that students
have the basic understanding that forms the basis of this diagnostic assessment. However, in most
cases, students for whom this assessment is appropriate will have this understanding.
Correct Response:
Less than (<)
• This item is not included in the determination of whether students have M1.
• Students with Misconception 1 will reason that 86 < 659, so 12.86 < 12.659.
• Students who only consider the numbers to the left of the decimal will select “Equivalent.”
Correct Response:
Greater than (>)
• Students with Misconception 1 will reason that 788 > 88, so 0.788 > 0.88.
• Students who only consider the numbers to the left of the decimal will select “Equivalent.”
Correct Response:
Less than (<)
• Students with Misconception 1 will reason that 65 > 9, so 3.65 > 3.9.
• Students who only consider the numbers to the left of the decimal will select “Equivalent.”
Correct Response:
Less than (<)
• Students with Misconception 1 will reason that 3 < 189, so 0.3 < 0.189.
Correct Response:
Greater than (>)
• Students who only consider the numbers to the left of the decimal will select “Equivalent.”
If students choose an incorrect response that does not indicate M1 thinking, review their explanations to determine what
difficulty they are having.
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Comparing Decimals I
»»Scoring
Pre-Assessment Analysis Process
Some important things to know about the analysis process for this diagnostic assessment:
• This diagnostic assessment has been validated to reliably predict the likelihood that a student has Misconception 1.
You can weigh the relative likelihood that your student has this misconception by considering whether the student’s
written responses provide “Strong Evidence” or “Weak Evidence” of Misconception 1.
• If a student is determined to show evidence of Misconception 1 on even just one of items 2, 3, 4, or 5, the student
is likely to have this misconception. (Item 1 is a baseline item and is not intended to provide information on the
presence of Misconception 1.)
• For each item, you need to look at both the selected response choice and the explanation. Students will show
evidence of Misconception 1 only if they select the M1 response choice and have an explanation that supports
Misconception 1. To learn more about how to tell whether an explanation supports Misconception 1, go to the
“Student Misconceptions” tab and watch the video provided or review the information on p. 3–4.
• An optional Scoring Guide Template is provided for your use when you score your own students’ diagnostic
assessments. In each row of the assessment, write a student’s name, then circle the appropriate information for
each item on the pre-assessment (shaded) and, later, the post- assessment (in white). If a student’s response does
not fit Correct or M1 but is “Other,” draw a strike-through line..
How to Determine If a Student Has the Misconception
1. For each item, look at Table 1 to determine what the selected response might indicate.
Table 1. Response Patterns for the Pre-Assessment
Item
Decimal Numbers
Being Compared
Correct Response
M1
Likely Response
1
0.352
0.476
Less than (<)
n/a
2
12.86
12.659
Greater than (>)
Less than (<)
3
0.788
0.88
Less than (<)
Greater than (>)
4
3.65
3.9
Less than (<)
Greater than (>)
5
0.3
0.189
Greater than (>)
Less than (<)
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Comparing Decimals I
»»Scoring
What if there’s no multiple-choice response selected?
In that case, carefully consider the explanation the student gives. If the explanation leaves no doubt that the student would
have selected the M1 response choice and about how the student is reasoning, you can code it as “Strong Evidence” of M1.
However, if the explanation leaves some question about what the student was thinking, code it as “Weak Evidence” of M1. For
additional guidance on determining the strength of the evidence, see the “What counts . . .” information in step 2 below.
2. For each item with the M1 response choice, note whether the evidence of M1 from the explanation is strong or weak.
If the student selects the M1 response choice, look next at the student’s explanation to determine whether it also
supports Misconception 1. An explanation can be categorized as “Strong Evidence” of M1, “Weak Evidence” of M1, or “No
Supporting Evidence” of M1.
What counts as “Strong Evidence” of M1 in the pre-assessment?
In general, responses with strong evidence of M1 include a clear indication that the student is focusing on the number of
digits to the right of the decimal point and is comparing those digits as whole numbers.
Below are three examples of student responses with strong evidence of M1, using pre- assessment items. To see additional
examples of student responses that illustrate this misconception, go to the “Sample Student Responses” tab and click on
the button to download the PDF or review the information on p. 35–38.
Example A: Strong Evidence of M1
“12.86 is smaller than
12.659. Because 12.659
has one more number
than the other”
This student chooses the M1 response (“Less than”) and specifically refers to the number of digits in each decimal
number.
