by Josh Rappaport
So many students ask: what’s math good for?
So in this article, I’ll show how to use simple math to do something useful — keeping track of days and dates, all in your head! This is a great thing to know whenever you need to figure out something for your schedule, but have no calendar handy.
So to start … for any given month, the first step is to figure out which weekday falls on the 7th. Whichever weekday that is, memorize it. Why? Because that weekday will also fall on all multiples of 7: the 14th, the 21st and the 28th. And that right there already gives you a skeletal grasp on the month. Call that weekday the “7-Day” of the month. And now we’re rolling.
Example: take the month we’re now in, April 2014
This April, the 7th is a Monday, so for this April, “7-Day” is Monday.
Based on this, we now know that all of the following are also Mondays: 4/7, 4/14, 4/21, and 4/28.
And since Friday comes four days after Monday, merely add 4 to each Monday date to get the Fridays of April:
7 + 4 = 11 // 14 + 4 = 18 // 21+ 4 = 25
This means that this month, the Fridays are: 4/11, 4/18, 4/25.
And don’t forget, there’s also the first Friday, 7 days before 4/11, so 4/4.
Once you know the Mondays and Fridays, it’s easy to figure out the workweeks, as they run from Monday through Friday. So for this month, the M-F workweeks are 4/7 – 11; 4/14 – 18; 4/21 – 25; and 4/28 – 5/2.
Not bad, huh? But that’s not all. Once you get the hang of this, it’s a cinch to figure out the “7-Day” of the following month, May in our case.
To do this, first absorb an important point.
The weekday on which one month ends is ALWAYS the “7-Day” of the following month. For example, if a month ends on Thursday, the 30th, the “7-Day” of the following month will be Thursday. Count it out, and you’ll see. [Fri, the 1st, Sat., the 2nd, Sun., the 3rd, Mon., the 4th, Tues., the 5th, Wed., the 6th, Thurs., the 7th]. Again, this shows that the weekday on which any month ENDS = the “7-Day” of the following month.
Now let’s return to our month: April 2014. My next point may at first seem strange, but bear with me for a moment. If, hypothetically, this April had only 28 days (thus ending on 4/28), that day would be a Monday, since Monday is this April’s “7-Day.” But further, since that would be the last day of April, hypothetically, Monday would be the “Seven-Day” of May as well.
So notice that if all months had 28 days, every month would have the same “7-Day” and therefore days and dates would be extremely regular.
But of course, things are more ‘messy.’ Months have different numbers of days, and April itself has 30, two days more than the “neat-and-clean” 28.
So how does this affect our calculations? It means that April ends two days after its “7-Day” of Monday. That means that April ends on a Wednesday (Monday + 2 days). But based on what we said just above, this means that Wednesday will be the “7-Day” of May.
Generalizing this concept, we see that for months with 30 days, the “7-Day” of the following month is always TWO weekdays beyond the “7-Day” of the month with 30 days. Example: if June (with 30 days) has a “7-day” of Wednesday, we can be certain that July will have a “7-day” of Friday (Wednesday + 2 days).
Similarly, for months with 31 days, the “7-Day” of the following month will always be THREE weekdays beyond the “7-Day” of the month with 31 days. Example: If July (with 31 days) has a “7-day” of Tuesday, that means that the next month, August, will have a “7-Day” of Friday (Tuesday + 3 days).
Finally, for non-leap-year February months (with 28 days), the “7-Day” of February will be identical to the “7-Day” of March. For once we don’t need to tack on extra days!
So to put this whole strategy in the proverbial “nutshell,” here are the main points for keeping track of dates mentally.
1st) Figure out which weekday is the “7-Day” for the month you’re in.
2nd) Once you know (and memorize) that, add 2 days to that weekday to get the “7-Day” of the following month, if your month has 30 days. Or add 3 days if your month has 31 days.
3rd) Once you know your month’s “7-Day” count ahead or back to find the Mondays for your month.
4th) From the Mondays, count ahead 4 days to find the Fridays of your month. Then put the Monday-Fridays together to get the workweek days for the month you’re in.
And voila! That’s essentially all you need to get started keeping track of dates in your head.
I find it’s useful to be able to do this mentally, and it also kind of impresses people, as a little side benefit.
Well, this piece, it turns out, is my final article for HERD. So let me say THANK YOU for being a great audience. I’ve enjoyed the process of writing these articles very much. And I wish all of you the very best on your continuing adventures through the fields of mathematics.
Josh Rappaport is the author of the Algebra Survival Guide and Workbook, which together comprise an award-winning program that makes algebra do-able! Josh also is the author of PreAlgebra Blastoff!, an engaging, hands-on approach to working with integers. All of Josh's books, published by Singing Turtle Press, are available on Amazon.com
So many students ask: what’s math good for?
