Click here [1] for the Problem Extension Worksheet version of the Problems of the Week.
Click here [2] for an MS Word version of the Problems of the Week.
Click here [3] for the Canadian Problem Extension Worksheet version of the Problems of the Week.
Click here [4] for a Canadian MS Word version of the Problems of the Week.
[5]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.
[6]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.
[7]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.
[8]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.