Unit 7: Proportional Reasoning

Outcome: Expand and demonstrate understanding of proportional reasoning related to: rates scale diagrams scale factor area surface area volume

DEFINITIONS Rate: Comparison of two amounts that are measured in different units; for example, keying 240 words/8 min Unit Rate: A rate in which the numerical value of the second term is 1; for example, keying 240 words/8 min expressed as a unit rate is 30 words/min. Similar Objects: Two or more 3-D objects that have proportional dimensions.

DEFINITIONS Scale Diagram: A drawing in which measurements are proportionally reduced or enlarged from actual measurements; a scale diagram is similar to the original. Scale: The ratio of a measurement on a diagram to the corresponding distance measured on the shape or object represented by the diagram. Scale factor: A number created from the ratio of any two corresponding measurements of two similar shapes or objects, written as a fraction, a decimal or a percent.

SECTION 8.1 COMPARING AND INTERPRETING RATES Example 1: Natasha bought a 12 kg turkey from her local butcher for $ The local supermarket has turkeys advertised in its weekly flyer for $1.49/lb. There are about 2.2 lb in 1 kg. Which store has the lower price? In order to compare the two prices, we need to use the same units. Since the Advertised price is per pound, let’s figure out what Natasha paid per pound. Convert ______________________ to pounds: To Convert from one unit to another, we want to change the units without changing the value of the number. What number can we multiply by that does not change the value of a number? How can you write 1 as a fraction? What other fractions have a value of 1? If the numerator is equal to the denominator then the fraction equals _______________.

When converting units, we multiply by a conversion factor where the numerator and denominator have the same value. The 26.4lb turkey cost $ How can we compare this price to the store that charges $1.49/lb? Since $1.49/lb is a ratio, we can write the butcher’s price as a ratio. We want ______________________ on top and ______________________ on the bottom. The more expensive turkey is… ____________________________________________

Example 2: When making a decision about buying a vehicle, fuel efficiency is often an important factor. The gas tank of Mario’s new car has a capacity of 55 L. The owner’s manual claims that the fuel efficiency of Mario’s car is 7.6 L/100 km on the highway. Before Mario’s first big highway trip, he set his trip meter to 0 km so he could keep track of the total distance he drove. He started with the gas tank full. Each time he stopped to fill up the tank, he recorded the distance he had driven and the amount of gas he purchased. On which leg of Mario’s trip was his fuel efficiency the best? Use unit rates to determine which leg was more fuel efficient. We can use a ratio of distance driven/gas used.  The distance driven on the first leg was 645km.  The distance driven on the second leg was ­­­__________________________________

8.1 Assignment: Nelson Foundations of Mathematics 11, Sec 8.1, pg. Questions 1, 4, 6, 9, 14