Math You Can See: Art, Nature, Patterns, Society, and More

SBAC OPT-OUT ASSIGNMENT: 

Do some reading from links below. Follow instructions on this form and fill it out for a site that interests you. If you were "invited" to join my SBAC Opt-Out class (by email to your PPS account), then when you join, you can click on the Reflections assignment, click on its form, fill in the form from there and submit it to me electronically! Cool!! It is also fine to save the form to your drive, fill it in, then share viewing privileges with me (jwright2@apps4pps.net or jwright2@pps.net), or to do a printed copy by hand and hand it in. Thanks -- I like reading about which sites interest you and what you learned!

GENERAL

Math Munch: A Weekly Digest of the Mathematical Internet: Something for everyone!

ART AND ARCHITECTURE

• Math Art Tools | Math Munch
  Fantastic online math art tools!
• Muslim rule and compass: the magic of Islamic geometric design | Alex Bellos, The Guardian
  Includes a step-by-step guide for an Islamic-style tiling pattern.
• Readers’ Gallery | Math Munch
  Fabric art and drawings from Math Munch readers that show math (especially geometry).
• {3,3,7} Honeycomb Meets Plane at Infinity | Visual Insight
  Gorgeous computer-generated image of "honeycomb in 3D hyperbolic space," etc. Just look at it.
• Henry Segerman's Math Art
  Mathematical art; 3-D sculptures & 2-D prints. Very cool colorful & printable dodecahedron on the "Autoglyphs" page!
• Bathsheba Sculpture on Shapeways | Bathsheba Grossman
• Impossible World: Art
  "Impossible art" by artists like MC Escher.
• Geometry of Iran's Mosques | Inhabitat

VISUAL PATTERNS AND VISUALIZATION OF MATH

• Visual Patterns Not just tiles! Dozens of visual patterns with drawings and some real objects like Legos.
• Factorization - Visual illustration of divisor pairs | GeoGebraTube
• The Harriss Spiral | Alex Bellos, The Guardian
  Pretty fractal curve made golden-ratio-style. This article has a great description of what is going on mathematically.
• Polyhedra from Cardstock (Slide-Togethers)
  George Hart's templates and demonstrations of polyhedral constructions that can be made from cardstock.
• Paper Clifford Torus | cutoutfoldup.com
• How To Teach Math With LEGOs | The Hub
  Fractions, area & perimeter, multiplication, statistics...

MUSIC

• The Saddest Thing I Know about the Integers | Evelyn Lamb
  Math shows that you can't get perfect octaves from a bunch of perfect fifths.
• What Pi sounds like | Michael Blake, YouTube
  Surprisingly beautiful.

SCIENCE, NATURE, AND FOOD

• Fibonacci Numbers in Nature
  Slides and photos.
• Huge 3200 Year Old Tree | Distractify
  BIIIIIIG.
• What 2000 Calories Looks Like - YouTube
• Incommensurate Cheez-Its | Christopher Danielson (Trianglemancsd)
  Are Big Cheez-Its REALLY "Twice the size!" of regular? Christopher and his kids are on the case.
• Gauss / Curvature & Strength (& Pizza) | WIRED

SOCIETY AND SOCIAL JUSTICE

• Are you reflected in the new Congress? | The Guardian
  Enter demographic info (sex, age, etc.) and find out how many members of Congress share it.
• Mapping Migration in the United States | New York Times
  Fascinating map showing where people living in each state in 1900, 1950, or 2012 were born.
• Parable of the Polygons | Vi Hart
  How small, harmless-seeming choices can make a harmful world: discrimination simulation.
• Math in the Real World | Get The Math
  Some "real world" math for various art/sports/jobs; some dubious connections, and some are better videos than others. The Math in Music one has some interesting proportions. 

Math 6: Decimal Games & Practice

(If you're looking for Math 8 Pythagorean Theorem homework, see the post below this!)

Here's a list of places you can practice your skills with decimals. I will keep updating it as I find more sites.

For Math 6 homework due Wednesday 3/4/15, your job is to read this list till you find the instructions for the "crazy word" that will tell me you looked at it. (Don't tell your friends -- make them look themselves so they definitely know how to find my website!)

