Math Puzzles

1.For a person, his childhood is 1/6 of life. Adolescence is 1/12. Marriage 1/7. A child born after 5 yrs. Child reaches half of father's age, child died. Person lived 4 more yrs. Person lived to (84).

2.I have 36 marbles. First person takes 1 then 1/7 of leftover. #2 takes 2 and 1/7 of what is left. #3 takes 3 and 1/7. ... Fair?

3.142,857 is magic. Times2, times3, ...

4.Arrange 10 coins in 5 rows and 4 coins are on each row. (Hint : star shape)

5.How do you reduce the leftover sentence to half for "A person served 4 yrs of his life sentence"?

6.35 horses divided amongst 3 people. 1/2, 1/3, 1/9. How?

7.1 person shared bread with 2. #2 provided 3 loaves and #3 provided 5. Loves wer cut into 3's and person #1 will pay 1 coin for each loaf (8 coins total). How many coins should #2 get?

8.Four 4's can make any #: 44-44, 44/44, 4/4 + 4/4, ...

9.There 7 full bottles of wine. 7 half bottles and 7 empty bottles. How 2 divide amongst 3 people so each has same amount of wine and same # of bottles?

10.3 men go and eat. At the end, each paid $10. The owner gave back a $5 and they left $2 for tips. They paid a total of $29 out, where is the last $1?

11.Perfect number: 28 is divisible by 1,2,4,7,14. Add them up = 28. Same with 6.

12.I have 30 melons to sell at 3 for $1. You have 30 to sell at 2 for $1. Can we just sell at 5 for $2?

13.Numbers who are friends. 220 is divisible by 1,2,4,5,10,11,22,44,55,110. 284 is divisible by 1,2,4,71,142. Many factors are the same. Add up factors of 220 will = 284 and vise v.

14.6 1 8
7 5 3
2 9 4 is a majic square.

4 5 16 9
14 11 2 7
1 8 13 12
15 10 3 6 is a majic sq.

15.90 marbles. #1 will sell 50, #2 30, and #3 10. Three people need to sell them at the same prices and get the same sum. (Hint : #1 sell 49 at 7 for $1 and last marble at $3 each)

16.I have between 200 and 300 coins. Div by 3 and throw away 1 remainder. Do this 3 more times. How many did I have at the beginning? (ans: 241)

17. Three people are charged to fill a large room with things he can buy with $1. #1: hay. #2: a candle lit, light fills the room. #3: burn a piece of paper and smoke fills room.

18.8 to the 3 power is 512. 5+1+2 = 8
27 is the same.

19.There are three red cards and 2 green cards. Three people will have 1 pasted to the back and they line up from 1 to 3 and they need to guess which color they have on the back. The last person (#3) can see the colors of #1 and #2. Person #2 can see the color of #1, Person #1 can see nothing. After a while, #1 got what color he has(red). How?

20. I have 8 coins and one weights less than the rest 7 which weight the same. I have a scale and I can only use the scale twice and no weight can be used.

21. There are 5 people. 2 with black eyes and 3 with blue. People with black eyes always tell the truth and Three with blue always lie. You can ask 2 questions (to 2 people) and find out which is which?

(Hint: Question #1:What is color of your eyes to the first? The answer is in Arabic so I can not understand.

Question #2:What did the first person answer? "She said her eyes are blue"

Question #3:What is the color of the eyes of the previous 2 people? Answer: The first black and second blue eyes.

Final answer:Bla, blu, bla, blu, blu)

Math in Denmark

Met two girls from Denmark on the plane to LA. They are 13 and 14 from a rural area. There is a girl and boy younger in the family. English is poor to medium.

They ride bicycles to school. There are about 8 classes each day. Classes are balanced. There is no soda available in school. They pay about $3.50 for lunch each day. Drug use is not much but they can get the stuff. Drinking is not common amongst friends.

I asked them to do some math:

They can add, subtract and multiply. They both had trouble dividing. They could not add fractions. They could not graph a point or solve a one variable equation.

Math curriculum in Taiwan

No calculator is used in all 12 years

G1S1: Count up to 30; Simple shapes; which side is more (blocks); who is taller; add; subtract (2 digits); read analog clock.
G1S2: Count up to 100; move up and down time on an analog clock; +, -; tally to a table.

