Lesson 3
1. Lesson 3
1.3. Explore 3
Module 6: Proportional Reasoning
A lot of the problems you have solved in this module have required you to use rates. For instance, you compared rates to find the best buy or to do conversions. Sometimes you need to use rates to solve for an unknown.
Read “Example 3: Reasoning to solve a rate problem” on page 456 of your textbook. Consider the following: What strategies did Mila and Joe use to determine how many boxes of dessert squares should be purchased? Which strategy do you prefer?
The strategy of unit analysis involves using conversion factors to reduce to a single unit in the second term (or denominator) of the rate.
You can solve a rate problem that involves an unknown by using a variety of strategies. Mila used unit analysis to solve her problem while Joe decided to use estimation. Unit analysis is also useful for converting from one unit to another. Consider the following situation.
Esther was training for a race and bought a pedometer to track her jogging speed. She was disappointed to see that the pedometer only displayed her speed in m/s. Her coach had been tracking Esther’s progress and recording her speed in km/h.
Esther decided to note her speeds from her pedometer and then do the conversions to km/h. Her top speed with her coach had been 6 km/h. With her new pedometer, Esther’s top speed had been 2 m/s. Had her speed increased, decreased, or stayed the same?
Esther can convert from km/h to m/s or vice versa. She decided to convert from m/s to km/h.
Then she can convert to km/h by dividing by 1000.
So, Esther ran faster with her pedometer than with her coach.