How to save car fuel through learn­ing ra­tios and com­par­a­tives

Panay News - - BUSINESS -  By Mar­c­nie C. Al­ba­son, Teacher II Capiz Na­tional High School

THIS IS the Math les­son that touches on ra­tios and com­par­a­tives with a warm up ac­tiv­ity in solv­ing for fuel econ­omy be­tween cars. Even­tu­ally, your stu­dents will ac­quire a car. It is ei­ther a dream, just like hav­ing their own house, or land­ing on their dream job, or their fu­ture work will re­quire them to use a car.

Whether it is for per­sonal or pro­fes­sional use, and given to­day’s gas prices, this les­son can pro­vide a re­al­ity check for stu­dents be­gin­ning to drive for the first time. Teach­ers can adapt this prob­lem and add an­other prob­lem solv­ing cat­e­gory of “cost of fi­nal trip or cost of each gal­lon of gas or ask would reg­u­lar, plus or pre­mium gas at 2.39/gal­l­lon; 2.99/gal­lon or 3:09/gal­lon get the bet­ter mileage for Stu­dent A and Stu­dent B’s trip?”

Be­fore the prob­lem can even be writ­ten, stu­dents need to have a work­ing vo­cab­u­lary. Pro­vide them with a dic­tionary or the glos­sary of the math book to write down the def­i­ni­tions with an ex­am­ple of the fol­low­ing words for this les­son: (1) Ra­tio is the com­par­i­son of two quan­ti­ties which can be ex­pressed as frac­tions, per­cents, dec­i­mals are in the form x:y. An ex­am­ple of a ra­tio could be the ra­tio of males to fe­males in the math class­room: 2 fe­males/5 males or a car trav­els at 60mph (miles per hour) or 60 miles/1 hour; and, (2) Rate is the com­par­i­son of quan­ti­ties with dif­fer­ent units.

The car trav­el­ing at 60 mph has the rate of 60 miles per hour should be writ­ten as 60 miles: 1 hours. An­other ex­am­ple would be found in a gro­cery store: Mac­in­tosh Ap­ples are $1.39/lb. and a Volk­swa­gen gets 35 miles per gal­lon in the city.

In learn­ing the ra­tios to mileage com­par­a­tives, let our warm-up prob­lem be: Stu­dent A’s car gets 42 miles to the gal­lon on the free­way. How much gas will Stu­dent A’s car use if it is driven 126 miles on the I-90 free­way? The an­swer is ra­tio would be to set up a scale to get the an­swer so have stu­dents fill in the blanks for “X.” If 42 miles per gal­lon = 42 miles : 1 gal­lon, X : 2 gal­lons and 126 miles : X gal­lons, X = 84 miles : 2 gal­lons and 126 miles : 3 gal­lons = blanks for ‘X.” Stu­dents can di­vide 126 miles/42 to get the cor­rect an­swer which would be 3 gal­lons.

Next, let’s use this prob­lem to prob­lem solve a com­par­ing fuel econ­omy prob­lem for real- life stu­dents: Marcy and Will.

The prob­lem is Marcy and Will got sum­mer jobs as coun­selors. They both drove to the same sum­mer camp us­ing al­ter­nate free­way routes. In com­par­ing the fuel econ­omy of their cars, each ar­gued that their car got the best gas mileage. How would you solve this prob­lem us­ing the in­for­ma­tion be­low: Marcy took I-90 and got to Camp Wood­mark and posted the fol­low­ing data: 323 miles : 20 gal­lons of gas. Will took I-405 and got to Camp Wood­mark and posted the fol­low­ing data: 278 miles : 16 gal­lons of gas. The an­swer is Marcy’s car went 323 miles/20 gal­lons = 16.2 miles/gal­lon. Will’s car went 278 miles/16 gal­lons = 17.4 miles/gal­lon.

Also, stu­dents can use the above data to make a pre­dic­tion ta­ble and an equa­tion to solve for the prob­lem: Whose car, Marcy or Will’s, will get the best fuel econ­omy if the trip took 450 miles or 515 miles? This math ac­tiv­ity can pro­vide stu­dents an op­por­tu­nity to cre­ate a rate ta­ble of gal­lons of gas and miles for Marcy and Will’s cars which could start at 323 miles: 20 gal­lons and 278 miles : 16 gal­lons re­spec­tively and in­clude the new data of 450 miles and 515 miles for prob­lem solv­ing.

Stu­dents can then graph the rate ta­ble to show which car is truly more fuel ef­fi­cient and cre­ate con­clu­sions and fur­ther pre­dic­tions. (

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