Q: At a hardware store, I can buy 1 for $0.75 and I can buy 2761 for $3.00. What am I buying?
A: House numbers
Monday, December 27, 2010
Thursday, November 11, 2010
November 2010 Brain Teaser Solution
Which is larger -- 8^98 or (8^99 - 8^98)? (8^98 means "8 to the 98th power")
You can put this into a calculator and it will give you back scientific notation because both these numbers are REALLY BIG.
so 8^98 is about 3.12 x 10^88 (10 to the 88th power) but 8^99 - 8^98 is about 2.22 x 10^89 (10 to the 89th power) therefore 8^99 - 8^98 is larger. But by how much?
Here is where the cool factoring comes in:
8^99 - 8^98 can be rewritten as: 8^98(8 - 1) making it 7 times bigger than 8^98.
You can put this into a calculator and it will give you back scientific notation because both these numbers are REALLY BIG.
Here is where the cool factoring comes in:
8^99 - 8^98 can be rewritten as: 8^98(8 - 1) making it 7 times bigger than 8^98.
Sunday, October 31, 2010
Sunday, October 17, 2010
October 2010 Brain Teaser Solution
Q: What is the greatest possible product of two positive whole numbers whose sum is 100?
A: 2500 (50 x 50)
Let x = one number then 100 - x = other number
So we want to maximize the product of this algebra, x(100 - x) = 100x - x^2
see the graph below:
This result can also be achieved through Calculus. If we take the derivative of the algebra and set that equal to 0, then solve for x.
The derivative of 100x - x^2 is 100 - 2x, when 100 - 2x = 0 is solved x = 50.
When we substitute 50 into 100x - x^2, we get
100(50) - (50)^2
5000 - 2500 = 2500
So the maximum point is at x = 50 -- at the (x,y) point (50, 2500).
The list below shows:
Column 1 first number
Column 2 100 - first number
Column 3 product of Column 1 and Column 2
1 99 99
2 98 196
3 97 291
4 96 384
5 95 475
6 94 564
7 93 651
8 92 736
9 91 819
10 90 900
11 89 979
12 88 1056
13 87 1131
14 86 1204
15 85 1275
16 84 1344
17 83 1411
18 82 1476
19 81 1539
20 80 1600
21 79 1659
22 78 1716
23 77 1771
24 76 1824
25 75 1875
26 74 1924
27 73 1971
28 72 2016
29 71 2059
30 70 2100
31 69 2139
32 68 2176
33 67 2211
34 66 2244
35 65 2275
36 64 2304
37 63 2331
38 62 2356
39 61 2379
40 60 2400
41 59 2419
42 58 2436
43 57 2451
44 56 2464
45 55 2475
46 54 2484
47 53 2491
48 52 2496
49 51 2499
50 50 2500
51 49 2499
52 48 2496
53 47 2491
54 46 2484
55 45 2475
56 44 2464
57 43 2451
58 42 2436
59 41 2419
60 40 2400
61 39 2379
62 38 2356
63 37 2331
64 36 2304
65 35 2275
66 34 2244
67 33 2211
68 32 2176
69 31 2139
70 30 2100
71 29 2059
72 28 2016
73 27 1971
74 26 1924
75 25 1875
76 24 1824
77 23 1771
78 22 1716
79 21 1659
80 20 1600
81 19 1539
82 18 1476
83 17 1411
84 16 1344
85 15 1275
86 14 1204
87 13 1131
88 12 1056
89 11 979
90 10 900
91 9 819
92 8 736
93 7 651
94 6 564
95 5 475
96 4 384
97 3 291
98 2 196
99 1 99
A: 2500 (50 x 50)
Let x = one number then 100 - x = other number
So we want to maximize the product of this algebra, x(100 - x) = 100x - x^2
see the graph below:
This result can also be achieved through Calculus. If we take the derivative of the algebra and set that equal to 0, then solve for x.
The derivative of 100x - x^2 is 100 - 2x, when 100 - 2x = 0 is solved x = 50.
When we substitute 50 into 100x - x^2, we get
100(50) - (50)^2
5000 - 2500 = 2500
So the maximum point is at x = 50 -- at the (x,y) point (50, 2500).
The list below shows:
Column 1 first number
Column 2 100 - first number
Column 3 product of Column 1 and Column 2
1 99 99
2 98 196
3 97 291
4 96 384
5 95 475
6 94 564
7 93 651
8 92 736
9 91 819
10 90 900
11 89 979
12 88 1056
13 87 1131
14 86 1204
15 85 1275
16 84 1344
17 83 1411
18 82 1476
19 81 1539
20 80 1600
21 79 1659
22 78 1716
23 77 1771
24 76 1824
25 75 1875
26 74 1924
27 73 1971
28 72 2016
29 71 2059
30 70 2100
31 69 2139
32 68 2176
33 67 2211
34 66 2244
35 65 2275
36 64 2304
37 63 2331
38 62 2356
39 61 2379
40 60 2400
41 59 2419
42 58 2436
43 57 2451
44 56 2464
45 55 2475
46 54 2484
47 53 2491
48 52 2496
49 51 2499
50 50 2500
51 49 2499
52 48 2496
53 47 2491
54 46 2484
55 45 2475
56 44 2464
57 43 2451
58 42 2436
59 41 2419
60 40 2400
61 39 2379
62 38 2356
63 37 2331
64 36 2304
65 35 2275
66 34 2244
67 33 2211
68 32 2176
69 31 2139
70 30 2100
71 29 2059
72 28 2016
73 27 1971
74 26 1924
75 25 1875
76 24 1824
77 23 1771
78 22 1716
79 21 1659
80 20 1600
81 19 1539
82 18 1476
83 17 1411
84 16 1344
85 15 1275
86 14 1204
87 13 1131
88 12 1056
89 11 979
90 10 900
91 9 819
92 8 736
93 7 651
94 6 564
95 5 475
96 4 384
97 3 291
98 2 196
99 1 99
100 0 0
Tuesday, September 21, 2010
24 x 12
The huge Excel handbook had been my intense focus as a potential deskside banker support person.
On a third round at a big investment bank, a banker asked "What's 24 x 12?"