Fruit Splat/Place Value Decimals: This game is great practice for thinking about place value in decimals and for adding using mental math. It's designed to have several different levels, and you can play in timed mode or "relaxed" mode.
Flower Power: put decimals in order of size -- a nice complicated game (read the directions)
Balloon Pop Decimals Level 1 and Balloon Pop Decimals Level 2: Pop the balloons from smallest decimal to largest. If a balloon won't pop, it's because you haven't found the smallest. Score is based on time, but you can ignore it if you want and still get the practice.
Balloon Pop Decimal Patterns: Pop the balloons that continue a pattern.
Hungry Puppies: add decimals (quick mental math; fun speed challenge, but problems are not terribly complicated)
phschool.com: the textbook company's site (you need the codes from me; ask me or email me); includes online quizzes. Your crazy word is your name backwards! For fractions, decimals, and percents, try any of the Bits and Pieces books' links. Try doing the easier 4 or 5 problems in each quiz without a calculator, and use an online calculator for the others.
Sheppard Software decimal activities: Most of the activities on this list are mainly useful if you're having trouble understanding what decimals mean.
IXL (for-profit site which lets non-members practice a few minutes with standard problems) is SURE to have other decimal practice, but I haven't found the exact links yet. You can probably find something useful by exploring.

COMING SOON: PERCENTS:
Decention: finding equivalent fractions, decimals, and percentages

Fraction/Decimal/Percent Jeopardy: quiz yourself on converting between these. Use "0.3..." for 0.3 with a bar (repeating decimal)
Troy's Toys: prices and percents: find out amounts of discount from percent, or vice versa; you pick the level of difficulty by picking the toys
Balloon Invaders: a good challenge for finding percents FAST! only works if you are quicker with the keyboard than I am!

Informal Proofs of the Pythagorean Theorem (Math 8)

We've explored some right triangles in class and found that if you make squares off each side of a right triangle and find their areas, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on the legs. (For the picture below, the blue area + the red area = the green area.) This relationship is one way of expressing the Pythagorean Theorem.



Author: Pythagorean.svg: en:User:Wapcaplet
Derivative work: CP QQY (talk)
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.

Therefore, the Pythagorean Theorem says that if a and b are the lengths of the legs of a right triangle and c is the length of the hypotenuse, then 

a2 + b2 = c2

There are LOTS of different ways to prove the Pythagorean Theorem holds true for right triangles. You will explore two of them online and sketch your results in your math notebook.

1. Open Hotmath's Pythagorean Theorem activity. (If that link doesn't work, try clicking on the Pythagorean Theorem activity at hotmath.com's Geometry activities. Don't click on "Geometry" at the side.)
2. By default, the tab at the top for Dissection is chosen. In geometry, dissection is about cutting up a shape and rearranging it to make another shape. The square sticking off the longer leg is cut into four quadrilaterals. See if you can drag these pieces and the square sticking off the shorter leg to make the square sticking off the hypotenuse. If you get stuck, or just for a review, hit Animation.
3. Next, click on the Chinese tab at the top to explore another proof. Follow the directions; if you get stuck, or to review, hit Animation.
4. In your notebook, for both of these methods, sketch the "before" and "after" pictures that show a2 + b2 = c2.

(If you have technical difficulties, have a parent write a brief, signed note in your notebook explaining, and I will excuse you from the assignment and add a note to that effect.)

Math Information and Practice Websites

This page lists some math websites middle school students might find useful for explanations of math topics and practice of math facts and procedures. I have mixed feelings about students using some of these sites, which you can read here, but they can also be quite helpful.

This page is a work in progress; I am reviewing, sorting, and updating math links I originally collected on my former website, so you may want to look there too.

General Math Websites

• Khan Academy is famous for how thorough its coverage of math topics is. As a stand-alone math program it has limitations, but as far as I know it has a good reputation for accuracy. You can explore their videos for free (just pick Math as the Subject from the top of the screen), or if you want to track your progress on their questions, you can create an account for free.
• IXL is a commercial website with lots of quiz questions for practice; it gives information on math procedures when you make a mistake. You can use it for free for a limited amount of time each day. It has a very extensive list of topics. The questions tend to be somewhat repetitive and the help is very focused on procedures, but several students have told me they found IXL helpful.
• Math Is Fun has lots of informative write-ups of math topics; their information on fractions may be especially useful. Information is followed by quizzes so you can get some practice.
• Sheppard Software has many different game options, especially for grade 6 and younger. Their games are a little more complicated than some and do require some understanding, but your success still mostly depends on how fast you can recall math facts.  
• Ask Dr. Math at the Math Forum has a lot of interesting posts in answer to people's questions. They are often more thought-provoking and far-ranging than the other math help options listed here. 