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Comparing Decimals I
»»Scoring
Example B: Strong Evidence of M1
“This one is greater
because it has more digits
after the decimal”
This student chooses the M1 response (“Greater than”) and is clearly paying attention to the number of digits after the
decimal point.
Example C: Strong Evidence of M1
This student chooses the M1 response (“Less than”) and clearly indicates that he or she is paying attention to the
digits to the right of decimal point and comparing them as whole numbers.
What counts as “Weak Evidence” of M1 in the pre-assessment?
Responses with weak evidence of M1 include some indication that the student is ignoring place value and is viewing the
digits to the right of the decimal point as a whole number. However, these responses also generally require making more
inferences about what the student was thinking, or they leave some question or doubt as to whether the misconception is
present or to what degree it is present.
Below are three examples of student responses with weak evidence of M1, using pre-assessment items. To see additional
examples of student responses that illustrate this misconception, go to the “Sample Student Responses” or review the
information on p. 35–38.
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Comparing Decimals I
»»Scoring
Example A: Weak Evidence of M1
“They would not be equile
[equal] because the first is
bigger”
This student chooses the M1 response (“Greater than”). However, the explanation (“the first is bigger”) leaves some
doubt as to what the student is thinking without having to make inferences. This makes it “Weak Evidence” of M1.
Example B: Weak Evidence of M1
“0.3 is smaller than 0.189
because its just a 0.3.”
This student chooses the M1 response (“Less than”) and explains that this decimal is smaller because it’s “just a 0.3.”
However, it’s not clear why the student sees it as smaller without having to make inferences about what the student is
thinking. This makes it “Weak Evidence” of M1.
Example C: Weak Evidence of M1
“Because there only is a
0.3 and on the other on
[one] is 0.189”
This student chooses the M1 response (“Less than”) and explains that “there only is a 0.3.” While the student clearly
sees this decimal number as smaller, there is no information about why the student sees it as smaller, which makes it
“Weak Evidence” of M1.
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Comparing Decimals I
»»Scoring
What counts as “No Supporting Evidence” in the pre-assessment?
If a student selects the M1 response choice but provides no explanation at all, this counts as “No Supporting Evidence” of
M1. If a student’s response choice suggests the possibility of M1 but the explanation does not support it, the item is not
considered to be indicative of the misconception and can also be scored as “No Supporting Evidence.”
3. After you have analyzed each item for a student, use the guidelines below to determine whether the student has
Misconception 1.
This diagnostic assessment has been validated to predict the possible presence of Misconception 1 for a student. If
a student is determined to show evidence of the misconception on even just one of items 2, 3, 4, or 5, the student is
likely to have Misconception 1, regardless of whether the evidence is coded as “Strong” or “Weak.” The relative number of
items with weak or strong evidence gives you information about how strongly the misconception may be present for the
student.
What if my student has only one item coded as M1 with “Weak Evidence,” and the rest are correct?
Even if your student has only one item with “Weak Evidence” of M1, this diagnostic assessment is validated to predict that it
is likely your student has this misconception. However, the presence of only one item with “Weak Evidence” of M1 suggests
that the misconception may not be very deeply rooted in this student’s thinking.
You may want to keep an eye on this student during regular classwork to watch for other evidence of this misconception.
What if the student’s explanation is contradictory to the multiple-choice response chosen?
If you come across a response in which the explanation seems to contradict the response choice, it is considered a possible
indication of M1. Look for additional evidence, either on these assessments or from the student’s comments in class.
14 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
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Comparing Decimals I
»»Scoring
(Optional) Scoring Practice Items—Pre-Assessment
The following sample student responses are provided as an optional practice set. If you would like to practice scoring
several items to further clarify your understanding of the scoring process, you may try scoring the following 10 items.
We recommend scoring one or two at a time and checking your scoring as you go against our key, found on p. 18.
Practice Example 1
“Becuase [Because] 65 is
big [bigger] than 9.”
Practice Example 2
“12.86 is smaller beause
[because] 86 is smaller
then [than] 659 and it won’t
work.”
Practice Example 3
“There’s an 8 in the tenths
place other has a 6 in the
tenths place”
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Practice Example 4
“0.189 is bigger because 0.3
is smaller then [than] 189”
Practice Example 5
“Because 189 is way bigger
than 3 and it has a 9 in the
thousands place”
Practice Example 6
“I looked at the place value.”
Practice Example 7
“30 > 18.9”
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Comparing Decimals I
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Practice Example 8
“07.88 is more than 0.88
because in 07.88 it has a 7
in the thousand place”
Practice Example 9
“If you compare the 6 and
8 the larger number is 8
so 12.86 is grater [greater]
than 12.659.”