I said "288" He asked me how -- "12 x 12 doubled is 24 12s" = 288
He responded 24 x 10 + 24 x 2 = 240 + 48 = 288
I then said 24 x 24 = 576 -- take half of this (12 24s)which is 288
Both of us were at least 30, so I then said:
"If you remember your high school algebra -- 24 and 12 are both 6 from 18 so you can write 24 x 12 as (18 + 6)(18-6) and when you FOIL that it becomes 18^2 + 6(18) - 6(18) - 6^2. which is 324 - 36 = 288!"
I got the job!
On a third round at a big investment bank, a banker asked "What's 24 x 12?"
I said "288" He asked me how -- "12 x 12 doubled is 24 12s" = 288
He responded 24 x 10 + 24 x 2 = 240 + 48 = 288
I then said 24 x 24 = 576 -- take half of this (12 24s)which is 288
Both of us were at least 30, so I then said:
"If you remember your high school algebra -- 24 and 12 are both 6 from 18 so you can write 24 x 12 as (18 + 6)(18-6) and when you FOIL that it becomes 18^2 + 6(18) - 6(18) - 6^2. which is 324 - 36 = 288!"
I got the job!
Thursday, September 09, 2010
September 2010 Brain Teaser Solution
When writing the whole numbers from 1 to 20, there are 12 1s (one in 1, 10, 12, 13, 14, 15, 16, 17, 18 and 19 and two in 11). When writing the whole numbers from 1 to 1000, how many 1s will you write?
1- 99 20
100 - 199 120
200 - 299 20
300 - 399 20
400 - 499 20
500 - 599 20
600 - 699 20
700 - 799 20
800 - 899 20
900 - 999 20
1000 1
Total 301
There are 12 1's from 1- 20
then 21, 31, 41, 51, 61, 71, 81, and 91
From 1 - 99, you will write a total of 20 ones
The same is true for 200 - 299, 300 - 399, 400 - 499, 500-599, 600 - 699, 700 - 799, 800 - 899, and 900-999. So from 200 - 999, there are a total of 160 ones (8 x 20)
From 100 - 199,
there are 20 ones in the second and/or third digit:
101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 131, 141, 151, 161, 171, 181, 191
plus all the ones that begin every number from 100 - 199 inclusive: 100
1- 99 20
100 - 199 120
200 - 299 20
300 - 399 20
400 - 499 20
500 - 599 20
600 - 699 20
700 - 799 20
800 - 899 20
900 - 999 20
1000 1
Total 301
There are 12 1's from 1- 20
then 21, 31, 41, 51, 61, 71, 81, and 91
From 1 - 99, you will write a total of 20 ones
The same is true for 200 - 299, 300 - 399, 400 - 499, 500-599, 600 - 699, 700 - 799, 800 - 899, and 900-999. So from 200 - 999, there are a total of 160 ones (8 x 20)
From 100 - 199,
there are 20 ones in the second and/or third digit:
101, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 121, 131, 141, 151, 161, 171, 181, 191
plus all the ones that begin every number from 100 - 199 inclusive: 100
Saturday, August 14, 2010
August 2010 Brainteaser Solution
Determine the smallest integral (whole number) value of x that will make the product 4840x a perfect cube.
Thefactors of 4840 = 484 x 10 = 22 x 22 x 10 = 2 x 11 x 2 x 11 x 2 x 5 (the prime factors)
To make a perfect cube, you need three of each factor:
you have enough 2s, so you need 2 5's and one 11.
5 x 5 x 11 = 275
Thefactors of 4840 = 484 x 10 = 22 x 22 x 10 = 2 x 11 x 2 x 11 x 2 x 5 (the prime factors)
To make a perfect cube, you need three of each factor:
you have enough 2s, so you need 2 5's and one 11.
5 x 5 x 11 = 275
Tuesday, August 10, 2010
Wednesday, July 21, 2010
July 2010 Newsletter Brain Teaser Solution
Which would you rather have? a) $1,000,000
or b) Doubling Pennies for 30 days
1 penny on day 1, 2 pennies on day 2, 4 pennies on day 3, 8 pennies on day 4, etc.
The doubling pennies become $5368709.12 on Day 30.
Day # of Pennies Dollars
1 1 0.01
2 2 0.02
3 4 0.04
4 8 0.08
5 16 0.16
6 32 0.32
7 64 0.64
8 128 1.28
9 256 2.56
10 512 5.12
11 1024 10.24
12 2048 20.48
13 4096 40.96
14 8192 81.92
15 16384 163.84
16 32768 327.68
17 65536 655.36
18 131072 1310.72
19 262144 2621.44
20 524288 5242.88
21 1048576 10485.76
22 2097152 20971.52
23 4194304 41943.04
24 8388608 83886.08
25 16777216 167772.16
26 33554432 335544.32
27 67108864 671088.64
28 134217728 1342177.28
29 268435456 2684354.56
30 536870912 5368709.12
or b) Doubling Pennies for 30 days
1 penny on day 1, 2 pennies on day 2, 4 pennies on day 3, 8 pennies on day 4, etc.
The doubling pennies become $5368709.12 on Day 30.
Day # of Pennies Dollars
1 1 0.01
2 2 0.02
3 4 0.04
4 8 0.08
5 16 0.16
6 32 0.32
7 64 0.64
8 128 1.28
9 256 2.56
10 512 5.12
11 1024 10.24
12 2048 20.48
13 4096 40.96
14 8192 81.92
15 16384 163.84
16 32768 327.68
17 65536 655.36
18 131072 1310.72
19 262144 2621.44
20 524288 5242.88
21 1048576 10485.76
22 2097152 20971.52
23 4194304 41943.04
24 8388608 83886.08
25 16777216 167772.16
26 33554432 335544.32
27 67108864 671088.64
28 134217728 1342177.28
29 268435456 2684354.56
30 536870912 5368709.12
Monday, July 19, 2010
Friday, July 09, 2010
Viewing the SAT as a Challenge and National Indicator
Viewing the SAT as a Challenge and National Indicator
in response to Washington Post article Your SAT Score Has Little to Do
As a Math peak performance coach, I have found that studying for the SAT can be challenging and entertaining while promoting brain fitness at any age. Although I graduated from college in 19XX, I took the SAT in 2009 to gain perspective, to have fun, and to boost mental fitness. I learned much reading and grammar while studying last summer.
Some fields of study use the SAT as a measure of being able to ‘keep up with the Joneses’. Engineering schools want high Math scores (to follow along with profs who write a dozen equations on the board); likewise, journalism schools want high verbal scores.