So in this article, I’ll show how to use simple math to do something useful — keeping track of days and dates, all in your head! This is a great thing to know whenever you need to figure out something for your schedule, but have no calendar handy.
So to start … for any given month, the first step is to figure out which weekday falls on the 7th. Whichever weekday that is, memorize it. Why? Because that weekday will also fall on all multiples of 7: the 14th, the 21st and the 28th. And that right there already gives you a skeletal grasp on the month. Call that weekday the “7-Day” of the month. And now we’re rolling.
Example: take the month we’re now in, April 2014
This April, the 7th is a Monday, so for this April, “7-Day” is Monday.
Based on this, we now know that all of the following are also Mondays: 4/7, 4/14, 4/21, and 4/28.
And since Friday comes four days after Monday, merely add 4 to each Monday date to get the Fridays of April:
7 + 4 = 11 // 14 + 4 = 18 // 21+ 4 = 25
This means that this month, the Fridays are: 4/11, 4/18, 4/25.
And don’t forget, there’s also the first Friday, 7 days before 4/11, so 4/4.
Once you know the Mondays and Fridays, it’s easy to figure out the workweeks, as they run from Monday through Friday. So for this month, the M-F workweeks are 4/7 – 11; 4/14 – 18; 4/21 – 25; and 4/28 – 5/2.
Not bad, huh? But that’s not all. Once you get the hang of this, it’s a cinch to figure out the “7-Day” of the following month, May in our case.
To do this, first absorb an important point.
The weekday on which one month ends is ALWAYS the “7-Day” of the following month. For example, if a month ends on Thursday, the 30th, the “7-Day” of the following month will be Thursday. Count it out, and you’ll see. [Fri, the 1st, Sat., the 2nd, Sun., the 3rd, Mon., the 4th, Tues., the 5th, Wed., the 6th, Thurs., the 7th]. Again, this shows that the weekday on which any month ENDS = the “7-Day” of the following month.
Now let’s return to our month: April 2014. My next point may at first seem strange, but bear with me for a moment. If, hypothetically, this April had only 28 days (thus ending on 4/28), that day would be a Monday, since Monday is this April’s “7-Day.” But further, since that would be the last day of April, hypothetically, Monday would be the “Seven-Day” of May as well.
So notice that if all months had 28 days, every month would have the same “7-Day” and therefore days and dates would be extremely regular.
But of course, things are more ‘messy.’ Months have different numbers of days, and April itself has 30, two days more than the “neat-and-clean” 28.
So how does this affect our calculations? It means that April ends two days after its “7-Day” of Monday. That means that April ends on a Wednesday (Monday + 2 days). But based on what we said just above, this means that Wednesday will be the “7-Day” of May.
Generalizing this concept, we see that for months with 30 days, the “7-Day” of the following month is always TWO weekdays beyond the “7-Day” of the month with 30 days. Example: if June (with 30 days) has a “7-day” of Wednesday, we can be certain that July will have a “7-day” of Friday (Wednesday + 2 days).
Similarly, for months with 31 days, the “7-Day” of the following month will always be THREE weekdays beyond the “7-Day” of the month with 31 days. Example: If July (with 31 days) has a “7-day” of Tuesday, that means that the next month, August, will have a “7-Day” of Friday (Tuesday + 3 days).
Finally, for non-leap-year February months (with 28 days), the “7-Day” of February will be identical to the “7-Day” of March. For once we don’t need to tack on extra days!
So to put this whole strategy in the proverbial “nutshell,” here are the main points for keeping track of dates mentally.
1st) Figure out which weekday is the “7-Day” for the month you’re in.
2nd) Once you know (and memorize) that, add 2 days to that weekday to get the “7-Day” of the following month, if your month has 30 days. Or add 3 days if your month has 31 days.
3rd) Once you know your month’s “7-Day” count ahead or back to find the Mondays for your month.
4th) From the Mondays, count ahead 4 days to find the Fridays of your month. Then put the Monday-Fridays together to get the workweek days for the month you’re in.
And voila! That’s essentially all you need to get started keeping track of dates in your head.
I find it’s useful to be able to do this mentally, and it also kind of impresses people, as a little side benefit.
Well, this piece, it turns out, is my final article for HERD. So let me say THANK YOU for being a great audience. I’ve enjoyed the process of writing these articles very much. And I wish all of you the very best on your continuing adventures through the fields of mathematics.
Josh Rappaport is the author of the Algebra Survival Guide and Workbook, which together comprise an award-winning program that makes algebra do-able! Josh also is the author of PreAlgebra Blastoff!, an engaging, hands-on approach to working with integers. All of Josh's books, published by Singing Turtle Press, are available on Amazon.com
