Chocomagic

1. Chocomagic • First of all, pick the number of times a day that you would like to have chocolate (more than once but less than 10) • Multiply this number by 2 (just to be bold) • Add 5 • Multiply it by 50 • If you have already had your birthday this year add 1759 .. If you haven't, add 1758. • Now subtract the four digit year that you were born. • You should have a three digit number • The first digit is the number of times you would like to have chocolate

2. Is it Magic or is it Math : Interesting ways to use Magic to Explore Important MathematicsMathemagic By: Amanda Meiners Nicole Maila Eden Malone

3. Re-gifting Robin • Re-gifting Robin http://www.regiftable.com/regiftingrobinpopup.html • Classroom use: Place Value • CC: Grade 5 Understanding place value, and analyzing patterns and relationships.

4. Can I guess your number? • Pick any 3 digit number • Rearrange the digits in reverse order • Subtract from the original. • Want a positive difference, subtract accordingly • Note: if this is equal to a two digit number, think of it as a “three” digit number with a zero in front when reversing the digits. • Take this new number and reverse again • This time add the two numbers • You will always get 1089. • Classroom use: Also the place value. Intro to Perfect squares • CC: High school-rational and irrational numbers

5. Proof • eg. 534 • Claim: Choose any three digit number with distinct digits represented abc. Reverse • the digits of this number so you have cba. Subtract the smaller of the two numbers from the larger one so you are left with a new number. Take this new number and reverse the digits again to make another new number. Add the two new numbers. Take the square root of that sum, and you will always be left with 33. • Note: if the first difference is equal to a two digit number, think of it as a “three” digit number with a zero in front when reversing the digits. • Proof: Imagine an arbitrary three digit number • Let the number abc be represented as 100a + 10b + c where a,b,c are distinct numbers in the set {0,1,2,3,4,5,6,7,8,9} • Reversing the digits would result in 100c + 10b + a • Subtract the second number from the first • 100a + 10b + c – (100c + 10b + a) = 100a + 10b + c – 100c – 10b – a • = 99a – 99c = 99(a - c) • Our new number is 99(a-c) • Let x represent a-c.

6. Since we know a and c are single digit numbers which do not equal each other, and the difference is at least 1, we know that 1 < x < 8 • We will take this case by case. • 99 * 1 = 099 099+990 = 1089 • 99 * 2 = 198 198+891 = 1089 • 99 * 3 = 297 297+792 = 1089 • 99 * 4 = 396 396+693 = 1089 • 99 * 5 = 495 495+594 = 1089 • 99 * 6 = 594 594+495 = 1089 • 99 * 7 = 693 693+396 = 1089 • 99 * 8 = 792 792+297 = 1089 • We always get 1089 in EVERY case. • The square root of 1089 is 33, hence you always get 33 as an answer.  • q.e.d.

7. The Magic Number 9 • Think of a four digit number in which all of the digits are different. • write the number down but don’t tell anyone what it is • Jumble up the four digits and write the new number below the first. • If it is smaller or above the first number if it is larger. • Subtract the smaller number from the larger number. • Add the digits of the total together • If the total of this calculation is a two digit number then these two digits should be added together as well. • Carry on like this until they are left with a single digit number. • Magically, this number will always be a 9! • Classroom use: Place Value • CC: Perform operations with multi digit whole numbers

8. Magic Card Trick • Give the tricky a set of nine cards and have them pick one without letting you know. Hand cards back with the card selected on top. • Place all other cards left in the deck back on top of this. • Start dealing the cards out in columns of 10, counting down from 10. • When counting down you deal the card value you say STOP and move onto the next column. • If you go all the way from 10 to 1, place a cap (turned over card) on the stack. • Continue to do this for 4 stacks.

9. Magic Card Trick (continued) • Once you have your 4 stacks count the values (uncapped) stacks together. (capped =0) • The added value is the number YOUR card is in the rest of the deck. • Reason: Know-the card is always going to be the 44th card, so you need to get through 43 cards. • Classroom use: Addition/ Subtraction of double digits involving 11’s

10. Speaking of 9’s… Does .999999=1? • Arithmetic • Algebra CC: 7th grade expressions and equations Early High school mathematics

11. Fold’m Eights • Fold the values up in a way so that when looked at read 1-8. • 7levels starting off with easy and getting more difficult as they go. • Make a check list that students need to mark off a certain number by a certain date or end of a chapter. • Great pre-curser to nets or a way to have students fill the last 5 minutes of class. • CC: Sixth grade Geometry ideas.

12. Magic Tables • Take a look at the 5 cards in front of your group, pick a secret number between 1 and 31. • Put all the cards with that number in the center of the group. • I will guess your number • Reason: Add all the numbers together on the first numbers of the cards given to you: Powers of 2 • Example: If the cards in the center have cards that start with 16 and 4, since when added together this would make their number be 20. • CC: sixth grade- evaluating exponents with whole numbers • Seventh grade- Use properties of operations to generate equivalent expressions • High school: rewrite exponential functions using multiple exponents.

13. CC: 7th grade students solving real life mathematical problems

14. Other fun Math-gical Ideas • Brain “Bus”ters • Equations that contain the initials of words that will make it correct. • Input-> Outputs • We fed in random inputs into a supercomputer and it came up with unique output. • Word Phrasing • Have students complete problems that match to answers and letters in the alphabet to complete a fun saying.