The SAT is important because there is no national standard of high school curriculum or a national exit exam. While the Core Standards have been in the works, the existing standard could be the SAT (or ACT or GED) as a unifier for a reasonable body of knowledge. http://www.corestandards.org/.
The GED is a formidable exam -- only 60% of high school graduates could pass the GED http://www.acenet.edu/Content/NavigationMenu/ged/etp/score.htm
If people could view the SAT like a marathon, it would give mental fitness a boost!! Test taking/studying just makes you smart just like working out makes you physically fit.
Try the free SAT Question of the Day!!
http://sat.collegeboard.com/practice/sat-question-of-the-day
Robin Schwartz
Author, Build Math Confidence e-newsletter
http://www.mathconfidence.com/
in response to Washington Post article Your SAT Score Has Little to Do
As a Math peak performance coach, I have found that studying for the SAT can be challenging and entertaining while promoting brain fitness at any age. Although I graduated from college in 19XX, I took the SAT in 2009 to gain perspective, to have fun, and to boost mental fitness. I learned much reading and grammar while studying last summer.
Some fields of study use the SAT as a measure of being able to ‘keep up with the Joneses’. Engineering schools want high Math scores (to follow along with profs who write a dozen equations on the board); likewise, journalism schools want high verbal scores.
The SAT is important because there is no national standard of high school curriculum or a national exit exam. While the Core Standards have been in the works, the existing standard could be the SAT (or ACT or GED) as a unifier for a reasonable body of knowledge. http://www.corestandards.org/.
The GED is a formidable exam -- only 60% of high school graduates could pass the GED http://www.acenet.edu/Content/NavigationMenu/ged/etp/score.htm
If people could view the SAT like a marathon, it would give mental fitness a boost!! Test taking/studying just makes you smart just like working out makes you physically fit.
Try the free SAT Question of the Day!!
http://sat.collegeboard.com/practice/sat-question-of-the-day
Robin Schwartz
Author, Build Math Confidence e-newsletter
http://www.mathconfidence.com/
Friday, July 02, 2010
Math Would Help People Land Jobs
Workers Need Better Skills
American workers need 9th grade level Math to gain jobs in the manufacturing sector. One of the slides shows 8th graders on a tour of a factory.
American workers need 9th grade level Math to gain jobs in the manufacturing sector. One of the slides shows 8th graders on a tour of a factory.
Tuesday, June 29, 2010
Solution for June 2010 Brain Teaser
Find the average of all multiples of 7 between 7 and 777, inclusive. Answer: 392
This is like the Gaussian problems (adding consecutive numbers) as it is the pairs of numbers that allow us to more easily solve these types of problems.
For example, adding the numbers 1 - 10 can be done by grouping the smallest and largest 1 and 10 to make 11, (then the next smallest and largest) 2 and 9 to make 11, 3 and 8, 4 and 7 and 5 and 6 to get 5 pairs of 11. So the sum of the numbers form 1 to 10 is 5 x 11 = 55.
From 7 to 777 inclusive is just like 1 to 111 inclusive (divide each by 7).
One of Math educator and writer Polya's methods: Solve a Simpler Problem. Step 2: Devise a Plan
Choosing easier numbers can often make the solution easier and simpler to understand.
To find the average of 1 to 111, find the average of each pair -- the average of 1 and 111 is 56 (1+111)/2.
The average of 2 and 110 is 56 and so on.
So the 392 is the average of 7 and 777 and also the average of 14 and 770 (the next two multiples) is also 392.
Please visit the Excel spreadsheet on docstoc and scroll down to see that the answer is 392!!
http://www.docstoc.com/docs/45498081/Math-Confidence-Brain-Teaser-June-2010
This is like the Gaussian problems (adding consecutive numbers) as it is the pairs of numbers that allow us to more easily solve these types of problems.
For example, adding the numbers 1 - 10 can be done by grouping the smallest and largest 1 and 10 to make 11, (then the next smallest and largest) 2 and 9 to make 11, 3 and 8, 4 and 7 and 5 and 6 to get 5 pairs of 11. So the sum of the numbers form 1 to 10 is 5 x 11 = 55.
From 7 to 777 inclusive is just like 1 to 111 inclusive (divide each by 7).
One of Math educator and writer Polya's methods: Solve a Simpler Problem. Step 2: Devise a Plan
Choosing easier numbers can often make the solution easier and simpler to understand.
To find the average of 1 to 111, find the average of each pair -- the average of 1 and 111 is 56 (1+111)/2.
The average of 2 and 110 is 56 and so on.
So the 392 is the average of 7 and 777 and also the average of 14 and 770 (the next two multiples) is also 392.
Please visit the Excel spreadsheet on docstoc and scroll down to see that the answer is 392!!
http://www.docstoc.com/docs/45498081/Math-Confidence-Brain-Teaser-June-2010
Monday, June 28, 2010
Saturday, June 12, 2010
On-Line Learning of 100 Pairs by Math Confidence
Quick, what number plus 43 adds up to 100? Studying 100 pairs (for example, 60 and 40 are 100 pair as they sum to 100) can help people with mental Math and cash register Math.
Math Confidence 100 Pairs Activity on Quia
Math Confidence 100 Pairs Activity on Quia
If you can't divide 300 by 2, should you qualify for a loan?
Weak Math Skills Linked to Default -- borrowers with poor Math skills were three times more likely to go into foreclosure.
This article starts off "If you can't divide 300 by 2, should you qualify for a loan?"
The survey led by a Columbia University prof, Stephan Meier, had five questions -- only two were in the article -- the one listed above and "How much is 10% of 1000?"
16% of the respondents got one of these 2 questions incorrect.
Financial education is heavily based on Math education and personal finance is an excellent application of understanding numbers and how they affect life. In addition, practicing problem-solving can build the mental skills and perseverance that can help people to read the fine print on a mortgage.
This article starts off "If you can't divide 300 by 2, should you qualify for a loan?"
The survey led by a Columbia University prof, Stephan Meier, had five questions -- only two were in the article -- the one listed above and "How much is 10% of 1000?"
16% of the respondents got one of these 2 questions incorrect.
