Transcript ICTM Presentation - Class Reunion Icebreakers, Games

Making Math Fun
by
Robert Greenlee
Wheaton Warrenville South High School
1993 Tiger Trail
Wheaton, IL. 60189
website:
http://www.greenleecds.com/mathhome.html
Home e-mail: [email protected]
School e-mail: [email protected]
Quotes
 “Good teachers are usually a little crazy.”
- Rooney, Andy (b. 1919) American journalist
 “A good teacher is one-fourth preparation
and three-fourths theater.”
- Godwin, Gail (b. 1937) American writer
Starting Class Activities

Pictionary/Charades
……………
Starting Class Activities

Pictionary/Charades
Starting Class Activities

Pictionary/Charades
Starting Class Activities

Pictionary/Charades
Starting Class Activities

Pictionary/Charades
(used with conic sections - parabolas)

Top Gun

Hoosiers

Rudy

Field of Dreams
Starting Class Activities

My beginning of the school year group activity
 One person describes, others draw,
and no one can ask any questions
 One person describes, others draw,
and anyone can ask any questions
“The only bad question is the one not asked!”
“Math is not a spectator sport!”
Starting Class Activities

Quick check - review problem or from
homework (usually a harder problem)

1st person correct 1 jolly rancher and 2 EC,

next person 1 jolly rancher and 1 EC,

third person 1 EC, everyone else nothing or
1 EC if only a few correct students
Starting Class Activities continued

Puzzles (see handout)
Given:group one contains the letters: M, T, U, V, W, Y
group two contains the letters: C, D, E, K
group three contains the letters: S, Z
group four contains the letters: H, O, X
group five contains the letters: F, G, J, L, P, Q, R
Each letter of BRAIN belongs in what group?
Answer: B in group two due to horizontal symmetry,
R in group five due to no symmetry, A in group one
due to vertical symmetry, I in group four due to all
types of symmetry, N in group three due to point
(rotational) symmetry
Note: I use this when I introduce symmetry and
also on parent night.
Starting Class Activities continued

Visual Puzzles (see handout)
(used with Trigonometric Identities)
Connect all nine dots by four lines without
retracing any line or part of a line or without picking
up the pencil. (Note: The lines can intersect.)
.
.
.
.
.
.
.
.
.
Starting Class Activities continued

More Puzzles continued
(see handout)
(used with Trigonometric Identities)
Given: (x - a) (x - b) (x - c) ... (x - z) = ?
The product of the given problem, the ?, has what numerical
answer?
Hint: I will take the Chicago Cubs and you take your favorite
major league baseball team. I will add up all the runs the
Cubs will score in each game played this season and you get
to multiply the runs scored by your team in each game played
this season. I bet that the Cub's sum will be greater than your
team's product. If you know the reason why it is a good bet
for the Cub's fan then it will help you to answer the original
problem.
Answer: 0 (zero) because x - x = 0
Starting Class Activities continued
•
Patterns (see handout)
(used with Sequences & Series)
 A famous one: 1, 1, 2, 3, 5, …

Timmy Tyler’s sequence:
2, 3, 10, 12, 13, 20, 21, …, 39, 200, 201, …, 399,
and Timmy Tyler happened to have a
cousin named Susie Swartz who lived by
the seashore:
6, 7, 16, …
Starting Class Activities continued
• Seeing the big picture
(used in geometry proofs and mathematical induction)
 Seurat’s painting
“Sunday Afternoon on the Island of LaGrande Jatte”
There is beauty in art and in math and one of
the beautiful things in math is logic.
Starting Class Activities continued
•
Neat Polar Graphs
\best stuff\alg2PreC\polar.doc
(see handout)
Starting Class Activities continued
•
Escalante – Standup/Sit-down:
(from the movie Stand and Deliver)
(used with trig. special angles and quadrants)
Name the quadrant or axis:
“Radians are like a foreign
language and you are not
fluent in radians until you stop
converting to degrees.”
-
4 radians
etc.
Starting Class Activities continued
• Illinois Six ball Lottery (used in probability & stats unit)





