EXT 3-6 Sampler

65 MultiplicationEquationswithModels Lesson26, 6ETeacherGuide 76 Objective56: To solvemultiplication equationsusing models, pictures and symbols. Materials: Rectangular rods (orpositive rectangular rods,Master 22), black andwhite cubes (orpositive andnegative integer squares,Master 22), paper bags (or envelopes) ModelingEquations InvolvingMultiplication The concept of avariable is abstract.Whenusingbags to represent anunknownnumber, emphasize that bags markedwith the same lettermust alwayshave the same number of cubes inside. Secretlyplace2black cubes into eachof 3bagsmarked x anddisplay thebags. Explain that the3bags altogether have avalueof 6. Writeon theboard: 3 x =6 Howmanyblackorwhite cubes are ineachbag? (2black cubes in eachbag)Pour out the cubes toverify. This is amultiplicationequation.What operationdo youuse to solveamultiplicationequation? (division) Writeon theboard: 3 3 x = 6 3 x =2 Divide the class into small groups of equal size. Distributeonebag (or envelope) to each student and a pileof black andwhite cubes (or integer squares) to each group. Instruct groupA to label all bags in their group with the letter a , groupBwith the letter b , etc. Then ask students in eachgroup to select a secret integer between 0 and7 andhave each student in that groupplace the selectednumber of cubes inhis orher bag. For example, if groupA selected2, each student ingroupAwould place twopositive cubes in thebag labeled a . Select anumber of bags fromgroupA, e.g., 4bags. Display the four bags, each clearlymarkedwith the letter a . Be sure that there are the samenumber of cubes in each bag. Tell the students the total number of cubes in all of thebags.Ask students toguess thenumber of cubes inside eachbag. Pour out the cubes inside eachof thebags and count the total number. In this case, if groupAhad selected2 as their secret number, the total number of cubeswouldbe8black cubes. If fourbags, each containing the secretnumber a , havea total of 8black cubes, howmany cubeswere inside eachbag? (2) Draw apicture: = a a a a Continue selecting adifferent number of bags from eachgroup.At the conclusion, elicit from the students the generalization that equations involvingmultiplicationof avariable are solvedbydividingby thenumber of bags. Writeon theboard: 4 a =8 4 a 4 = 8 4 a =2 Read the explanation together.Model the solution usingbags and cubes and thenusing a rectangular rod for eachbag.Have studentsusebags and cubes to solve theodd-numberedproblemswith apartner. Have studentswork the even-numberedproblems independently. Skill Builders 56-3 76 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. Multiplicationand divisionare inverse operations. Oneoperation undoes the other. You can divide both sides of an equation by the same number tomaintain equality. There are 12 flowers and 3 vases. If the same number of flowers are togo into each vase, howmany flowerswill go into each vase? Let x = number of flowers in1 vase. 3 x = 12 Usemodels to solve the equations. 3. 2 x =8 x =________ 6. 4 x =8 x =________ 9. 3 x =9 x =________ 4. 5 x = 10 x =________ 7. 4 x = 4 x =________ 10. 2 x = 6 x =________ 5. 3 x = 6 x = ________ 8. 2 x = 10 x = ________ 11. 3 x = 0 x =________ 1. = x =________ 2. = x =________ = or x =4 SolvingMultiplicationEquationswithModels = 12. Jamiehas $45. Hehas3 times asmuchmoney ashis sister. If x is the amount ofmoneyhis sister has, writean equation that describesher money. Usewords to explainhow to findhowmuchmoneyhis sister has. Divide bothsides by3. 3 4 2 3 2 1 3 2 5 0 2 3x = $45Divide bothsides by3 tofindout howmuchmoney his sister has. 6.EE.5, 6.EE.7 Students learn todivide both sidesof anequation by the samenumber to understandmultiplication. Grade6 PartB