Take a risk: Be square in your math classroom! · Mathematical mindsets: Unleashing students'...

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.)

marymsullivan@comcast.net

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