Video Solutions to help Grade 6 students learn how to solve constant rate work problems by calculating and comparing unit rates.

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Lessons for Grade 6

Common Core For Grade 6

• Students solve constant rate work problems by calculating and comparing unit rates.

• 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.

Example 1: Fresh-Cut Grass

Suppose that on a Saturday morning you can cut 3 lawns in 5 hours, and your friend can cut 5 lawns in 8 hours.
Your friend claims he is working faster than you. Who is cutting lawns at a faster rate? How do you find out?

Example 2: Restaurant Advertising

Next, suppose you own a restaurant. You want to do some advertising, so you hire 2 middle school students to
deliver take-out menus around town. One of them, Darla, delivers 350 menus in 2 hours, and another
employee, Drew, delivers 510 menus in 3 hours. You promise a $10 bonus to the fastest worker since time is
money in the restaurant business. Who gets the bonus?

Example 3: Survival of the Fittest

Which runs faster: a cheetah that can run 60 feet in 4 seconds or gazelle that can run 100 feet in 8 seconds?

Example 4: Flying Fingers

What if the units of time are not the same in the two rates? The secretary in the main office can type 225
words in 3 minutes, while the computer teacher can type 105 words in 90 seconds. Who types at a faster
rate?

1. Who walks at a faster rate: someone who walks 60 feet in 10 seconds or someone who walks 42 feet in 6 seconds?

2. Who walks at a faster rate: someone who walks 60 feet in 10 seconds or someone who takes 5 seconds to walk 25 feet? Review the lesson summary before answering!

3. Which parachute has a slower decent: a red parachute that falls 10 feet in 4 seconds or a blue parachute that falls 12 feet in 6 seconds?

4. During the winter of 2012-2013, Buffalo, New York received 22 inches of snow in 12 hours. Oswego, New York received 31 inches of snow over a 15 hour period. Which city had a heavier snowfall rate? Round your answers to the nearest hundredth.

5. A striped marlin can swim at a rate of 70 miles per hour. Is this a faster or slower rate than a sailfish, which takes 30 minutes to swim 40 miles?

6. One math student, John, can solve these 6 math problems in 20 minutes while another student, Juaquine, can solve them at a rate of 1 problem per 4 minutes. Who works faster?

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