Archive | November, 2009
November 18, 2009 

Easy task high credit, tough task low credit, reasonable results.

If you are assigning scores to questions on a test, I used to make hard questions worth more points than easy questions, because I thought that they should carry a greater reward for correct answers. This caused problems because many students who had a decent level of understanding of material were not getting the questions worth the most points on their assessments.

My current approach is the exact opposite, an easy question should be worth lots of points, and a tough questions should be worth a few. The few points are enough to separate out kids who are good from those who are excellent, but students who do well on a test should not be receiving terrible scores. This tends to agree with our intuition about what a student’s total score should be.

I think I figured this out sometime last year, and I’ve been thankful for it ever since.

November 15, 2009 

What day of the week where you born on?

I’ve been reluctant to post lately because I haven’t felt like I have much worth sharing. I’m using BetterLesson, and I’m slowly getting my curriculum updated to it. I’ve spent a lot of time putting together some units, the units are composed of an Overview (a pdf containing lists of skills and links to other pdf worksheets and Smart Board files that relate to the unit), worksheets, notes, and multiple versions of tests with answer keys written in LaTeX and the package eqExam and the AcroTex bundle by DP Story.

I did a little research this afternoon, and thought I’d put it up here. I’ll be giving this the run through tomorrow in my “mathletics” math competition class. Here goes.

Big Question
What day of the week do you think you were born on? Take a guess.

Some Info For you to Consider
1. The number of days in a month can be easily remembered using your knuckles.

Thanks to the Mnemonics Guide at EUDesign

Thanks to the Mnemonics Guide at EUDesign

2. If today, November 15th, 2009 is a Sunday, and you want to know what day it was on March 18th, 2009, find the number of days that have elapsed, divide by 7, and use the remainder to determine the day of the week.

Number of days elapsed since March 18th:
March: 18th to 31st is 13 days. 30 days elapsed in April, May is 31, June, 30. July, 31, August, 31, Sep, 30, Oct, 31 and Nov: 15. For a total of 13 + 30 + 31 + 30 + 31 + 31 + 30 + 31 + 15 for a total of 242 days. Since 242/7 = 34\frac{4}{7}, March 18th, 2009 was (Sat, Fri, Thus, Wed), 4 days prior in the week relative to today, so it was a Wednesday.

3. 365 divided by 7 has a remainder of 1. So generally, if the a date in year N is Monday, the date in year N + 1 is a Tuesday. But leap years have 366 days, so if a date in year N is Monday, and a February 29th falls within the range of dates in the next year, the date in year N + 1 will be a Wednesday. Note that 2008 was a leap year.

For practice, I’d show how to calculate my own birthday. Here’s a fake example to protect my millions in offshore bank accounts and student loans. Say I was born on July 13th, 1980.

1. Number of Days elapsed since July 13th, 2009, remember today is Sunday, November 15th:
18 + 31 + 30 + 31 + 15 = 125.

2. 125 / 7 = 17 r 6. So 17 and 6/7 weeks have elapsed since July 13th, making July 13th fall six days earlier in the week. July 13th, 2009 must have been a Monday.

3. Years from July 13th, 1980 until July 13th, 2009 = 29. For each year the week days shift forward one, but for leap years they shift by two. Of the 29 years there were 7 leap years. In reverse order they were 2008, 2004, 2000, 1996, 1992, 1988, 1984 (1980 would not count since July 13th would have occurred after February 29th of the leap year). Increment another 7 days from the leap years giving 36 weekdays to account for. 29 + 7 = 36, which has remainder 1. Therefore, July 13, 1980 must have been a Sunday.

Explore
Have each student determine the day of their birthday and the day of a friends.

I’ll be giving them a set of mathcounts problems, that include some day of the week calculation.