Pi Day!

Why are so many people excited about today, 3/14/15? It's "Pi Day," so called because the number pi rounded to the nearest ten-thousandth is 3.1415. If you want to round off to the nearest billionth, pi is 3.141592654, so if you trust your clock enough, you can get especially rapturous over Pi Day at 9:26 and 54 seconds! (I'm posting this after the morning 9:26, but you can still celebrate the evening one... the last 3/14/15 9:26 of the century.)

Long Division Practice Sites

Good long division practice sites! Click on the option to get help if you need it.

Easier (divisor has 1 digit)
Harder (divisor has 2 digits)

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.)

Solving and Graphing Linear Equations: Practice Games

• 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. Clicking on blocks instead of dragging can reduce the tedium.
• Interactivate Equation Solver: You provide steps for solving an equation, along with reasons ("additive inverse" if you're "undoing" an addition or subtraction or "multiplicative inverse" if you're "undoing" a multiplication or division). The program responds with the new equation that would follow from doing what you suggest to both sides of the equation. Keep going till you get x by itself and know what its value is. (Leave "Use Identity Properties" off unless you want to have to do extra steps saying adding 0 or multiplying by 1 can be ignored.)
• 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).
• 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. 
• 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 after you've succeeded at easier levels in previous games; I'm not sure how you can save this if you play at school, however.
• Algebra vs. the Cockroaches: Cockroaches on your graph paper! Annihilate them! Choose your weapon, which will fire in the straight line whose equation you provide, hopefully hitting the cockroaches before they breed. Read the instructions (they're quick). Remember growth/change = slope = rise/run; they all say how much y increases (or decreases) when x increases by 1. Some time pressure; try using hints if this gets frustrating.

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. 

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?