ANSWER KEYS - Teacher Use Only

Understanding Rates | Grade 6

Student Concept Worksheet Answers
1
15 miles per hour
45 miles / 3 hours = 15 mph
2
$2.00 per pound
$10.00 / 5 pounds = $2.00 per pound
3
30 words per minute
120 words / 4 minutes = 30 wpm
4
30 miles per gallon
240 miles / 8 gallons = 30 mpg
5
Store A: $1.50/notebook | Store B: $1.40/notebook | Better buy: Store B
Store A: $6.00/4 = $1.50 per notebook. Store B: $8.40/6 = $1.40 per notebook. Store B has lower unit price.
Practice Worksheet Answers

Part A: Finding Unit Rates

# Problem Answer Work
1150 miles in 3 hours50 mph150/3 = 50
2$24 for 6 pounds$4 per pound24/6 = 4
3200 words in 5 min40 wpm200/5 = 40
4360 miles on 12 gallons30 mpg360/12 = 30
5$35 for 7 hours$5 per hour35/7 = 5
672 beats in 60 seconds1.2 beats/second72/60 = 1.2

Part B: Finding Unit Prices

# Problem Answer Work
74 pens for $3.00$0.75 per pen3.00/4 = 0.75
810 oz for $4.50$0.45 per oz4.50/10 = 0.45
93 lb for $12.60$4.20 per pound12.60/3 = 4.20
108 bananas for $2.00$0.25 per banana2.00/8 = 0.25

Part C: Comparing Rates

11
Store A: $0.0625/oz | Store B: $0.06/oz | Better: Store B
A: $4.00/64 = $0.0625/oz. B: $2.88/48 = $0.06/oz. Store B is cheaper per ounce.
12
Brand X: $1.40/roll | Brand Y: $1.25/roll | Better: Brand Y
X: $8.40/6 = $1.40/roll. Y: $10.00/8 = $1.25/roll. Brand Y is cheaper per roll.
13
Car A: 60 mph | Car B: 54 mph | Faster: Car A
A: 240/4 = 60 mph. B: 270/5 = 54 mph. Car A is faster.

Part D: Word Problems

14
75 toys per hour
450 toys / 6 hours = 75 toys per hour
15
$84
Unit rate: $63/9 = $7/hour. For 12 hours: $7 x 12 = $84
16
15 minutes
Unit rate: 48/4 = 12 pages/min. For 180 pages: 180/12 = 15 minutes
17
8 gallons
256 miles / 32 mpg = 8 gallons
18
315 pages
Unit rate: 135/3 = 45 pages/day. For 7 days: 45 x 7 = 315 pages

Challenge Questions:

#19: Store A: $45/3 = $15 per shirt. Store B: $70/5 = $14 per shirt. Store C: $52/4 = $13 per shirt. Store C is the best deal at $13 per shirt.

#20: Train: 90/1.5 = 60 mph. Car: 120/2.5 = 48 mph. Train is faster by 12 mph (60 - 48 = 12).

FAST Practice Quiz Answers
1
A) 70 miles per hour
280 miles / 4 hours = 70 mph. B adds instead of divides. C multiplies. D divides wrong way.
2
B) $1.75 per pound
$8.75 / 5 pounds = $1.75 per pound. A multiplies. C and D are calculation errors.
3
A) Brand A ($0.30 per oz)
Brand A: $3.60/12 = $0.30/oz. Brand B: $5.12/16 = $0.32/oz. Brand A has lower unit price.
4
Select: $4.50 per pound, 55 miles per hour, 15 words per minute
$4.50 per pound - YES (per 1 pound)
120 miles in 2 hours - NO (not per 1)
55 miles per hour - YES (per 1 hour)
$24 for 8 items - NO (not per 1)
15 words per minute - YES (per 1 minute)
5
C) 105 pages
Unit rate: 42/6 = 7 pages/min. For 15 min: 7 x 15 = 105 pages.
6
A) She earns $7 per hour, so she would earn $91 for 13 hours
$56/8 = $7/hour. For 13 hours: $7 x 13 = $91. B has wrong hourly rate. C has wrong multiplication.
FAST Quiz Scoring Guide
Score Interpretation Recommended Action
6/6 Mastery Ready for proportional relationships and percent problems.
4-5/6 Approaching Mastery Review unit rate calculation or applying rates. Check which type caused errors.
2-3/6 Developing Reteach division for unit rates. Use concrete examples like money and shopping.
0-1/6 Needs Intervention Small group instruction. Start with simple unit prices before moving to speed and other rates.
FAST Success Kit | Grade 6 | FL B.E.S.T. Standards: MA.6.AR.1.3, MA.6.AR.1.4 | Answer Key - Teacher Use Only