Primary Type: Formative Assessment
Status: Published
This is a resource from CPALMS (www.cpalms.org) where all educators go for bright ideas!
Resource ID#: 63165
Comparing Four Tenths
Students are asked to consider two grids with different sized wholes and determine if both models show four-tenths.
Subject(s): Mathematics
Grade Level(s): 4
Intended Audience: Educators
Freely Available: Yes
Keywords: MFAS, compare, hundredths, tenths, grids
Resource Collection: MFAS Formative Assessments
ATTACHMENTS
MFAS_ComparingFourTenths_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 Comparing Four Tenths worksheet and reads the following aloud to the student:
When some students look at these two grids, they believe that both grids show four tenths because each has four parts shaded in. Is this reasoning correct? Why or
why not?
2. If necessary the teacher can prompt by asking, “What do you notice about the two models?”
TASK RUBRIC
Getting Started
Misconception/Error
The student does not understand that decimal comparisons are only valid when referring to the same sized whole.
Examples of Student Work at this Level
The student says that the reasoning is correct because both models have four shaded in. When prompted, the student says that the two wholes do not need to be the
same size.
page 1 of 3 Questions Eliciting Thinking
What is the same about the models? What is different?
Can we compare decimals using area models if they are not the same size? What would that show us?
How many total squares are in the model? What fraction of the model is shaded?
What does one square represent on a 10 x 10 grid? What does one column represent?
Can you write the decimal (or fraction) for the second model?
Instructional Implications
Demonstrate that comparisons are only valid when the decimals refer to the same size whole using the same size partition (e.g., tenths or hundredths). Provide
opportunities for the student to use models (10 x 10 grids or base ten blocks) to compare decimal numbers. Reinforce the relationship between decimals and fractions and
guide the student to understand and compare decimals by thinking about them as fractions.
It may be helpful to relate the decimals to money. Relate the place value to the corresponding coin (e.g., the tenths place represents dimes). For example, when
comparing 0.4 and 0.04, the student can say that 0.4 is four dimes, or forty cents, and 0.07 is seven pennies, or seven cents. Guide the student to observe that 0.07 is
less than 0.4 since seven cents is less than forty cents.
Model reading decimals appropriately (e.g., read 0.4 as “four tenths” rather than as “zero­point­four”).
Consider using the MFAS task Comparing Four Fifths and Three Fourths (4.NF.1.2) which assesses this same idea using fractions.
Making Progress
Misconception/Error
The student is unable to clearly explain the difference in the models.
Examples of Student Work at this Level
The student struggles to clearly explain that the model is flawed because the two wholes are not the same size. After prompting from the teacher, the student may be
able to describe that decimal comparisons are only valid when the two wholes are the same size.
Questions Eliciting Thinking
What is different about the two models? Why is that difference important?
Can we compare fractions using area models if they are not the same size? What would that show us?
How many total squares are in the model? What fraction of the model is shaded?
If you write each number as a decimal (or fraction) can you compare them?
How could you represent each of the models as a fraction?
Instructional Implications
Guide the student to interpret 0.04 as four hundredths and to interpret 0.4 in its equivalent form, 40 hundredths. Model explaining that 0.04 is less than 0.4 because 4
hundredths is less than 40 hundredths. Encourage the student to provide place value explanations when comparing decimals.
Partner the student with a “Getting Started” student. Have the student model for the “Getting Started” student how to compare decimal numbers using place value
understanding.
Provide the student with problems in context to compare decimals with different wholes. For example, Mary had 0.75 of one milliliter of liquid and Zak had 0.5 of a liter of
liquid. Explain why Zak has more liquid than Mary.
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 says that the reasoning is incorrect because the models do not have the same size whole and comparisons of decimals are only valid when they refer to the
same size whole. The student may also note that the decimal grid showing 0.4 has a greater fraction of area shaded than the decimal grid showing 0.04.
Questions Eliciting Thinking
How could we make the models comparable in this example?
What would you tell another student to convince them that the models are not equivalent?
page 2 of 3 Can you represent the value shown by each model on the same number line?
How can you use benchmark fractions (0,
Is
always less than
,
,
, and 1) to compare 0.49 and 0.8?
? Why or why not?
Instructional Implications
Ask the student to use strategies other than visual models to compare decimals (e.g., place value and benchmark decimals). Guide the student to reason about the size of
the decimal and to see that some decimals can be easily compared using place value or benchmark decimals. Guide the student to be flexible in his or her choice of
strategies based on the decimals being compared.
ACCOMMODATIONS & RECOMMENDATIONS
Special Materials Needed:
Comparing Four 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.3.7:
Description
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.
page 3 of 3