Multiplication, Division, Multiples, and Factors

• Penguin Jump: For your 12 x 12 multiplication facts, check your knowledge (and speed) in a competitive way. You can join a game or create your own. If you create a private game, you can play against the computer. You can also make custom settings to play (for instance) only up to 10 x 10.
• Sigma Prime: I think this factoring game is fun! Shoot the appropriate prime factors at the invading number ships.
• Hit the Button: "Number Bonds" is about addition & subtraction; the others are multiplication & division.
• Times Tables Quiz at Crickweb: Solve multiplication problems in a "millionaire"-style quiz.

Fractions, Decimals, and Percents

• Melvin's Make a Match: Match written fractions with equivalent pictures. Good design.
• Fraction Booster: "Enter Activities" and then select Level 4 to practice putting fractions on a number line or Level 5 to find reduced fractions.
• Ordering Fractions: Sort fractions with different denominators in order of size.
• Match Fractions, Decimals and Percentages: Like it sounds.
• Decention: Find equivalent fractions, decimals, and percentages.
• Treefrog Treasure: Sophisticated game design; math seems to be basic identification of percents and decimals on number-line-like scales.
• Sheppard Software Fraction Games: PacMan-type games and others, giving practice in improper fractions and mixed numbers, equivalent fractions, adding fractions, subtracting fractions, among others.
• Fruit Splat/Place Value Decimals: This game is great practice for thinking about place value in decimals and for adding using mental math. It's designed to have several different levels, and you can play in timed mode or "relaxed" mode.
• Flower Power: put decimals in order of size -- a nice complicated game (read the directions).
• Balloon Pop Decimals Level 1 and Balloon Pop Decimals Level 2: Pop the balloons from smallest decimal to largest. If a balloon won't pop, it's because you haven't found the smallest. Score is based on time, but you can ignore it if you want and still get the practice.
• Balloon Pop Decimal Patterns: Pop the balloons that continue a pattern.
• Hungry Puppies: add decimals (quick mental math; fun speed challenge, but problems are not terribly complicated)
• Sheppard Software decimal activities: Most of the activities on this list are mainly useful if you're having trouble understanding what decimals mean.
• Fraction/Decimal/Percent Jeopardy: quiz yourself on converting between these. Use "0.3..." for 0.3 with a bar (repeating decimal)
• Troy's Toys: prices and percents: find out amounts of discount from percent, or vice versa; you pick the level of difficulty by picking the toys
• Balloon Invaders: a good challenge for finding percents FAST! only works if you are quicker with the keyboard than I am!

Solving Algebraic Equations

• Solving Equations Connect Four: Loads slowly. I recommend setting the timer to a longer time, or no time at all. Play with a partner or your imaginary friend. Experiment with the different difficulty levels and settings till you find the right difficulty (except don't do "Quadratic" for Math 8).
• Model Algebraic Equations with a Balance Scale: A bit confusing to start, but fantastic for visual thinkers. Build the equation, then keep the scales balanced by doing the same thing to both sides until you have solved for x.
• Manga High Algebra Meltdown: Complicated, fun, some time pressure. You have to provide the "input" (solution) that will "go through the machine" (equation) to give the desired output. You can adjust the difficulty level.
• Solving Equations Hangman: Ignore the letters! Good equations for practice; gamewise, not terribly exciting. Solve each problem (on scratch paper) and enter the answer. Mistakes cause a part of the hangman to be drawn. 

When or Why You Should or Shouldn't Use Math Practice Websites

Elsewhere on this blog, I've been making a list called Math Information and Practice Websites. This page is about my mixed feelings about this kind of practice.

The games and pages on that list have some nice features. They help you practice and memorize useful "math facts" (addition, subtraction, multiplication, or division of two numbers), and give you practice at recalling them. Many people find them fun. Some of the pages give lots of information and explanations that can help you remember or learn math topics.

Some possible disadvantages to these games are that they:

• often emphasize speed and scoring, which can be stressful for some people and aren't all that related to math understanding
• generally don't lead to deep thinking about math concepts (the games on my Math Websites with Creative or Complicated Games list tend to be better for this)
• usually do not connect different math ideas; the problems are narrowly focused on certain skills
• hardly ever require complicated problem solving strategies
• may not meet middle school Common Core standards
• often do not involve "real world" problems or make you curious

These websites could definitely make your life easier by speeding up certain calculations, and some of the math teaching information is excellent. But remember: if you find a game on that list is stressing you out, or you're just learning how to move through a Pacman-type maze fast but not actually improving your recall of any new math facts, the game is not making your life easier and maybe you should go do something more fun or thought-provoking! Just make sure to stop and think every once in a while about whether the game is helping with your learning goals or not.

