 # Standard 3 : Understand decimal notation for fractions, and compare decimal fractions. (Major Cluster) (Archived)

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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.

### General Information

Number: MAFS.4.NF.3
Title: Understand decimal notation for fractions, and compare decimal fractions. (Major Cluster)
Type: Cluster
Subject: Mathematics - Archived
Domain-Subdomain: Number and Operations - Fractions

#### Related Standards

This cluster includes the following benchmarks
 Code Description MAFS.4.NF.3.5: Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 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. MAFS.4.NF.3.7: 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.

#### Related Access Points

This cluster includes the following access points.

#### Access Points

 Access Point Number Access Point Title MAFS.4.NF.3.AP.5a: Find the equivalent fraction with denominators that are multiples of 10. 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. MAFS.4.NF.3.AP.7a: Use =, <, or > to compare two decimals (decimals in multiples of .10). MAFS.4.NF.3.AP.7b: Compare two decimals expressed to the tenths place with a value of less than 1 using a visual model. MAFS.4.NF.3.AP.7c: Compare two decimals expressed to the hundredths place with a value of less than 1 using a visual model.

#### Related Resources

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

#### Original Student Tutorials

 Name Description Fractions at the Fair: Equivalent Tenths and Hundredths: Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial. 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.

#### Formative Assessments

 Name Description Using Models to Compare Decimals: Students are asked to compare decimals by drawing a visual model and record the comparison using the less than, greater than, or equal to symbol. Tenths and Hundredths: Students are asked if an equation involving the sum of two fractions is true or false.  Then students are asked to find the sum of two fractions. Comparing Decimals in Context: Students are asked to compare two pairs of decimals in the context of word problems and to record a comparison using an inequality symbol. Adding Five Tenths: Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to another fraction with a denominator of 100. Comparing Four Tenths: Students are asked to consider two grids with different sized wholes and determine if both models show four-tenths. Compare Decimals: Students are asked to compare four pairs of decimals using the less than, greater than, or equal to symbols. Using Benchmark Decimals on a Number Line: Students are asked to use benchmark decimals to place four fractions on a number line. Hundredths and Tenths: Students are asked if an equation is true or false. Then students are asked to find the sum of two fractions. Fractions to Decimals: Students are given four fractions and asked to write each in decimal form. Seven Tenths: Students express a fraction with a denominator of 10 as an equivalent fraction with a denominator of 100 and are then asked to add the fraction to another fraction with a denominator of 100. 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 Adding Tenths and Hundredths: The purpose of this task is adding fractions with a focus on tenths and hundredths. 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. Fraction Equivalence: Students may not articulate every detail, but the basic idea for a case like the one shown here is that when you have equivalent fractions, you have just cut the pieces that represent the fraction into more but smaller pieces. Explaining fraction equivalences at higher grades can be a bit more involved (e.g. 6/8=9/12), but it can always be framed as subdividing the same quantity in different ways. 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. Using Place Value: Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

#### Tutorials

 Name Description Adding Two Fractions with Denominators 10 and 100: The Khan Academy tutorial video presents a visual fraction model for adding 3/10 + 7/100 . Comparing Two Decimals with a Visual Model: In this Khan Academy tutorial video two decimals are compared using grid diagrams. 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. Visually Converting from Tenths to Hundredths: In this Khan Academy video a fraction is converted from tenths to hundredths using grid diagrams. 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

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

#### Original Student Tutorials

 Title Description Fractions at the Fair: Equivalent Tenths and Hundredths: Learn about equivalent 10ths and 100ths and how to calculate these equivalent fractions at the fair in this interactive tutorial. 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

 Title 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.

 Title Description Adding Tenths and Hundredths: The purpose of this task is adding fractions with a focus on tenths and hundredths. 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. Fraction Equivalence: Students may not articulate every detail, but the basic idea for a case like the one shown here is that when you have equivalent fractions, you have just cut the pieces that represent the fraction into more but smaller pieces. Explaining fraction equivalences at higher grades can be a bit more involved (e.g. 6/8=9/12), but it can always be framed as subdividing the same quantity in different ways. 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. Using Place Value: Each part of this task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

#### Tutorials

 Title Description Adding Two Fractions with Denominators 10 and 100: The Khan Academy tutorial video presents a visual fraction model for adding 3/10 + 7/100 . Comparing Two Decimals with a Visual Model: In this Khan Academy tutorial video two decimals are compared using grid diagrams. 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. Visually Converting from Tenths to Hundredths: In this Khan Academy video a fraction is converted from tenths to hundredths using grid diagrams. 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

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