Financial education is heavily based on Math education and personal finance is an excellent application of understanding numbers and how they affect life. In addition, practicing problem-solving can build the mental skills and perseverance that can help people to read the fine print on a mortgage.
Monday, June 07, 2010
Monday, May 31, 2010
The SAT vs the Marathon
When I took the SAT in October 2009, the students thought I was the proctor! It was helpful to relive the test-taking experience plus I learned a lot of grammar. A marathon is an interesting comparison as preparation for an athletic event is very similar to an academic event.
There is a peak performance aspect -- the preparation is the key -- actual timed practice as well as self-care (sleep, food, etc) help with mental and physical performance. At the end of the day regardless of the results, the payoff is in the energy and effort expended.
I was inspired by a 2009 Wall Street Journal article written by a reporter whose teenage son dared her to take the SATs What I Learned from the SATs.
SAT vs. Marathon
4.5 hours Variable
Indoors Outdoors
Teens Various age levels
Increase cognitive abilities Improve physical fitness
There is a peak performance aspect -- the preparation is the key -- actual timed practice as well as self-care (sleep, food, etc) help with mental and physical performance. At the end of the day regardless of the results, the payoff is in the energy and effort expended.
I was inspired by a 2009 Wall Street Journal article written by a reporter whose teenage son dared her to take the SATs What I Learned from the SATs.
SAT vs. Marathon
4.5 hours Variable
Indoors Outdoors
Teens Various age levels
Increase cognitive abilities Improve physical fitness
Monday, May 24, 2010
Final Exam Success Tip 1: Don't Write on Your Review Sheet
A review sheet is a gift ;)
Most teachers are giving away much of the exam on their review sheets!!
Don't write the answers on your review sheet!
It's the independent practice of reworking the problems that will boost learning, confidence and scores.
Review Sheet Tip from Math Confidence Blog
Review Sheet Tip from Math Confidence Blog
Tuesday, May 18, 2010
May 2010 Newsletter Brain Teaser Solution
Tom can beat Dick by one-tenth of a mile in a five-mile race. Dick can beat Harry by one-fifth of a mile in a five-mile race. By how much can Tom beat Harry in a five-mile race?
Tom runs 5 miles in the time it takes Dick to run 4.9 miles. This is a rate of 98% or .98.
Dick runs 5 miles in the time it takes Harry to run 4.8 miles. This is a rate of 96% or .96.
So the rate of Harry to Dick is (0.98)(0.96)5 so Harry was 4.704 miles along when Tom finished.
So Tom beat Harry by 0.296 miles.
Tom runs 5 miles in the time it takes Dick to run 4.9 miles. This is a rate of 98% or .98.
Dick runs 5 miles in the time it takes Harry to run 4.8 miles. This is a rate of 96% or .96.
So the rate of Harry to Dick is (0.98)(0.96)5 so Harry was 4.704 miles along when Tom finished.
So Tom beat Harry by 0.296 miles.
Sunday, May 02, 2010
Friday, April 30, 2010
April 2010 Brain Teaser Answer
Using all the digits from 0,1,2...9, form two 5-digit numbers so that their sum is the
a)smallest sum: 34047
One example: 20468 + 13579
Another example is: 10468 + 23579
You cannot have a leading zero (the number cannot start with a zero) so for the least sum, start with 1 for the first number and 2 for the second number. Then make 0 the second digit of one of them and 3 the other second digit. Then continue with 4 and 5 and so on.
b)greatest sum: 183951
One example is: 97531 + 86420
Another example is: 87531 + 96420
For the greatest sum: First digits 8 or 9, Second digits 6 or 7 and so on.
a)smallest sum: 34047
One example: 20468 + 13579
Another example is: 10468 + 23579
You cannot have a leading zero (the number cannot start with a zero) so for the least sum, start with 1 for the first number and 2 for the second number. Then make 0 the second digit of one of them and 3 the other second digit. Then continue with 4 and 5 and so on.
b)greatest sum: 183951
One example is: 97531 + 86420
Another example is: 87531 + 96420
For the greatest sum: First digits 8 or 9, Second digits 6 or 7 and so on.
Career and College Ready
According to this Washington Post article: http://voices.washingtonpost.com/answer-sheet/no-child-left-behind/what-is-being-college-and-care.html, only 23% of college students do not remediation. The article quotes an ACT spokeswoman "Readiness for college means not needing to take remedial courses."
High schools and society would do well to focus on college and career readiness in addition to graduation rates. While there is no high school exit exam, only 60% of high school graduates could pass the GED (according to the GED).
High schools and society would do well to focus on college and career readiness in addition to graduation rates. While there is no high school exit exam, only 60% of high school graduates could pass the GED (according to the GED).
Thursday, April 15, 2010
Saturday, April 10, 2010
Financial Literacy as a School Subject
NYT article on Financial Literacy in School
Often students and parents will ask "When I am ever going to use this Math?". Studying trig and algebra will make you smarter and therefore you will have the capacity to understand Finance and Economics. An excellent topic mentioned in the article is Time Value of Money. A good example is:
How much will you have if you invest $100 for 3 years at 10% compounded annually?
This question inspires dialogue and learning on interest rates, banking, decimals, percents, exponents as well as opening a window into understanding the way the world works.
Often students and parents will ask "When I am ever going to use this Math?". Studying trig and algebra will make you smarter and therefore you will have the capacity to understand Finance and Economics. An excellent topic mentioned in the article is Time Value of Money. A good example is:
How much will you have if you invest $100 for 3 years at 10% compounded annually?
This question inspires dialogue and learning on interest rates, banking, decimals, percents, exponents as well as opening a window into understanding the way the world works.
Friday, April 09, 2010
Identifying Problems...ok Math Opportunities
Metacognition (thinking about thinking) is the feedback loop or the "little voice in your head that you hear when you do Math -- such as add 4 to each side and divide both sides by 2".
Self-awareness of knowledge and skills can be achieved by categorizing Math problems into types of problems. The ability to identify problem types can refine learning and bring clarity while increasing the enjoyment and flow of Math opportunities. This is especially important in Math as gauging the level of challenge can help students know what to study and how to invest their time and energy under peak perfromance coniditions (tests).
It is a problem that they call them problems -- so how about Math opportunities?
