2. Worksheet to review basics of trig. Great review before ACT! http://www.edhelper.com/math/trigonometry90.htm 

3. Fun worksheet to practice graphing in the four quadrants-

http://www.math-aids.com/cgi/graphing_four_ordered_puzzle.pl?skill=2&language=0&memo=&answer=1&x=95&y=24 

4. Challenge Problem

At McDonalds you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number such that you can not order any combination of the above to achieve exactly the number you want?

SOLUTION:

For any desired number if it is divisible by 3 it can easily be made with 6 and 9 packs, except if the number is 3 itself. If you can't use all six packs then use one 9 pack and you can do the rest with six packs.

If the number is not divisible by 3 then use one 20 pack. If the remaining number is divisible by 3 then use the above method for the rest.

If the number still isn't divisible by 3 use a second 20 pack. The remainder must be divisible by 3, in which case use the 6 and 9 packs as above.

The largest impossible number would be such that you would have to subtract 20 twice to get a remainder divisible by 3. However, you can't make 3 itself with 6 and 9 packs. So the largest impossible number is 2*20+3=43.

Mathproblems.info
By Michael Shackleford, A.S.A.
 

 Math Youtube Video Links

- Tricks

5. http://youtu.be/9qQAYEYLCoU (how to do long multiplication faster)

6. http://www.youtube.com/watch?v=WhH8WMbxPEU (fun card trick that anyone can do with just a little math)

- Applications

7. http://www.ted.com/talks/dan_meyer_math_curriculum_makeover.html (high school  teacher gives example of how to contextualize high school education)

8. http://www.ted.com/talks/lang/en/sean_gourley_on_the_mathematics_of_war.html (how math can be used to analyze war)

- Fun ways to Remember math

9. http://www.youtube.com/watch?v=OFSrINhfNsQ (Teach me how to factor...quadratic rap)

10. MATH FOOTBALL- REVIEW GAME

How to Play

1. The class should split into two groups.
2. A member of the offense is asked by the umpire to pick the level of difficulty of their question – 10 yards, 20 yards, 30 yards or 40 yards.
3. The umpire selects and asks a 10 yard, 20 yard, 30 yard or 40 yard question.
4. If the student answers correctly, the ball advances the appropriate number of yards on the field.
5. If the question is answered incorrectly, a "bad pass" is called, and the question goes to a player of the team that is "on defense."
   • After "bad pass" is called, there will be pause before a defensive player is called to answer the question.
   • Answering the question correctly gives the defense the opportunity to "sack the quarterback" for a ten yard loss when the offense picks a 10-yard question, or to intercept a 20, 30, or 40-yard pass play when the respective pass play was selected. Sacking a quarterback in the offensive endzone is worth 2 points.
   • If the defensive player misses the question, the pass has been dropped and play continues without a change in the yard line.
6. After each touchdown, the ball begins on the offensive team's 20 yard line.
7. An offensive team has 4 downs to gain 10 or more yards. If 10 or more yards are attained in 4 or less downs, then the offensive team is awarded another 4 downs to gain 10 or more yards.
8. There are no fieldgoals.
9. On fourth down, the offensive team can select to punt. No question is asked on a punt. The defensive team gains possession of the ball on their 20 yard line.

11. MATH HANGMAN- REVIEW GAME

How to Play

1. The class should split into four groups.
2. With each question, a representative of the team is selected to write on the board. Each team's representative goes to the board.
3. A question is asked.
4. All team members can contribute by suggesting to the representative at the board what to write.
5. When a representative is done, he/she yells "done" and sits down.
6. The remaining groups continue to work on the problem until all groups complete the problem or time is called.
7. The group that finishes first with the correct answer is awarded a chance to guess a letter on their hangman board.
8. A team is awarded a score when they guess all the correct letters of their word.

 13. Challenge Problem:

A town consists of only one street in the form of a circle. The town authorities give out four licenses for a particular kind of business. The inhabitants of the town live in equal density along the circle and will always go to the closest business for what they need. Business A gets to choose a location first, then business B, then C, and finally D. Each business desires to carve out as much business for themselves as possible but each knows the others all have the same motive. Assume that if a business is indifferent between locating in two different sections of the circle it will choose a section at random. Also assume that the business that goes last will choose a location in the middle of the largest (or one of the largest) sections. Where should business B choose relative to the location of A?

 14. "Cheat Sheet" for Algebra II. Could be given to studetns at begining of the year, or could be used on tests so they dont ahve to memorize all the fomulas and rules. http://tutorial.math.lamar.edu/pdf/Algebra_Cheat_Sheet.pdf

15. "Cheat Sheet" for calculus. Shows most the main derviative/integral rules, and it shows some of the most common derivatives and integrals. http://tutorial.math.lamar.edu/pdf/Common_Derivatives_Integrals.pdf 

ACT PREP:

17. Gives sample problems and some strategies. Problems are broken up by mathematical topics. http://www.act-math-practice.com/act-math-prep.htm

18. Full math section practice exam. Free and a great practice for the real test. http://www.actstudent.org/sampletest/math/math_01.html

21. Holey Sphere!

You don't need calculus to solve this problem (but if you know how to do it using calculus, go ahead) as long as you know the volume of a sphere is (⁴/₃)π r³.

SOLUTION:

Plan A -- the easy way to answer this problem.

The easiest solution is to start off by assuming the problem has a solution.  This problem seems to be missing some critical information that you would think would be required to solve the problem, such as the radius of the sphere and the radius of the hole.  But since this information wasn't supplied, you would be right to conclude that either the problem can't be solved in the manner requested (an exact real number) or else this information isn't needed.  As it turns out (see below for the full scoop) this information isn't needed, so you can assume any values of the sphere's radius and the hole's radius that are consistent with a 6-inch wall of the hole.  So what if you assume the hole is infinitesimally small, i.e. zero?  That works, and the answer is the volume of a 6-inch diameter sphere, which is 36π.