Practice Example 10
“3 is smaller than 189 so
0.189 is big.”
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Comparing Decimals I
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Scoring Practice Items Answer Key—Pre-Assessment
Practice Example 1
“Becuase [Because] 65 is
big [bigger] than 9.”
This is an example of M1 with “Strong Evidence.” The student is clearly focusing on the digits to the right of the
decimal point and comparing them as whole numbers.
Practice Example 2
“12.86 is smaller beause
[because] 86 is smaller
then [than] 659 and it won’t
work.”
This is an example of M1 with “Strong Evidence.” The student is clearly focusing on the digits to the right of the
decimal point and comparing them as whole numbers.
Practice Example 3
“There’s an 8 in the tenths
place other has a 6 in the
tenths place”
This is an example of a “Correct” response with “Strong Evidence” (though making any distinction between strong and
weak correct responses is not necessary for this diagnostic assessment; it simply gives you more information about
your student). This student is clearly paying attention to place value in order to compare the decimal numbers.
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Comparing Decimals I
»»Scoring
Practice Example 4
“0.189 is bigger because 0.3
is smaller then [than] 189”
This is an example of M1 with “Weak Evidence.” Although the student selects the correct response for this item
(“Greater than”), the explanation states the opposite: that 0.189 is bigger and 0.3 is smaller. It is difficult to know how
this student is reasoning without making inferences, so this is considered “Weak Evidence” of M1.
Practice Example 5
“Because 189 is way bigger
than 3 and it has a 9 in the
thousands place”
This is an example of M1 with “Strong Evidence.” The student’s explanation specifically focuses on the digits to the
right of the decimal and compares them as whole numbers. However, there is also an interesting reference to the 9 in
the “thousands” place, suggesting that this student has some partial or flawed understanding of place value.
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Comparing Decimals I
»»Scoring
Practice Example 6
“I looked at the place value.”
This is an example of a “Correct” response with “Weak Evidence” (though making any distinction between strong and
weak correct responses is not necessary for this diagnostic assessment; it simply gives you more information about
your student). The student selects the correct response for this item (“Greater than”); however, while place value is
mentioned, the student does not explain what it is about the place value that helped the student decide. It is unclear
from the student’s explanation how the student is thinking about place value, making it “Weak Evidence” that the
student is thinking correctly.
Practice Example 7
“30 > 18.9”
This is an example of a “Correct” response with “Weak Evidence” (though making any distinction between strong and
weak correct responses is not necessary for this diagnostic assessment; it simply gives you more information about
your student). The student selects the correct response for this item and moves the decimal point two places to the
right for each number to compare them; the student offers no other explanation.
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»»Scoring
Practice Example 8
“07.88 is more than 0.88
because in 07.88 it has a 7
in the thousand place”
This is an example of M1 with “Weak Evidence.” The student selects the M1 response for this item (“Greater than”), and
the explanation says that 07.88 “has a 7 in the thousand place,” which suggests that the student is thinking of whole
numbers. However, this statement is both unclear and incorrect (i.e., in the decimal numbers presented, 7 is in the tenths
place), leaving it unclear how the student is thinking about the comparison. This makes it “Weak Evidence” of M1.
Practice Example 9
“If you compare the 6 and
8 the larger number is 8
so 12.86 is grater [greater]
than 12.659.”
This is a “Correct” example with “Strong Evidence” (though making any distinction between strong and weak correct
responses is not necessary for this diagnostic assessment; it simply gives you more information about your
student). The student is clearly paying attention to place value in order to compare the decimal numbers. The student
underlines the numbers in the tenths place and explains how to compare them.
Practice Example 10
“3 is smaller than 189 so
0.189 is big.”
This is an example of M1 with “Strong Evidence.” The student’s explanation specifically focuses on the digits to the right of
the decimal and compares them as whole numbers.
21 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
POST-ASSESSMENT
Post-Assessment Items
The post-assessment is structured exactly the same as the pre-assessment, comprising five items with specific attributes
associated with comparing decimals. Each item may elicit information about the students’ understanding of place value
when comparing decimals.

Item
Correct response:
Less than (<)
Understandings and Misconceptions
• NOTE: This item is considered a “baseline” item; it is included in the assessment to confirm
that students actually understand the basic concept of reading decimal numbers. A lack of
understanding of this concept would invalidate the rest of the diagnostic assessment, so this
item is a “double check” that students have the basic understanding that forms the basis of
this diagnostic assessment. However, in most cases, students for whom this assessment is
appropriate will have this understanding.
