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Taking Risks in the New Frontier:
Rigor, Reasoning and Relevance
ATMIM Spring Conference
Worcester State University
Friday, March 24, 2017
SHAPE NUMBERS
GAMES HISTORY
Dr. Mary M. Sullivan
Rhode Island College (Ret.)
Take a risk:
Be square in
your math
classroom!
1
Dividing square regions
Separate the square region into a congruent pair by drawing a path connecting vertices from the 16
given. Paths are different if they produce different congruent pairs.
2
Latin Squares
Ken-Ken provides arithmetic clues as hints to the numbers to go in each square. Solve this puzzle.
Copy the values of your solution into the second grid. In the third grid, create a different set of Ken-Ken
clues. The values in the second grid should be the solution.
Grade level determines size of square and operations used. Create a 4 x 4 Latin Square or solve this Ken-
Ken puzzle to have one. Using the same values, create a different set of clues.
Sudoku Mini
3
Screenshots from iPad app 100! (Also iPhone version, 1010!) Goal is to complete rows and columns on the 10 x 10 grid, using pieces given
4
Checkerboard Paper
5
Checkerboard
6
Dissecting Squares:
Demonstrate how you can cut each square into 4, 5, 6, … squares. Describe your thinking process.
7
The area of Square A is 64 square units; the area of square B is 81 square units. Determine the
dimensions of FIND.
Dissecting Squares
A B F I
D N
8
Magic Squares: sum of each row, column, and diagonal is the same “magic constant.”
2 7 6 4 14 12
b g f
9 5 1 18 10 2
i e a
4 3 8 8 6 16
d c h
a b c d e f g h i
b + g + f =
d + c + h =
b + i + d =
f + a + h =
b + e + h =
f + e + d =
i + e + a =
g + e + c =
A prime number has exactly two factors: itself and 1. See if you can construct magic squares that
contain from 1 to 8 prime numbers.
10
11
References and Resources
Complex Instruction (Smarter Together)
Boaler, Jo. (2016). Mathematical mindsets: Unleashing students' potential through creative math, inspiring messages and innovative teaching. San Francisco, CA: Jossey-Bass Publishers.
Cohen, E. G., & Lotan, R.A. (Eds.) (1997). Working for equity in hetereogeneous classrooms: Sociological
theory in practice. New York: Teachers College Press.
Cohen, E. G., & Lotan, R.A. (2014). Designing groupwork: Strategies for the heterogeneous classroom, Third Edition. New York: Teachers College Press.
Featherstone, H., et al. (2011). Smarter Together! Collaboration and Equity in the Elementary Math Classroom. Reston, VA: National Council of Teachers of Mathematics.
https://ww2.kqed.org/mindshift/2016/05/23/how-a-strengths-based-approach-to-math-redefines-who-is-smart/
http://cimath.org/
Mathematics
Kenney, M. J., Bezuszka, S.J., & Martin, J. (1992). Informal geometry explorations. Palo Alto, CA: Dale Seymour Publications.
Kenney, M. J., & Bezuszka, S.J. (2015). Number Treasury3. Singapore: World Scientific Publishing Co.
Article on dissecting squares into squares of different sizes
http://celebrationofmind.org/archive/miller-squares.html
Constructing Latin Squares of order 4
https://en.wikipedia.org/wiki/Small_Latin_squares_and_quasigroups#Order_4
Tasks sources
https://www.youcubed.org/tasks/
http://www.celebrationofmind.org/
http://cimath.org/more-information/
Tricks for squaring numbers
Compare Pankaj Rattan’s https://www.youtube.com/watch?v=aiwLSm9KHUI
with this one https://www.youtube.com/watch?v=mdsqHAIHlyA
