Wednesday, August 9, 2017

Math Dice Games for Factors and Multiples GCD LCM

Games of chance are a fun way to learn arithmetic.  Here are four games that I use to teach properties of factors, multiples, greatest common factors (GCFs), and least common multiples (LCMs). In each case, play the game a few times, and try to work with the other players to determine the best winning strategies. I want to emphasize this last point.  If you are going to take the time to play these games, it's important to reflect on the mathematics underlying them. Understanding why the winning strategies are what they are will shed a lot of light on the nature of factors and multiples and the relationship between these two ideas.

Each game requires dice, pencil, and paper.  If you don't have the required dice on hand, you could buy a 7-die standard set, and in the mean time, you can use a cut deck of playing cards, or even put numbers on scraps of paper and pull them from a hat.

1. Zonk Game:

Set up: Each player makes their own board of 16 numbers.
The numbers are chosen from the factors of the numbers 1 through 12.
You can repeat factors as often as you like.
For example, a game board can look like this:
1  1  1   2
2  2  3   3
4  5  6   7
8  9  11 12

Play: Roll 1D12 (in other words, roll one 12-sided die or pick a card from Ace to Queen).
Each player crosses out all of the factors of the roll that they have on their board.  For example, if the roll is 9, each player crosses out one of each of 1, 3, and 9 on their board. In the board above, the player would cross out one 1 and one 3.

Goal: First player to cross out all numbers on their board wins.

2. Zink Game:

Set up: Each player makes their own board of 16 numbers.
The numbers are chosen from the multiples of the numbers 1 through 6.
You can repeat numbers as often as you like.
For example, a game board can look like this:
1     2     3    4
5     6     6   6
10  12  14  15
16  25  30  30

Play: Roll 1D6.
Each player crosses out all of the multiples of the roll that they have on their board.  For example, if the roll is 3, each player crosses out one of each multiple of 3 on their board. In the board above, the player would cross out 3, 6, 9, 12, 15. 30. 60. and 120.

Goal: First player to cross out all numbers on their board wins.

Question: Is it possible to win the game on the first roll?


3. Zonker Game:

Set up: Each player makes their own board of 5 numbers.
The numbers are chosen from the number of factors of the numbers from 1 through 100.
You can repeat numbers as often as you like.
For example, a game board can look like this:
1  2  2  3  5

Play: Roll 2D10 to make a number from 1 to 100.
Count the number of factors of that number.  Each player crosses out that number if they it have on their board.  For example, if the roll is 25, then 25 has 3 factors (1, 5, and 25). So, each player crosses out the number 3 on their board, if they have it. If the roll is 29, then each player can cross out a 2 because 29 is prime, and prime numbers have exactly 2 factors.

Goal: First player to cross out all numbers on their board wins.

Questions: How many rolls have 1 factor? How many rolls have 5 or more factors?  


4. GCD Times LCM Game:

Play: Roll 2D12 to get numbers x and y.
Find GCD(x,y) and LCM(x,y).
Multiply them to get your score.
Players alternate turns.

Bonus points: If GCD times LCM equals x times y, then take a bonus 99 points.

For example, if the rolls are 3 and 4. then GCD = 1 and LCM = 12.  1 times 12 equals 12, so the score is 12.  Also 1 times 12 equals 3 times 4. So this roll gets a 99 bonus for a total of 111 points.

Goal: First player to 1000 points wins.

Question: Which rolls give the bonus points?

Sunday, November 8, 2015

Math Inspiration for the Curious (and the not so curious)

Do you have a curious child that wants to explore math beyond the classroom?  Do you have a smart child that is unmotivated by their math class? Does your child just need some extra help with their math homework?  My goal is to teach the beauty and wonder of mathematics to your child from preschool through calculus. No matter their grade level or ability, your children can learn more mathematics than they get in their classes at school. Your child and I can work directly from any math book, I can create tailored math lessons for your child, or anything in between. If your child likes math and wants to learn more, she should learn all the cool fun bits that got weeded out of the curriculum. (Yes, algebra is FULL of cool fun bits!) If your child is under-achieving in math right now, he could be learning from lessons that tap directly into his strengths and interests. 

