 dansmath4kids |
 2/03 |
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- Finding Math in the World Patterns & Numbers (back to top)
- Finding Math in the World Patterns & Numbers (back to top)
- As a math teacher, one of
the most-often asked questions I get is:
- "What are we gonna use this stuff for?" I try to find some area of math
- that applies to their favorite interest, even if it's music, art, or dance!
- "What are we gonna use this stuff for?" I try to find some area of math
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- Physics: Where would this world be without the laws of physics? Right where it is, but we
- couldn't understand it or the rules that govern its gravity and motion without knowing math!
- Advertising: How much should we spend on TV commercials & newspaper ads this year?
- Some ads will increase sales, but too many ads will backfire and some customers will leave.
- Music: The chromatic scale (C, C#, D, D#, ... , B, C) is made up of notes defined by frequencies
- that grow in a "geometric progression" whose ratio is the 12th root of 2 ; spanning one octave!
- Art: Many of the movements in classical, impressionist, or modern art have been based upon
- geometric principles: Cubism, OpArt of the 1960's, and Digital Illustration rely heavily on math.
- Dance: George Balanchine of the New York City Ballet was obsessed with geometric patterns
- and movements for his dancers. His choreography stressed straight lines and intricate timing.
- Physics: Where would this world be without the laws of physics? Right where it is, but we
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- Puzzle Problems: (back to top)
- Puzzle Problems: (back to top)
- [ Number Problems | Geometry Problems | Train Problems | Logic Problems ]
-
- Problems are labeled Elementary,
Middle, High; either 'school' or 'difficulty' level!
- No answers are provided, that makes it more of a 'treasure hunt' for you.
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- Number Problems . . . back to top
- N1. a) Find a Fibonacci number, bigger than 1, that's a perfect
- square. (E) b) Any more square Fibs under a million? (M)
- N2. Which numbers from 1 to 100 tie for the most divisors? (M)
- N3. Find a three-digit number, without any 0's, that equals the
- sum of the cubes of its digits. (M)
- N4. What number (under 1000) leaves a remainder of 3 when divided
- by 7, a rem of 4 when div by 11, and rem 5 when div by 13? (H)
- Geometry Problems . . . back to top
- G1. How many circular cookies of diameter 4" will fit onto a
- round plate of radius 6"? (E)
- G2. What's the inside corner angle of a STOP sign (8-sided) ? (M)
- G3. How do you cut a 4" by 9" rectangle into three easy pieces
- that can be rearranged into a square? What size square? (M/H)
G4. What's the diameter of the
small circle in the corner? (H)
- Train Problems . . . back to top
- T1. Two trains, each going 20 meters per second, approach
- each other from 6,000 meters apart starting at noon.
- When will they meet? (E)
- T2. On your vacation, your train, traveling at 45 mph,
- passed a train in the opposite direction going 36 mph.
- You saw the second train take 6 seconds to pass your eye.
- How long was the second train? (mph is miles per hour) (M)
- T3. You fell asleep on the train halfway to your destination.
- You slept until you had half as far to go as you went while
- you slept. What fraction of the trip were you sleeping? (H)
- Logic Problems . . . back to top
- L1. My younger niece is 13 years old, but her older sister just
- had her fourth birthday. How is this possible? (E)
- L2. Can you plant ten trees in four rows of five trees each? I can! (M)
- L3. You see two twins from your class; one always tells the truth, and
- the other always lies, and you don't know which one is which. You
- want to know if there will be a test today. What one question
- can you ask one random twin so you'll know for sure? (H)
- Math Activities and Ideas for Parents . . from www.dansmath.com . . (back to top)
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- 1. Be positive about math and about learning; kids listen more than you know!
- Most kids will enjoy a subject
if there aren't negative preconceptions; try not to say things
like
- "I was never any good at math," or "math is hard," or "you probably won't need to know that."
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- 2. Encourage fun and exploration, not just grades and competition.
- Math isn't about A's, drills,
and endless practice; it's a classical subject, a universal language,
- and a beautiful structure of patterns and logic. It's also a place to learn problem solving.
- Achievement in the usual subjects of arithmetic, algebra, geometry, trig, and calculus will
- happen only when students invest mental energy in doing math; so make it relevant and fun!
- and a beautiful structure of patterns and logic. It's also a place to learn problem solving.
- 3. Be sure to provide a good place for your kid to study.
- Have a room, desk, or table
that isn't in the line of sight of a TV set. Math can be done
well
- with or without a computer; web surfing while studying can be distracting. Got three kids in
- a one-bedroom apartment? Carve out a corner of the kitchen and set up a lamp and small
- bookshelf; allow for your kid's concentration time without noise or frequent interruptions.
- with or without a computer; web surfing while studying can be distracting. Got three kids in
- 4. Allow computer exploration on the internet; at least to a list of websites you select.
- There are some amazing places
to see (including dansmath.com), and some of them are at a
- more advanced level than your kid might be, but that doesn't mean they can't go there.
- Try mathworld.wolfram.com or Ask Dr.Math or visit Dan's Favorite Links.
- more advanced level than your kid might be, but that doesn't mean they can't go there.
- 5. Look for mathematical
patterns together (numerical
and geometric) in the
world around you.
- a) Did you know that a soccer ball is really a geometric solid called a "truncated icosahedron"?
- b) What are triangular numbers,
and where can you find them besides bowling?
- c) What's the story of Pi (
=
3.14159265 . . . ) and
why do the decimals go on forever?
- d) What's so special about numbers like 60; why do they have so many divisors?
- c) What's the story of Pi (
- a) Did you know that a soccer ball is really a geometric solid called a "truncated icosahedron"?
Lesson Plans and Ideas for Teachers 
(coming soon) (back to top)The greatest thing about my job is that I teach what I love, and (for the most part) nobody tells me how to teach it. But what if you want someone to tell you what to do? Read on!
- The Usual Suspects: Arithmetic, Algebra, Geometry, Trigonometry
- Be sure to browse my free math lessons on all these topics!
- Some Tangential Topics: Number Theory, Tessellations, Polyhedra
- On The Fringe: Chaos & Fractals, Math Sounds, Any-Pointed Stars
- Be sure to browse my free math lessons on all these topics!
Graphics & Animations You can view, print, or steal these! (back to top) This is a "3D space curve"
with its shadows on two walls
and floor! (Done in Mathematica)
- It's a soccer ball! No,
it's a spherical
- projection of a truncated icosahedron!
- Here every corner is the meeting place
- of two hexagons and one pentagon.
- projection of a truncated icosahedron!
This is the picture proof of the
famous Pythagorean Theorem;
comparing the yellow areas we
can see that a^2 + b^2 = c^2 .
(I showed this in my job interview!)
- I like to blur the line
- between Math and Art.
- This is a surface generated
- by Mathematica, showing
- the red space curve and a
- progression of curves along
- normal vectors at each point.
- between Math and Art.
This is the simplest
dissection of a rectangle
into incongruent squares
(diff sizes) rectangle is 32 x 33.
- This animation, used in calculus,
explains
- that the (red) secant lines that connect two
- points P and Q approach a limiting tangent
- line (blue) at P, as Q approaches P.
- (Click Reload or Refresh if it's not moving.)
- that the (red) secant lines that connect two
(back to top)
