MAFS.4.NF.3.6

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
Assessed: Yes
Test Item Specifications

  • 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

Sample Test Items (2)

Related Courses

This benchmark is part of these courses.
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 and beyond (current))
5020110: STEM Lab Grade 4 (Specifically in versions: 2016 - 2022 (current), 2022 and beyond)
5012065: Grade 4 Accelerated Mathematics (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)
5012015: Foundational Skills in Mathematics 3-5 (Specifically in versions: 2019 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.4.NF.3.AP.6a: Identify the equivalent decimal form for a benchmark fraction.
MAFS.4.NF.3.AP.6b: Match a fraction (with a denominator of 10 or 100) with its decimal equivalent (5/10 = 0.5).
MAFS.4.NF.3.AP.6c: Read, write, or select decimals to the tenths place.
MAFS.4.NF.3.AP.6d: Read, write, or select decimals to the hundredths place.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 4 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Sample 3 - Fourth Grade Math State Interim Assessment:

This is a State Interim Assessment for fourth grade.

Type: Assessment

Educational Games

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.

Type: Educational Game

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.

Type: Educational Game

Formative Assessments

Using Benchmark Decimals on a Number Line:

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

Type: Formative Assessment

Fractions to Decimals:

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

Type: Formative Assessment

Using Benchmark Fractions on a Number Line:

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

Type: Formative Assessment

Decimals to Fractions:

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

Type: Formative Assessment

Lesson Plans

What Sort of Decimal Do You Have?:

This is a thought-provoking fraction/decimal comparison task. The fractions and decimals have been selected for this task to promote the use the following strategies when suitable:
• comparing to benchmark fractions,
• finding a common denominator,
• finding a common numerator.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

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.

Type: Lesson Plan

Farming Fractions:

This lesson begins with a whole-group flower garden anchor chart activity. Independent practice follows with students using a 100"s grid to plant a ten-row vegetable garden with four kinds of vegetables. They write equivalent fractions and decimals for the part of the garden in which each vegetable is planted. Decimals are then written in expanded form.

Type: Lesson Plan

Cookies and Treats:

Fourth graders will help Cookies and Treats find eco-friendly packaging for its cookies. Students will work with decimals and data in order to develop a procedure for ranking and choosing packaging for cookies.

Type: Lesson Plan

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 (specifically tenths and hundredths).

Type: Lesson Plan

Fractions Undercover!:

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

Type: Lesson Plan

Dynamic Decimals, Fractions and Money!:

In this lesson, students will realize the connection between fractions, decimals and money through the use of a 100 grid.

Type: Lesson Plan

Happy Hundredths (Lesson 2 of 3):

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 3 in a unit on fraction and decimal concepts

Type: Lesson Plan

Shopping with Tenths and Hundredths (Lesson 3 of 3 in a Unit):

This is the third lesson of a three-lesson unit about tenths and hundredths. Please see "happy hundredths" and "terrific tenths" before attempting this lesson. Students will work with math manipulatives to understand that it takes 100 hundredths or 10 tenths of something to make one whole. They will understand that it takes 10 hundredths to make 1 tenth. They will use manipulatives with money (pennies, dimes, dollars), fractions (one hundredth pieces, one tenth pieces, one whole pieces), and base ten blocks (units, rods, wholes) to show different values. They will express values with combinations of the given manipulatives and draw their solutions.

Type: Lesson Plan

Terrific Tenths (Lesson 1 of 3):

In this lesson, students will work with math manipulatives to understand that it takes 10 tenths of something 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 express values with combinations of the given manipulatives and draw their solutions.

This is lesson one in a three lesson unit.  Lesson two (HAPPY HUNDREDTHS) deals with hundredths and lesson three deals with combining and solving problems with tenths and hundredths (SHOPPING WITH TENTHS AND HUNDREDTHS).

Type: Lesson Plan

Original Student Tutorials

Return to Deciland: Locating Decimals on a Number Line:

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

Type: Original Student 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.

Type: Original Student Tutorial

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorials

Decimals as Words:

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

Type: Tutorial

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.

Type: Tutorial

Grid Representations of Decimals:

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

Type: Tutorial

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.

Type: Tutorial

Virtual Manipulative

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.

Type: Virtual Manipulative

STEM Lessons - Model Eliciting Activity

Cookies and Treats:

Fourth graders will help Cookies and Treats find eco-friendly packaging for its cookies. Students will work with decimals and data in order to develop a procedure for ranking and choosing packaging for cookies.

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.

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.

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.

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.

MFAS Formative Assessments

Decimals to Fractions:

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

Fractions to Decimals:

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

Using Benchmark Decimals on a Number Line:

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

Using Benchmark Fractions on a Number Line:

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

Original Student Tutorials Mathematics - Grades K-5

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.

Return to Deciland: Locating Decimals on a Number Line:

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

Student Resources

Vetted resources students can use to learn the concepts and skills in this benchmark.

Original Student Tutorials

Return to Deciland: Locating Decimals on a Number Line:

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

Type: Original Student 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.

Type: Original Student Tutorial

Educational Games

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.

Type: Educational Game

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.

Type: Educational Game

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorials

Decimals as Words:

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

Type: Tutorial

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.

Type: Tutorial

Grid Representations of Decimals:

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

Type: Tutorial

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.

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Tasks

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

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.

Type: Problem-Solving Task

Tutorial

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.

Type: Tutorial