Students fill out 2 lottery cards, with the same numbers
on each, and turns one in to the teacher.
Each day pick 6 random numbers between 1-52.
Do this for 5 days.
I have the students play 2 grids the first day, 4 the next ,
6 the next, 8 the next, and then all 10 grids the 5th day.
See how many students get 3, 4, 5, or 6 of those
numbers.
(see the next slide for a summary)
Starting Class Activities continued
• Lottery continued (Spreadsheet template on the CD)
MATH 6 BALL ILLINOIS LOTTO (52 total balls) Spreadsheet
Class
Amt Bet
Grand
2nd
3rd
4th
.
(6 out of 6)(5 out of 6)(4 out of 6)(3 out of 6)
Day 1
1st Hour
$11
4th Hour
$14
5th Hour
$18
1 Day Total
$43
$0.00
$0.00
$0.00
$0.00
Day
Day 2
1st
4th
5th
Day
Hour
Hour
Hour
2
$26
$32
$40
$98
$141
1st
4th
5th
Day
Hour
Hour
Hour
3
$48
$45
$60
$153
$294
1st
4th
5th
Day
Hour
Hour
Hour
4
$60
$68
$80
$208
$502
1st
4th
5th
Day
Hour
Hour
Hour
5
$75
$80
$100
$255
$757
2 Day Total
Day 3
3 Day Total
Day 4
4 Day Total
Day 5
5 Day Total
Total Grids Played:
Probability of Winning
# That Should Have Won
# of Actual Winners
Our Prob. of Winning
1514
1
to
1
to
2
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
$6.00
$6.00
2
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
$0.00
3
$11.48
$17.48
$0.00
$0.00
2
2
4
$15.60
$33.08
2
5
1
4
$0.00
$0.00
$12.75
$19.13
$0.00
$0.00
$12.75
$52.20
% of Total Money Paid Out as Winnings: 8.58%
Grand
2nd
3rd
4th
20,358,520 73,762
1,311
67
0.0
0.0
1.2
22.6
0
0
1
26
0
0
1514
58
Starting Class Activities continued
•
Math Aerobics
best stuff\alg2PreC\AEROBICS.DOC
(used with lines or translations of basic graphs)
Aerobics Explanation
The aerobics is a fun activity where I pick, usually on a Friday, 2 students - a
cheerleader and a football player to be the leaders in front of the class but
facing the same way as all the other students who are all standing up. I
have one other volunteer who does not want to do the aerobics stand at the
overhead and slowly show each function going down each column and
covering up the other columns. I would do this but I like doing (modeling)
the aerobics with the students. I have music playing that would be good for
aerobics. The person uncovering the functions has to time it so they do not
go too fast especially when doing horizontal shifts nor too slow also.
Starting Class Activities continued
• Math Aerobics continued (Algebra class)
y=x
y = -x
y=x
y=0
x=0
y=x
y = 2x
y = -x
y = -2x
x=0
y=0
y=x
y = ½x
y = 2x
a horizontal line
a vertical line
y = -x
y = -½x
a line with no slope
a line with zero slope
y=x
y=x+1
y=x–1
Starting Class Activities continued
• Math Aerobics continued
(Algebra 2 or Precalculus class)
Whenever x2 (just x2) shows up everyone raises
their hands above their heads claps once and
then makes a U shape with their arms. A -x2 has
the students put their hands down in a upside
down U shape, a x2+1 they stand up on their toes,
a x2-1 they bend their knees, an (x-1)2 they shift
one step right, and an (x+1)2 they shift one step
left. For x3 one arm is up and one down and they
are to slap their thigh whenever just x3 or -x3
shows up etc.
Starting Class Activities continued
x2 (clap hands)
-x2 (slap legs)
x4
-x4
x2 + 1
-x2 + 1
(x + 1)2
x2 (clap hands)
-(x + 1) 2
-x2 (slap legs)
x2 – 1
x2 (clap hands)
-x2 - 1
x2 (clap hands)
(x - 1) 2
-x2 (slap legs)
-(x - 1)2
(x + 1)2 + 1
(x + 1)2 + 1
x2 (clap hands)
-(x + 1)2 - 1
x2 (clap hands)
-(x - 1)2 + 1
x2 (clap hands)
-(x - 1)2 - 1
x2 (clap hands)
x3 (slap leg)
-x3 (slap leg)
x3 (slap leg)
x5
-x3 (slap leg)
-x5
x3 (slap leg)
x3 + 1
-x3 (slap leg)
-x3 + 1
(x + 1)3
-(x + 1) 3
-x3 (slap leg)
(x - 1)3
x3 (slap leg)
-(x - 1)3
-x3 (slap leg)
(x + 1)3 + 1
etc.
1/x
-[x] i.e. -int(x)
[x] i.e. int(x)
After Test or End of Period Activity
• Snafooz
http://www.iqpuzzles.com
(then scroll down to snaffoz picture)
http://www.mindwareonline.com
(then search for snafooz)
Homework