• This item is not included in the determination of whether students have M1.
• Students with Misconception 1 will reason that since 41 < 187, 2.41 < 2.187.
• Students who only consider the numbers to the left of the decimal will select “Equivalent.”
Correct response:
Greater than (>)
• Students with Misconception 1 will reason that since 899 > 99, 0.899 > 0.99.
• Students who only consider the numbers to the left of the decimal will select “Equivalent.”
Correct response:
Less than (<)
• Students with Misconception 1 will reason that since 34 > 8, 6.34 > 6.8.
• Students who only consider the numbers to the left of the decimal will select “Equivalent.”
Correct response:
Less than (<)
• Students with Misconception 1 will reason that since 2 < 175, 0.2 < 0.175.
• Students who only consider the numbers to the left of the decimal will select “Equivalent.”
Correct Response:
Greater than (>)
If students choose an incorrect response that does not indicate M1 thinking, review their explanations to determine what
difficulty they are having.
22 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Post-Assessment Analysis Process
Some important things to know about the analysis process for this diagnostic assessment:
• This diagnostic assessment has been validated to reliably predict the likelihood that a student has Misconception 1. You
can weigh the relative likelihood that your student has this misconception by looking at the number of responses
coded as either “Strong Evidence” or “Weak Evidence” of Misconception 1.
• If a student is determined to show evidence of Misconception 1 on even just one of items 2, 3, 4, or 5, the student is
likely to have this misconception.
• For each item, you need to look at both the selected response choice and the explanation. Students will show
evidence of Misconception 1 only if they select the M1 response choice and have an explanation that supports
Misconception 1. To learn more about how to tell whether an explanation supports Misconception 1, go to the
“Student Misconceptions” tab and watch the video provided or review the information on p. 3–4.
How to Determine If a Student Has the Misconception
The post-assessment uses the same scoring process as the pre-assessment. If you are not already familiar with the steps
for scoring the assessment, please review that section starting on p. 10.
1. For each item, look at Table 2 to determine what the selected response might indicate.
Table 2. Response Patterns for the Post-Assessment
Item
Decimal Numbers
Being Compared
Correct Response
M1
Likely Response
1
0.279
0.345
Less than (<)
n/a
2
2.41
2.187
Greater than (>)
Less than (<)
3
0.899
0.99
Less than (<)
Greater than (>)
4
6.34
6.8
Less than (<)
Greater than (>)
5
0.2
0.175
Greater than (>)
Less than (<)
23 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
What if there’s no multiple-choice response selected?
In that case, carefully consider the student’s explanation. If the explanation leaves no doubt that the student would have
chosen the M1 response and about how the student is reasoning, you can code it as “Strong Evidence” of M1. However, if
the explanation leaves some question about what the student was thinking, code it as “Weak Evidence” of M1. For additional
guidance on determining the strength of the evidence, see the “What counts . . .” information in step 2 below.
2. For each item with the M1 response choice, note whether the evidence of M1 from the explanation is strong or weak.
If the student selects the M1 response choice, look at the student’s explanation to determine whether it also supports
Misconception 1. An explanation can be categorized as “Strong Evidence” of M1, “Weak Evidence” of M1, or “No
Supporting Evidence” of M1.
What counts as “Strong Evidence” of M1 in the post-assessment?
Responses with strong evidence of M1 include a clear indication that the student is focusing on the number of digits to the
right of the decimal point and is viewing those digits as whole numbers.
Below are three examples of student responses with strong evidence of M1, using post-assessment items. To see additional
examples of student responses that illustrate this misconception, go to the “Sample Student Responses” tab and click on
the button to download the PDF, or review the information on p. 35–38.
Example A: Strong Evidence of M1
“It is greater because it’s
in the hundreds and the
other one has 1 diget
[digit]”
This student chooses the M1 response for this item (“Greater than”) and says that 0.175 is greater “because it’s in the
hundreds” and that 0.2 only has one digit, clearly viewing them as whole numbers.
24 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Example B: Strong Evidence of M1
“It’s greater than 0.2
because it hase [has] more
numbers.”
This student chooses the M1 response for this item (“Greater than”) and is clearly using the number of digits in each
as a way to compare the two decimals.
Example C: Strong Evidence of M1
“I chose this because
2.41 is less than 2.187
by [because?] 41 is much
smaller than 187”
This student chooses the M1 response for this item (“Less than”) and is clearly paying attention to the digits to the
right of the decimal and comparing them as whole numbers.