Great Math 8 Resources for CPM Algebra

The publisher of our Algebra Connections textbook, CPM (College Preparatory Mathematics), has a terrific homework help resource on the web. For each homework problem, it has tips, sample work, suggestions, and/or a few answers to check against as you work.

There are lots of other things for families on cpm.org in addition to the homework help, including extra practice worksheets, technology resources, resource pages to go with lessons (the same ones provided in class), and advice and guides for parents. Hope you find lots of useful things! If you have particular recommendations, please leave them in the comments.

Fun Puzzle Websites

This is nowhere close to a complete list! There's so much fun stuff out there!

Oregonian's Puzzle Kingdom: Lots of logic puzzles of all sorts, including Battleships, Sudoku, Pic-a-Pix, Kakuro, and Hashi.
Maths Resources (the British call it maths): Dozens of fun puzzles and games, including classic card and board games as well as newer online games like 2048.
KenKen: Includes various difficulty levels. Great practice for thinking about numbers (especially factoring) and logic!
Numbrix: another neat logic puzzle. Try the easier levels first to get the hang of it.
Brain Teasers from the National Council of Teachers of Mathematics' Illuminations website
Calculation Nation online math games (also from NCTM)
Hotmath math games are at various levels; pick one that is appropriate for you (the cockroach one is pretty funny)
NRICH Enriching Mathematics: Lower secondary is probably the most appropriate level here
Vi Hart has a lot of amazing videos on YouTube. I haven't watched all of these, and some rely on high school or college math.
Lure of the Labyrinth is a computer game designed for pre-algebra middle schoolers. It has a storyline in which you are rescuing a lost pet from monsters in a labyrinth by solving complicated math puzzles. You can set up a free account to try it. I have not investigated it much yet. If you try it, let me know what you think of it!
Lewis Carroll Puzzles: How can you go wrong? I also strongly recommend reading Alice in Wonderland and Through the Looking Glass if you have not already!

Math Websites with Creative or Complicated Games

Here are some math websites I recommend for middle school students. This page is a work in progress; I am reviewing, sorting, and updating math links I originally collected on my former website, so you may want to look there too.

Calculation Nation: All free, no ads. Click on "GUEST PASS" or create a login at home with your family. I recommend READING DIRECTIONS before playing any game. Any are fine, but some are more fun or better for math than others. My favorites are:

• Square Off: Capture spaceships with rectangles with certain perimeters. Math concept level: high. Strategy level: high. Time pressure: medium.
• Factor Dazzle: Get points by finding factors, and keep your opponent's score low by giving them numbers without many factors. Can you figure out ahead of time how many points you will get from a certain move? Very similar to NCTM Illuminations' Factor Game but has a little extra fun. Math concept level: high. Strategy level: medium. Time pressure: low.
• Drop Zone: "Drop" your fractions on other fractions to add up to 1. More fun than it sounds! Math concept level: high. Strategy level: medium. Time pressure: low.
• Fraction Feud: Make a fraction (less than 1) smaller or larger than the one you’re “jousting” against. Consider using the Fraction Bar Chart. Try to figure out which cards are generally best to use or keep for later. Math concept level: high. Strategy level: high. Time pressure: low.
• Times Square: Tic-tac-toe with times tables, basically. Math concept level: medium. Strategy level: medium. Time pressure: low.
• Flip-n-Slide: Capture ladybugs with a triangle by translating, rotating, and reflecting it. Complicated; could turn out fun after several sessions. Math concept level: medium to high. Strategy level: high. Time pressure: low.
• neXtu: I haven't really played this, but it basically looks like a fun board game. Math concept level: low. Strategy level: high. Time pressure: low.

Fraction Game (NCTM Illuminations): Click on '+' symbols for information. Use equivalent fractions and estimation of fraction sizes to "play" fraction cards on fraction number lines. Play several times. How few cards can you use? What are good strategies to reduce the number of cards you use?

Troy's Toys: Percent discount game. In Level 1, find a discounted price from the original price and the percent discount. In Level 2, find the mystery discount percent from the price and discount. Not super creative, but fairly realistic and thorough.