Math worksheets

Creative Publications, Pizzazz
Homework

Graphs - have points or curves that
when connected make a shape
Anyone do it with lines, ellipses, parabolas,
circles or other figures?

Crossword puzzles
(create your own puzzles)
http://www.puzzlemaker.com
Homework continued

Crossmatics
45 sophisticated puzzles reinforce basic number
understanding and problem-solving skills. Students fill in
crossword-like grids using numerical clues. Grades 7-12.
Homework continued

Nonograms (also called Griddlers,
CryptoPics, CrossPix, and Pic-A-Pix)
These grid puzzles are good for deductive reasoning.
The first website has the directions and the second is one
of many websites where you can play online.
http://www.geocities.com/activityworkshop/
puzzlesgames/nonograms/index.html
http://www.puzzle-nonograms.com/
see next slide for an example
Homework continued

Nonograms continued
Checking HW
 Which one is wrong
 Certain problem correct
 Predict how many got a certain
one correct
(can also be used with lecture for checking for understanding)
Use Tickets

Prizes or Drawings

Free Homework

Extra Credit on quiz or test
Selecting Groups

Snowball fight
Directions
Students take their given card and crumple it up into a ball.
They have a “snowball” fight, throwing the balls across the room.
Lay down some ground rules first about hitting each other’s
faces and attacking you!
When time is called, they must pick up the nearest snowball and
then that is used to find a group.
Variation:
You can also have problems on the cards and then when time is
called, they must work that problem.
They then crumple it back up and have another snowball fight to
get a second problem to complete.
Selecting Groups

Matching puzzle piece

Playing Cards (all the Kings are a group etc.)
Find your category:
 Joey Rachel Monica Chandler
 Izzie Christina Meredith George
 Bears Packers Cowboys Giants
 Cubs
White Sox Brewers Dodgers
 Boston Miami New York Philadelphia
 Seattle San Francisco Los Angeles
San Diego
 Others?

Miscellaneous
 Posters with funny sayings
ex.) Tiger posters
 Polar Valentine Card:
In my
(see handout)
- 1 and in my r  4  4sin 
you are as lovely as a r  4cos2 !
In my eyes and in my heart
you are as lovely as a rose!
Miscellaneous
 Math Graffiti
(source: Denisse R. Thompson University of South Florida)
exponet
para
p
e
r
p
e
factor!al
e
oot
ndicular
Songs
 Commercial Sources:
 Bob Garvey (CD $19.95)
www.mathmadness.org
(to the tune of YMCA: y = mx + b)
 Alex Kajitani (2 CD’s each $24.99)
www.mathraps.com
(low level/middle school)
Songs continued
 Sources:
 on CD - Math Songs And Poems
(89 pages, 150 items)
 on CD - Poems for Teachers
(19 pages, 31 poems)
Songs continued
 Three of the songs I play in class:
 “Take it to the Limit” by the Eagles
(used with limit section)
 “Signs” by Five Man Electric Band
(used with sum, difference, double,
and half angle trig formula sections)
sign, sign everywhere a sign
 “The Good, the Bad, and the Ugly” the movie
Calculator fast draw used with this also
(used with sum and difference trig angle
formula section)
 The Good: puzzles i.e. identity proofs
 The Bad: sin(α+β)
 The Ugly: 5π/12
Songs continued
 Quadratic Formula Songs:
 “Pop Goes the Weasel”
 “Notre Dame Fight Song”
 “Frarajaka”
 “Happy Birthday”
 “Take Me Out to the Ballgame”
by Jim Warwick from WWSHS (see next slide)
Quadratic Formula Song
by Jim Warwick
Sung to the tune of “Take Me Out to the Ballgame”
Negative b plus or minus, the square root of b squared
(Take me out to the ballgame, take me out to the crowd)
Minus 4 times a times c
(Buy me some peanuts and Cracker Jack)
All over 2 times a
(I don’t care if I ever get back)
For there’s root root root in the numerator (point to the root sign)
(For it’s root root root for the game team)
If no b squared (point to b squared in the numerator), it’s a shame
(If we don’t win it’s a shame)
For there’s one two three terms in all in this old formula.
(point to the three terms)
(For it’s one two three strikes you’re out at the old ball game.)
Memorization Tricks
 SOH CAH TOA
Some old hag
Came a hoppin
Through our attic
Some old horse
Caught another horse
Taking oats away
Some old hairy (or heavy)
Cows are hairier (or heavier)
Than others are
Some old hippie
Caught another hippie
Tripping on acid
others?
Memorization Tricks
 SOH CAH TOA
Some old hag
Came a hoppin
Through our attic
Some old horse
Caught another horse
Taking oats away
Some old hairy (or heavy)
Cows are hairier (or heavier)
Than others are
Some old hippie
Caught another hippie
Tripping on acid
others?
Memorization Tricks continued

