Unit 4

Decimal Fractions

Math

Unit Length and Description:

20 days

In unit 4, students extend their understanding of finding equivalent fractions to change fractions with a denominator of 10 to a denominator of 100.  As students prepare for their initial work with decimal numbers, previous experiences with building equivalent fractions should support their work of changing tenths to hundredths.  As they connect fractions to decimal representations, students should realize that decimal place value units are special fraction units:  0.7, 7 tenths, and  are different representations for the same number.

During this unit, students extend their work with whole number place value to include decimal places on the place value chart.  Students are provided with many experiences to show concrete representations and numerical representations of decimals, and read decimal numbers to hundredths.

Students explore adding and subtracting tenths plus hundredths using models and visual representations.  Fluency makes an important role in this unit as students begin to add and subtract fractions with unlike units, for example, 3 tenths + 4 hundredths = 30 hundredths + 4 hundredths.  As students begin to understand the relationship among decimals places, they use models and visual representations to compare decimals that refer to the same whole.  Finally, students apply their understanding of decimal fractions to solve measurement word problems.

Standards:

 Major Cluster: Number and Operations-Fractions Understand decimal notations for fractions, and compare decimal fractions. 4.NF.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.  (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general.  But addition and subtraction with unlike denominators in general is not a requirement at this grade.) 4.NF.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. 4.NF.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. Supporting Cluster:  Measurement and Data Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit 4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. Standards for Mathematical Practices 1.   Make sense of problems and persevere in solving them. 2.   Reason abstractly and quantitatively. 3.   Construct viable arguments and critique the reasoning of others. 4.   Model with mathematics. 5.   Use appropriate tools strategically. 6.   Attend to precision. 7.   Look for and make use of structure. 8.   Look for and express regularity in repeated reasoning.

Enduring Understandings:

·         Fractions can be expressed as decimals.

·         Decimals can be represented visually and in written form.

·         Decimals are a part of the base ten system.

·         Tenths can be expressed using an equivalent fraction with a denominator of 100.

·         Comparisons of two decimals are only valid when the two decimals refer to the same whole.

Essential Questions:

·         What is a decimal fraction and how can it be represented?

·         How are decimal numbers and decimal fractions related?

·         How can I model decimals fractions using the base-ten and place value system?

·         What are the characteristics of a decimal fraction?

·         What patterns occur on a number line made up of decimal fractions?

·         When we compare two decimals, how do we know which has a greater value?

4.NF.A.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.  (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general.  But addition and subtraction with unlike denominators in general is not a requirement at this grade.)

Activities and Resources

·         Decimal Designs

·         Decimal Fraction Cards

·         Dismissal Duty Dilemma

·         Equivalent Fractions with a Denominator of 100 Problems

·         Fraction Go Fish

·         Sums of 1

·         Dimes and Pennies

·         Equation Check

·         Model Z

Illustrative Mathematics

·         How Many Tenths and Hundredths?

·         Expanded Fractions and Decimals

·         Dimes and Pennies

·         Fraction Equivalence

Online Resources

Teachers please be aware that many free online resources are supported by advertisements. Although they may be excellent for use with students, we as educators are legally obligated to make sure our students are not exposed to these advertisements. Please screen all online resources before showing to students. If a game has a “full screen” mode or requires that you begin the game to move past the ads, please do so before allowing student access.

·         Thinking Blocks – Model and Solve Fraction Word Problems

·         Thinking Blocks – Modeling Tool

·         Decimal Number Bonds, Make 1

Illuminations

LearnZillion

·         Express Fractions with a Denominator of 10 as Equivalent to Fractions with Denominators of 100

·         Express a Fraction with Denominator 10 as an Equivalent Fraction with Denominator 100

·         Convert Between Fractions and Decimals

·         Comparing Decimal Fractions and Understanding Notation (Unit)

* Contain standards from more than one domain

4.NF.A.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.

Activities and Resources

·         Decimal Fraction Cards

·         Decimal Hundreds Chart

·         Decimals: Hundredths Grids 1

·         Decimals: Hundredths Grids 2

·         Decimal Squares

·         Decimals to Fractions

·         Diving for Decimals

·         Representing Decimals

·         Show What You Know:  Multiple Representations of Decimals and Fractions

·         Expanding Decimals with Money

Illustrative Mathematics

·         How Many Tenths and Hundredths?

·         Expanded Fractions and Decimals

·         Dimes and Pennies

Online Resources

Teachers please be aware that many free online resources are supported by advertisements. Although they may be excellent for use with students, we as educators are legally obligated to make sure our students are not exposed to these advertisements. Please screen all online resources before showing to students. If a game has a “full screen” mode or requires that you begin the game to move past the ads, please do so before allowing student access.

o   Thinking Blocks – Model and Solve Fraction Word Problems

o   Thinking Blocks – Modeling Tool

o   Place Value Number Line (choose decimal place)

o   Line Mine

Gizmos

·         Modeling Decimals (Area and Grid Models)

·         Treasure Hunter (Decimals on the Number Line)

Illuminations

·         What’s the (Decimal) Point?:  Using Models to Understand Decimal Place Value

LearnZillion

·         Use Decimal Notation for Fractions with Denominators 10 or 100

4.NF.B.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.

Activities and Resources

·         Comparing Decimals

·         Decimal Board Activities

·         Decimal Line Up

·         Deci-Mill Dunk

·         Deci-Moves

·         Decimal Sort

·         Decimal Squares

·         I am the Greatest

·         Running the Race

llustrative Mathematics

·         Using Place Value

Online Resources

Teachers please be aware that many free online resources are supported by advertisements. Although they may be excellent for use with students, we as educators are legally obligated to make sure our students are not exposed to these advertisements. Please screen all online resources before showing to students. If a game has a “full screen” mode or requires that you begin the game to move past the ads, please do so before allowing student access.

·         Compare Money Amounts

·         Fruit Splat Compare

LearnZillion

·         Compare Two Decimals to Hundredths

4.MD.A.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Activities and Resources

·         Metric Relationships

·         Number Lines for Hundredths

·         Number Lines for Tenths

·         Meter Stick Compare Fractions

Online Resources

Teachers please be aware that many free online resources are supported by advertisements. Although they may be excellent for use with students, we as educators are legally obligated to make sure our students are not exposed to these advertisements. Please screen all online resources before showing to students. If a game has a “full screen” mode or requires that you begin the game to move past the ads, please do so before allowing student access.

·         Thinking Blocks – Modeling Tool

LearnZillion

·         Represent Fractional Distance Measurement Quantities Using Diagrams

·         Represent Quantities of Money by Using Diagrams

·         Convert Larger Units to Smaller Units in Money Problems