Lower Elementary
Question: Christine has $2. If she buys 3 pencils for 25¢ each and 2 erasers for 50¢ each, how much money does she have left?
Answer: 25¢
Solution: Christine bought 3 pencils for 25¢. Together the 3 pencils cost 75¢ (25¢ + 25¢ + 25¢ = 75¢). She also bought 2 erasers for 50¢ each. Together the 2 erasers cost $1.00 (50¢ + 50¢ = $1.00). Combined, the pencils and erasers cost a total of $1.75 (75¢ + $1.00 = $1.75).
To find how much money she has left we ask,
“how far is it from $1.75 up to $2.00?”
After paying for the pencils and erasers, Christine has 25¢ left.
Upper Elementary
Question: A frog is at the bottom of a 25–foot well. Each day he climbs up 3 feet, and each night he slips down 2 feet. How many days will it take the frog to reach the top of the well?
Answer: 23 days
Solution: During the day the frog climbs 3 feet and falls 2 feet at night, effectively only climbing 1 foot for every whole day. Many students will try and say that the frog takes 25 days to climb out, but this is not correct. After 22 whole days, the frog has climbed a total of 22 feet. The next day he climbs 3 feet to 25 feet and gets out, only taking the frog 23 days.
Middle School
Question: Some rattlesnakes can shake their rattles at a rate of 50 times per second and keep rattling at the same rate for 3 hours. At this rate how many times does a snake shakes its rattle in the 3 hour span?
Answer: 540,000 shakes
Solution: Let’s start by finding how many times the snake shakes its rattle in a minute, then an hour, and finally 3 hours.
1 minute: 60 × 50 shakes = 3000 shakes
1 hour: 60 × 3000 shakes = 180,000 shakes
3 hours: 3 × 180,000 shakes = 540,000 shakes
Algebra and Up
Question: How many 1500 kilobyte pictures can you fit on a 3 terabyte hard drive?
Answer: 2142857
Solution: To find how many kilobyte pictures fit on to a 3 terabyte hard drive, we need to first convert kilobytes into terabytes. Then in accordance with the Law of SAMEness, they will have the same name allowing us to divide. You may need to hint to students that there are 1024 kilobytes in a megabyte, 1024 megabytes in a gigabyte, and 1024 gigabytes in a terabyte.
Number of kb per tb:
1024 kb/mb × 1024 mb/gb × 1024 gb/tb = 1073741824 kb/tb
(or about 1.07 × 10^9 kb/tb)
Capacity of the hard drive in kb:
3 tb × 1073741824 kb/tb = 3221225472 kb
(or about 3.21 × 10^9 kb)
Capacity of the hard drive in 1500 kb pictures:
3221225472 kb / 1500 kb/picture = 2147483.648 pictures
(or about 2.14 × 10^6 pictures)
Because we cant have 0.648 of a picture, we round down to 2,147,483
(or about 2,140,000 pictures).
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