All Students Take Calculus
The letters ASTC signify the order of the trigonometric
functions to which of the functions are positive, starting in
the top right quadrant, and moving counterclockwise.
 In Quadrant I, A for All, all trigonometric functions are positive
 In Quadrant II, S for Sine, sine functions are positive
 In Quadrant III, T for Tangent, tangent functions are positive
 In Quadrant IV, C for Cosine, cosine functions are positive
Others:
 All Snow Tastes Cold
 A Smart Trig Class
 All Strippers Take Cash
source "http://en.wikipedia.org/wiki/All_Students_Take_Calculus"
Memorization Tricks continued

F A C T OR – find a common term or else…

Order of Operations
PEMDAS or Please Excuse My Dear Aunt Sally

Numerical Mnemonics
(Note: The number of letters in each word represents a digit.)

e Mnemonic (2.718281828)
“I’m forming a mnemonic to remember a function
in analysis.”

Pi Mnemonic (3.14159265358979)
“How I need a drink, alcoholic in nature, after the
heavy lectures involving quantum mechanics!”
*Find out who has Pi memorized the most places.
Memorization Tricks continued

Fred Foil or his sister Floi Foil
Guess and check factor: x2 + 5x + 6
F – First times First
L – Last times Last
O – Outside times Outside +
I – Inside times Inside
(x + 2 ) (x + 3 )
Check for Understanding Activities
• Step Forward & Take a Bow
1) Assign a number or figure to some students
ex. rectangle, square, rhombus, quadrilateral
2) Have them stand in front of room
3) Give clue
ex. Your diagonals are perpendicular.
If that student’s figure fits then they step
forward and take a bow.
Note: Can do with whole class but they remain
seated and stand when their item fits the
description.
Check for Understanding Activities
• Concentration Puzzle
Format: Groups or whole class using PowerPoint (see next slide)
Directions
1) One student is named “runner” for the team.
2) The runner picks up a problem and returns to the group where all group
members complete the problem on their worksheet.
3) The runner presents the solution to the teacher that gives the team the
next problem and a puzzle piece.
4) Repeat the process 8-12 times.
5) Groups must tape together their puzzle and write the phrase/sentence
depicted by the puzzle on the back of the paper.
6) All papers are collected and graded on correctness.
Modifications
1) Runners can be switched after each problem.
2) Penalty questions can be given for incorrect solutions that are presented
to the teacher.
3) Different number of questions for groups or different levels of puzzles.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
Check for Understanding Activities
• Concentration Puzzle continued
Answer: Britney Spears
Check for Understanding Activities
• Scavenger Hunt Directions
Around the room in random locations is an answer
to a problem and on the back side is the next
problem to be done. Make 2 copies of each to put
around the room. Students (in groups of 2) go to a
sheet and do the problem on the back side. They
then look around the room for the answer. Once
they find it they do the problem on the back side of it
and then look for that answer. You must plan it out
so each problem leads to an answer etc and the last
one loops back to the first one. Make 2 copies of
each so students do not just follow the group in front
of them and there is not a jam up at any one
problem.
Check for Understanding Activities
• Prize Show PowerPoint Directions
Pick a problem to work on. When finished, a prize
will be revealed. This is the prize you do not get.
The final prize is the one the class will receive.
Prizes include: Extra credit, candy, donuts, and
raffle tickets. However, some problems have no
prize!!
Candy
1.

