Decimals to Fractions

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Resource ID#: 61925 Primary Type: Formative Assessment

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Students are given four decimals and asked to write each as a fraction.

General Information

Subject(s): Mathematics, Mathematics (B.E.S.T. - Effective starting 2022-2023)

Grade Level(s): 4

Intended Audience: Educators

Keywords: MFAS, fraction, decimal, tenths, hundredths

Instructional Component Type(s): Formative Assessment

Resource Collection: MFAS Formative Assessments

Attachments

MFAS_DecimalsToFractions_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.

The teacher provides the student with the Decimals to Fractions worksheet.
The teacher says, “Write each of the following decimals as fractions.”

Three-tenths

Eighty seven hundredths

Five hundredths

Nine-tenths

TASK RUBRIC

Getting Started

Misconception/Error

The student does not understand how to represent a decimal as a fraction.

Examples of Student Work at this Level

The student is unable to identify the appropriate denominator.

The student includes the decimal point in the numerator (e.g., writing $begin mathsize 12px style fraction numerator 0.87 over denominator 100 end fraction end style$ ).

Questions Eliciting Thinking

What do the decimal places tell you about the denominator of the fraction?

Can you read aloud the number 0.75? How would you write the fraction for that number?

What is the denominator of 0.2? What is the denominator or 0.05?

What happens to the decimal point when you write the decimal as a fraction?

Instructional Implications

Model for the student how to read decimals and write them as fractions. Guide the student to understand that the number of digits to the right of the decimal indicates the number of zeros in the denominator of the fraction. Begin with decimals such as 0.6 and 0.93. Next, introduce decimals with zeros in the tenths or hundredths place such as 0.40 and 0.07. Use place value blocks, 10 by 10 grids, and money to model the equivalence of decimals such as 0.8 and 0.80 and the corresponding fractions of $begin mathsize 12px style 8 over 10 end style$ and $begin mathsize 12px style 80 over 100 end style$ .

Provide opportunities for the student to use place value mats, blocks, and 10 by 10 grids to represent decimals as fractions with denominators of 10 and 100.

Consider implementing the MFAS task Fractions to Decimals.

Making Progress

Misconception/Error

The student makes errors when there is a zero in the tenths or hundredths place.

Examples of Student Work at this Level

The student writes 0.09 as $begin mathsize 12px style 9 over 10 end style$ .

The student writes 0.60 or $begin mathsize 12px style 6 over 100 end style$ or $begin mathsize 12px style 60 over 10 end style$ .

Questions Eliciting Thinking

Can you explain how 0.3 and 0.03 are different when written as fractions?

Look at the number 0.09. What is the place value of the nine? What will be the denominator of the fraction?

Can you read aloud the number 0.6? What will be the denominator of the fraction?

When you look at a decimal, how do you know the numerator of the fraction? How do you know the denominator?

Instructional Implications

Use place value blocks, 10 by 10 grids, and money to model the equivalence of decimals such as 0.8 and 0.80 and the corresponding fractions of $begin mathsize 12px style 8 over 10 end style$ and $begin mathsize 12px style 80 over 100 end style$ . In a similar fashion, model the difference between decimals such as 0.09 and 0.9 and the corresponding fractions.

Provide opportunities for the student to use place value mats, blocks, and 10 by 10 grids to represent decimals as fractions with denominators of 10 and 100. Give the student additional practice with decimals such as 0.4 and 0.04, 0.8 and 0.08, and 0.1 and 0.01.

Consider using the MFAS task Tenths and Hundredths.

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 represents each decimal: 0.6 as $begin mathsize 12px style 6 over 10 end style$ , 0.87 as $begin mathsize 12px style 87 over 100 end style$ , 0.09 as $begin mathsize 12px style 9 over 100 end style$ , and 0.23 as $begin mathsize 12px style 23 over 100 end style$ .

Questions Eliciting Thinking

Is 0.6 the same as 0.60? How do you know that? Can you represent this visually?

Can you write the fraction for 0.007?

How would you add $begin mathsize 12px style 7 over 10 end style$ and $begin mathsize 12px style 19 over 100 end style$ ? Can you write the sum as a decimal?

Instructional Implications

Challenge the student to add decimals by expressing them as fractions with like denominators of 10 or 100 (e.g., add 0.6 to 0.14 by writing $begin mathsize 12px style 60 over 100 end style$ + $begin mathsize 12px style 14 over 100 end style$ = $begin mathsize 12px style 74 over 100 end style$ ).

Ask the student to compare fractions and decimals to the hundredths place by reasoning about their size and writing them in common formats (e.g., compare $begin mathsize 12px style 7 over 10 end style$ and $begin mathsize 12px style 60 over 100 end style$ or compare 0.4 and $begin mathsize 12px style 23 over 100 end style$ ).

Allow the student to work with a Making Progress student to explain how decimals can be written as fractions with tenths and hundredths.

Consider using the MFAS Task Using Benchmark Decimals on a Number Line.

Accommodations & Recommendations

Special Materials Needed:
- Decimals to Fractions 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

* Please note that examples of resources are not intended as complete curriculum.

Aligned Standards

This vetted resource aligns to concepts or skills in these benchmarks.

Related Resources

Other vetted resources related to this resource.

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Decimals to Fractions

General Information

Attachments

Formative Assessment Task

Instructions for Implementing the Task

TASK RUBRIC

Getting Started

Making Progress

Got It

Accommodations & Recommendations

Special Materials Needed:

Source and Access Information

Aligned Standards

Related Resources

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