Overview Students will wrk in cperative grups t slve a real-wrd prblem by using the bk Hw D yu Lift a Lin? Using a ty lin and a lever, students will discver hw much wrk is needed t raise the ty lin. They will use prprtins t determine the frce needed t lift a real lin. Grade Levels: 4 6 Cncepts Multiplicatin Measurement Prblem slving Frce Simple machines Divisin Rati Wrk Energy Materials TI-15 Explrer calculatrs Hw D yu Lift a Lin? Wells, Rbert E. (Park Ridge, IL: Albert Whitman and Cmpany, 1996) Paper, pencils Ruler Pster paper Meter stick r thin, but nt pliable, bard with meter stick 3 pencils taped tgether in a triangular prism shape r ther bject fulcrum Small ty lin (r ther small bean-bag type animal) Stacking gram masses, r balls f clay r washers weighing abut 1 5 grams each Student activity sheet Assessment Thrughut the activities, questins are included fr frmative assessment. Student wrk samples shuld be used as a check fr understanding. Have the students use the TI-15 t shw their calculatins. 2016 Texas Instruments Incrprated 1 educatin.ti.cm
Intrductin Read the first sectin f the bk Hw D Yu Lift a Lin? by Rbert E. Wells t the students. Discuss with the students the parts f a lever shwn in the bk. Demnstrate making a lever by using a 12-inch ruler with a pencil as a fulcrum. (Nte: D nt use the meter stick fr the demnstratin since ding s will reveal part f the slutin.) Place a 5-gram mass (lad) at ne end f the ruler. Place the pencil (fulcrum) at the 6-inch mark. Have students guess hw much weight it will take t lift the 5 grams. Place masses n the ther end f the ruler until the 5-gram mass is lifted. Mve the pencil t anther lcatin clser t the 5-gram mass. Have students predict hw much weight it will take t lift the 5-gram mass. Place masses n the ther end f the ruler until the 5-gram mass is lifted. Repeat the prcess with the fulcrum in tw ther lcatins. Write the infrmatin in a chart and have students lk fr patterns. Presenting the Prblem 1. Review the fur steps f prblem slving with the students: understanding the prblem making a plan carrying ut the plan evaluating the slutin 2. Have the students read the Prblem page and paraphrase the prblem. Make sure the students are clear n what the prblem asks. 3. Discuss with students infrmatin n the Prblem page. Make sure they understand hw t create a lever with the meter stick r bard and pencils. Remind them f the prcedures used in the Intrductin t lift the 5-gram mass. 4. If grups have difficulty with the prblem, use the Things t Cnsider page. This page prvides guiding questins t help the students cmplete the prblem-slving steps. 5. The presentatin shuld include the mathematics used t predict hw much weight it wuld take t lift the real lin. 2016 Texas Instruments Incrprated 2 educatin.ti.cm
Evaluating the Results 1. After the presentatins are made, have students examine the varius slutins presented. Questins fr Students: v Hw are the presentatins similar? v Hw are the presentatins different? 2. Ask them t cmpare the numbers used. Questins fr Students: v Did all grups use the same numbers? v Why d yu think this is s? 3. Ask them t determine the reasnableness f the results. Questins fr Students: v Did each grup answer the questin? v D the numbers used make sense? v Did all f the grups cnsider all f the variables? 4. Ask them t evaluate hw each grup used the calculatr t slve the prblem. 5. Ask them t extend their thinking. Questin fr Students: v Hw des the weight f the lad impact the amunt f frce needed t lift it with a lever? 2016 Texas Instruments Incrprated 3 educatin.ti.cm
SOLUTIONS Lifting a Lin The Prblem: Hw much effrt will it take t lift a lin with a lever? In the first part f the activity, team members will make a chart shwing the amunt f wrk it takes t lift a ty lin with the fulcrum at varius distances frm the lin. Then they will predict the amunt f wrk it will take t lift a real lin with the fulcrum at different distances. Students will write an explanatin abut their slutin prcess. Answers will vary based n the explanatins. Using the Calculatr Using Prprtins Use the TI-15 calculatr t slve this prblem: Ms. Kleid is helping plan the refreshments fr Field Day. She wanted t knw everyne s favrite ice cream flavr s she culd rder enugh ice cream. She surveyed her class. Out f her class f 22 students, 10 students preferred chclate ice cream, 8 preferred vanilla, and 4 preferred strawberry. Ms. Kleid knws there are 531 students at schl. Hw can she predict hw many ice cream cups in each flavr she needs? Ms. Kleid decided she needs t knw the fractinal part f her class that likes each flavr. Since there are 22 students in her class, 10 8 4 like chclate, like vanilla, and 22 22 22 like strawberry. She decides t simplify the fractins. Hw des the result help Ms. Kleid? The display shws: 5 11 Pssible answer: The fractin is easier t calculate with, but it des nt help her. 2016 Texas Instruments Incrprated 4 educatin.ti.cm
Ms. Kleid decided that simplifying the fractins desn t help at all. She needs t knw what 10 f 531 students is. Next she tries this: 22 The display shws: 8 241 22 Des this answer make sense fr the number f peple in the schl wh like chclate ice cream? Hw d yu knw? What shuld Ms. Klein d abut the fractin part? What wuld happen if she simplified the mixed number? The display shws: 4 241 11 Pssible answer: Yes the answer makes sense because a little less than half f the students in Ms. Kleid s class preferred chclate ice cream and 241 is a little less than half f 531. Ms. Kleid shuld rund the fractin part up t the nearest ne. Des the simplified fractin help? Pssible answer: n Try the ther tw fractins and multiply by 531 t predict the number f students wh will prefer vanilla r strawberry ice cream. D yu have fractinal parts? What shuld Ms. Kleid d with the fractinal parts t make sure there is enugh ice cream fr everyne? 1 193 11 students in the schl prefer vanilla ice cream and 6 96 11 students prefer strawberry ice cream. Yes there are fractinal parts. Mrs. Kleid shuld rund the fractinal parts up t the nearest whle number. 2016 Texas Instruments Incrprated 5 educatin.ti.cm