Saturday, March 14, 2015

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.)

Tuesday, March 3, 2015

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) 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.

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!

Monday, March 2, 2015

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'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.)