What counts as “Weak Evidence” of M1 in the post-assessment?
Responses with weak evidence of M1 include some indication that the student is ignoring place value and is viewing the
digits to the right of the decimal point as a whole number. However, these responses also generally require making more
inferences about what the student was thinking, or they leave some question or doubt as to whether the misconception is
present or to what degree it is present.
Below are three examples of student responses with weak evidence of M1, using post-assessment items. To see additional
examples of student responses that illustrate this misconception, go to the “Sample Student Responses” or review the
information on p. 35–38.
25 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Example A: Weak Evidence of M1
“I got less than because
the number on the left is
less than the number on
the right”
This student chooses the M1 response for this item (“Less than”). The explanation, however, basically restates the
student’s selected response and leaves some question as to why the student selected “Less than.” This lack of clarity
makes it “Weak Evidence” of M1.
Example B: Weak Evidence of M1
“I think less than because
(2.187) looks bigger than
(2.41).”
This student chooses the M1 response (“Less than”). However, it is unclear why the student thinks 2.187 looks bigger
than 2.41 without having to make inferences about the student’s thinking. Therefore, it is considered “Weak Evidence”
of M1.
Example C: Weak Evidence of M1
“I think 0.175 is greater
than 0.2 because it has
bigger numbers”
This student chooses the M1 response for this item (“Greater than”), but it is unclear what the student means by “has
bigger numbers” without having to make inferences about the student’s thinking. Therefore, it is considered “Weak
Evidence” of M1.
26 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
What counts as “No Supporting Evidence” in the post-assessment?
If a student selects the M1 response choice but provides no explanation at all, this counts as “No Supporting Evidence of
M1.” If a student’s response choice suggests the possibility of M1 but the explanation does not support it, the item is not
considered to be indicative of the misconception and can also be scored as “No Supporting Evidence.”
3. After you have analyzed each item for a student, use the guidelines below to determine whether the student has
Misconception 1.
This diagnostic assessment has been validated to predict the possible presence of Misconception 1 for a student. If a
student is determined to show evidence of the misconception on even just one of items 2, 3, 4, or 5, the student is likely
to have Misconception 1, regardless of whether the evidence is coded as “Strong” or “Weak.” The relative number of
items with weak or strong evidence gives you information about how strongly the misconception may be present for the
student.
27 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
(Optional) Scoring Practice Items—Post-Assessment
The following sample student responses are provided as an optional practice set. If you would like to practice scoring
several items to further clarify your understanding of the scoring process, you may try scoring the following 10 items.
We recommend scoring one or two at a time and checking your scoring as you go against our key, found on p. 31.
Practice Example 1
“9 in 0.99 is bigger than 8 in
0.899”
Practice Example 2
“34 is grater [greater] than
8.”
Practice Example 3
“I picked less than becaus
[because] the aligater
[alligator] whants [wants]
to eat the bigest [biggest]
number.”
28 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Practice Example 4
6/8 > 6/34
Fractions
Practice Example 5
“0.175 is greater than 0.2
beacause [because] on the
right its only 0.2”
Practice Example 6
“Because the bigger number
eats the smaller number”
Practice Example 7
“Even though theres the
number zero befor [before]
it the one on the left is still
bigger.”
29 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Practice Example 8
“8 is bigger than 3”
Practice Example 9
“34 is a hieghr [higher]
number than 8.”
Practice Example 10
“189 is more than 3.
Because three is more
than 1.”
30 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Scoring Practice Items Answer Key—Pre-Assessment
Practice Example 1
“9 in 0.99 is bigger than 8 in
0.899”
This is an example of a “Correct” example with “Strong Evidence” (though making any distinction between strong and
weak correct responses is not necessary for this diagnostic assessment; it simply gives you more information about
your student). The student is clearly paying attention to place value in order to compare the decimal numbers.
Practice Example 2
“34 is grater [greater] than
8.”
This is an example of M1 with “Strong Evidence.” The student is clearly paying attention to the digits to the right of the
decimal point and is comparing them as whole numbers.
Practice Example 3
“I picked less than because
[because] the aligater
[alligator] wants to eat the
bigest [biggest] number.”
This is an example of M1 with “Weak Evidence.” This student chose the M1 response for this item (“Less than”). This
student has clearly heard the mnemonic about alligators and inequality signs, but it is unclear how the student is
deciding which is the bigger number without having to make inferences about the student’s thinking. Therefore, it is
considered “Weak Evidence” of M1.