Self-awareness of knowledge and skills can be achieved by categorizing Math problems into types of problems. The ability to identify problem types can refine learning and bring clarity while increasing the enjoyment and flow of Math opportunities. This is especially important in Math as gauging the level of challenge can help students know what to study and how to invest their time and energy under peak perfromance coniditions (tests).
It is a problem that they call them problems -- so how about Math opportunities?
Math can Build Non-Cognitive Skills too!
Studying Math may seem like a purely academic endeavor but it improves focus, persistence and self-advocacy which are takeaways that are "life skills". This article quotes Dan Pink author of Drive on parents focusing on academics at the expense of "life skills" but school can also fuel these skills and talents that can then be applied to any endeavor whether academic, athletic or otherwise.
New York Times on Determination and Deliberate Practice
New York Times on Determination and Deliberate Practice
Wednesday, March 31, 2010
Planning for Success in Math and Life
A planner is vastly different than a calendar. A calendar keeps track of appointments and scheduling but a planner focuses on prioritization and short- and long-term planning!
The Personal Digital Assistant (PDA) has become a common tool in school and business and many people use their phone to store their calendar and appointments. While the Treo phone has a very basic calendar --I went back to the low-tech paper version of Franklin Covey Planners -- the Weekly pocket format.
The planner inspires vision and goals which leads to thinking about the Important but Not Urgent tasks such as studying for next week's exam, filing your taxes or scheduling an annual checkup. In addition to feeling more inspired and organized, perusing your paper planner is more socially correct than glancing at your phone. A zipperable planner protects your plans from the elements (like a water bottle!) and offers a place to store a pen or pencil. Zippered Planner Binders
Franklin Covey offers Plan Plus Online which can be reached from any web browser -- planning on paper or on-line can raise productivity and motivation to stay focused and reach goals.
The Personal Digital Assistant (PDA) has become a common tool in school and business and many people use their phone to store their calendar and appointments. While the Treo phone has a very basic calendar --I went back to the low-tech paper version of Franklin Covey Planners -- the Weekly pocket format.
The planner inspires vision and goals which leads to thinking about the Important but Not Urgent tasks such as studying for next week's exam, filing your taxes or scheduling an annual checkup. In addition to feeling more inspired and organized, perusing your paper planner is more socially correct than glancing at your phone. A zipperable planner protects your plans from the elements (like a water bottle!) and offers a place to store a pen or pencil. Zippered Planner Binders
Franklin Covey offers Plan Plus Online which can be reached from any web browser -- planning on paper or on-line can raise productivity and motivation to stay focused and reach goals.
Thursday, March 25, 2010
March 2010 Brain Teaser Solution
Amanda went to the mall to buy supplies. She spent 1/2 of what she had plus $2.00 in the first store. Then she went to the second store and spent 1/2 of what she had left plus $1.00. In the third store, she spent 1/2 of what she had left plus $1.00. In the fourth store and last, she spent 1/2 of what she had left. After all of her purchases, she was left with only $3.00. How much money did she start with and how much did she spend in each store?
Amanda started with $64
she spent $34 in store 1
$16 in store 2
$8 is store 3
$3 in store 4
she spent a total of 34 + 16 + 8 + 3 = 61
therefore she has $3 left
After store 1 she has x - (1/2x + 2) which becomes 1/2x -2
then store 2
1/2 of answer 1 - 1
so 1/2(1/2x - 2) - 1
1/4x - 1- 1
so after store 2: 1/4x - 2
then store 3
1/2(1/4x-2) - 1
1/8x - 1- 1
so after store 3:1/8x - 2
then store 4:
1/2(1/8x - 2)
1/16x - 1
this is = 3
1/16x - 1 = 3
add 1 to both sides
1/16x = 4
x = 64
After store 1 she has 1/2(64)-2 = 30
so after store 2: 1/4x - 2 = 1/4(64) - 2 = 14
so after store 3:1/8x - 2 = 1/8(64) -2 = 6
then store 4: 6/2 = 3
Amanda started with $64
she spent $34 in store 1
$16 in store 2
$8 is store 3
$3 in store 4
she spent a total of 34 + 16 + 8 + 3 = 61
therefore she has $3 left
After store 1 she has x - (1/2x + 2) which becomes 1/2x -2
then store 2
1/2 of answer 1 - 1
so 1/2(1/2x - 2) - 1
1/4x - 1- 1
so after store 2: 1/4x - 2
then store 3
1/2(1/4x-2) - 1
1/8x - 1- 1
so after store 3:1/8x - 2
then store 4:
1/2(1/8x - 2)
1/16x - 1
this is = 3
1/16x - 1 = 3
add 1 to both sides
1/16x = 4
x = 64
After store 1 she has 1/2(64)-2 = 30
so after store 2: 1/4x - 2 = 1/4(64) - 2 = 14
so after store 3:1/8x - 2 = 1/8(64) -2 = 6
then store 4: 6/2 = 3
Wednesday, March 17, 2010
How Far Can Math and Patience Take Kids?
Patience is a virtue!! Math builds space telescopes and also life skills such as persistence and endurance.
Washington Post article on Math and Hubble -- the sky is the limit! has some great quotes from Neil deGrasse Tyson, director of the Hayden Planetarium in New York, "who gets to peer into the starry great beyond for clues to the origin of the universe. "
"Tyson earned a bachelor's degree in physics from Harvard and a doctorate in astrophysics from Columbia, but it was at the Bronx High School of Science in New York where he learned to not to be deterred when the going gets rough. "
"I remember the transition from algebra to calculus and thinking: 'I will never in my life figure this out. I better try something else.' How many people do we lose because they don't think they are getting it as fast as they should? What I did was take a little bit at a time. Over the months, it was [as] though a misty fog began to dissipate and I was slowly emerging with a fluency in the new and powerful symbols of calculus."
Author Courtland Milloy encourages schools and parents to inspire students by showing an interest in Math and Science ;)
Washington Post article on Math and Hubble -- the sky is the limit! has some great quotes from Neil deGrasse Tyson, director of the Hayden Planetarium in New York, "who gets to peer into the starry great beyond for clues to the origin of the universe. "
"Tyson earned a bachelor's degree in physics from Harvard and a doctorate in astrophysics from Columbia, but it was at the Bronx High School of Science in New York where he learned to not to be deterred when the going gets rough. "
"I remember the transition from algebra to calculus and thinking: 'I will never in my life figure this out. I better try something else.' How many people do we lose because they don't think they are getting it as fast as they should? What I did was take a little bit at a time. Over the months, it was [as] though a misty fog began to dissipate and I was slowly emerging with a fluency in the new and powerful symbols of calculus."
