Description of Presentation Appropriate use of technology is an - PDF document

NCTM 2012 Presentation no video.notebook April 26, 2012 Preparing Smart Teachers to Teach with SMART TM Technology NCTM Annual Conference April 26, 2012 Philadelphia, PA Mary Lou Metz (mlmetz@iup.edu) Edel Reilly Francisco Alarcon Indiana University of PA Metz, Reilly & Alarcon 1

NCTM 2012 Presentation no video.notebook April 26, 2012 Description of Presentation Appropriate use of technology is an essential component of preparing pre­ service teachers to teach mathematics. We will share smart technology lessons, activities, strategies, and tools we have used in our work with pre­service mathematics teachers at the elementary, middle school, and secondary levels. Metz, Reilly & Alarcon 2

NCTM 2012 Presentation no video.notebook April 26, 2012 Agenda • Example from Geometry • Example from Algebra • Example from Number Theory • Example from Fraction Concepts Metz, Reilly & Alarcon 3

NCTM 2012 Presentation no video.notebook April 26, 2012 Examples from Geometry • Methods Course for PreK ­ 4 Education Majors • Lesson: Teaching Geometry concepts ­ Four NCTM content goals for geometry Shapes and properties Transformations Location Visualization ­ Five van Hiele levels of geometric thought 0: Visualization 1: Analysis 2: Informal Deduction 3: Deduction 4: Rigor Metz, Reilly & Alarcon 4

NCTM 2012 Presentation no video.notebook April 26, 2012 Shapes and Properties - Level 0 Click here to check your answer. Metz, Reilly & Alarcon 5

NCTM 2012 Presentation no video.notebook April 26, 2012 Metz, Reilly & Alarcon 6

NCTM 2012 Presentation no video.notebook April 26, 2012 Shapes and Properties - Level 1 Back to Geometry Goals Metz, Reilly & Alarcon 7

NCTM 2012 Presentation no video.notebook April 26, 2012 Transformations - Level 1 Click here to check your answer. • Reflect the shape across the x- axis. • Reflect the shape across the y-axis. Click here to check your answer. Back to Geometry Goals Metz, Reilly & Alarcon 8

NCTM 2012 Presentation no video.notebook April 26, 2012 Visualization - Level 0 Pentominoes Using 5 squares, make as many DIFFERENT shapes as you can. Each square must share a side with at least one other square. Click here to check your answer. Metz, Reilly & Alarcon 9

NCTM 2012 Presentation no video.notebook April 26, 2012 Metz, Reilly & Alarcon 10

NCTM 2012 Presentation no video.notebook April 26, 2012 Examples from Algebra • Grades 4 through 8 Algebra Course • Modeling the simplification of expressions. Distributive property Adding and subtracting polynomials Multiplying and factoring polynomials • Graphing equations Metz, Reilly & Alarcon 11

NCTM 2012 Presentation no video.notebook April 26, 2012 Distributive Property Use the same concept that was applied with multiplication of integers, think of the first factor as the counter. The same rules apply. 3( x + 2) x 1 Metz, Reilly & Alarcon 12

NCTM 2012 Presentation no video.notebook April 26, 2012 Addition and Subtraction of Polynomials 1. (x 2 + 2x + 1) + (x 2 ­ x ­ 4) x 2 x x 1 ­x ­1 ­1 ­1 ­1 x 2 Metz, Reilly & Alarcon 13

NCTM 2012 Presentation no video.notebook April 26, 2012 4. (2x 2 + 2) ­ (x 2 + 2x ­ 1) x 2 x 2 1 1 ­x x 1 ­1 Metz, Reilly & Alarcon 14

NCTM 2012 Presentation no video.notebook April 26, 2012 Substitution Algebra tiles can be used to model substitution. Represent original expression with tiles. Then replace each rectangle with the appropriate tile value. Combine like terms. 3 + 2 x let x = 4 x 1 Metz, Reilly & Alarcon 15

NCTM 2012 Presentation no video.notebook April 26, 2012 Multiplication Binomials­­Using Algebra Tiles (x + 3)(x + 2) x 1 1 1 x 1 1 x 1 x 2 Metz, Reilly & Alarcon 16

NCTM 2012 Presentation no video.notebook April 26, 2012 Make a collection of 2 big squares, 7 rectangles, and 6 ones. How many ways can they be arranged? Which set looks aesthetically pleasing (in a rectangle)? What are the dimensions of the rectangle? This will lead to factoring. x 1 x 2 Metz, Reilly & Alarcon 17

NCTM 2012 Presentation no video.notebook April 26, 2012 3. x 2 + 6 x + 8 x 1 x 2 Metz, Reilly & Alarcon 18

NCTM 2012 Presentation no video.notebook April 26, 2012 A rational function is a function f that is a quotient of two polynomials, that is, p(x) f(x) = q(x) where p(x) and q(x) are polynomials and where q(x) is not the zero polynomial. The domain of f consists of all inputs x for which q(x)≠ 0. y 2 1 x ­10 ­5 0 5 10 ­1 ­2 Metz, Reilly & Alarcon 19

NCTM 2012 Presentation no video.notebook April 26, 2012 y 2 1 x ­5 0 5 10 Metz, Reilly & Alarcon 20

NCTM 2012 Presentation no video.notebook April 26, 2012 y 30 20 10 x ­10 ­5 0 5 10 ­10 ­20 Metz, Reilly & Alarcon 21

NCTM 2012 Presentation no video.notebook April 26, 2012 Example from Number Theory • Introduction to Number Theory for secondary mathematics education majors • Lesson: introduction to divisibility and proof techniques Metz, Reilly & Alarcon 22

NCTM 2012 Presentation no video.notebook April 26, 2012 Some Other Number Theory Magicians Euclid Fibonacci Diophantus of Alexandria Carl Friedrich Gauss Euler Metz, Reilly & Alarcon 23

NCTM 2012 Presentation no video.notebook April 26, 2012 Metz, Reilly & Alarcon 24

NCTM 2012 Presentation no video.notebook April 26, 2012 Metz, Reilly & Alarcon 25

NCTM 2012 Presentation no video.notebook April 26, 2012 Onto some magic with numbers ... Metz, Reilly & Alarcon 26

NCTM 2012 Presentation no video.notebook April 26, 2012 Metz, Reilly & Alarcon 27

NCTM 2012 Presentation no video.notebook April 26, 2012 Was this really a magic trick? Is there a pattern you notice? Metz, Reilly & Alarcon 28

NCTM 2012 Presentation no video.notebook April 26, 2012 Metz, Reilly & Alarcon 29

NCTM 2012 Presentation no video.notebook April 26, 2012 Definition : An integer b is divisible by an integer a ≠ 0 if and only if b = a c for some integer c. Theorem : An integer is divisible by 9 if and only if the sum of its digits is divisible by 9 Metz, Reilly & Alarcon 30

NCTM 2012 Presentation no video.notebook April 26, 2012 Making a Video of the Class Class April 18 2011.wmv Metz, Reilly & Alarcon 31

NCTM 2012 Presentation no video.notebook April 26, 2012 Examples from Fraction Concepts Metz, Reilly & Alarcon 32

NCTM 2012 Presentation no video.notebook April 26, 2012 Smart Pen background Metz, Reilly & Alarcon 33

NCTM 2012 Presentation no video.notebook April 26, 2012 Fraction Concepts Task 1: = 1 = ? = ? Video of Task 1 Metz, Reilly & Alarcon 34

NCTM 2012 Presentation no video.notebook April 26, 2012 Metz, Reilly & Alarcon 35

Attachments fractions1.pdf