Fraction and Decimal Equivalency - ODE - Ohio Department of ...

Fraction and Decimal Equivalency – Grade Four787 rods 8 units = 100= 0.78606 rods 0 units = 106= 100= 0.6 = 0.60506. Have students place five rods on the flat. Discuss what part of the whole this is ( 105, 100, 0.5,50.50). Lead discussion for other ways to say 10using the example of five dimes (50 pennies)5 50is equal to a half-dollar: 5 dimes = one half dollar = 10= 100= 0.5 = 0.50 = 21. Discuss other5examples to prove 10(0.5) = 21, e.g.:• 5 is half of ten1• 5 apples are 2of 10 apples25 1Continue with examples to show 100= 0.25 = 4(just as one quarter is one-fourth of a dollar)75 3 3and 100= 4(just as three quarters are 4of a dollar).107. Have students cover the flat with 10 rods to lead discussion of how to read and write this: 10100= 1.0 = 1.00. Continue with more examples, e.g.:= 1001010of a candy bar = one whole candy bar100100 pennies = 100of a dollar = $1.00Part Two8. Pass out a copy of 10 x 10 Grid, Attachment E, to each student. Have students cut out thelarge grid. Ten by ten grids may be cut from one-inch grid paper as an alternative. Make achart on the overhead projector, board or chart paper for display to record information to helpstudents notice patterns.Fraction of grid Number of small squares Decimal100100 1.00, 1.0100Instructional Tip:Throughout this part, relate how tenths of a whole are the same as dimes in a dollar andhundredths are like pennies in a dollar. Example:7 ten strips = 107= 0.7 just as 7 dimes = $0.709. Tell students to think of this grid as one whole.a. How many small squares are in the large square? (100, just as 100 pennies are in onedollar)b. How would we write a fraction to show all the small squares in the large square? ( 100c. As a decimal? (1.00, 1.0)100)5

Fraction and Decimal Equivalency – Grade Four72• Write the fraction 100below the grid. How many small squares should we shade? (72)How would you write this as a decimal? (0.72)1• Shade 2of the whole square. How many small squares would this be? (50) How would50you write the fraction? ( 105, 100or 21) How would you write the decimal? (0.5 or 0.50)• Shade the whole square. How many small squares is this? (100) How would you write10 100this as a fraction? ( 10, 100) How would you write this as a decimal? (1.0, 1.00)Instructional Tip:When working together, allow time for students to try to answer questions on their own, withimmediate feedback as to correct solution. Allow time for and encourage questions. Circulate toassist while instructing.21. Have students turn over Class Worksheet, Attachment C. They may look back to thisworksheet if they continue to have difficulty relating fractions and decimals, but encouragethem to try the next part on their own. Pass out copies of Independent Worksheet, AttachmentD. Working independently, students will continue to shade grids and write fractions anddecimals for problems seven through twelve. Examples are given on the board or overheadand presented orally:• Shade 6 tenths.• Shade 6 hundredths.• Shade 3 tenths and 4 hundredths.55• Show 100.50• Shade 100. Write two fractions and two decimals.• Shade the whole square.22. Collect Class Worksheet, Attachment C, and Independent Worksheet, Attachment D, toevaluate students’ progress.23. Have students independently write about what they learned in their mathematical journal.Have students draw models of fractional parts and label using decimals, fractions and words.Circulate to ask questions of individuals to help them clarify thinking such as:• How are fractions and decimals alike?• What does it mean to have a repeating decimal?• What can you do to find a decimal equivalent for a fraction?• A fractional part can be represented by different fractions such as one-half is the same astwo-fourths and three-sixths. Can decimals be represented by different fractions? (No,0.2 can not be represented as a decimal in any other way.)Allow time for partners to share their ideas with each other. Randomly choose students toshare their journal entries with the class. Review terms whole, fraction, decimal, tenths,hundredths, and how common fractions can be expressed as decimals. Record ideas on chartpaper to display.8

