I recently discovered that the way that prices are shown on rate signs for motor vehicle fuel varies quite a bit. Some display the current price in dollars, some in cents and some, confusingly, show both dollars and cents. None of the signs that I found actually showed the units being displayed ($, ¢, L, gal., etc). I decided that it would be a good topic for a Which One Doesn't Belong discussion that would focus in on decimals, place value and fractions as well as currency and volume measurement.
Here are some suggestions why each image might not belong as well as some additional information for discussion:
Top Left: This is the only fuel price sign with both a decimal and a fraction. It is from a Costco in Oregon. The price is $2.29 and 9/10¢ per gallon. Both dollars and cents are used in this price. If you assumed that the entire price was listed in dollars, then $2.29 and $9/10 would actually give a price of $2.29 + $0.9 = $3.19.
Top Right: This is the only fuel price sign with just one decimal. It is from a Shell station in Halifax, NS and is in Canadian cents per litre. In Nova Scotia, the price often doesn't end with the standard 9/10¢ since the price is regulated by the Nova Scotia Utility and Review Board and only changes once per week.
Bottom Left: This is the only fuel price sign with two decimals. It is from an Atlantic Superstore gas station in Dartmouth, NS. Similar to the sign above it (top left), it displays a price of $1.00 and 0.5¢ per litre. While probably not confusing to the average motorist, I find the use of two decimals to be mathematically troubling. Why not just list the price as $1.005?
Bottom Right: This is the only fuel price sign with no decimals. It is from a 76 gas station in Oregon and is in US cents per gallon. It is interesting to note that Oregon and New Jersey are the only two US states with laws prohibiting self serve at gas stations. This sign mentions "Mini Serve" to note that an attendant operates the pumps but does not provide any of the other services you'd expect with full service.
Nova Scotia Mathematics Curriculum Outcomes
Grade 5 N09 - Students will be expected to relate decimals to fractions and fractions to decimals (to thousandths).
Grade 5 N10 - Students will be expected to compare and order decimals (to thousandths) by using benchmarks, place value, and equivalent decimals.
Grade 6 N01 - Students will be expected to demonstrate an understanding of place value for numbers greater than one million and less than one-thousandth.
Grade 7 N07 - Students will be expected to compare, order, and position positive fractions, positive decimals (to thousandths), and whole numbers by using benchmarks, place value, and equivalent fractions and/or decimals.
Students and Staff at J.L. Ilsley High School recently returned from a March break trip to Italy. Their stories about Rome and pizza and gelato inspired this "Would You Rather?" math question. Most students are pretty familiar with pizza and have strong opinions to share on their favourite type and restaurant for pizza.
Would you rather have a slice of pizza from New York or from Rome? The New York pizza costs $2.75 US per slice. The Rome pizza costs 1,50€ per 100 grams.
In Rome, pizza by the slice or "pizza al taglio" is typically sold in rectangular pieces by weight. Prices are often listed per 100 grams. Prices can vary greatly depending upon the type and location of restaurant. Restaurants close to major tourist attractions in Rome are often much more expensive. The price I quote above is from Pizza Florida in Rome. Estimating the weight of a typical slice of pizza might be difficult for students. How much does a typical piece of pizza weigh? According to Pizza Pizza, a 1/10 slice of a 14 inch diameter pizza is approximately 110 grams. There is also the issue of currency conversion. You could ask for 3 Euros worth of pizza, but how much will that cost you in Canadian dollars? An online currency conversion website or app can help with currency exchange.
The Nova Scotia Mathematics 10 curriculum has outcomes on both currency exchange and SI to imperial unit measurement conversions so I thought this would be a nice warm up question to be used in that course.
In case you were wondering where you should go to eat pizza, here are the 14 top cities for pizza, as identified on the Conde Nast Traveler Best Pizza in the World list. Note that a Canadian city, Edmonton, made the list.
Nova Scotia Mathematics Curriculum Outcomes
Mathematics 10 - M02 Students will be expected to apply proportional reasoning to problems that involve conversions between SI and imperial units of measure.
Mathematics 10 - FM01 Students will be expected to solve problems that involve unit pricing and currency exchange, using proportional reasoning.