G2S1: Count and use numbers up to 200; + and - vertically; analog clock, dates; cm; multiply; measure length.
G2S2: Count up to 1000 and work with those numbers; meter; multiplication table; line, plane; tell amount of money; concept of horizontal and vertical; point, edge,face; concept of fractions.

G3S1: Count up to 2000 and + - X / of these numbers. plane shapes (triangle, four sided poligons); perimeter; volume; kg, g; area;; division; compare fractions.
G3S2: 10,000 and under (count and + - X /); time (hr vs. min, min vs. sec); multiply and divide large numbers; angle; circle basics; + - of fractions; mm, decimal numbers.

G4S1:Count under 100,000 and (+ - X /);parallel and perpendicular lines; mixed fractions and operations of; area of squares and rectangles; orders ofoperations; add and subtract time; measure with a protractor; adding angles

G4S2: Switch amongst fractions, percent, and decimals; more conceptual operations of fractions(4 times how much is 4/5); proportion; X and / of decimals vertically; speed; how to truncate.

G5S1: + - X / of all huge numbers; km; + - X / with approximation; work with decimals up to three digits; divide to form a mixed fraction; volume; names and characteristics of different types of triangles and shapes with 4 sides; line graph and bar graph.

G5S2: common factors and common multiples; simplify fractions; numberline; graph decimals and fractions; find area by counting unit squares; area of parallelograms and trapezoids; ton; kg.

G6S1: + - X / of negative numbers; absolute values; exponents; sci. notations; distributive property a (x + y) = ax + ay; solve complex equations with just one variable.

G6S2: Solve linear inequalities; solve systems; graph ordered pares;
graph ax + by = c; inverse variation; variables and functions.

*** Middle School ***

G7S1: distributive, foil,polynomial operations (+ - X /); factoring ax2+bx+c; squareroot; pythagoream theorem; solve quadratic equations.

G7S2:sequence;
geometry: copy line segment, copy angle, area; circle (central angle, arc length, shaded area); polygon( internal angles and area); prism and pyramid (surface area and volume); triangle proofs; perpendicular and parallel line proofs; parallelogram, kite, trapezoids.

G8S1: similar triangles (size and area); similar shapes; circle (tangent, secant, angles)

G8S2: quadratic equations, switching amongst forms and graphing;
Stat, tables, box plots, mean medium mode; probability, sampling.

G9: review of sets, functions, rational and real numbers, XY plane; imaginary numbers and graphing; series, sequence; polynomial operations (alg2 level).

*** High S ***

G10: index; log; trig(up to precalc level).

G11: vectors, matrix used to solve systems of equations; 3D coordinates.

G12: conics; seq; probability; stat (sampling, standard deviation).

Open Mathematics

by Jo Boaler, Stanford U. (1996)

Students are encouraged to take responsibility for their own actions and to be independent thinkers.

Students work on open-ended projects in mixed-ability groups at all times.

In these classes, very little control or order is imposed.

The lessons have no structure.

Math teaching in US

US math teachers do not teach connections but teach procedures.

We need to change. We should change a bit everyday. After a long time, there will be a big difference and it will stay.

Integrated math from Glencoe

Four year math integrating algebra1, geometry, algebra2, calculus.

The IMP curriculum looks and feels dramatically different from the
programs that have existed in most schools for many years.
• It is problem-centered.
• It is integrated.
• It expands the content scope of high school mathematics.
• It focuses on developing understanding.
• It includes long-term, open-ended investigations.
• It can serve students of varied mathematical backgrounds in
heterogeneous classrooms.