31 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Practice Example 4
6/8 > 6/34
Fractions
This is an example of a response that is neither correct nor an indicator of M1. The student selects the correct
response for this item (“Greater than”) but then changes the decimals into fractions incorrectly to compare them.
While 6/8 is indeed greater than 6/34, there is no evidence that the student is comparing 8 to 34 in order to compare
the decimals.
Practice Example 5
“0.175 is greater than 0.2
beacause [because] on the
right its only 0.2”
This is an example of M1 with “Weak Evidence.” This student chooses the M1 response for this item and in the
explanation says it’s “only 0.2,” suggesting possible whole-number reasoning. However, there is not enough
information in the explanation to determine this without making inferences about the student’s thinking. Therefore, it
is considered “Weak Evidence” of M1.
32 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Practice Example 6
“Because the bigger number
eats the smaller number”
This is an example of a “Correct” response with “Weak Evidence” (though making any distinction between strong and
weak correct responses is not necessary for this diagnostic assessment; it simply gives you more information about
your student). The student chooses the correct response for this item but does not provide sufficient evidence that he
or she understands why 2.41 is greater than 2.187.
Practice Example 7
“Even though theres the
number zero befor [before]
it the one on the left is still
bigger.”
This is an example of M1 with “Weak Evidence.” This student chooses the M1 response for this item (“Greater than”)
and says “the one on the left is still bigger.” While this suggests possible whole-number reasoning, there is not enough
information in the explanation to determine this without making inferences about the student’s thinking. Therefore, it
is considered “Weak Evidence” of M1.
Practice Example 8
“8 is bigger than 3”
This is an example of a “Correct” response with “Strong Evidence” (though making any distinction between strong and
weak correct responses is not necessary for this diagnostic assessment; it simply gives you more information about
your student). The student is clearly paying attention to place value in order to compare the decimal numbers.
33 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Scoring
Practice Example 9
“34 is a hieghr [higher]
number than 8.”
This is an example of M1 with “Strong Evidence.” The student is clearly paying attention to the digits to the right of the
decimal point and is comparing them as whole numbers.
Practice Example 10
“189 is more than 3.
Because three is more
than 1.”
This is an example of M1 with “Weak Evidence.” The student selects the M1 response (“Less than”). However, the
explanation seems contradictory: The student is clearly comparing 3 and 189 as whole numbers, but then says, “Because
three is more than 1,” suggesting the use of place value. Because it’s unclear how the student is thinking about this
comparison, it is considered “Weak Evidence” of M1.
34 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
Sample Student Responses
»»Review examples of student responses to assessment items.
To determine the degree of understanding and misunderstanding in the student work, it’s important to consider both the
answer to the selected response and the explanation text and representations. The example above is one of many student
work samples that provide insight into student thinking about the misconception targeted in these diagnostic assessments
(see the “Research-Based Misconceptions” tab for more information and a video about this misconception).
We encourage you to look at the collection of student work examples provided here.
The Comparing Decimals 1 diagnostic assessment focuses on a particular misconception that students have regarding
how to compare decimal numbers. Sample student responses indicative of this misconception are provided separately
below, along with samples of correct student responses. To determine the degree of understanding and misunderstanding,
it’s important to consider both the student’s answer to the selected response and the student’s explanation text and
representations.
»» Misconception 1 (M1): Using Whole-Number Thinking / A Focus on “Longer Is Larger”
Students with this misconception consistently compare decimals by comparing the numbers to the right of
the decimal point as if they were comparing whole numbers (e.g., they consider 0.34 to be greater than 0.8
because 34 is greater than 8). Because they are accustomed to thinking of numbers with more digits as larger,
they overgeneralize from their experiences with whole-number comparisons and extend this rule to decimals.
(For more information, go to the “Research-Based Misconceptions” tab.)
Students typically do not apply this thinking when comparing numbers with different digits in the ones place,
such as 2.36 and 5.1. Instead, they tend to appropriately compare the values of the digits in the ones place, in
this case reasoning that since 5 is greater than 2, 5.1 is greater than 2.36.
35 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Sample Student Responses
The following student responses show examples of this misconception.
Item
Sample Student Responses with Evidence of
Misconception 1
Pre-Assessment
#3
Notes
• The misconception selected response is
chosen
AND
• The student says the first decimal number
is bigger because it has more numbers
“0.788 is bigger because it has 1 more number than 0.88”
Pre-Assessment
#2
• The misconception selected response is
chosen
AND
• The explanation focuses on which decimal
number has more digits
“I think 12.659 is biger [bigger] becsse [because] it has
more digets [digits].”
