EXT 3-6 Sampler

57 MultiplyingFractionsbyFractions Lesson10, 6ETeacherGuide 29 Objective19: To find thepattern formultiplying fractions. To relate theword “of” to theoperationofmultiplication. Materials: Paper, FractionBars (orFractionStripsmade fromMaster 14) Pattern forMultiplyingFractions Students can learn the algorithmor rule formultiplying fractionswith little conceptual understandingbecause the ideas they learned forwholenumbermultiplication also workwith fractions (multiply thenumerators;multiply thedenominators). Therefore, instruction shouldbegin withvarious problem-solving strategies that help students find themultiplicationpattern. These strategies also help studentsunderstandwhy a fractionof a fraction or a fractionof awholenumberwill be less than the original number. Writeon theboard: Youhaveone-half of apizza left over fromdinner. For abedtime snack, you eat one-half of your leftoverpizza. What fractional part of thewholepizzadidyou eat for a bedtime snack? Ask students to read theproblem anddiscusswith a partnerdifferentways to solve theproblem. Somepossible solutions are actingout theproblemwith a real pizza, modeling theproblemwith apieceof clayor round tortilla, drawing apicture andpaper folding. Draw apicture: Paper folding: Fold a circle into2 equal parts. Eachpart is½. Fold the½circle into two equal parts. Each small part is¼. Writeon theboard: 1 2 of 1 2 1 4 Whydoes itmake sense to say that “of”means multiplication? (Becausemultiplying thedenominators gives you the total number of parts andmultiplying the numerators gives you thenumber of parts taken.) 1 4 1 2 1 4 1 2 Demonstrate the sameproblemusing½FractionBars anddraw the solutionon theboard: What is thepattern formultiplying fractions? (Multiply thenumerators andmultiply thedenominators. Simplify if possible.) Read the information together at the topof thepage. Fold apieceof paper todemonstrate½of¼=⅛.Draw a pictureof a fractionbardivided intoone fourths and shade one fourth. Ifwedrawadotted line to show½of¼,what fractional part is½of¼? (⅛)Have studentsdrawdotted lines to solveproblem4.Note that the answers to some problemswill need tobe simplified. Skill Builders 19-1 1 2 1 2 1 4 1 2 of or 29 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. 12. Genemade a cake and cut it into six equal parts. He then cut each part into 2 equal pieces and ate one of the pieces. What fraction of the cake did he eat? ________ 13. Jesse had of a pizza. He ate of his pizza after school. What fraction of thewhole pizzawas eaten after school? ________ Multiplying Fractions by Fractions paper folding 1 2 of 1 4 = 1 8 1 4 cutting the fractionbar into equal parts Rule: Multiply the numerator by thenumerator and the denominator by the denominator. Simplify theanswer. } } Hereare someways tomultiply a fraction by a fraction. Use the pictures to find the products. 1 2 of 1 4 = 1 8 1. 2. 3. of = of = of = Draw in dotted lines to show themultiplication. Shade to show the solution. 4. 5. of = ______ of = ______ 6. × = _________ 9. × = _________ 7. × = _________ 10. × = _________ 8. × = _________ 11. × = _________ Multiply. Simplify if necessary. When two fractions aremultiplied, what can you say about the size of the answer? Justifywhy this happens using diagrams, words, and symbols. 1 6 1 12 1 18 1 9 1 12 1 6 1 20 3 35 1 10 12 25 1 8 1 6 1 3 1 4 1 12 Studentsusemodels, paper folding, anddrawingpictures todiscover andgain conceptual understandingofmultiplying fractions. Students canusepaper folding togain understanding ofmultiplying a fraction times a fraction. Grade6