Thumbs
Up
Nothing
2.
3.
A pop
4.
quiz!!
Stickers
5.  Donuts!!
6. 
A big smile
EC 
5 pts8.
EC  2 pts9.
7.

A pat on the
back
10.

Applause
11.

High Five
12.

Review
 Games
 Basketball:
 1 pt correct answer
 1 pt for basket made
(using a wiffle ball in wastebasket
from short distance away
- only get to shoot if question
answered correct)
 2 pts for long shot across the room
(only get to shoot if 1st shot was
made)
Review continued

Games continued

Millionaire

Jeopardy - on CD:
 Prealgebra (21)
 Algebra (2)
 Geometry (3)
 Algebra 2 / Precalculus (3)
best stuff\anyClass\MILLION.DOC
Review continued

Games continued

MATHO (on CD is an exel template that will make 36
random cards with the answers automatically filled in)
Directions: Pick any 25 of the answers in the slots below and put them on your MATH-O
card. Cross off each answer below as you use it, so you do not repeat any answers.
slope
3
y=x+1
y = 7x – 5
vertical perpendicular
2
y=x+1
–2
parallel
–1
zero
y=3
11
13
y-intercept
y=4
x=3
undefined
y=x
horizontal y = – 5x + 7 y = –2x + 3
-5
x =4
M A T H O
y = 2x + 3
My Favorite Problems / Worksheets
• Pythagorean Problem
(on CD)
(PreAlgebra, Algebra, or Geometry)
Take a long rope, tie it to the bottom of the goal post at one
end of a football field. Then run it across the length of the
field (120 yards) to a goal post at the other end. Stretch it
tight, and then tie it to the bottom of that goal post, so that
it lies flat against the ground. Now suppose that I add just 1
foot of slack to the rope, so that now I can lift it off the
ground at the 50-yard line. How high can I lift it up?
A. not high enough to fit my finger under it
B. just high enough to crawl under
C. just high enough to walk under
D. high enough to drive a semi-truck under
180.5 ft
?
?2 = 180.5 2 - 1802
180 ft
Surprise answer: D
It will be 13.43 feet high at the 50-yard line!
My Favorite Problems / Worksheets

Put steps in order (on web & CD best stuff\alg1\COMPSQR.DOC)
(used in Algebra completing the square or
Geometry proofs)
A) Original Problem
x2 + 3 = -4x
A) x2 + 4x + 3 = 0
A) x2 + 4x = -3
A) x2 + 4x + 4 = -3 + 4
A) (x + 2)2 = 1
A) x + 2 = ±1
A) x = -1 or x = -3
My Favorite Problems / Worksheets

Exponential / Log WS
(used in Algebra 2/Precalc)
(on website & CD: ..\best stuff\alg2PreC\logws2)
a) If Columbus invested 1¢ ($0.01) at 2% interest compounded
continuously with a Native American banker when he landed
in the 'New World', how much would be in the account today
rounded to the nearest cent?
0.01e(2009-1492)*0.02
answer: $309.46
b) If Columbus invested 1¢ ($0.01) at 4% interest compounded
continuously with a Native American banker when he landed
in the 'New World', how much would be in the account today
rounded to the nearest cent?
0.01e(2009-1492)*0.04
answer: $9,576,576.76
My Favorite Problems / Worksheets

Exponential / Log WS
(used in Algebra 2/Precalc)
(see handout and on web & CD: ..\best stuff\alg2PreC\drinking)
Answer the following using the website:
http://www.onlineconversion.com/bac.htm
Directions: For #1) - 4) below, use 2 hours for time drinking and use 4.5
for the % alcohol content.
The percent risk, R, of an auto accident can be found by: R = e21.4 b
where b is the blood alcohol percent level of the driver.
1) What is your weight?
2a) For 24 ounces (2 drinks) what will be your blood alcohol content ?
b) Calculate your percent chance of having an accident using the
formula
3a) For 60 ounces (5 drinks) what will be your blood alcohol content ?
b) Calculate your percent chance of having an accident
4a) For 96 ounces (8 drinks) what will be your blood alcohol content ?
(Note: Death from blood alcohol poisoning occurs at 0.4% to 0.5%)
b) Calculate your percent chance of having an accident.
My Favorite Problems / Worksheets

