Standard #: MAFS.4.NF.3.6 (Archived Standard)


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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.



General Information

Subject Area: Mathematics
Grade: 4
Domain-Subdomain: Number and Operations - Fractions
Cluster: Level 1: Recall
Cluster: Understand decimal notation for fractions, and compare decimal fractions. (Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

Date Adopted or Revised: 02/14
Content Complexity Rating: Level 1: Recall - More Information
Date of Last Rating: 02/14
Status: State Board Approved - Archived
Assessed: Yes

Test Item Specifications

    N/A

    Assessment Limits :
    Denominators are limited to 10 and 100. Decimal notation is limited to tenths and hundredths. Items may contain decimals or fractions greater than 1 and/or mixed numbers
    Calculator :

    No

    Context :

    No context





Related Courses

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5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
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5020110: STEM Lab Grade 4 (Specifically in versions: 2016 - 2022, 2022 and beyond (current))
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022, 2022 and beyond (current))
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022, 2022 and beyond (current))


Related Resources

Educational Games

Name Description
Fraction Quiz

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Decimal and Fraction

This interactive Flash applet has students match fractions with their equivalent one- or two-place decimals. Students have a chance to correct errors until all matches are made.

Formative Assessments

Name Description
Using Benchmark Decimals on a Number Line

Students are asked to use benchmark decimals to place four fractions on a number line.

Fractions to Decimals

Students are given four fractions and asked to write each in decimal form.

Using Benchmark Fractions on a Number Line

Students are asked to use benchmark fractions to place four decimals on a number line.

Decimals to Fractions

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

Lesson Plans

Name Description
Field Day Fractions

This is a Model Eliciting Activity (MEA) activity which requires the students to convert fractions to decimals, order the decimals, and then design a process for ranking the classrooms from quantitative and qualitative data and then re-test their procedure on a new set of data. Ultimately, the students have to write a letter explaining and supporting the step-by-step process they used.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Cookies, Fractions and Decimals, Oh My!

This lesson asks students to recommend which cookie the owners of The Cookie Jar should add to their menu. Before they make their decision, the students have to convert decimal notation and fractions with denominators 10 and 100 to fractions with like denominators. Then they will be able to see exactly how many people voted for each cookie and they can factor in that information along with additional cookie facts to make their final recommendation.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

We All Scream for ICE CREAM - MEA

In this MEA, students will work in collaborative groups to solve multi-step problems with whole numbers, fractions, decimals and percent by using different mathematical operations. The students will be asked to assist an ice cream shop owner, who is planning a promotional program "Flavor of the Month," to rank the ice cream flavors based on the data provided. Students will need to read a data table, rank the flavors, convert the fraction amount to a percent and decimal and per serving costs to a decimal as well. A twist is added to the problem when one of the flavors is too expensive to make because of seasonal availability but two new flavors are added to be calculated. An additional twist is given by adding an adult survey to the second data table. The students will need to recalculate the new percent and decimals for the additional flavors.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Donuts and Decimals

In this MEA, students will convert fractions into decimals and then compare the decimals to decide which donut a donut shop should add to their menu.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Supermarket Sweep!

In this lesson, students will use a grocery store ad to select items for purchase, working within the constraint of making their purchases with a $50 gift card. After their initial plan, they have some emergency expenses that change the amount of the gift card unexpectedly, and they must alter their list and re-compute how much money would remain on their gift card after their planned purchases are made.


Cookies and Treats

Fourth graders will help Cookies and Treats find cost-effective and eco-friendly packaging for its cookies. Students will organize data and compare prices using decimal notation in order to develop a procedure for choosing packaging for cookies.  Students will use multiplication and division of whole numbers to plan for how many packages to order.

Model Eliciting Activities, MEAs, are open-ended, interdisciplinary problem-solving activities that are meant to reveal students’ thinking about the concepts embedded in realistic situations. Click here to learn more about MEAs and how they can transform your classroom.

Equivalency Detectives: Fractions and Decimals!

This is a lesson intended to reinforce students' ability to find equivalent fractions and decimals. The lesson requires prior essential vocabulary knowledge, and a basic understanding of converting fractions to decimals and decimals to fractions  (tenths and hundredths).

Fractions Undercover!

Students will correctly model and discover fractions and their decimal equivalents through the use of decimal grids and base ten blocks.

Dynamic Decimals, Fractions and Money!

This lesson is a practice lesson for student’s knowledge on connecting decimals, money and fractions. 

Happy Hundredths (Lesson 2 of 2)

In this lesson, students will work with math manipulatives to understand that it takes 100 hundredths of something to make one whole. They will use manipulatives with money (pennies and dollars), fractions (one hundredth pieces and one whole pieces), and base ten blocks (units and wholes) to show different values. They will express values with combinations of the given manipulatives and draw their solutions.