Author Courtland Milloy encourages schools and parents to inspire students by showing an interest in Math and Science ;)
Tuesday, March 16, 2010
Academic Support Is Helpful ;)
At Xavier, Nun Works Out Players' Academic Side
Many students can benefit from this type of support.
It is great to see an article on academic coaching even if the main focus is on sports.
Robin Schwartz
Founder, www.mathconfidence.com
Author, Build Math Confidence e-newsletter
Many students can benefit from this type of support.
It is great to see an article on academic coaching even if the main focus is on sports.
Robin Schwartz
Founder, www.mathconfidence.com
Author, Build Math Confidence e-newsletter
Friday, March 12, 2010
Helping Students Know What They Don't Know
This is in response to Willingham Helping Students Know What They Know in the Washington Post's Answer Sheet column with guest columnist Daniel Willingham.
Test taking is a skill that can be developed -- especially if one focuses on thinking about their thinking processes (metacognition).
As a Math peak performance coach (and former engineer / MBA), I help students to know what they know and know what they don't...to know where the traps are and what could go wrong. Often students do know the material better than their test scores show -- points can be lost due to not reading/answering the questions carefully!!
Engineering school taught us this attention to detail --please click on this link to my mathconfidence blog:
http://mathconfidence.blogspot.com/search/label/metacognition
Robin Schwartz
Founder, www.mathconfidence.com
Author, Build Math Confidence monthly e-newsletter
Test taking is a skill that can be developed -- especially if one focuses on thinking about their thinking processes (metacognition).
As a Math peak performance coach (and former engineer / MBA), I help students to know what they know and know what they don't...to know where the traps are and what could go wrong. Often students do know the material better than their test scores show -- points can be lost due to not reading/answering the questions carefully!!
Engineering school taught us this attention to detail --please click on this link to my mathconfidence blog:
http://mathconfidence.blogspot.com/search/label/metacognition
Robin Schwartz
Founder, www.mathconfidence.com
Author, Build Math Confidence monthly e-newsletter
Thursday, March 11, 2010
Core Standards Team Members...add Industry and GED
The Math Core Standards Team Members includes many Math educators from colleges, K-12 teachers and supervisors at the district level. Also included are people from the College Board and Achieve. From the academic perspective, GED experts would add to the discussion.
It would be also be interesting to add people from industry/corporate to see what employers would like to see in employees.
It would be also be interesting to add people from industry/corporate to see what employers would like to see in employees.
Common Core Standards Draft Released
The Common Core Standards are an initiative to standardize American public education.
Each state has had its own disparate (sometimes a very long list) standards.
The comments are open to the public until April 2nd.
In New York, the link is: Toolkit for Common Core Standards NY
To post comments: http://www.forms2.nysed.gov/emsc/ocis/ccssm.cfm
Each state has had its own disparate (sometimes a very long list) standards.
The comments are open to the public until April 2nd.
In New York, the link is: Toolkit for Common Core Standards NY
To post comments: http://www.forms2.nysed.gov/emsc/ocis/ccssm.cfm
Thursday, March 04, 2010
Do Not Pass Go, Do Not Collect $200 (Math as a gatekeeper)
COMPASS Placement Test Pre-Algebra and Algebra provides sample questions and info about the test.
Practicing for this placement test will help students potentially avoid remedial classes saving time and money and keep them on track to their educational and career goals.
Sunday, February 28, 2010
Near(ly) Perfect Squares
Perfect squares are great landmarks for Mental Math. Math has changed since 19XX as calculators have changed the way that Math is taught and learned and tested. Increasing Mental Math ability increases confidence, empowerment and self-reliance.
Nearly Perfect Squares
Perfect squares (like 4^2 = 16 and 5^2 = 25) can help people find close facts like 3 x5 and 4 x 6 (answers are both one less than the perfect squares) .
This will work for:
9 x 11 (99) = 1 less than 10^2 (100)
19 x 21 (399) = 1 less than 20^2 (400)
29 x 31 (899) = 1 less than 30^2 (900)
and for any number!!
(x-1)(x+1) = x^2 - 1 always one less than x^2
Somewhat Nearly Perfect Squares
Perfect squares (like 4^2 = 16 and 5^2 = 25) can help people find somewhat close facts like 2 x 6 and 3 x 7 (answers are both four less than the perfect squares) .
This will work for:
8 x 12 (96) = 4 less than 10^2 (100)
18 x 22 (396) = 4 less than 20^2 (400)
28 x 32 (899) = 4 less than 30^2 (900)
and for any number!!
(x-2)(x+3) = x^2 - 4 always four less than x^2
Nearly Perfect Squares
Perfect squares (like 4^2 = 16 and 5^2 = 25) can help people find close facts like 3 x5 and 4 x 6 (answers are both one less than the perfect squares) .
This will work for:
9 x 11 (99) = 1 less than 10^2 (100)
19 x 21 (399) = 1 less than 20^2 (400)
29 x 31 (899) = 1 less than 30^2 (900)
and for any number!!
(x-1)(x+1) = x^2 - 1 always one less than x^2
Somewhat Nearly Perfect Squares
Perfect squares (like 4^2 = 16 and 5^2 = 25) can help people find somewhat close facts like 2 x 6 and 3 x 7 (answers are both four less than the perfect squares) .
This will work for:
8 x 12 (96) = 4 less than 10^2 (100)
18 x 22 (396) = 4 less than 20^2 (400)
28 x 32 (899) = 4 less than 30^2 (900)
and for any number!!
(x-2)(x+3) = x^2 - 4 always four less than x^2
February 2010 Brain Teaser answer and solution
Solve for a, b, c, d, and e.
a (b + c + d + e) = 128
b (a + c + d + e) = 155
c (a + b + d + e) = 203
d (a + b + c + e) = 243
e (a + b + c + d) = 275
a (b + c + d + e) = 128
a(5 + 7 + 3 + 11) = hey this doesn't work
ok let's try 243 = 9 x 27 so d = 9
a(5 + 7 + 9 + 11) = a ( 32) therefore a = 4
4(5 + 7 + 9 + 11) = 128
a (b + c + d + e) = 128
b (a + c + d + e) = 155
c (a + b + d + e) = 203
d (a + b + c + e) = 243
e (a + b + c + d) = 275
Check out the prime factors of each of the numbers.
