Sunday, October 5, 2014

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. 

Friday, October 3, 2014

Geometry: Exploration of Triangle Similarity

Conditions for triangle similarity: Try the SAS tab first, then select SSA at the top and experiment with that.

If two triangles have a proportional pair of side lengths and the angles between those sides are congruent, must they be similar?

If two triangles have a proportional pair of side lengths and the angles between one of those sides and the other side are congruent, must they be similar?

Thursday, October 2, 2014

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.