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News from Mathnasium of Columbus Bradley Park

The Ghosts of Christmas Math

Dec 12, 2019

Happy Holidays! We hope you're all spending your winter breaks (whenever they may be) in good cheer. If you find yourself in need of a holiday spirit boost, we have you covered with some extra sets of Problems of the Week from Christmases past!

Lower Elementary:

Question 1: Paul hung 13 ornaments on the Christmas tree. Quinn hung 19 ornaments on the Christmas tree. Reagan hung 17 ornaments on the Christmas tree. How many ornaments are on the Christmas tree?

Question 2: Santa can write 24 names on each foot of his list. How many names can Santa fit onto a list that is 4 feet long?

Upper Elementary:

Question 1: Danielle made cookies to leave for Santa. Half of the cookies she made are chocolate chip, one third of the cookies are oatmeal raisin, and the remaining 3 cookies are peanut butter. How many total cookies did Danielle leave for Santa?

Question 2: Santa can write 24 names on each foot of his list. How many names can Santa fit onto a list that is 4 feet long?

Middle School:

Question 1: Benji is driving to his grandparents’ house to celebrate Christmas Eve. He traveled 60 miles to get to the house. Because of traffic, Benji’s average speed was 45 miles per hour. How long did it take Benji to get to his grandparents’ house in minutes?

Question 2: Rachel the Christmas elf can wrap 8 presents in 3 minutes. How long will it take Rachel to wrap 28 presents?

Algebra and Up:

Question 1: Penelope is wrapping presents. She has a cube-shaped gift that has a volume of 512 cubic inches. If she wants to use an exact amount of wrapping paper to wrap the gift, how much wrapping paper does she need to wrap the gift?

Question 2: A dreidel has 4 sides. If a player spins the dreidel and it lands with “nun” facing up, the player does nothing. If “gimel” faces up, the player gets all the tokens. If “hey” faces up, the player gets half the tokens. If “shin” faces up, then the player must add a token to the pot. What is the probability that four people playing a round of dreidel will each take tokens if the round starts with 8 tokens in the pot?

Lower Elementary:

Solution 1:  To find the total number of ornaments hanging on the tree, we add the number of ornaments each person put on the tree. So, we add 13 + 19 + 17. It would be easier to add 13 and 17 first since the ones place values add to 10. 13 + 17 = 30, and 30 + 19 = 49, so there are 49 ornaments on the tree.

Solution 2:  We can either add 24 + 24 + 24 + 24, or we can multiply. Twenty-four is one away from 25, and 25 × 4 = 100. That’s one extra, four times. 24 × 4 is the same as 100 – 4 = 96 names.

Upper Elementary:

Solution 1:  First we need to find the fractional part that the peanut butter cookies represent. 1 – 1/2 – 1/3 = 1 – 3/6 – 2/6 = 1/6. So the peanut butter cookies represent 1/6 of the cookies. Since there are 3 peanut butter cookies, there is a total of 3 × 6 = 18 cookies.

Solution 2:  Each reindeer has 2 more jingle bells than the last. After Prancer with 15 bells, Vixen has 17, Comet has 19, Cupid has 21, Donner has 23, Blitzen has 25, and Rudolph has 27. The sum of all the jingle bells is 171.

Hint: A good strategy to use to add up all 9 addends is to match pairs of digits in the ones place that add up to 10 (e.g. 1 and 9).

Middle School:

Solution 1:  Benji’s grandparents live 60 miles away and he travels 45 miles per hour. After 1 hour, Benji will have traveled 45 miles, so he still needs to travel 15 more miles. 15 is 1/3 of 45, so it will take Benji 1 1/3 hours to get to his grand parents’ house. There are 60 minutes in an hour, so it took Benji 1 1/3 × 60 = 80 minutes.

Answer 2:  10 minutes and 30 seconds

Solution 2:  Eight presents goes into 28 presents 3½ times. So, Rachel needs 3 minutes, 3½ times to wrap 28 presents. 3 × 3½ = 10 minutes, or 10 minutes and 30 seconds.

Algebra and Up:

Answer 1:  384 square inches of wrapping paper

Solution 1:  The volume of a cube is the side length cubed. To find the side length, we take the cube root of the volume. The cube root of 512 = 8, so the side lengths are 8 inches. The surface area of the cube is the area of one face times the number of faces. The area of one face is 8 × 8 = 64 square inches. A cube has 6 faces, so the surface area of the box is 64 × 6 = 384 square inches.

Answer 2:  1 out of 128

Solution 2:  There are 2 ways to win tokens, “gimel” and “hey,” but in order for the everyone to have tokens available to them, only the last person can spin a “gimel.” For the first 3 players, the probability of getting “hey” is 1/4. The probability of the last player getting either “gimel” or “hey” is. So, the probability that each player will get tokens is 1/4 × 1/4 × 1/4 × 1/2 = 1/128.