EXT 3-6 Sampler

45 Equivalent Fractions Objective12: To find all sets of equivalent fractions from a set of fractionbars. To identify and change a fraction to lowest terms. Materials: FractionBars orFractionStrips (Master 16) Vocabulary: lowest terms Equivalent Fractions fromFractionBars Arrange the students in small groups andgive each group a set of FractionBars. Haveoneperson inyourgroup select and list all thebarswherenoparts are shaded. (0⁄12, 0⁄10, 0⁄6, 0⁄5, 0⁄4, 0⁄3, 0⁄2) Makea towerwithyourbarsbyputting ⁄ for the bottom story, ⁄ for thenext story, ⁄ for thenext storyand soon. Show the towerwitha set of overhead fractionbars. Twoormore fractions that represent the samenumber are calledequivalent fractions.Beginningwith the ½markonyourgreenbar, identify theother fraction barswhichareequivalent to½.Write thenameof these equivalencieson the chart on the studentpage. Students mayuse a ruler or a sheet of paper to find that½ is equivalent to 2⁄4, 3⁄6, 5⁄10 and 6⁄12. (½linesupwith 2⁄4, 3⁄6, 5⁄10 and 6⁄10.) You can see that½is the sameas ⁄.What operation is usedoneach term to change½to ⁄? (Multiplyboth terms by2.) Writeon theboard: Howwouldyou change ⁄back to½? (Divideboth terms by2.) What is thepattern for findingequivalent fractions? (Multiplyordivideboth terms of the fraction by the samenumber.) Writeon theboard: When thenumeratorand thedenominatorhaveno common factorsother than1, the fraction is expressed in lowest terms . Identify½as the lowest terms fraction for the items on theboard. Repeatwith the⅓bar (⅓linesupwith 2⁄6 and 4⁄12).Again, ask for thepatterns to change⅓to 2⁄6 andvice versa. After filling in the chart, allow students time to share their observations about the equivalent fractions theyhave written. All fractions in the same rowareequivalent.The fractions in the far left columnare said tobe in lowest terms.Howdoyouknow if a fraction is in lowest terms? (Thenumerator and thedenominatorhaveno common factors other than1.) Forproblems 20–23, students are supposed to fill in the boxwith thenumber that creates an equivalent fraction. Discusswith studentshow they candetermine that number. Whatpart of the fractionwith themissing numberdoweknow? (denominator) Howdowemake equivalent fractions? (multiplyordivideboth the numerator anddenominator by the samenumber) Doyou multiplyordivide to change2 into4? (multiply) What numberdoyoumultiplyby? (2) Sowhatnumbermustwe multiply thenumeratorby? (2) Whatnumberbelongs in thebox? (2) Why? (because1 2=2) Skill Builders 12-1 2 4 1 2 x2 x2 = 1 2 2 4 ÷2 ÷2 = - Lesson10, 5ETeacherGuide 33 33 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. 1. 1 2 2. 1 1 3. 1 3 4. 2 3 5. 1 4 6. 3 4 7. 1 5 8. 2 5 9. 3 5 Equivalent Fractions Forproblems1–18,findallof thesetsofequivalent fractions. Lowest Terms Equivalent Fractions in Higher Terms Lowest Terms Equivalent Fractions in Higher Terms 1 3 1 4 1 5 1 6 1 1 0 1 1 2 1 2 2 4 2 4 3 6 5 10 6 12 3 3 4 4 5 5 6 6 10 10 12 12 1 3 1 4 1 5 1 6 1 1 0 1 1 2 10. 4 5 11. 1 6 12. 5 6 13. 1 1 0 14. 1 3 0 15. 1 7 0 16. 17. 18. 1 1 2 1 9 0 1 5 2 19. The value of a fraction is not changedwhen you _____________or ______________ the numerator and denominator by the same number. Find themissingnumerator in eachequivalent fraction. 20. = 1 2 4 21. = 3 4 12 22. = 2 5 10 23. = 5 6 12 2 6 2 10 4 10 6 10 9 12 4 6 8 10 4 12 8 12 2 12 3 12 10 12 2 9 4 10 multiply divide Students learn togeneralize as theydiscover the important pattern found inequivalent fractions. Grade5