Standard #: MA.4.FR.1.2


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Use decimal notation to represent fractions with denominators of 10 or 100, including mixed numbers and fractions greater than 1, and use fractional notation with denominators of 10 or 100 to represent decimals.


Clarifications


Clarification 1: Instruction emphasizes conceptual understanding through the use of manipulatives visual models, number lines or equations.

Clarification 2: Instruction includes the understanding that a decimal and fraction that are equivalent represent the same point on the number line and that fractions with denominators of 10 or powers of 10 may be called decimal fractions.



General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 4
Strand: Fractions
Status: State Board Approved

Benchmark Instructional Guide

Connecting Benchmarks/Horizontal Alignment

 

Terms from the K-12 Glossary

  • NA

 

Vertical Alignment

Previous Benchmarks

 

Next Benchmarks

 

Purpose and Instructional Strategies

The purpose of this benchmark is to connect fractions to decimals. Students extend their understanding of fraction equivalence (MA.3.FR.2.2) to include decimal fractions with denominators of 10 or 100. The connection will continued in grade 6 (MA.6.NSO.3.5) and completed in grade 7 (MA.7.NSO.1.2). 
  • Instruction should help students understand that decimals are another way to write fractions. The place value system developed for whole numbers extends to fractional parts represented as decimals. The concept of one whole used in fractions is extended to models of decimals. It is important that students make connections between fractions and decimals in models. 
  • Instruction should provide visual fraction models of tenths and hundredths, number lines, and equations so that students can express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100. 
  • Students reinforce understanding that the names for decimals match their fraction equivalents (e.g., seven tenths, 7 tenths, 0.7, 710, seventy hundredths, 70 hundredths, 0.70 and 70100 are all equivalent). 

  • This benchmark is a connection point to the metric system and will be explored in MA.4.M.1.2.

 

Common Misconceptions or Errors

  • Students often confuse decimals such as 6 tenths and 6 hundredths. Students should use models and explain their reasoning to develop their understanding of the connections between fractions and decimals.
  • Some students may not understand that fractions and decimals are different presentations of the same thing. Number lines and other visual models will help students gain a better understanding of this concept.

 

Strategies to Support Tiered Instruction

  • Instruction includes building fractions and their decimal equivalents using base ten blocks. 
    • For example, students build 210 “two-tenths” and 20100 “twenty hundredths” with base ten blocks while using vocabulary that will help students see the decimal connection as well. Students realize that the numbers have the same value.
base 10 blocks

 

Instructional Tasks

Instructional Task 1 (MTR.6.1

Read the following numbers and use the benchmark fractions to place them on the number line. 
  • a. 0.8 
  • b. 0.32 
  • c. 0.6 
  • d. 0.17
number line

 

Instructional Items

Instructional Item 1 

A value is shown.
2 5100

What is the value in decimal form? 
  • a. 0.25 
  • b. 2.05 
  • c. 2.5 
  • d. 25.100

*The strategies, tasks and items included in the B1G-M are examples and should not be considered comprehensive.



Related Courses

Course Number1111 Course Title222
5012060: Mathematics - Grade Four (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))
7712050: Access Mathematics Grade 4 (Specifically in versions: 2014 - 2015, 2015 - 2018, 2018 - 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 Access Points

Access Point Number Access Point Title
MA.4.FR.1.AP.2 Use decimal notation to represent fractions less than one with denominators of 10 or 100 and use fractional notation with denominators of 10 or 100 to represent decimals less than one.


Related Resources

Educational Games

Name Description
Flower Power: An Ordering of Rational Numbers Game


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

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.

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
Wondrous Water Parks

This activity requires students to apply their knowledge of unit conversions, speed calculation, and comparing fractions to solve the problem of which water park their class should choose to go on for their 5th grade class trip.

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. 

Fraction Measuring With Cuisenaire Rods

In this lesson, students will use Cuisenaire rods to measure lengths and generate equivalent fractions. This is a concrete way to introduce how to generate equivalent fractions by finding patterns in the numerators and denominators.

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.

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
Flower Power: An Ordering of Rational Numbers Game:


This is a fun and interactive game that helps students practice ordering rational numbers, including decimals, fractions, and percents. You are planting and harvesting flowers for cash. Allow the bee to pollinate, and you can multiply your crops and cash rewards!

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.

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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