155 = 5 x 31...therefore b = 5
203 = 7 x 29...therefore c = 7
243 = 3 x 81...therefore d = 3
275 = 11 x 25...therefore e = 11
155 = 5 x 31...therefore b = 5
203 = 7 x 29...therefore c = 7
243 = 3 x 81...therefore d = 3
275 = 11 x 25...therefore e = 11
a (b + c + d + e) = 128
a(5 + 7 + 3 + 11) = hey this doesn't work
ok let's try 243 = 9 x 27 so d = 9
a(5 + 7 + 9 + 11) = a ( 32) therefore a = 4
4(5 + 7 + 9 + 11) = 128
Check:
5(4 + 7 + 9 + 11) = 5(31) = 155
7(4 + 5 + 9 + 11) = 7(29) = 203
5(4 + 7 + 9 + 11) = 5(31) = 155
7(4 + 5 + 9 + 11) = 7(29) = 203
9(4 + 5 + 7 + 11) = 9(27) = 243
11(4 + 5 + 7 + 9) = 11(25) = 275
so: a = 4,b = 5, c = 7, d = 3, e = 11
Thursday, February 25, 2010
GED as a Possible Standard
http://voices.washingtonpost.com/class-struggle/2010/02/crawling_toward_national_tests.html
How about using the GED as a high school standard?According to the ACE that administers the GED, "Only 60% of graduating high school seniors would pass the GED Tests on their first attempt". http://www.acenet.edu/Content/NavigationMenu/ged/pubs/GED_Testing_Program_Fact_Sheet_v1_2010(3).pdf
Since institutions already accept the GED as an established standard, it would be interesting to consider the GED as an exit exam rather than defining new ones.
For lower grades, SAT or ACT (or placement tests like Accuplacer or COMPASS) could be used as goals (whether or not these exams cover what is needed, they are already an accepted standard).
How about using the GED as a high school standard?According to the ACE that administers the GED, "Only 60% of graduating high school seniors would pass the GED Tests on their first attempt". http://www.acenet.edu/Content/NavigationMenu/ged/pubs/GED_Testing_Program_Fact_Sheet_v1_2010(3).pdf
Since institutions already accept the GED as an established standard, it would be interesting to consider the GED as an exit exam rather than defining new ones.
For lower grades, SAT or ACT (or placement tests like Accuplacer or COMPASS) could be used as goals (whether or not these exams cover what is needed, they are already an accepted standard).
Wednesday, February 17, 2010
Math Helps People Think Better
Seth Godin writes:
Can you factor this?
If you're like most people, you get a little queasy at the thought. And when you were in tenth grade, you surely wondered why they were bothering you.
(the answer is (x-2) times (x-2), in case you were curious.)
It turns out that the real reason you needed to do this work was to be able to play with numbers in your head. Abstract numerical thought is an important skill among educated people.
My response:
Great analogy...except no queasiness ;)
Can you factor this?
If you're like most people, you get a little queasy at the thought. And when you were in tenth grade, you surely wondered why they were bothering you.
(the answer is (x-2) times (x-2), in case you were curious.)
It turns out that the real reason you needed to do this work was to be able to play with numbers in your head. Abstract numerical thought is an important skill among educated people.
My response:
Great analogy...except no queasiness ;)
Sunday, February 14, 2010
Why Take Math comment on about.com
http://math.about.com/b/2010/02/08/why-take-math.htm#gB3
Instilling Core Values with the Life Skill and Discipline of Math
Instilling Core Values with the Life Skill and Discipline of Math
Friday, February 12, 2010
Info for Parents on Math Ed
http://www.wheresthemath.com/Pages/informationforparents.aspx
This advocacy group based in Seattle has been a strong proponent of parental involvement and curriculum choice.
This advocacy group based in Seattle has been a strong proponent of parental involvement and curriculum choice.
Thursday, February 11, 2010
Checking Up on Student Understanding
http://www.denverpost.com/education/ci_14350149
In this the article, the reference is to POP (Proof of Purchase) -- some call them exit slips. Sometimes I call them checkpoints. A short quiz at the end of class or at the end of a lesson (within a class) can help both students and teachers assess what they know and what they still need to learn.
Wednesday, February 10, 2010
The GED is a Common Standard
http://www.acenet.edu/Content/NavigationMenu/ged/test/math.htm
A Common Core accepted standard is the GED.
A Common Core accepted standard is the GED.
Tuesday, February 09, 2010
Kids Need Work to Do
http://voices.washingtonpost.com/answer-sheet/homework/give-kids-homework-while-schoo.html?referrer=emaillinkpg
With beforeschooling and afterschooling, just add snowschooling ;)
With beforeschooling and afterschooling, just add snowschooling ;)
Monday, February 08, 2010
Letters on Playing to Learn
http://www.nytimes.com/2010/02/08/opinion/l08teach.html?ref=opinion
Two of the letter writers would like to see elementary Math education to go beyond the four operations.
"In addition, in any mathematics curriculum, including early childhood, children are capable of learning much more than the four basic operations. Where are geometry and early algebra? What about logic, measurement and estimation?"
The same letter writer as quoted above also points out the lack of social studies in Engel's ideal early schooling.
Two of the letter writers would like to see elementary Math education to go beyond the four operations.
"In addition, in any mathematics curriculum, including early childhood, children are capable of learning much more than the four basic operations. Where are geometry and early algebra? What about logic, measurement and estimation?"
The same letter writer as quoted above also points out the lack of social studies in Engel's ideal early schooling.
Sunday, February 07, 2010
What should a 12 year old know?
http://www.nytimes.com/2010/02/02/opinion/02engel.html?ref=opinion
Reading out loud is a terrific skill to develop!
However, by age 12, other Math concepts can be added to the four operations -- especially the middle school merry-go-round of fraction/decimal/percent.
Reading out loud is a terrific skill to develop!
However, by age 12, other Math concepts can be added to the four operations -- especially the middle school merry-go-round of fraction/decimal/percent.
Sunday, January 31, 2010
Division with Fractions 1 and 3/4 divided by 1/2
This is an example from Liping Ma's book:
Using Decimals
How much is 1.75 divided by .5?
