Rewards for Problems of the week:
5 stars for the correct answer at your level; 10 stars for the next level; 20 stars each for 2+ levels up.
Lower Elementary:
Question: What are the next 4 numbers in the pattern below?
100, 95, 96, 91, 92, _____, _____, _____, _____
Answer: 87, 88, 83, 84
Solution: There are 2 steps in the pattern. To get from 100 to 95, we subtract 5. To get from 95 to 96, we add 1. Then the pattern repeats.
Upper Elementary:
Question: Pauline gets on her bike at home and rides 2 miles north to the post office. From there, she rides 3 miles west to the library. Then, she rides 4 miles south to the park, then 5 miles east to the farmer’s market. Finally, Pauline rides her bike 2 miles north to her friend Max’s house. How far away is Max’s house from Pauline’s house?
Answer: 2 miles east
Solution: Instead of solving this mentally, students can use a coordinate plane and put Pauline’s house on the origin. The post office is at (0, 2). The library is at (–3, 2). The park is at (–3, –2). The farmer’s market is at (2, –2). Finally, Max’s house is at (2, 0), which is 2 miles to the right, or east, of Pauline’s house.
Middle School:
Question: The figure below is horizontally and vertically symmetrical. What is its area?
Note: The figure is not drawn to scale.
Answer: 104 square centimeters
Solution: We can find the area of the shape by turning thinking of it as 3 shapes stuck together— triangle ABF, triangle DCE, and rectangle BCEF. Triangle ABF has a width of 4 + 4 = 8 and a height of 1/2 (16 – 10) = 3, so its area is 1/2 × 8 × 3 = 12. Triangle DCE has the same width and height as triangle ABF. Rectangle BCEF has an area of 8 × 10 = 80. So, altogether, the area of the shape is 12 + 12 + 80 = 104 square centimeters.
Algebra and Up:
Question: In the figure below, AG is a line and the measure of x is two times the measure of y. What is the value of y?
Answer: 40°
Solution: Since AG is a line, 6z = 180°. So, z = 180° ÷ 6 = 30°. We also know that x + y + 2z = 180°, or x + y + 60 = 180°, or x + y = 120°. If x = 2y, then we can conclude that 3y = 120°. So, y must be 120° ÷ 3 = 40°.
To make the result equal zero, you need to change some of the addition signs to subtraction, multiplication, or division.
Answer: 
Mathnasium of Lake Boone is a math-only learning center for K-12 students in Raleigh, NC. Trusted by over a million parents, Mathnasium uses personalized learning plans and the proprietary Mathnasium Method™ to help students catch up, keep up, and get ahead on their math journey.
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