Biorhythms (used in Algebra 2/Precalc)
(see handout and on website & CD:
..\best stuff\alg2PreC\BIORHYTHM)
Based on the graphs of 3 sine functions answer questions
about when you will, within the next month, have the best or
worst day emotionally, intellectually , and physically
(maximum/minimum points).
Also find out when you will be accident prone, where the
physical graph crosses the horizontal axis.
Some people claim that biorhythm patterns can help you
make the best use of your time and energies and help avoid
potential problems by knowing your high, low, and critical
days. Others feel that by generating life-cycle data we are
creating a "self-fulfilling prophesy".
What is your position on this issue and why?
My Favorite Problems / Worksheets
• Lottery (see handout)
(used in probability unit)
A favorite problem from Lotto Worksheet 1:
(on website & CD: ..\best stuff\alg2PreC\lotto1)
If each of the combinations from the Illinois lotto 20,358,520 (52C6) - represents a penny and it takes
18 pennies to stack to be 1 inch then how many
miles will this answer be?
answer: 17.9 miles
My Favorite Problems / Worksheets

Directed Graphs WS
(used in Discrete Math/Precalculus)
(on website & CD: ..\best stuff\alg2PreC\directed)
High School Soap Opera:
Brenda
Gail
Faye
Abby
Eric
Debbie
Colleen
My Favorite Worksheets for All Classes

Glyph (used in statistics unit)
(see handout and on web & CD: best stuff\anyClass\GLYPHG)
hair length - hair length
reading - eye width
computer use - eye width
studying - eye height
phone use - ear height
watching TV - eye height
work - nose length
music - ear height
height - head height
eating - mouth width
talking to parents mouth length
weight training - neck width
socializing - shoulder length
weight - head width
My Favorite Worksheets for All Classes

An Exercise in "Logical" Thinking 2 WS
(see handout and on website & CD:
best stuff\anyClass\LOGIC1b.doc)
A favorite “logic” problem (#25 on handout):
Mary’s mother has a tendency to name her four
children after U.S. coins. Her first child was
named Quartaro (for quarters), the second child
was Dimetrius (for dimes), the third was Nicole
(for nickels), and the last child was named what?
Answer: Mary
My Favorite Worksheets for All Classes

A Number Game
(see handout and on website & CD:
best stuff\anyClass\ NUMBERSA.DOC)
ex.1) 60 = M in an H.
Answer: 60 = Minutes in an Hour
My Favorite Worksheets for All Classes

A Frame Game
(see handout and on website & CD:
best stuff\anyClass\ frames1.DOC)
school
decimal,
decimal,
decimal,…
high
school
repeating
decimal
L
L
I
I
N
N
E
E
L
L
I
I
N
N
E
E
parallel lines
square roots
Math Humor

Silly - Mom’s Proof (Geometry proof)
(on website & CD: best stuff\geometry\proofkey.doc)
Definitions: Time is Money
Money is the root of all Evil.
Given:
Teenage Girls = Time x Money
Prove:
Teenage Girls = Evil
Statements
Step 1: Teenage Girls = Time x Money
Step 2: Time = Money
Step 3: Teenage Girls = Money x Money
Step 4: Teenage Girls = Money2
also
Step 5: Money = Evil
Step 6: Money2 = Evil 2
Step 7: Money2 = Evil
therefore
Step 8: Teenage Girls = Evil
Reasons
the Given
by Definition
Substitution - steps 1 and 2
Arithmetic Substitution
by Definition
Algebra Property - squaring both sides
Simplification
Substitution - steps 4 and 7
Math Humor
Answer: Cross out the common n
Answer: You are on your own …
Math Jokes

If a math problem, that is too hard to
figure out by mental math, was given to a
constipated math student what did the
student do?
Answer:
The student worked it out with a pencil.

How is the homework procrastinating
math student like the butcher who backed
into the meat-grinder?
Answer:
They both got a little behind in their work.
Thanks
for
Attending!
Thanks for Attending!
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