FERMI ESTIMATES
Estimate how many pencils a school uses in a school day.
About 1,000–5,000 depending on the school size
Write the ratio of 12 apples to 3 bananas.
12:3 or 4:1.
If you have 3 shirts and 2 pants, how many outfits can you make?
6 outfits
A grade is 40% tests and 60% homework. If a student has a 90 test average and 80 homework average, what’s the total grade?
84
In plurality voting, who wins?
The candidate with the most first-place votes
Estimate how many minutes you spend brushing your teeth in a year.
About 730 minutes (2 minutes × 365)
If 5 pencils cost $3, how much do 20 pencils cost?
$12
A coin is flipped and a spinner with 4 colors is spun. How many total outcomes?
8
You earn $12/hr for 10 hours and $20/hr for 5 hours. What is your weighted average hourly wage?
$14.67/hr
What is the Borda count?
Points assigned to ranked choices; the highest total wins
Estimate how many slices of pizza are eaten in the U.S. per day if 1 in 8 people eat pizza daily.
40 million slices
Solve the proportion: 8/12 = x/18
x = 12
License plates have 2 letters followed by 2 digits. How many plates are possible?
26² × 10² = 67,600
A class has 10 students scoring 80 and 5 students scoring 100. What is the weighted average?
86.7
A cake is divided fairly using the “divider-chooser” method. How does it work?
One cuts, the other chooses
Estimate the number of hairs on a human head
100,000 hairs.
A map uses a scale of 1 inch = 8 miles. How many miles are 3.5 inches?
28 miles
An ice cream shop has 3 cones, 4 flavors, and 2 toppings. How many combinations?
24
A student raises her quiz average (worth 30%) from 70 to 90. If tests (worth 70%) average 85, what is the final average?
86.5
In a ranked-choice election, what happens if no candidate has a majority?
The last-place candidate is eliminated and votes are redistributed
Estimate the number of steps you take in a year if your average is 7,000 per day.
2.5 million steps.
A recipe uses a ratio of 2 cups sugar to 5 cups flour. How much sugar is needed for 25 cups of flour?
10 cups sugar
Use the fundamental counting principle: How many 5-digit codes can be made using digits 1–9 (no zeros) if digits can repeat?
9⁵ = 59,049
A bag contains 30% blue marbles, 50% red, and 20% green. What is the expected score if blue = 1 point, red = 2, and green = 5?
2.3 points
Three roommates split rent of $1,500 using fair share so each feels they get at least ⅓ value. What amount represents each person’s fair share?
At least $500 worth of value per person