Lower Elementary
Question: Rachael wants to read a book that is 168 pages long. If she reads 12 pages each day, how many weeks will it take Rachael to read the entire book?
Answer: 2 weeks
Note: If Rachael can read 12 pages in one day, then in order to find out how many days it takes her to read 168 pages, divide: 168 / 12 = 14. That means it would take 14 days to read the book. 7 days = 1 week so that means 14 days = 2 weeks.
The problem could also be solved by finding out how many books Rachael can read in 1 week. Since 1 week = 7 days. To find out how many pages Rachael reads in 1 week, multiply: 12 x 7 = 84 pages. That means in another week Rachael can read 84 more pages. That means for 2 weeks she can read (84 + 84) 168 pages.
Upper Elementary
Question: In Chicago, Illinois the temperature was 4oF(ahrenheit) at 6 am. By 12 pm the temperature had risen 14o F. Then, the temperature dropped 27o F by 8 pm. What was the temperature at 8 pm?
Answer: -9o F
Middle School
Question: The 28 students in Mr. Smith’s gym class chose to participate in track and field events during the class. 9 students chose the long jump, 12 students chose the 100-meter dash and 4 students chose both. How many students chose neither?
Answer: 11 students
Note: Drawing a Venn diagram can help find the answer. In this problem the only events of concern are the long jump and the 100-meter dash.
From the Venn diagram you can see that 5 students chose the long jump and not the 100-meter dash, 8 students chose the 100-meter dash and not the long jump. Since there were 4 students who chose both, the total number of students participating in either of these two events is 17. To find the student participating in neither subtract the 17 students from the two events from the total number of students. 28 – 17 = 11.
Another method for solving this problem is to know that the total number of students participating in the two events is the union of the students from both events minus the intersection of the two events.
The union of the two events is 9 + 12 = 21 (total students who chose the long jump + total students who chose the 100-meter dash). The intersection of the two events is 4 (the number of people who chose both)
21 – 4 = 17. Now subtract the total number of students participating in either event from the total number of students in the class 28 – 17 = 11.
Algebra and Up
Question: Frank is building an entertainment center. He wants to put a circular cable with a 3 cm circumference through a square opening with a perimeter of 4 cm. Will the cable go through the opening? Explain why or why not?
Answer: Yes. In order for the cable to go through the square opening the diameter of the cable has to be less than the width and height of the square opening. Since the diameter of the cable is approximately .955 centimeters and the width and height of the square is 1 cm the cable will go through.
Note: Drawing a picture may help visualize what needs to happen in order for the cable to fit through the hole. From the picture we can see that in order for the cable to fit perfectly through the square opening (to be inscribed) the diameter of the cable must be less than or equal to the width and height of the opening.
Since the perimeter of the square opening is 4 cm, that means the length of each side is 1 cm. In order for the cable to fit through the diameter must be less than or equal to 1 cm.
We can find the diameter of the cable by using the formula for circumference. C = pi*d. Let pi = 3.14.
In this case the circumference = 3 cm. Solving for diameter we have that d = C / pi = 3 / 3.14 d ≈ .995 cm.
Since .995 < 1, the cable will fit through the opening.