1.75/.5 = 3.5
Using Fractions
1 and 3/4 divided by 1/2
1 and 3/4 = 7/4
7/4 divided by 1/2
How many half cups are in 7/4 cups?
1 half cup = 1/2
2 half cups = 2/2 = 1
3 half cups = 3/2
4 half cups = 4/2 = 2 -- this is too much
7/4 divided by 1/2
multiply 7/4 by the reciprocal of 1/2
7/4 x 2/1 = 14/4 = 7/2 = 3 and 1/2
Division with Fractions is "a topic at the summit of arithmetic". In the introduction, she asks a division with fractions question: 13/4 divided by 1/2 and offers three additional problem-solving methodologies (besides Keep, Change, Flip) -- Dividing Using Decimals, Applying the Distributive Law and You Don't Have to Multiply.
Using Decimals
How much is 1.75 divided by .5?
1.75/.5 = 3.5
Using Fractions
1 and 3/4 divided by 1/2
1 and 3/4 = 7/4
7/4 divided by 1/2
How many half cups are in 7/4 cups?
1 half cup = 1/2
2 half cups = 2/2 = 1
3 half cups = 3/2
4 half cups = 4/2 = 2 -- this is too much
7/4 divided by 1/2
multiply 7/4 by the reciprocal of 1/2
7/4 x 2/1 = 14/4 = 7/2 = 3 and 1/2
Division with Fractions is "a topic at the summit of arithmetic". In the introduction, she asks a division with fractions question: 13/4 divided by 1/2 and offers three additional problem-solving methodologies (besides Keep, Change, Flip) -- Dividing Using Decimals, Applying the Distributive Law and You Don't Have to Multiply.
Saturday, January 30, 2010
Checking Multiplication with Casting Out Nines
Multiplication can be checked using Casting Out Nines. (rather than long division)
By studying the digits in the problem and comparing them to the digits in the answer, we can gain confidence that we have done the problem correctly.
Here are some examples:
12 x 12 = 144
The digits in 12 add up to 3 (1+2)
The digits in the other 12 add up to 3 (1+ 2)
3 x 3 = 9 (144 adds up to 9)
13 x 13 = 169
The digits in 13 add up to 4 (1+3)
The digits in the other 13 add up to 4 (1+ 3)
4 x 4 = 16 (169 adds up to 16)
We could also add up the digits in the 16 of 4 x 4 and get 7
and get 7 in the answer by casting out the 9 in the 169 so we are left with a 16 that add up to 7.
125 x 4 = 500
The digits in 125 add up to 8 (1+2+5)
The 4 is just a 4
8 x 4 = 32 and the digits in 32 add up to 5
The answer 500 also adds up to 5.
By studying the digits in the problem and comparing them to the digits in the answer, we can gain confidence that we have done the problem correctly.
Here are some examples:
12 x 12 = 144
The digits in 12 add up to 3 (1+2)
The digits in the other 12 add up to 3 (1+ 2)
3 x 3 = 9 (144 adds up to 9)
13 x 13 = 169
The digits in 13 add up to 4 (1+3)
The digits in the other 13 add up to 4 (1+ 3)
4 x 4 = 16 (169 adds up to 16)
We could also add up the digits in the 16 of 4 x 4 and get 7
and get 7 in the answer by casting out the 9 in the 169 so we are left with a 16 that add up to 7.
125 x 4 = 500
The digits in 125 add up to 8 (1+2+5)
The 4 is just a 4
8 x 4 = 32 and the digits in 32 add up to 5
The answer 500 also adds up to 5.
Wednesday, January 27, 2010
What You Know About Math?
Great and enthusiastic fun video about the TI-84
http://www.youtube.com/watch?v=Ooa8nHKPZ5k
http://www.youtube.com/watch?v=Ooa8nHKPZ5k
Learning Math Takes Patience
Feature on an award-winning Calc teacher in North Carolina who emphasizes practice for improvement and likens the process to bettering athletic ability. The article also talks about how Math attitude affects students and performance.
Tuesday, January 26, 2010
Personal Finance Classes in High School
This is such a needed app for Math and Life!!
Economics is also terrific but can be theoretical rather than practical.
Math provides the foundation for processing and understanding personal finance and economic terms to increase savviness and savings while reducing debt.
Economics is also terrific but can be theoretical rather than practical.
Math provides the foundation for processing and understanding personal finance and economic terms to increase savviness and savings while reducing debt.
Monday, January 25, 2010
Singapore Math Success
Singapore Math in Focus is hailed by students and teachers.
http://www.kentucky.com/142/story/1109176.html
http://www.kentucky.com/142/story/1109176.html
Saturday, January 23, 2010
ACCUPLACER: College Placement Exam
The ACCUPLACER is used by many colleges for placement into Math and English.
Passing these tests is important in order to avoid non-credit remediation classes.
The title link goes to a page with a pdf of sample questions for both Math and English.
Tips for the ACCUPLACER:
http://www.collegeboard.com/student/testing/accuplacer/accuplacer-tips.html
Passing these tests is important in order to avoid non-credit remediation classes.
The title link goes to a page with a pdf of sample questions for both Math and English.
Tips for the ACCUPLACER:
http://www.collegeboard.com/student/testing/accuplacer/accuplacer-tips.html
Tuesday, January 12, 2010
Where is the GED?
While states are spending money and resources on exit exams, it would be interesting to think about using the GED as a standard. According to this document, only 60% of graduating high school seniors would pass the GED Tests on their first attempt:
http://www.acenet.edu/Content/NavigationMenu/ged/pubs/GED_Testing_Program_FactSheet_20092.pdf
GED sample questions:
http://www.acenet.edu/Content/NavigationMenu/ged/test/prep/sample_questions.htm
http://www.acenet.edu/Content/NavigationMenu/ged/pubs/GED_Testing_Program_FactSheet_20092.pdf
GED sample questions:
http://www.acenet.edu/Content/NavigationMenu/ged/test/prep/sample_questions.htm
Monday, January 11, 2010
Math Show for Preschoolers
This new Nickelodeon preschool show will debut on January 25th.Web site of show
http://www.nickjr.com/team-umizoomi/
http://www.nickjr.com/family-entertainment/kids-books/nickjr-quick-picks/best-math-books-for-kids.html
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