How do I do these things? I am a former Cal Poly (SLO) Mathematics Professor with a Ph.D. in Mathematics Education and an M.S. in Mathematics. I worked in mathematics classrooms in public schools and universities for 15 years. My specialty as a professor was the mathematical education of teachers. I taught math, and I taught people how to teach math. I have worked with a couple thousand students and hundreds of teachers. I am also an accomplished mathematical artist, and I use art as a way of exploring mathematical ideas.

Why Do I love Teaching Math?
My entire life, I have explored in the wonder and beauty of mathematics, and my goal is to inspire that wonder people around me. Math is fascinating and beautiful, and I love watching students’ faces light up when they learn something new. Your child can learn far more math than their classes and textbooks teach them. My challenge is to learn about your child and craft lessons to fit their specific needs and skills. I especially enjoy applying math to the visual arts and making beautiful and instructive things. In addition to doing their homework, your child can learn that same math through paper folding and cutting, manipulating blocks, toys, games, fabric, beads, felt, and even cookie dough. Math can be very engaging when you know how to do it.

Process for Working with New Customers
When meeting a new student, the first thing I try to do is learn about them and what their goals are. I ask questions to learn what interests and motivates each student. For example, does your child like to play games? I can design games so he will role dice, count blocks, and move markers. Does she like making things with her hands? We can fold and cut paper or sew things. Does he like to move around a lot? We can move while we do math.

Once I understand your goals, together, we solve math problems.  We can work from any math book you want, or I can develop lessons for you. While we do math problems together I watch and listen carefully to assess what your child already knows and is able to do. We will communicate through words, symbols, graphs, tables, equations, or whatever is relevant to the math at hand. Your child and I will build mathematical objects with our hands and in our minds. Your child can learn through custom math lessons that suit their needs, interests, and abilities.

My goals are that your child learns how to solve problems, organize their thinking, and if you desire, clearly present their ideas on paper. Your child can become fluent in calculating, learn number sense, and improve their grades in school.

I build relationships with my students and their parents. I am very patient, and I have successfully worked with many students with disabilities including ADD, ADHD, ASD, dyslexia, and vision disorders.

Qualifications
*Tenured Professor of Mathematics at Cal Poly State University, SLO (2001-2007)
*Ph.D. in Curriculum & Instruction (Mathematics Education)
University of Wisconsin, Madison (2001)
*M.A. in Mathematics
University of California, Santa Barbara
*Associate Editor, Journal of Mathematics and the Arts (2007-present)

Invited talks
*MoMath (The National Museum of Mathematics)
*Gathering 4 Gardner
*Meetings of the Mathematical Association of America 
*Bridges Meetings
*Meetings of the Minds
*Julia Robinson Math Festival

I am a leader in mathematical art, both as an innovator and evangelist.

I have 15 years of math classroom teaching experience in public schools and universities in California and Wisconsin.  I have taught complete courses across the entire school mathematics curriculum including arithmetic, pre-algebra, algebra, geometry, trigonometry, pre-calculus, calculus for engineering, calculus for business, introduction to proofs, math for elementary school teachers, math for high school teachers, teaching methods for high school math teachers, and math and visual art.  

Rates
Please inquire about my hourly and half daily rates. I can drive to your home or I can teach your child at my home in Sunnyvale, California.  I can travel anywhere in the San Francisco Bay Area, including Sunnyvale, San Jose, Cupertino, Santa Clara, Hillsborough, Mountain View, Palo Alto, Saratoga, Los Gatos, Los Altos, Fremont and other towns in the vicinity.

Contact
Gwen Fisher gwen [at] beadinfinitum [dot] com 

References
Available upon request