Fraction and Decimal Equivalency – Grade FourPart Five24. On the board or on chart paper, draw a number line labeled 0 on the left end and 1 on theright end. Have each pair of students make a number line horizontally in their mathematicsjournal or on a sheet of 8 21x 11 inch paper.0 125. Distribute a copy of Fractions and Decimals, Attachment F, to each pair of students. Havestudents cut apart the fractions and decimals and collaborate to decide about where on thenumber lines the fractions and decimals would go. After placing these in order on their desk,students put a point for each fraction and decimal on their number lines and write the fractionor decimal below the point. If students have difficulty ordering fractions and decimals havethem make models or visual representations using 10 by 10 grids.26. When all students have their number lines finished, begin placing fractions on the largenumber line using tape or gummy adhesive. Randomly choose students to place fractions ordecimals on the number line. Have chosen students explain their strategies for placement onthe number line. Class participates by using “thumbs up” for agreement” or “thumbs down”for disagreement. Choose students to correct any errors.Instructional Tip:Parallel number lines may be drawn directly above or below the instructional number line todivide into thirds, fourths and tenths. By lining up the number lines, students will be able to placetheir fraction more accurately on the instructional number line.27. Cover the number line at the board. In math journal or on paper, have students turn paperhorizontally to draw a number line beginning with 0 and ending with 1. Tell students to put amark and label the number line with these fractions and decimals: 41, 21, 43, 31, 1.00, 0.50,0.10, and 0.6.28. Have students confer with partners to compare number lines, discuss placement of fractionsand decimals and, if necessary, change their positions. For feedback, show all students thenumber line used during instruction and review thinking strategies to find correct placementsof the fractions and decimals.Differentiated Instructional Support:Instruction is differentiated according to learner needs, to help all learners either meet the intentof the specified indicator(s) or, if the indicator is already met, to advance beyond the specifiedindicator(s).• Students showing evidence of not meeting expectations may need extra practice andindividual assistance using the base-ten blocks. They may benefit from using play money(dollars, dimes and pennies) to model each decimal.• Working with partners will increase attention, confidence and development of skills.• Students demonstrating evidence of exceeding expectations may be utilized as peer tutors forstudents needing extra practice.9

Fraction and Decimal Equivalency – Grade Four• Use calculators to find decimals for fractions (i.e., thirds, eighths, twelfths, etc.).• Challenge students to create equivalent fractions by multiplying the numerator and1 1000denominator by the same number. (Example: 10002x1000=2000) Students may check equivalentfractions using a calculator. (Does 1 divided by 2 equal the same decimal as 1000 divided by2000?)Extension:Use this bulletin board idea to extend learning into students’ daily lives. Divide the board intofour columns; (fraction, decimal, what it looks like diagrams, divided geometric shapes, coinsand number line 0 – 1, with points to designate each fraction and decimal. Include at least 10rows to display commonly used fractions and decimals.Home Connections:• Students are encouraged to bring in samples from any print media (newspapers, magazines,catalogs, etc.) or other printed information (net weights from boxed or canned foods, labelsfrom liquids, etc.) that show decimals. They may add these to a related point on a largenumber line (0-10) at the bottom of the Fraction/Decimal bulletin board.• Parents may encourage their children to go on a “fraction hunt” or decimal hunt” in theirhouses or at the store and discuss how each fraction would be stated as a decimal or howeach decimal could be stated as a fraction. (Example: Write a money amount as both afraction and a decimal on a check)Materials and Resources:The inclusion of a specific resource in any lesson formulated by the Ohio Department ofEducation should not be interpreted as an endorsement of that particular resource, or any of itscontents, by the Ohio Department of Education. The Ohio Department of Education does notendorse any particular resource. The Web addresses listed are for a given site’s main page,therefore, it may be necessary to search within that site to find the specific information requiredfor a given lesson. Please note that information published on the Internet changes over time,therefore the links provided may no longer contain the specific information related to a givenlesson. Teachers are advised to preview all sites before using them with students.For the teacher: chalkboard or chart paper, markers, transparency of Attachment C, 10 x 10grid, overhead markers, set of overhead base-ten blocks, gummed adhesive ortapeFor the student:cet of base-ten blocks for each group of four, sheet of chart paper for eachgroupVocabulary:• decimal• equivalent• fraction• fractional part10

