Crypt Arithmetic Problems That Are Simple to Explain
Students in 5th grade math challenge at Seward.
Please perform both checks and write on paper.
Write your name and your E2 teacher's name on
the paper and hand in to Karen Utter on Monday
Nov 5 or Wed Nov 7.
2012 6th Grade Math Challenge Problem #1
162
+XD
-----
2D7
D must equal 5 so we have:
162
+X5
-----
257
When we add X to 6, we must get 5 and a carry of 1.
So, 6 + X = 15, or X = 9
162
+95
-----
257
Check: Do the above with a calculator and verify that it is correct.
2012 6th Grade Math Challenge Problem #5
ON + ON + ON + ON = GO
Adding ON 4 times is the same as multiplying by 4.
ON
x4
-----
GO
Try various values for N.
N can't be zero because then, N and O would be the same.
If N is 1, O = 4 and 4 x O would be 16, generating a carry
and giving a three-digit answer.
If N is 2, O = 8 and 4 x O would be 32, again generating a
carry and giving a three-digit answer.
If N is 3, 4 x 3 = 12. That makes O = 2 with a carry of 1.
G = 4 x 2 + 1, or 9.
This gives:
23
x4
----
92
Check: 23 + 23 + 23 + 23 = 92
Verify this with a calculator.
Sunday, October 28, 2012
Tuesday, February 24, 2009
Problems 1 through 4 of 2008 Team Round #3
These are just hints:
1) The total number of sandwiches can be divided by 7 with nothing left over. Divide total by 7, multiply the result by 2.
2) L = 4/3 W Area is LW (note: LW means L times W) LW = 300, but when you substitute L=4/3 W, you get a formula for W squared. Take the square root, you know W. Then use L=4/3 w to get L. Note: the problem asks for "length."
3) The smallest 3-digit number divisible by 11 is 110. Since 110 is divisible by 2 with nothing left over, it can't be the answer. Try 121, it meets all the conditions.
Another way, the answer has to be 1 plus a multiple of 60. It can't be 61, because 61 is not a 3-digit number. But it could be 120 plus 1, or 121. This is "educated guessing" I don't know any other way to do it. "Sixty" is the least common multiple of 2,3,4,and 5.
4) When an elevator goes from first floor to third floor, it really goes up 2 "spaces:" draw a picture. So, when it goes from first floor to 20th floor, it goes up 19 spaces.
1) The total number of sandwiches can be divided by 7 with nothing left over. Divide total by 7, multiply the result by 2.
2) L = 4/3 W Area is LW (note: LW means L times W) LW = 300, but when you substitute L=4/3 W, you get a formula for W squared. Take the square root, you know W. Then use L=4/3 w to get L. Note: the problem asks for "length."
3) The smallest 3-digit number divisible by 11 is 110. Since 110 is divisible by 2 with nothing left over, it can't be the answer. Try 121, it meets all the conditions.
Another way, the answer has to be 1 plus a multiple of 60. It can't be 61, because 61 is not a 3-digit number. But it could be 120 plus 1, or 121. This is "educated guessing" I don't know any other way to do it. "Sixty" is the least common multiple of 2,3,4,and 5.
4) When an elevator goes from first floor to third floor, it really goes up 2 "spaces:" draw a picture. So, when it goes from first floor to 20th floor, it goes up 19 spaces.
Friday, January 23, 2009
Watching Planet Venus
You go out at a specified time and watch Venus.
How long can you watch until Venus
sets? On a scale with North 0, East 90, South 180
and West 270, show where Venus sets, if possible,
show a local landmark.
Times are given for Mendota Heights, MN but are
accurate for Minneapolis as well. See worked example
at the end of the data.
Data below!
