Exploring Decimals (Grade 4/5) - By: Amy Benjamin

Exploring DecimalsBy: Amy BenjaminMath- Grade 4/56 day unit planTechnologies Used:*Computers*Class set of calculators(TI80)* TI-84+ graphing calculator*Overhead unit for calculator*Overhead projector*Overhead manipulatives (transparent decimal gridpaper,transparent fractions squares and overhead calculator)*Fraction cubes

Overall ObjectivesStudents discuss common uses of decimals. They will becomefamiliar with a calculator, representing decimals on grids and the use of anoverhead with manipulatives.Standards AddressedNCTMNumber and Operations*understand numbers, ways of representing numbers, relationships amongnumbers, and number systems*understand meanings of operations and how they relate to one anotherProblem Solving*build new mathematical knowledge through problem solvingConnections*recognize and use connections among mathematical ideas* understand how mathematical ideas interconnect and build on oneanother to produce a coherent whole*recognize and apply mathematics in contexts outside of mathematicsNew York StateContent Strand- Number Systems*5.N.4- Create equivalent fractions, given a fraction*5.N.5- Compare and order fractions including unlike denominators*5.N.9- Compare fractions ,=*5.N.11- Understand that percent means part of 100, and write percents asfractions and decimals*5.N.19-Simplify fractions to lowest termsResourcesAkers, Joan.Investigations in Number, Data and Space: Name that Portion, TeacherNotes .Cambridge,Mass:TERC; 1998Dennis, J. Richard. Fractions are parts of things. New York:Thomas Y.Crowe; 1971.Ernst, Lisa Campbell. Sam Johnson and the Blue Ribbon Quilt. New York:Lothrop, Lee and Shepard, 1983Page Two

Materials and Equipment Needed*Computers*Class set of calculators(TI80)*Overhead projector*Overhead manipulatives (transparent decimal gridpaper,transparent fractions squares and overhead calculator)*Fraction cubes*Newspaper sports sectionsOverviewDay One- “Interpreting Decimals”Students discuss common uses of decimals. Using a calculator to solvedivision problems. To explore application of decimals children can choosesports teams to follow over a two week period, keeping track of win/lossrecords and making predictions and changes in the “percentage” of gameswon.Day Two- “Decimals on Grids”Students represent tenths and hundredths on grids. Then they play adecimal game. Fill Two, which involves combining decimals on grids.Day Three and Four- “Decimal Games”Students will rotate between 3 decimal games that involve ordering decimalnumbers expressed in tenths, hundredths, and thousandths: Smaller toLarger, Decimals in-between and Capture Decimals.Day Five and Six- “Fractions to Decimals”Students find decimals of up to three digits that have a value between thatof two given decimals. Students then find decimal equivalents for fractionson the calculator, making a Fraction to Decimal Division Table for allfractions with numerators and denominators from 1 to 12. They identify andexplain patterns within the table.Page Three

“Interpreting Decimals”Lesson SummaryStudents discuss common uses of decimals. Using a calculator, theyfind several division problems that have answers of 0.5,0.25,0.75, and otherfamiliar decimals.MaterialsCalculatorsTI-84+ calculatorOverhead adapterNewspaper sports sectionOpeningShow students the following examples of decimals:Car odometer- 47364.3Baseball player’s batting average- .346Rainfall in the last 24 hours- 0.25 inchTotal rain for the month- 5.43 inchesAllow a few minutes for students to read each decimal number anddecide with your partner what it means. Listen for student understandingabout decimals. Do they recognize that 0.25 inch is ¼ inch or that 5.43inches is almost 5 ½ inches?Lesson DescriptionWrite on the board: 0.5 0.25How would you read these decimals?(one- place decimal-tenths, two-place decimal-hundreths)What familiar fractions are these decimals equal to?0.5= ½ 0.25= ¼If fractions and decimals are two ways of writing the same thing, why doyou think we need both forms?Decimals are easier to work with. Decimals are always expressed inmultiples of 10-tenths,hundredths, and thousands Fractions have all kindsof different denominators-thirds, sevenths,twelfthsI want to express these fractions (1/2 , ¼) as decimals, but I didn’t knowhow. Who knows how I can use my calculator to find out?Remind students that a fraction is another form of division. Any fractioncan be thought of as a division problem. The line between the numbers islike a division sign. (1/2 represents 1 divided by 2- 1 divided into 2 parts)Doing the division on the calculator gives us the decimal equivalent on thedisplay.Page Four

