7th graders: please click on the following link for review problems before the Final Exam on Monday and Tuesday


Problem of the Week


Harry’s Broom

Harry needed to put his 4-foot long broom in a box. He found a box that was 2 feet long by 3 feet wide, and while his broom didn't fit on the bottom, it did fit in the box. What's the shortest the height of the box could be?



Square root of 3.  The shortest height for the box would have the broom lying diagonally. Using the Pythagorean Theorem, the minimum length is the square root of 3.



A Day at the Fairs


It seems that a humble merchant visited three fairs. At the first fair, early in the morning, he doubled his money selling his products, but spent $30 in food and buying other items. 


At midday at the second fair, he tripled his money and spent $54. At the third fair in the afternoon he quadrupled his money but spent $72. 

Upon his return home to his wife and ten children, late that day, he counted the money he had in his bag; there was $48. 


How much did the man gain or lose during the day? 


The merchant gained $19 during the day.  The equation to solve is:

48 = 4[3(2x-30) – 54] – 72

x = 29, representing how much money the merchant began the day with. 48 – 29 = $19 gain.


Squares Rectangles and Rhombuses


All squares are both rectangles and rhombuses. All rhombuses and rectangles are parallelograms.  On a sheet of paper Josh draws 19 rectangles, 15 rhombuses, and 7 squares. How man parallelograms did Josh draw?


In a Venn diagram, the area where rectangles and rhombuses overlap represents squares.  In this region, there are 7 squares, leaving 12 non-square rectangles and 8 non-square rhombuses for a total of 27 parallelograms.


Fair Die


A fair die is tossed four times. What is the probability that it lands with either 5 or 6 on top at least once?

65/81 or approximately .80247. 

The number of possible ways to roll four dice is 64, or 1296: six choices for each of the four rolls. 

There are four ways to roll a single die once and not get a 5 or 6 (that is, to get a 1, 2, 3, or 4), so the number of ways to roll a die four times and not get a 5 or a 6 is 44, or 256. 

Then 1296 - 256, or 1040, ways (the rest of the possibilities) exist to roll the die four times and get a 5 or 6 at least once. 

Therefore, the probability of rolling a die four times and getting a 5 or a 6 at least once is 1040/1296, or 65/81, which is approximately .80247.