Hot Air Balloons

Fall is a beautiful time of year to take a hot air balloon ride! You may not be able to take a balloon ride, but we hope you enjoy solving this week’s problems.

Melrose’s hot air balloon is a sphere of diameter 100 feet. How many cubic feet of air will Melrose’s hot air balloon hold when completely filled? Express your answer as a decimal to the nearest tenth.

Moving Day

The summer months are the most popular time to move to a new home. Janet’s family is moving, and she suddenly realizes just how much stuff they have in their current home. Once the moving company finishes packing everything in boxes, they begin the task of numbering them. A sticker is placed on every box and on every item that is too large to fit in a box. Janet notices that stickers in three distinct colors are used. There are blue stickers numbered 239 through 262, green stickers numbered 163 through 178 and yellow stickers numbered 453 through 492.

Road Work Ahead

A construction crew places orange barrels on both sides of a particular road to indicate a work zone. On each side of the road, the distance between the centers of consecutive barrels is 15 feet. If this work zone is 1.5 miles long, what is the total number of barrels that will be used?

Happy Pi Day

 

This Wednesday (3/14) was Pi Day. Here are a few questions in honor of the day.

If Celia ate 1/4 of 2/3 of 1/2 of a pie, what fraction of the whole pie did she eat? Express your answer as a common fraction.

Celia ate (1/4)(2/3)(1/2) = 1/12 of the whole pie.

 

A Mathy Valentine

On a coordinate grid, graph the following segments:

y = x, for 0 ≤ x ≤ 2
y = 2x − 2, for 2 ≤ x ≤ 3
x = 3, for 4 ≤ y ≤ 6
y = −x + 9, for 2 ≤ x ≤ 3
y = 7, for 1 ≤ x ≤ 2
y = x + 6, for 0 ≤ x ≤ 1

Now reflect each of the segments over the y-axis.  What popular shape have you drawn?

Happy New Year!

Happy New Year! Now that 2018 is here, let’s have some fun with this number!

What is the last digit of 20182018?

The units digits of the powers of 2018 are the same as the units digits of the powers of 8, and they form a pattern that repeats every four powers. The pattern of units digits is 8, 4, 2 and 6. Since 2018 is 2 more than a multiple of 4, it follows that the units digit of 20182018 is the second digit in this pattern, which is 4.

 

Baking Fruit Cake

Allie plans to make a fruit cake for her family plus four more to give away to friends. Shown here is a list of the ingredients required to make a fruit cake according to Allie’s recipe. How many ounces of mixed fruit are needed for Allie to make five fruit cakes, according to her recipe?

fruit cake ingredients.eps

O, Christmas Tree

Although, Franklin Pierce, the 14th U.S. President, originally brought the Christmas tree tradition to the White House, it was Calvin Coolidge, the 30th U.S. President, who, in 1923, started the National Christmas Tree Lighting Ceremony now held every year on the White House lawn. Last week, the president and first family continued that tradition by lighting a tree on the White House lawn. And speaking of trees, try to solve the following Christmas tree-themed problems.