Grade 6 Unit 3

 Grade 6 Unit 3: Unit Rates & Percentages

Who biked faster: Andre, who biked 25 miles in 2 hours, or Lin, who biked 30 miles in 3 hours? One strategy would be to calculate unit rates. A unit rate is created by writing a ratio as something “per 1.” For example, Andre’s rate could be written as “1212 miles in 1 hour” or “1212 miles per 1 hour.” Lin’s rate could be written “10 miles per 1 hour.” By finding the unit rates, we can compare the distance each person went in 1 hour to see that Andre biked faster. Every ratio has two unit rates. In this example, we could also compute hours per mile: how many hours it took each person to cover 1 mile. Although not every rate has a special name, rates in “miles per hour” are commonly called speed and rates in “hours per mile” are commonly called pace. Deciding which unit rate to calculate for a given ratio is part of the work of Unit 6.3.

• Using “miles per hour” or speed, Andre biked 12.5 miles per hour while Lin biked 10 miles per hour. Since Andre traveled more miles in the same amount of time, he is the faster biker.

Andre:

row 1	miles	hours
row 2	25	2
row 3	1	0.08

Lin:

row 1	miles	hours
row 2	30	3
row 3	1	0.1

Ask your student to explain the mathematics they are learning. Encourage them to use their notes or other work as they illustrate their ideas:

• What is a way you can compare ratios?
• How would you describe a unit rate? Can you show me some examples?

 Percentages 

Let’s say 440 people attended a school fundraiser last year. If 330 people donated more than $30, your student may be asked what percent of people donated more than $30. If it’s expected that the attendance this year will be 125% of last year, your student may be asked to find the number of attendees expected this year. A double number line can be used to reason about these questions.

Students will use their understanding “rates per 1” to find percentages, which we can think of as “rates per 100.” Double number lines and tables continue to support their thinking. The example above could also be organized in a table:

row 1	number of people	percentage
row 2	440	100%
row 3	110	25%
row 4	330	75%
row 5	550	125%

Toward the end of the unit, students develop more sophisticated strategies for finding percentages by noticing that every time they find P% of a number, they have to find P100 times that number. In the example above, finding 125% of 440 attendees is the same as 125100⋅440 attendees. By the end of the unit, students use these efficient strategies and understand why they work. Ask your student to explain the mathematics they are learning. Encourage them to use their notes or other work as they illustrate their ideas:

• See a coupon with a percentage discount? Ask your student how they would calculate the dollar amount saved.
• Can you describe a strategy for finding 25% of a number? 75% of a number?