Problems of the Week (POWs) Assignments

Instructions: Type your solutions neatly on stapled sheets of paper with your name on top of each page. Your solution will be graded according to the official Oregon Scoring Guide (you can look it up at http://www.octm.org/assess.html), and thus your write up should include all your reasoning, and not just a final answer.

The emphasis of these assignments is on clear, complete and precise explanations. Please write your solutions in a way that a "typical" student in the 5-8^th grade range will be able to follow it.

These problems were taken from the following NCTM sources:

The Mathematics Teacher

Mathematics Teaching in the Middle School

The Math Forum at Drexel University

A. POW 1 Due 6/22

A merchant paid $30 for an article. He wishes to place a price tag on it so that he can offer a 10 percent discount on the price marked on the tag and still make a profit of 20 percent on the cost. What price should he mark on the tag?

B. POW 2 Due 6/24

Five years ago, I planted a four-foot tall tree in the front yard. It has grown the same amount each year, and last year it was twice as tall as it was at the end of the first year. How tall is the tree now?

C. POW 3 Due 6/29

The town of Hippity-Hoppity has a population of 17, 480. Five percent of the people are one-legged. One-half of the remaining population goes barefooted. Sandals are the only footwear worn. How many sandals (not pairs) are worn in Hippity-Hoppity?

D. POW 4 Due 7/1

While sitting at my computer, my attention wandered to the digital time display. It showed the following time:

1:44

(I prefer a 12-hour clock showing only hours and minutes.)

"That's rather curious," I thought. "If I remove the two dots, I'll have the number 144, which is the square of 12. I wonder how often that sort of thing happens."

If a "day" starts at 7 am and ends at 7 pm, during which hour of the day am I most likely to see a square number on my time display? How many times total during the day does this happen?

E. POW 5 Due 7/6

Find the sum of all positive integers less than 1,000 that are divisible by 3 but not by 2.