Lesson Topic: Problem- Solving Using Rates, Unit Rates, and Conversions Lesson Objective: I can… Solve constant rate work problems by calculating and comparing unit rates
Let’s Review: Finding a common denominator
Example 1 - Fresh-Cut Grass If I cut 3 lawns in 5 hours, what fraction of a lawn can I cut per hour? If my friend cuts 5 lawns in 8 hours, what fraction of a lawn can she cut per hour? How can we compare the two fractions? Who is cutting lawns at a faster rate? By how much?
Example 2 – Flying Fingers The secretary types 225 words in 3 minutes and the computer teacher types 105 words in 90 seconds. What 2 rates can I pull out of this situation? Who types at a faster rate?
Group Practice – Do With Your Row If you’re a #1, you’re the timer for your group – Grab a stopwatch. If you’re a #2 or a #3, you’re a walker. #2 will walk 2 laps and #3 will walk 3 laps. #2 goes first. Try to walk at a constant speed as we are doing constant rate work problems today. Determine who walks at a faster rate by comparing the fractions of laps/seconds. When you’re done, #1 becomes #2, #2 becomes #3, and #3 becomes the timer.
Example 3 – Survival of the Fittest A cheetah runs 60 feet in 4 seconds and a gazelle runs 100 feet in 8 seconds. What 2 fractions can I pull out of this situation? Which runs faster?
Example 4 – Restaurant Advertising Darla delivers 350 menus in 2 hours and another employee, Drew, delivers 510 menus in 3 hours. What 2 fractions can I pull out of this situation? Who is faster?
Lesson Summary… Constant rate problems always count or measure something happening per unit of time. The time is always in the denominator. Sometimes the units of time in the denominators of two rates are not the same. One must be converted to the other before calculating the unit rate of each. Dividing the numerator by the denominator calculates the unit rate; this number stays in the numerator. The number in the denominator of the equivalent fraction is always 1.
Evaluate Your Learning How will you “Sharpen Your Saw”?