Post-Assessment
#3
• The misconception selected response is
chosen
AND
• The digits after the decimal point are
labeled “thous” and “hun,” as if they were
whole numbers
Post-Assessment
#4
• The misconception selected response is
chosen
AND
• The student removes the decimal point and
compares the decimal numbers as whole
numbers
“6.8 is less than 6.34 because 68 is less than 634”
Post-Assessment
#2
“2.41 is less than 2.187 because this one has tree [three] #s”
36 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
• The misconception selected response is
chosen
AND
• The explanation states that the larger
decimal number is the one with more
numbers
ASSESSMENT
Comparing Decimals I
»»Sample Student Responses
Incorrect Reasoning That Is Not an Example of This Misconception
Some students exhibit another common difficulty when they compare decimal numbers by looking only at the digits to the
left of the decimal point and then determining that the decimal numbers are equivalent.
Note: This diagnostic probe is not validated to test for this other common difficulty. However, it may still be helpful to be
aware of it, since you may notice this type of reasoning as you look through your students’ work.
The following student response shows an example of this other common difficulty.
Item
Sample Student Response
with other Incorrect Reasoning
Pre-Assessment
#4
“I looked at the three and I was thinking if it was equivalent.”
Notes
• The selected response, “Equivalent,” is an
indicator of this difficulty
AND
• The explanation makes it clear that the
student is focusing on the digit to the left of
the decimal point
Some students may try to convert the decimal numbers into fractions (often incorrectly) and then compare the fractions.
Here are two examples:
Item
Sample Student Responses
with other Incorrect Reasoning
Not on the
Pre- or PostAssessment
Post-Assessment
#4
37 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
Notes
• The selected response is neither correct
nor the M1- aligned response
AND
• The student incorrectly converts the
decimal numbers into fractions (although
the student’s comparison of the value of
the fractions is correct, in that they both
equal 0)
• The student selects the correct response
HOWEVER
• The student incorrectly converts the
decimal numbers into fractions (although
the student’s comparison of the value of
the fractions is correct, in that 6/8 is greater
than 6/34)
ASSESSMENT
Comparing Decimals I
»»Sample Student Responses
Correct Reasoning
Students with correct reasoning about comparing decimals are often able to do one or more of the following:
• Correctly name the place values of different digits to the right of the decimal point
• Compare digits in corresponding place values in each decimal number
Item
Sample Student Responses
with Correct Reasoning
Pre-Assessment
#3
Notes
• The student selects the correct response
AND
• The student names the place values
correctly and identifies corresponding digits
to compare the decimal numbers
“It doesn’t matter how many numbers, it matters
what’s in the tenths place”
Pre-Assessment
#5
“0.3 > 0.189
0.3 is larger because 3 tents [tenths] is bigger
than almost 2 tenths.”
Pre-Assessment
#4
• The student selects the correct response
AND
• The student correctly names each decimal
number
AND
• The student draws accurate pictures of the
numbers using base 10 block images
• The student selects the correct response
AND
• The explanation describes how to compare
the decimal numbers by comparing digits
with corresponding place values
“3 and 3 are equal so you have to look at the 9 and
6 and 9 is bigger than 6 on the number line”
38 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
Administering the Post-Assessment
»»Learn how to introduce the post-assessment to your students.
If the Comparing Decimals 1 pre-assessment shows that any of your students
have the misconception outlined in the Scoring Guide, plan and implement
instructional activities designed to increase students’ understanding. The postassessment provided here can then be used to determine if the misconception
has been addressed.
Post-Assessment [Student Version]
See Appendix A for the student
version of the Post-Assessment.
Prior to Giving the Post-Assessment
• Arrange for 15 minutes of class time to complete the administration
process, including discussing instructions and student work time. Since
the post-assessment is designed to elicit a particular misconception
after instruction, you should avoid using or reviewing items from the
post-assessment before administering it.
Comparing Decimals I Post Assessment Name_________________________ Date__________ Class___________
Compare the two decimals provided. Select the choice that shows the relationship between the two decimals.
1)
Explain your thinking.
Greater than (>)
0.279 Less t han ( <) 0.345 Equivalent (=)
Explain your thinking.
2)
Greater than (>)
2.41 Less t han (<) 2.187 Equivalent (=)
Explain your thinking.
3)
Greater than (>)
0.899 Less than ( <) 0.99 Equivalent (=)
Administering the Post-Assessment
Copyright © 2015, Education Development Center, Inc. All rights reserved.
