Problems of the Week July 22

HERE ARE AGE APPROPRIATE PROBLEMS OF THE WEEK. SCROLL TO THE BOTTOM FOR THE ANSWERS:

Lower Elementary:
Question: What are the next 4 numbers in the pattern below?

100, 95, 96, 91, 92, _____, _____, _____, _____

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?
 

Middle School (use the first image below):
Question: The figure below is horizontally and vertically symmetrical. What is its area?
Note: The figure is not drawn to scale.
 

Algebra and Up (use the second image below):
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?
 

ANSWERS ARE NEXT! NO PEAKING UNTIL YOU HAVE TRIED!

Lower Elementary 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:

96 – 5 = 91
91 + 1 = 92
92 – 5 = 87
87 + 1 = 88
88 – 5 = 83
83 + 1 = 84

Upper Elementary 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 Answer:  104 square centimeters

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 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°.