MENDOTA HEIGHTS, MINNESOTA
Location: W 93°07'48.0", N44°53'24.0",
(Longitude referred to Greenwich meridian)
Time Zone: 6h 00m west of Greenwich (Central Standard Time)
Date Set Azimuth Begin observing at
(Zone) h m ° h m
2009 Feb 01 (Sun) 21:25 272 19:45
2009 Feb 02 (Mon) 21:26 273 19:30
2009 Feb 03 (Tue) 21:26 274 19:45
2009 Feb 04 (Wed) 21:27 274 19:30
2009 Feb 05 (Thu) 21:28 275 19:45
2009 Feb 06 (Fri) 21:28 276 19:30
2009 Feb 07 (Sat) 21:28 276 19:45
2009 Feb 08 (Sun) 21:29 277 19:30
2009 Feb 09 (Mon) 21:29 277 19:45
2009 Feb 10 (Tue) 21:29 278 19:30
2009 Feb 11 (Wed) 21:29 279 19:45
2009 Feb 12 (Thu) 21:29 279 19:30
2009 Feb 13 (Fri) 21:29 280 19:45
2009 Feb 14 (Sat) 21:29 280 19:30
2009 Feb 15 (Sun) 21:28 281 19:45
2009 Feb 16 (Mon) 21:28 281 19:30
2009 Feb 17 (Tue) 21:27 282 19:45
2009 Feb 18 (Wed) 21:27 283 19:30
2009 Feb 19 (Thu) 21:26 283 19:45
2009 Feb 20 (Fri) 21:25 284 19:30
2009 Feb 21 (Sat) 21:24 284 19:45
2009 Feb 22 (Sun) 21:22 284 19:30
2009 Feb 23 (Mon) 21:21 285 19:45
2009 Feb 24 (Tue) 21:19 285 19:30
2009 Feb 25 (Wed) 21:18 286 19:45
2009 Feb 26 (Thu) 21:16 286 19:30
2009 Feb 27 (Fri) 21:14 287 19:45
2009 Feb 28 (Sat) 21:11 287 19:30
Example: suppose I begin observing at 19:30 on February 1. Venus sets at 21:25.
I can't subtract 30 from 25, so I "borrow" an hour from 21, an hour is 60 minutes.
Now I am subtracting 19:30 from 20:85. Subtracting hours from hours & minutes
from minutes, I observe for 1 hour and 55 minutes. The sun sets at angle 272 degrees,
which is just a little north of west, behind the houses on the opposite
side of the street. (Note: I will observe tonight and improve this).
Monday, November 10, 2008
Mother of all Teachable Moments, Part III
Right now (November 10 2008) the canvass process is going on; this means that the outputs of the mark-sense machines are being added up. The actual ballots are not looked at yet. the mark-sense machines are not networked (probably a good thing) so the results have to be read off of counters and typed into a data base. Also, some absentee ballots are being entered but others are not because of disputes.
This is a canvass, not a recount. The canvass will surely show that a recount must be done.
The difference between Coleman and Franken is now about 200 votes out of 3 million, with Coleman ahead.
The disputes will be resolved later. Also, later, ballots will be examined to see if the intent of the voter is clear from the marked ballot even if rejected by a machine. Later, I will send you examples of mis-marked ballots from the Star Tribune.
Here is about 50 minutes audio of Mark Ritchie, The Secretary of State of Minnesota from Friday November 7, 2008.
http://minnesota.publicradio.org/www_publicradio/tools/media_player/popup.php?name=minnesota/news/programs/2008/11/07/midday/midday_hour_1_20081107_64
This is a canvass, not a recount. The canvass will surely show that a recount must be done.
The difference between Coleman and Franken is now about 200 votes out of 3 million, with Coleman ahead.
The disputes will be resolved later. Also, later, ballots will be examined to see if the intent of the voter is clear from the marked ballot even if rejected by a machine. Later, I will send you examples of mis-marked ballots from the Star Tribune.
Here is about 50 minutes audio of Mark Ritchie, The Secretary of State of Minnesota from Friday November 7, 2008.
http://minnesota.publicradio.
Thursday, November 6, 2008
Minnesota Senate Election
Answers below:
The 2008 Senatorial Election in Minnesota was predicted to be a "statistical dead heat" and has turned out to be nearly a tie.
The results, according to the Minnesota Secretary of State, http://www.sos.state.mn.us , are:
Coleman, Republican: 1 211 538
Franken, DFL : 1 211 196
Barkley, Independence: 437 376
Minor Parties: 25 164
The eligible voters are: 3 741 514 (not all eligible voters are registered). Minnesota State Law mandates a recount if the difference in the two leading candidates is less than 0.5% of all votes cast. The losing candidate may waive this if he or she does so in writing. I don't think Franken is likeley to do so (although Coleman has suggested it).
Questions: is an automatic recount mandated in this case?
What percentage of the total votes cast did each of Coleman, Franken and Barkley get? Express as a percentage, with three decimal places, for example, 43.xxx%
Compare to pre-election polls, which gave Franken 43%, Coleman 36% and Barkley 16% with a sampling error of plus or minus 5%.
If you go to the Secretary of State website and look at the Recount Manual, you will see (page 8) many examples of mis-marked ballots. If the intention of the voter is clear, such ballots, which optical scan machines will not count, can be counted by hand. In my experience, about 1% of student multiple choice exams are defective. If that is true in this case, how many mismarked ballots might there be?
What percentage of eligible voters actually voted?
-------------------------------------
The total number of voters was: 2 885 274
The difference between Coleman and Franken was 342 votes, this is o.012 percent, less than the 0.500 percent required for a mandatory recount.