Challenge students to find several other ways to get the same decimals onA calculator, using different division problems.When we divide 1 by 2 on the calculator, we get 0.5 on the display. Whatother numbers could you divide to get 0.5?Write 0.5 on the board, and list the division problems that studentssuggest. Write them both with a division sign and fractions. As a challengegive then part of another problem, such as 50 divided by ?0.51 divided by 2 ½2 divided by 4 2/43 divided by 6 3/650 divided by ? 50/?AssessmentExplain that students will be making similar lists for some other decimalsthey have seen. Write 0.25 and a few other decimals familiar to students,such as 0.75, 0.1 and 2.5. Students take a moment to think and talk to theirneighbors about what fractions these decimals are equivalent to. Then theysearch with a calculator for 3 or 4 division problems that result in eachdecimal, keeping a list of each one.HomeworkStudents could be given a list of fractions to be converted to decimals.Page Five

“Decimals on Grids”Lesson SummaryStudent use a model decimal grid representing tenths andhundredths on grids. Then they play a decimal game, “Fill Two” whichinvolves combining decimals on a grid.MaterialsBlank squares**Decimal grids (tenths, hundredths,thousandths,ten-thousandths)**Decimal grid transparency**Decimal cards (set A and B)**Directions for Fill TwoOverhead projectorCrayons/MarkersOpeningShow students the blank square you have prepared. Explain that thisis one whole. Place a transparency of Decimal Grids on the overheadprojector.These grids are similar to those you used to show fractions and percents,but these show how one whole can be divided into decimals. How are thefour grids different?Allow students time to figure and discuss the number of parts ineach grid. The first grid is divided into 10 equal parts, the second into 100,the third into 1000, and the fourth into 10,000.Lesson DescriptionWrite 0.1 on the board or overhead. Have volunteers come to theoverhead and color in one-tenth on each of the grids.Which grid clearly shows one-tenth? How would we write one tenth ashundredths,as thousandths, and as ten-thousandths. For each grid write itboth as decimal and a fraction.Students discuss the question in small groups, write down theiranswers and then share responses.Write 0.25 and 0.3 on the board.Which of these decimals is greater?Invite students to illustrate answers on their grids.Write 0.05,0.5 and 0.50 on the board.What’s the difference between these three decimals? Which is worththe least? How do you know?Encourage students to discuss this in small groups.Page Six

Assessment/HomeworkIntroduce the game “Fill Two”. Two students can model the game forothers. Circulate and assess while students are playing the game. Cardsand directions can be copied for play at home.** Some students may find it helpful to write the percent equivalents on allthe Decimal Cards. Have them write it lightly in pencil on their cards.Remind students to record below the grid each decimal they color in.Page Seven

“Decimal Games”2 day lessonLesson SummaryStudents will play three decimal games that involve ordering decimalnumbers expressed in tenths, hundredths, and thousandths. Their workwill focus on reading and writing decimals, ordering decimals and addingdecimals.Materials**Decimal Cards (set A and B)**Decimal Grids**Directions for “Smaller to Larger” (student sheet)“Decimals in Between” (student sheet)“Capture Decimals” (see below)OpeningGames can be introduced by modeling. Teacher and student orstudent to student with the teacher facilitating.Allow students time to practice each game.Capture DecimalsCapture decimals is played by pairs. The deck of decimal cards isdealt out into two facedown piles, one for each player. Both players turntheir top card faceup at the same time. The player who turns up the highestvalue takes both cards and puts them aside. As in the other two games,encourage students to use Grids or to try writing the decimals as fractionswhen they need help comparing the value of the two decimals.AssessmentSee Teacher Checkpoint “Observing Decimal Games”HomeworkAll games and cards can be reproduced to play at home.Page Eight

“Fractions Decimals”2 day lessonLesson SummaryStudents find decimals of up to three digits that have a valuebetween two given decimals. Students then find decimal equivalents forfractions on the calculator, making a Fraction to Decimal Division Table forall fractions with numerators and denominators from 1 to 12. They identifypatterns within the table.MaterialsCalculatorsOverhead projector**Student Sheet (Fraction to Decimal Division Table)OpeningThis is a division table. It is similar to a multiplication table: Thenumbers we start with are shown across the top and down the left side,and the answers are recoreded in the inside boxes. You can use thisdivision table for recording fraction and decimal equivalents. The numbersin the top row represent numerators of fractions. The numbers in the leftcolumn are denominators.Model the procedure for completing the table. For example, point to 1in the top row and 2 in the left column, ask students what fraction thatwould represent , or what the decimal equivalent is (0.5), and where thatnumber should be recordedDistribute student sheet- Fraction to Decimal Table for students tocomplete. Students start by filling in decimal equivalents for fractions theyalready know before using the calculator. Encourage students to stop andlook for patterns.AssessmentStudents can be given a list to find equivalentsHomeworkAdditional charts can be completed at home.Page Nine