How the IMP Classroom Is Different

IMP’s rich curriculum and its focus on understanding require changes in the
classroom. The discussion below looks at several aspects of this change:
• An expanded role for the teacher
• A more active role for the student
• Extensive oral and written communication by students
• Both teamwork and independence for students
• Assessment using a variety of criteria
• Use of graphing calculator technology

Math acceleration

Just Saying No–to Accelerated Math
June 10, 2008 by SwitchedOnMom

Last week the Washington Post ran a story on the a topic I’ve blogged on before: the uneasiness many parents are feeling about willy-nilly math acceleration in MCPS. You can read the story, “Accelerated Math Adds Up to a Division over Merits,” (yuk, yuk) here.
While parents support rigor and the opportunity for acceleration, many are uneasy that it’s being approached backwards, being carried out by fiat. The word has come down from on high that students who complete algebra before high school are more “successful.” Thus it should be so–regardless of whether there are/exist numbers/percentages of students to meet these targets (20% of 6th graders, 40% of 7th graders, 80% of 8th graders taking algebra in 8th grade). To make it so, the math curriculum is being back-mapped into elementary school, with acceleration starting abruptly in 2nd grade. As the article notes, concern seems to be greatest in the less affluent “red zone” schools.

The result–at least what I’m hearing anecdotally–is kids who are rushed through a compacted curriculum, who are stressed out, and who have decided that they aren’t good at math and in fact hate it. Down the line, there are reports of a watered down algebra and kids with weaknesses who fall apart when they hit Algebra 2 in high school and lack a truly solid footing in math.
Last night I had dinner with a good friend. She told me she had informed the “math content specialist” that her 4th grader (who has been doing combined 5th and 6th grade math this year) was going to repeat the same level math class next year. (Her child was in agreement and parents have ultimate say on placement.) The content specialist said it should be no problem.
A few days later, however, the mom got word that the principal wanted to see her. She went into a meeting with the principal, vice principal and math content specialist. To her surprise, the principal was under the impression that it was the mom who had requested the meeting. She told the principal that no, they were the ones who had requested to meet with her. The principal then asked why she wanted her child to repeat math next year, as the grades on the cumulative unit tests (which he had in front of her/him) were quite good. (It should be noted that the school thinks “mastery” is earning a “C.”)

To the prinical’s astonishment the mom said that in her opinion the scores were essentially meaningless. The tests were given over two days, and her child had confided that she had been told by the teacher which questions were wrong–and which he/she needed to answer correctly the next day in order to get a higher grade. The principal sputtered that the mom had just robbed her/him of any argument against the mom’s decision. The principal was clearly not pleased and as the mom was leaving told the others present to stay behind.

The only question is, was the principal angry that the testing was being manipulated? Angry that she/he didn’t know that the data was being manipulated? Angry that there would now be one less child on the accelerated math track? Angry that a parent had discovered this? Some of this? All of this?

8th graders lost in algebra

THE MISPLACED MATH STUDENT:
LOST IN EIGHTH-GRADE ALGEBRA
Washington, D.C.
Wednesday, October 22, 2008

ANDERSON COURT REPORTING 706 Duke Street, Suite 100 Alexandria, VA 22314

Abstract:

Scores in math have been rising. They’ve been rising since the early ’90s and they’ve made tremendous gains from 2000 to 2007. But the kids enrolled in our top classes have been declining. Now, that’s not to say anything about those classes themselves. As you’ll soon see, their composition has changed. They’ve been enrolling more kids who score at low levels.

And you can see now our misplaced kids, our 10th percentile kids, they scored 211. So my kind of ballpark estimate of where they function in mathematics is approximately at the second grade level. And they are enrolled, once again, in algebra, algebra 2, or geometry in eighth grade.

Now, to get an idea of what these students can and cannot do in mathematics, here is a sample item from NAPE. This is a public release item. It deals with percentages. By the way, all eighth graders have trouble with this item. You can see that overall only 36 percent of eighth graders can do it. In case you can’t do it, I checked the right answer for you there

There were 90 employees in a company. This year, the number of employees increased by 10 percent. How many employees are in the company this year?

So you have to compute 10 percent of 90 and you get 9 and then you add that onto 90 and you get 99. If you don’t do those two steps accurately, you miss the item.

You can see that in the advanced classes only about half the kids got that item right. So this item is missed by a lot of eighth graders. But our misplaced 10th kids, the 10th percentile kids, they really had trouble with it. Less than 10 percent, 9.8 percent got this item correct.

Recommendations:

Let’s make our goal that more students will learn algebra, not that they’ll take courses

The second recommendation is to teach and assess prerequisite skills leading up to algebra. Let’s make sure, for instance, they know fractions.