• hundredths• repeating decimal• tenths• thousandthsFraction and Decimal Equivalency – Grade FourTechnology Connection:Use available software programs and Web sites for students to practice and reinforce skillsrelating fractions and decimals.Research Connections:Cawletti, Gordon. Handbook of Research on Improving Student Achievement. Arlington, Va.:Educational Research Service, 1999.Marzano, Robert J., Jane E. Pollock and Debra Pickering. Classroom Instruction that Works:Research-Based Strategies for Increasing Student Achievement, Alexandria, Va.: Association forSupervision and Curriculum Development, 2001.General Tips:• Stress that representing thirds in decimal form is only accurate when using a repeatingdecimal line (0.3 ). Using 0.33 for one-third or .067 for two-thirds is an approximation.• Fraction and decimal equivalency is a key aspect of fourth grade mathematics. Present theconcepts using models and visual representations to provide concrete connections betweenthe concepts. Part Two of this lesson may take multiple days.Attachments:Attachment A, Fraction ReviewAttachment B, Pre-AssessmentAttachment C, Class WorksheetAttachment D, Independent WorksheetAttachment E, 10 x 10 GridAttachment F, Fractions and DecimalsAttachment G, Post-Assessment11

Fraction and Decimal Equivalency – Grade FourAttachment AFraction ReviewName_______________________________Date__________________________1.__________2.__________________3.__________4.____________________12

Fraction and Decimal Equivalency – Grade FourAttachment BPre-AssessmentName_______________________________ Date__________________________1. Shade four parts. What fraction of the bar is shaded? ________2.How many parts of the bar are shaded? __________What fractional part of the bar is shaded? __________What fractional part of the bar is not shaded? __________3. Shade one circle.What fractional part of the set is shaded? __________Write the fraction for the part of the set that is not shaded. __________4.How many circles are shaded? __________Write the fraction for the shaded part of the set. __________Write other names we can use for this illustration.________________________________________________________________________5. Draw a picture to show 107(0.7).________________________________________________________________________13

Fraction and Decimal Equivalency – Grade FourAttachment CClass WorksheetName ________________________________Date ______________________1. ________ ________fraction decimal2. ________ ________fraction decimal3. ________ ________fraction decimal4. ________ ________fraction decimal14

Fraction and Decimal Equivalency – Grade FourAttachment DPractice WorksheetName ________________________________Date ______________________1. ________ ________fraction decimal2. ________ ________fraction decimal3. ________ ________fraction decimal4. ________ ________fraction decimal15

Fraction and Decimal Equivalency – Grade FourAttachment E10 by 10 Grid16

Fraction and Decimal Equivalency – Grade FourAttachment FFraction and Decimal Cards12 0.5014 0.250.75 1.00243410101318780.1 0.90 0.617

Fraction and Decimal Equivalency – Grade FourAttachment GPost-AssessmentName_______________________________Date__________________________Directions: Shade each grid as directed. Write the fraction(s) and decimal below each grid.1. Shade 2 tenths and 5 hundredths. 2. Shade 5 small squares._______ _______fraction decimal fraction decimal3. Shade 75 small squares. 4. Shade 30 small squares._______ _______ _______ _______fraction decimal fraction decimal18

Fraction and Decimal Equivalency – Grade FourAttachment G (continued)Post-Assessment5. Shade 5 columns of the grid. 6. Write the fraction using words, numbersand decimals to represent the shaded part ofthe grid in number 5._____________________________________________________________________________________________________________________________________fraction_______decimal7. Shade 2 columns of the grid. 8. Write the fraction using words, numbersand decimals to represent the shaded part ofthe grid in number 7._______________________________________________________________________________________________________________________________fraction_______decimal19

Fraction and Decimal Equivalency – Grade FourAttachment G (continued)Post-AssessmentName_______________________________ Date__________________________Direction: Write these fractions and decimals to go with the appropriate on the number line. You may write above or below thenumber line.0.25130.9 0.5 0.101010340 120