Click here for the Problem Extension Worksheet version of the Problems of the Week.
Click here for an MS Word version of the Problems of the Week.
Click here for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here for a Canadian MS Word version of the Problems of the Week.

Lower Elementary:
Question: Rachel the Elf is trying to count reindeer, but she’s only tall enough to count their legs. If Rachel counts 24 reindeer legs, then how many reindeer are there?
Answer: 6 reindeer
Solution: Each reindeer has 4 legs, so Rachel can count the reindeer by grouping the legs by 4. She counts 4, 8, 12, 16, 20, 24 legs, so there must be 6 reindeer.

Upper Elementary:
Question: For every 7 gingerbread people Tyler decorates, Sophia decorates 5. If they decorate 60 gingerbread people in total, then how many gingerbread people did Sophia decorate?
Answer: 25 gingerbread people
Solution: Sophia decorated 5 out of 5 + 7 = 12 of the gingerbread people. So, since 5/12 of 60 is 25, Sophia decorated 25 gingerbread people.

Middle School:
Question: Madison is 6 feet tall and casts a 15-foot shadow. He decorates an 8-foot-tall tree with ornaments, garlands, and a star on top. If the shadow cast by the decorated tree is 23 feet and 9 inches long, then how much height does the star add to the tree?
Answer: 11/2 feet
Solution: Since 6 × 21/2 = 15, we know that we multiply the real-life object by 21/2 to find the length of its shadow. So, the decorated tree’s height must be 233/4 ÷ 21/2 = 95/4 × 2/5 = 91/2 feet. That means that the star must have added 91/2 – 8 = 11/2 feet to the height of the tree.

Algebra and Up:
Question: Nora builds a hemispherical igloo with an interior diameter of 18 feet. The walls of the igloo are 1 foot thick, and the entrance takes up the space of 4π cubic feet of snow. What is the volume of snow used to create the walls of the igloo?
Answer: 1762/3π cubic feet
Solution: The interior of the igloo has a radius of 18 ÷ 2 = 9 feet, so the whole igloo has a radius of 9 + 1 = 10 feet. The volume of a sphere is 4/3πr3, so the volume of a hemisphere is 2/3πr3. That means the volume of the whole igloo is 2/3 × π × 103 = 6662/3π cubic feet. If we subtract the volume of the interior (2/3 × π × 93 = 486π cubic feet) and the snow carved out for the entrance, we get 6662/3π – 486π – 4π = 1762/3π cubic feet of snow.

Note: There will not be a new set of Problems of the Week for the week of December 25.