The percentages were Coleman 41.991%
Franken 41.978%
Barkley 15.158%
Polls predicted Franken would get 38 to 48%, Coleman 31 to 41%, and Barkley 11 to 21%. The sampling error margins are approximate, Coleman was at the high end of the predicted range, the other two candidates within the predicted range.
There might be about about 29 000 mis-marked ballots.
77% of the eligible voters actually voted. The percentage of registered voters is higher, since not all eligible voters are registered.
The 2008 Senatorial Election in Minnesota was predicted to be a "statistical dead heat" and has turned out to be nearly a tie.
The results, according to the Minnesota Secretary of State, http://www.sos.state.mn.us , are:
Coleman, Republican: 1 211 538
Franken, DFL : 1 211 196
Barkley, Independence: 437 376
Minor Parties: 25 164
The eligible voters are: 3 741 514 (not all eligible voters are registered). Minnesota State Law mandates a recount if the difference in the two leading candidates is less than 0.5% of all votes cast. The losing candidate may waive this if he or she does so in writing. I don't think Franken is likeley to do so (although Coleman has suggested it).
Questions: is an automatic recount mandated in this case?
What percentage of the total votes cast did each of Coleman, Franken and Barkley get? Express as a percentage, with three decimal places, for example, 43.xxx%
Compare to pre-election polls, which gave Franken 43%, Coleman 36% and Barkley 16% with a sampling error of plus or minus 5%.
If you go to the Secretary of State website and look at the Recount Manual, you will see (page 8) many examples of mis-marked ballots. If the intention of the voter is clear, such ballots, which optical scan machines will not count, can be counted by hand. In my experience, about 1% of student multiple choice exams are defective. If that is true in this case, how many mismarked ballots might there be?
What percentage of eligible voters actually voted?
-------------------------------------
The total number of voters was: 2 885 274
The difference between Coleman and Franken was 342 votes, this is o.012 percent, less than the 0.500 percent required for a mandatory recount.
The percentages were Coleman 41.991%
Franken 41.978%
Barkley 15.158%
Polls predicted Franken would get 38 to 48%, Coleman 31 to 41%, and Barkley 11 to 21%. The sampling error margins are approximate, Coleman was at the high end of the predicted range, the other two candidates within the predicted range.
There might be about about 29 000 mis-marked ballots.
77% of the eligible voters actually voted. The percentage of registered voters is higher, since not all eligible voters are registered.
Friday, September 5, 2008
Travel with $4 per gallon gas
A true story, August 2008.
A family drove from the Twin Cities to Yellowstone Park and return, possibly with some side trips. The family spent $475.90 on gasoline. If they paid $4 per gallon, how many gallons did they consume?
If their car traveled 22.5 miles per gallon, how far did they travel?
The round trip distance from the Twin Cities to Yellowstone Park and return is about 2040 miles. Compare your result to this distance.
Answers: CXIX gallons (rounded to the nearest gallon).
MMDCLXXVII miles (rounded to the nearest mile, and greater than 2040 miles, telling us they made 600 or 700 miles of side trips).
A family drove from the Twin Cities to Yellowstone Park and return, possibly with some side trips. The family spent $475.90 on gasoline. If they paid $4 per gallon, how many gallons did they consume?
If their car traveled 22.5 miles per gallon, how far did they travel?
The round trip distance from the Twin Cities to Yellowstone Park and return is about 2040 miles. Compare your result to this distance.
Answers: CXIX gallons (rounded to the nearest gallon).
MMDCLXXVII miles (rounded to the nearest mile, and greater than 2040 miles, telling us they made 600 or 700 miles of side trips).
Thursday, August 14, 2008
Speeds in meters per second
A typical walking speed is two meters per second. Probably the fastest speed for running (by people) is about ten meters per second -- 100 meters in 10 seconds.
An American Football field is 91.44 meters long, from goal line to goal line. At two meters per second, you can walk that far in 45 or 46 seconds.
Timing yourself with a watch with a second hand, how long does it take you to walk 91.44 meters?
(Mathematical experiment.)
The distance between bases on a baseball field is 27.432 meters. You can time a batter from home plate to first base to estimate the batter's speed. Somebody stealing second base might not start from first base, but if a player "tags up" you can time between other bases.
An American Football field is 91.44 meters long, from goal line to goal line. At two meters per second, you can walk that far in 45 or 46 seconds.
Timing yourself with a watch with a second hand, how long does it take you to walk 91.44 meters?
(Mathematical experiment.)
The distance between bases on a baseball field is 27.432 meters. You can time a batter from home plate to first base to estimate the batter's speed. Somebody stealing second base might not start from first base, but if a player "tags up" you can time between other bases.
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