I give full credit if you take advantage of information given away in the statement of the problem.  Or to put it another way, I allow you to assume the problem can be solved as a starting point to answering it.  If you're in high school or college, this is a useful trick, which will help you on tests.

Plan B -- a slightly harder way to answer this problem.

But still no calculus is needed, well, not really...

Now, suppose you set out to answer the question in the absence of such specific direction as to how the answer should be given.  We're going to set this sphere down on an x-axis centered right down the middle of the cylindrical hole.

let x=0 be the center of the sphere, 
let r be the radius of the sphere, and
let h be the radius of the cylindrical hole.

The relationship between h and r, which we'll need later, is h² + 3² = r²

Now consider this slice of the holey sphere: Plane P is perpendicular to the axis of the hole at a directed distance of "x" from the center of the sphere, -3 ≤ x ≤ 3.  The slice is the intersection of plane P with the sphere and its interior, minus the cylindrical hole.  It is a pair of concentric circles, and consists of the larger circle and the points that are inside it but not inside the smaller one.

The radius of the smaller circle is h, and the radius of the larger circle is sqrt(r²-x²)

So the area of this slice is π(r²-x²)-π(h²) = π(r²-x² -h²)

Since r²=h²+3², (remember?), the area of this slice is π(h²+3²-x²-h²) = π(3²-x²)

This is the same as the area of a slice through a sphere of radius 3 with no hole, or a hole whose radius is zero.

Since the cross-section area at distance x from the center of the holey sphere is the same as the cross-section area at the same distance from the center of an ordinary sphere of radius 3, it follows that the volume of the holey sphere, which is the integral of all these cross-section areas, is the same as the volume of the ordinary sphere.

The answer is (⁴/₃)π(3³) = 36π

22. This link takes you to a fun game that where you have to use your knowledge of math to ask the computer questions and try to guess their secret number which is any number 1-100. Challenge your peers by saying you can guess it with fewer questions asked!!

http://www.theproblemsite.com/games/secretnumber.asp

 23. This site shows 5 cool apps students with Ipad or Iphones could download. If I could get a few Ipads for the class through a grant or if my class was 1 to 1 with tablets, I could also have them download these. 

24. Another cool site that can show you how to use an Ipad to teach mathematics.

25. Just a simply wicked demonstration of how SMART boards can be used to teach math -specifically geometry and algebra. 

26. Review worksheet for the basics of geometry- if students ask for extra help

27. Review game- Jeopardy. Free download-able template to make the review game look and function like the real thing in a class room setting. 

28. A free and easily to use tool to customize my seating chart.

29. Interesting webquest for solving story problems. Could be easily adapted to fit into any class, but I think it shoulds like a fun lesson!

30. Free sample test questions for the AP calculus test! Use this to help students get ready to take the test if they need to in order to get credit for it.

 31. This site has a free online graphing calculator. Can use this for students who can't afford a graphing calculator, especially if the school is 1 to 1...why make students buy them?

32. TANGRAM REVIEW GAME

Tangram is an ancient Chinese game that is also known as "the wisdom puzzle." The objective of this puzzle is to fit together the seven pieces, called tans, (shown below) so that they form a given shape.

Many shapes are possible. Several possibilities are shown below:

What are the rules for using the pieces to form these shapes? They are quite simple. You must use all seven tans, and they must lay flat. They must touch, and none may overlap. It can be harder than it appears and can be a lot of fun. We will use this ancient game to help us review!

How to Play

1. The class should split into four groups.
2. With each question, a representative of the team is selected to write on the board. Each team's representative goes to the board.
3. A question is asked.
4. All team members can contribute by suggesting to the representative at the board what to write.
5. When a representative is done, he/she yells "done" and sits down.
6. The remaining groups continue to work on the problem until all groups complete the problem or time is called.
7. The group that finishes first with the correct answer is awarded a point and 15 seconds to work on the tangram.
8. A team is awarded 3 points when they place all of the pieces of the tangram correctly to create the desired picture within their 15 second allotment.

33. Intresting application of pascals triangle. Looking at the remainders of a certain and discovering patterns in the triangle. Can be used as a starting point for a lesson involving the triangle.

34.  Fun activity to introduce set theory. You assign rules for three sets, then drag objects into a tripe venn diagram according to the rules you set. Easy to do, but shows the concept very well!

35. Fun game to Investigate the first quardant of the Cartesian coordinate system by directing a robot through a mine field laid out on the grid. Can be used to simply review the coordinate system or expanded for distance formula, ect.

 36. WILD images of geometry in nature. Possible introduction to course, day after a test, or even review day activity (name what element of geometry you see in each picutere)

 37. Explanation of the link between matrices and robotics. Interesting applications of matrices that could be worked into a lesson. Would be awesome in a class if you could actually program a basic robot using matrices.

 38. Challenge Problem:

How many of the three digit numbers that can be made from all of the the digits 1, 3 and 5 (used only once each) are prime?

Solution:

None of them! All permutations of 135 are multiples of 3.

 39. Mathematics on facebook App. Fun way to combine mathematics with something all students like and can indentify with. There are little quizzes, games, problems, ect, and it's all on FACEBOOK! (the link wont work because you have to download the app...if logged in facebook, just search for mathematics and it should be in the first three that show up.)

 40. The shortest proof of pythagorean theorem! This website also has tons of "fun facts" that could be used to introduce awide variety of lessons.