Transcript A Family Reunion - Illinois Council of Teachers of Mathematics

By: Amanda Meiners
Western Illinois University
[email protected]
Illinois Weather
If today is zero degrees outside, and
tomorrow is predicted to be twice as
cold. How cold is it going to be?
A Family Reunion
One grandfather, one grandmother, two fathers,
two mothers, fours children, three grandchildren,
one brother, two sisters, two sons, two daughters,
one father-in-law, one mother-in-law, and one
daughter-in-law attended a family reunion. If both
halves of a relationship attended (i.e. the father and
the son), how many people showed up?
Grandmother
Mother In Law
Grandfather
Father In Law
Father
Son 1 Child 1
Daughters 1
Sister 1 Child 2
Mother
Daughter In Law
Son 2
Child 3
Daughters 2
Sister 2 Child 4
The Brain Games
• Based from a book: The Big Book of Brain Games by
Ivan Moscivich
• My version of the Hunger Games.
• Challenges that are more about thinking than math
all the time. Let students “play” with math ideas
without instructing them how to go about solving the
problem.
• Opens up the critical thinking and reasoning skills
students will need to use in the real world.
What is the level of math would you prefer
teach? Click all that apply
A. 6th grade
B. 7th grade
C. 8th grade
D. 9th grade
E. 10th grade
F. 11th grade
G. 12th grade
H. College and beyond.
0%
0%
0%
0%
0%
0%
0%
A.
B.
C.
D.
E.
F.
G.
0%
H.
How many homework problems do you plan
to assign each day?
17%
17%
17%
17%
17%
17%
A.
B.
C.
D.
E.
F.
I never assign any work outside of class.
1-5 problems
5-10 problems
10-15 problems
15-20 problems
20 or more problems a night
How much time do you expect students to
spend on their daily assignment?
A. 15 minutes
0%
B. 30 minutes
C. 45 minutes
D. 1 hour
E. 2 hours
A.
B.
C.
D.
E.
Common Core aligned materials
(Option 2)
Manga High
http://www.mangahigh.com/en_us/
Aligned to Common Core
Math based only
750 Prodigi and Games
Response to Intervention
Pros and Cons
Study Aid
Quizlet.com
www.quizlet.com
Free online/mobile device
Have 8 free classes
Self made OR use what's out there .
MTV (Math Television)
• Allow students to make their own (school
appropriate) math music video.
• Allows students to use the vast amount of math
vocabulary they have learned in a particular chapter,
unit, or year.
• ABC’s of Math
Twister Slope
• Bring the games students enjoy playing into class.
• Buy yourself a twister board and place real number values
on the spots.
• I had student keep the numbers positive if their right foot/ hand
was on the number. If their left foot/hand was on the number it
is a negative value.
• Composed a worksheet to help students walk through
the different ways to convert between the different types
of linear equations. (Algebra I)
• Could also use this idea when teaching students to
compose equations with particular zeros (Algebra II)
Where in the World is Variable Equation?
• Play on the shows we have/ students like
Carmen Santiago
• Allows students to learn while they are being
assessed under the multiple different equations
they will see.
• Build confidence in solving lots of equations
and having the option to come and ask the
“Chief” (teacher) questions as they arise.
Jeopardy Conics
• This is just one chapter this applies.
• Chapters with generalized ideas and/or lots of
formulas are great for this kind of review/
assessment.
• This can be interactive, you could even allow small
groups assess their knowledge.
Who Wants to be a Geo-iare?
• Millionaire.
• Able to work on formulas such as perimeter, area, volume,
Etc. building and building
• When using the template make sure you place the RIGHT
answer in the green box. It will not show up green initially in
the presentation, but if students get the answer right it will
show green then.
• Could also use to test proofs or any other math topics that
are more need to know
• Test math facts with powers and other items that students
need to know in High School
Other Game Shows Setups that are out
there.
• Family Feud
• Are You Smarter than a ____ Grader
• Deal or No Deal
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
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.
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.
Fold’m Eights
Fold the values up in a way so that when looked at read 1-8.
8 levels 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.
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
Magic Tables Continued
• 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.
CC: 7th grade
students solving real
life mathematical
problems
Thank you for coming!