This lesson 2 of 2 in a unit on fraction and decimal concepts

Terrific Tenths (Lesson 1 of 2)

Students will work with math manipulatives to understand that it takes 10 tenths to make one whole. They will use manipulatives with money (dimes), fractions (one tenth pieces), and base ten blocks (rods) to show different values. They will use decimal notation to record these tenths. 

This is lesson one in a two part lesson unit. Lesson two (HAPPY HUNDREDTHS) deals with hundredths.

Original Student Tutorials

Name Description
Return to Deciland: Locating Decimals on a Number Line

Learn how to locate decimals on a number line and compare decimals to save the Decis from a wizard's spell in this interactive tutorial.

Deci Land Escape

Help Rich escape Deci Land by learning how to write decimals that are related to fractions with denominators of 10 and 100 in this interactive tutorial.

Problem-Solving Tasks

Name Description
How Many Tenths and Hundredths?

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Expanded Fractions and Decimals

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Dimes and Pennies

The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.

Tutorials

Name Description
Decimals as Words

In this Khan Academy video decimals are written and spoken in words.

Decimals and Fractions from Grid and Number-Line Representations

The Khan Academy video uses grid diagrams and number-line representations to say and write equivalent decimals and fractions.

Grid Representations of Decimals

The Khan Academy video illustrates how to determine and write the decimal represented by shaded grids.

Introduction to Decimals

This tutorial for student audiences will provide a basic introduction to decimals. The tutorial presents a decimal as another way to represent a fraction. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer gaining an orange circle and a wrong answer graying out. Some "Try This" sections will read the decimal to the students as well.

Virtual Manipulative

Name Description
Fraction Models

An interactive tool to represent a fraction circle, rectangle, or set model with numerators and denominators ranging from 1 to 100. The decimal and percent equivalents of the created fraction are also displayed.

Student Resources

Original Student Tutorials

Name Description
Return to Deciland: Locating Decimals on a Number Line:

Learn how to locate decimals on a number line and compare decimals to save the Decis from a wizard's spell in this interactive tutorial.

Deci Land Escape:

Help Rich escape Deci Land by learning how to write decimals that are related to fractions with denominators of 10 and 100 in this interactive tutorial.

Educational Games

Name Description
Fraction Quiz:

Test your fraction skills by answering questions on this site. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. You can even choose difficulty level, question types, and time limit.

Decimal and Fraction:

This interactive Flash applet has students match fractions with their equivalent one- or two-place decimals. Students have a chance to correct errors until all matches are made.

Problem-Solving Tasks

Name Description
How Many Tenths and Hundredths?:

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Expanded Fractions and Decimals:

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Dimes and Pennies:

The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.

Tutorials

Name Description
Decimals as Words:

In this Khan Academy video decimals are written and spoken in words.

Decimals and Fractions from Grid and Number-Line Representations:

The Khan Academy video uses grid diagrams and number-line representations to say and write equivalent decimals and fractions.

Grid Representations of Decimals:

The Khan Academy video illustrates how to determine and write the decimal represented by shaded grids.

Introduction to Decimals:

This tutorial for student audiences will provide a basic introduction to decimals. The tutorial presents a decimal as another way to represent a fraction. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer gaining an orange circle and a wrong answer graying out. Some "Try This" sections will read the decimal to the students as well.



Parent Resources

Problem-Solving Tasks

Name Description
How Many Tenths and Hundredths?:

The purpose of this task is for students to finish the equations to make true statements. Parts (a) and (b) have the same solution, which emphasizes that the order in which we add doesn't matter (because addition is commutative), while parts (c) and (d) emphasize that the position of a digit in a decimal number is critical. The student must really think to encode the quantity in positional notation. In parts (e), (f), and (g), the base-ten units in 14 hundredths are bundled in different ways. In part (e), "hundredths" are thought of as units: 14 things = 10 things + 4 things. Part (h) addresses the notion of equivalence between hundredths and tenths.

Expanded Fractions and Decimals:

The purpose of this task is for students to show they understand the connection between fraction and decimal notation by writing the same numbers both ways. Comparing and contrasting the two solutions shown below shows why decimal notation can be confusing. The first solution shows the briefest way to represent each number, and the second solution makes all the zeros explicit.

Dimes and Pennies:

The purpose of this task is to help students gain a better understanding of fractions through the use of dimes and pennies.

Tutorial

Name Description
Introduction to Decimals:

This tutorial for student audiences will provide a basic introduction to decimals. The tutorial presents a decimal as another way to represent a fraction. Students will be able to navigate the teaching portion of the tutorial at their own pace and test their understanding after each step of the lesson with a "Try This" section. The "Try This" section will monitor students answers and self-check by a right answer gaining an orange circle and a wrong answer graying out. Some "Try This" sections will read the decimal to the students as well.



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