• Inform the students about the assessment by reading the following:
Today you will complete a short individual activity, which is designed to help
me understand how you think about comparing decimals, a topic we have been working on in class.
• Distribute the assessment and read the following:
This activity includes five problems. For each problem, choose your answer by completely filling in the circle to
show which answer you think is correct. Because the goal of the activity is to learn more about how you think
about comparing decimals, it’s important for you to include some kind of explanation in the space provided.
This can be a picture, words, a combination of pictures and words, or something else that shows how you
chose your answer.
You will have about 15 minutes to complete all the problems. When you are finished, please place the paper
on your desk and quietly [read, work on ____] until everyone is finished.
• Monitor the students as they work on the assessment, making sure that they understand the directions. Although
this is not a strictly timed assessment, it is designed to be completed within a 15-minute timeframe. Students may
have more time if needed. When a few minutes remain, say:
You have a few minutes to finish the activity. Please use this time to make sure that all of your answers are
as complete as possible. When you are done, please place the paper face down on your desk. Thank you for
working on this activity today.
• Collect the assessments
39 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
ASSESSMENT
Comparing Decimals I
»»Administering the Post Assessment
After Administering the Post-Assessment
Use the analysis process (found in the Scoring Guide PDF document under the Scoring Process section and found on
p. 7 of this document) to analyze whether your students have this misconception:
»» Misconception 1 (M1): Using Whole-Number Thinking / A Focus on “Longer Is Larger”
Some students who previously had the misconception will no longer have it—the ideal case. Consider your instructional
next steps for those students who still show evidence of the misconception.
40 Eliciting Mathematics Misconceptions | Assessment 1: Comparing Decimals 1
Comparing Decimals I Scoring Guide
Student:
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Str
Student:
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Str
Student:
Str
Post # 1
Str
Student:
Wk
Likelihood?
Str
Student:
Str
Pre # 5
Str
Student:
Wk
Pre # 4
Str
Student:
Str
Pre # 3
Str
Student:
Wk
Pre # 2
Str
Student:
Str
Pre # 1
Str
Student:
Wk
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Pre # 1
Pre # 2
Pre # 3
Pre # 4
Pre # 5
Likelihood?
Post # 1
Post # 2
Post # 3
Post # 4
Post # 5
Likelihood?
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Cor M1
Cor M1
Cor M1
Cor M1
Cor M1
M1
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Str
Wk
Str
Wk
Str
Wk
Str
Wk
Str
Wk
None
Comparing Decimals I Pre Assessment Name_________________________ Date__________ Class___________
Compare the two decimals provided. Select the choice that shows the relationship between the two decimals.
1)
Explain your thinking.
Greater than (>)
0.352 Less t han ( <) 0.476 Equivalent (=)
Explain your thinking.
2)
2)
Greater than (>)
12.86 Less t han ( <) 12.659 Equivalent (=)
Explain your thinking.
3)
3)
Greater than (>)
0.788 Less than ( <) 0.88 Equivalent (=)
Copyright © 2015, Education Development Center, Inc. All rights reserved.
Comparing Decimals I Pre Assessment Name_________________________ Date__________ Class___________
Compare the two decimals provided. Select the choice that shows the relationship between the two decimals.
Explain your thinking.
4)
Greater than (>)
3.65 Less t han ( <) 3.9 Equivalent (=)
Explain your thinking.
5)
5)
Greater than (>)
0.3 Less t han ( <) 0.189 Equivalent (=)
Copyright © 2015, Education Development Center, Inc. All rights reserved.
Comparing Decimals I Post Assessment Name_________________________ Date__________ Class___________
Compare the two decimals provided. Select the choice that shows the relationship between the two decimals.
1)
Explain your thinking.
Greater than (>)
0.279 Less t han ( <) 0.345 Equivalent (=)
Explain your thinking.
2)
2)
Greater than (>)
2.41 Less t han (<) 2.187 Equivalent (=)
Explain your thinking.
3)
3)
Greater than (>)
0.899 Less than ( <) 0.99 Equivalent (=)
Copyright © 2015, Education Development Center, Inc. All rights reserved.
Comparing Decimals I Post Assessment Name_________________________ Date__________ Class___________
Compare the two decimals provided. Select the choice that shows the relationship between the two decimals.
Explain your thinking.
4)
4)
Greater than (>)
6.34 Less t han ( <) 6.8 Equivalent (=)
Explain your thinking.
5)
5)
Greater than (>)
0.2 Less t han ( <) 0.175 Equivalent (=)
Copyright © 2015, Education Development Center, Inc. All rights reserved.