Lower Elementary:
Question: The United States Declaration of Independence was signed on July 4, 1776. How old will the United States Declaration of Independence be on July 4, 2013?
Answer: 237
Solution: To find the age of the United States Declaration of Independence, take the original date and subtract it from the current date. 2,013 – 1,776 = 237. The United States Declaration of Independence will be 237 years old on July 4, 2013.
Upper Elementary:
Question: For a 4th of July barbeque, Mark went to the store and bought hot dogs and hot dog buns. Hot dogs come in packs of 8 while the hot dog buns come in packs of 6. What is the smallest amount of each pack that Mark bought so that there is the same amount of hot dogs as hot dog buns?
Answer: 3 packs of hot dogs and 4 packs of hot dog buns
Solution: To solve this problem, first find the smallest number where equal groups of 8 is the same as equal groups of 6. This is the same as finding the least common multiple of 8 and 6.
8, 16, 24
6, 12, 18, 24
The least common multiple of 8 and 6 is 24. Since 8 × 3 is 24 and 6 × 4 is 24, so Mark bought 3 packs of hot dogs and 4 packs of hot dog buns.
Middle School:
Question: When Betsy Ross made the first flag, it had 13 stars and 13 stripes to represent the 13 states when the Declaration of Independence was signed. For one of her first flags, she had a 20 foot by 13 foot white cloth. She put a 7 foot by 7 foot blue square in the upper right corner. She then cut out the 13 star shapes from the blue fabric, taking out 1 square foot of blue fabric for each star. She then cut four 13 foot by 1 foot and three 20 foot by 1 foot red stripes and placed them 1 foot apart so that the flag would alternate red, white, red, white, red, white, red, white, red, white, red, white, red. What is the area of the flag that showed white?
Answer: 112 square feet
Solution: One way to solve this problem is to count up all the areas that are showing white. Let’s start with the stars. Since there are 13 stars, and each star is 1 square foot, there are 13 square feet of white showing for the stars.
Now let’s find the area of the stripes. Since the blue cloth covers 7 feet widthwise, that means that there are 7 stripes that are 13 feet by 1 foot and 6 stripes that are 20 feet by 1 foot. Since the alternating pattern starts with red, there are 3 white stripes that are 13 feet by 1 foot, or 13 square feet, and there are 3 white stripes that are 20 feet by 1 foot, or 20 square feet. So the total area for the stripes is 99 square feet (3 × 13 + 3 × 20 = 39 + 60 = 99).
Add the area of the stars and the area of the stripes to get the area of the total. 13 + 99 = 112. The flag has 112 square feet of white showing.
Algebra and Up:
Question: Fireworks follow a parabolic path before they explode in the sky. The pyrotechnics created a set of fireworks so that they would explode at the vertex of their parabolic path. They line up 2 fireworks right next to each other. One has a parabolic path of g(x) = –2x2 + 12x and the other has a path of h(x) = –x2 + 9x where x is measured in kilometers. How far apart on the x-axis are the fireworks when they explode?
Answer: 1.5 kilometers
Solution: First, we need to find the x-coordinate of the vertex for each fireworks. The standard equation for a parabola is f(x) = ax2 + bx + c. One way to find it is to use the formula for the x-coordinate of the vertex, x = –b/2a.
g(x): –b/2a = –12/2(–2) = –12/–4 = 3
h(x): –b/2a = –9/2(–1) = –9/–2 = 4.5
The x-coordinate of the vertex for the first firework is 3 and the x-coordinate of the vertex for the second firework is 4.5. So, the difference between the fireworks is 4.5 – 3 = 1.5. The fireworks will be 1.5 kilometers apart on the x-axis when they explode.
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