My letter to board of education

Dear Board Members:

I saw a nice boy who has failed algebra1 five times here at Magruder HS. According to his teacher, he is too low to pass. Although he is a unique person, more students like him are appearing. They are coming from closed learning centers. Their lack of knowledge is a result of excessive acceleration of mathematics in their younger years. Most of them are minority students and they do not see much hope of graduation.

Is it possible to bring MAPS1, MAPS2 back or make new courses in pre-algebra for them? These young folks can actually improve from current levels and become more capable. My own daughter passed high school with MAPS, algebra1, PGA, and geometry.

Best Regards,

Ed Hsu Magruder Mathematics 2/2009

Math practices

By ERIC WALSTEIN BrookevilleSunday, March 1, 2009; Page C07 Washington Post

As a teacher in the Montgomery County Science, Mathematics, Computer Science Magnet program, I have the privilege of teaching some of the best young minds in the United States. But even as standardized test scores have risen and the county has claimed great strides in math instruction, our program has had to offer a week of remedial math classes during the summer for our entering ninth-graders.

This past summer, the teachers administered a test of concepts we thought the students should know coming out of algebra, geometry, and algebra II. I constructed the test, and the other teachers reviewed it. We grouped the students into four levels based on their magnet qualifications. We gave them one hour to complete the exam. We did not let them use calculators. It had 27 questions and yielded eye-opening results.

I was assigned to the top group, which averaged only 15 questions right. The other groups scored commensurately lower, some as few as three or four questions right. Students found many of the ideas of algebra and geometry foreign, reporting that many core ideas had never been taught. This process of giving summer math help has been going on for five years now, and the knowledge trend has been down each year. This is a direct consequence of policy decisions of the Montgomery County Board of Education to eliminate course objectives, to push students to take algebra earlier -- often before they are ready -- and to rely heavily on calculators.

Cumulatively, these decisions leave students in an untenable position. They lack the rich math background to fully understand their current work. So, to get their work done, they have no option but to memorize the current work and punch unfamiliar buttons on a calculator. This technique masks their lack of connection between current tasks and previous concepts they supposedly know.

Calculators used incorrectly enable children to "solve" problems they don't actually understand. They not only hide the intellectual connections between ideas that mathematicians seek to have students understand, but they also impair math strategy, long a staple of math curriculum design. Used correctly, calculators can be an important tool. Used incorrectly, they subjugate mathematical progress and reasoning to a list of questions with a corresponding list of answers.
A Montgomery school official once told me that calculators are important because they give more students "access to math." That's wrong. They give students access to answers disconnected from math concepts. Many of my current students complain that curriculum acceleration made them move too quickly without proper understanding. Take the calculators away, as we did, and even the county's brightest bulbs now get a failing grade on material they supposedly have learned with top marks.

Our magnet program students bring to the table a significant amount of mathematical knowledge and talent. Their work ethic is impressive; they make extensive use of the additional materials that a school with real resources can provide.

The students have the ability, but the school system is not matching their commitment.

How math acceleration hurts poor kids

Acceleration in math usually means either skipping parts of the curriculum or hurrying through them.

Rich students have parents, tutors, and computers to bridge the gap. Poorer students may not have any assistance so they fall behind.

Math Rushing

One hundred twenty thousand students are misplaced in their eighth-grade math classes.

They have not been prepared to learn themathematics that they are expected to learn.
This unfortunate situation arose from good intentions and the worthy objective of raising
expectations for all American students.

Two groups of students pay a price. The misplaced eighth graders waste a year of mathematics,
lost in a curriculum of advanced math when they have not yet learned elementary
arithmetic. They should be taught whole number and fraction arithmetic so that
they can then move on to successfully learn advanced mathematics.

Their classmates also lose—students who are good at math and ready for algebra.
These well-prepared but ill-served students also tend to be black and Hispanic and to
come from low socioeconomic backgrounds.

Teachers report that classes of students with widely diverse mathematics preparation
impede effective teaching, that too many students arrive in algebra classes unmotivated
to learn, and that they wish that elementary schools gave greater emphasis to basic skills
and concepts in math. When algebra teachers have to depart from the curriculum to
teach arithmetic, the students who already know arithmetic and are ready for algebra are
the losers.

Math acceleration