1. A Review of the Best Pre-made Interactive GeoGebra Activities Dr. Carol A. Marinas Barry University Miami, Florida Dr. Joseph M. Furner Florida Atlantic University Jupiter, Florida 28 th International Conference on Technology in Collegiate Mathematics Atlanta, Georgia USA March 12, 2016 Copyright 2016 Carol A. Marinas, Joseph M. Furner

2. Can you identify the US City where these photos were taken? Can you see some mathematical idea within the photo? Starters Problems Two-minute Math Starters Starters Problems Two-minute Math Starters Copyright 2016 Carol A. Marinas, Joseph M. Furner

3. Using Daily Images to Teach Math Munakata and Vaidya (2012) based on their research found that students do not consider mathematics and science to be creative endeavors, though the traditional artistic disciplines rank high in this regard. To address this problem in perception, the authors used photography as a means to encourage students to find the deep-rooted connections between science and mathematics and the arts. The photography project was used in a formal classroom setting as well as an outside activity, i.e. in a more informal setting. The project found student interest and motivation were peaked when photography was part of the instructional strategies to teach new material while making meaningful connections to the math using the photography. Munakata, M., and Vaidya, A. (2012). Encouraging creativity in mathematics and science through photography. Teaching Mathematics and Its Applications: An International Journal of the IMA, 31(3),121-132. Copyright 2016 Carol A. Marinas, Joseph M. Furner

4. Connecting Math and Real-World Images Copyright 2016 Carol A. Marinas, Joseph M. Furner We, as educators, believe that GeoGebra can provides that visual connection!

5. Relating and understanding real- world problems through the use of interactive technology like GeoGebra and connecting them to photography to make important connections in math and make learning more meaningful for learners. Relationships between Real-World Applications, Mathematics, & GeoGebra Relationships between Real-World Applications, Mathematics, & GeoGebra Copyright 2016 Carol A. Marinas, Joseph M. Furner

6. GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus in one easy-to-use package. http://www.geogebra.org/cms/en/info Copyright 2016 Carol A. Marinas, Joseph M. Furner GeoGebra

7. It is important we encourage our learners to recognize that geometry and shapes/mathematics surround us! “Of all of our inventions for mass communication, pictures still speak the most universally understood language.” --- Walt Disney Company What Math do you see in these Photos? One can insert all of these images into GeoGebra and then draw the math relationships on top of the images. Copyright 2016 Carol A. Marinas, Joseph M. Furner

8. Using PreMade GeoGebra Activities in the Teaching of Mathematics For this presentation, we reviewed many GeoGebra GGB files. We chose files for a variety of grades. We covered a wide variety of Math Standards (CCSS). We selected ones that were appealing and user-friendly for teachers and students. Copyright 2016 Carol A. Marinas, Joseph M. Furner

9. Integers Copyright 2016 Carol A. Marinas, Joseph M. Furner Walking Integers CCSS.MATH.CONTENT.6.NS.C.6.A Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.

10. Decimals Copyright 2016 Carol A. Marinas, Joseph M. Furner Decimal Order CCSS.MATH.CONTENT.4.NF.C.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

11. Fractions Copyright 2016 Carol A. Marinas, Joseph M. Furner Adding Fractions CCSS.MATH.CONTENT.3.NF.A.3.B Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3. Explain why the fractions are equivalent, e.g., by using a visual fraction model.

12. Coordinate Geometry Copyright 2016 Carol A. Marinas, Joseph M. Furner Graphing Points CCSS.MATH.CONTENT.4.G.A.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.

13. Algebra/Slope Copyright 2016 Carol A. Marinas, Joseph M. Furner Slope of a Line CCSS.MATH.CONTENT: 8.EE.B.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. CCSS.MATH.CONTENT.8.F.A.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

14. Algebra/Solving Equation Graph Copyright 2016 Carol A. Marinas, Joseph M. Furner Solving Systems of Equations CCSS.MATH.CONTENT.HSA.CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. CCSS.MATH.CONTENT.HSA.REI.C.6 Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

15. Probability Copyright 2016 Carol A. Marinas, Joseph M. Furner Bag of Marbles CCSS.MATH.CONTENT.7.SP.C.7.A Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl will be selected.

16. Probability and Statistics Copyright 2016 Carol A. Marinas, Joseph M. Furner Roll the Dice CCSS.MATH.CONTENT.7.SP.C.8.B Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., "rolling double sixes"), identify the outcomes in the sample space which compose the event. CCSS.MATH.CONTENT.6.SP.B.5.D Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered.

17. Statistics/Measures of Central Tendency Copyright 2016 Carol A. Marinas, Joseph M. Furner Measure of Center CCSS.MATH.CONTENT.6.SP.B.5.C Giving quantitative measures of center (median and/or mean) and variability (interquartile range and/or mean absolute deviation), as well as describing any overall pattern and any striking deviations from the overall pattern with reference to the context in which the data were gathered.

18. Similar Triangles Copyright 2016 Carol A. Marinas, Joseph M. Furner Similar Triangles CCSS.MATH.CONTENT.HSG.SRT.A.2 Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

19. Pythagorean Theorem Copyright 2016 Carol A. Marinas, Joseph M. Furner CCSS.MATH.CONTENT.8.G.B.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. Pythagorean Theorem

20. Trigonometry/Unit Circle Copyright 2016 Carol A. Marinas, Joseph M. Furner Ferris Wheel CCSS.MATH.CONTENT.HSF.TF.A.2 Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

21. Parabolas Over the past several years, we developed many GGB Files to teach math. This year we wanted to explore existing pre-made GGBs that teachers can use to cover many math topics and show where to find them on the Internet. Parabolas Over the past several years, we developed many GGB Files to teach math. This year we wanted to explore existing pre-made GGBs that teachers can use to cover many math topics and show where to find them on the Internet. Copyright 2016 Carol A. Marinas, Joseph M. Furner Parabolas Parabolas (Our ggb file we created) CCSS.MATH.CONTENT.HSG.GPE.A.2 Derive the equation of a parabola given a focus and directrix. http://www.intmath.com/blog/mathematics/is-the- gateway-arch-a-parabola-4306

22. Cover the CCSS while using technology Make connections and relationships between math concepts and real-world examples Employ emerging technologies in math with the real world in class Show practical applications to math in life Employ innovative teaching in the classroom Stimulate excitement through images to understanding mathematics Use existing materials that make it easier for the instructor In Summary… Why is it important to use these GeoGebra files and activities? In Summary… Why is it important to use these GeoGebra files and activities? Copyright 2016 Carol A. Marinas, Joseph M. Furner

23. Intrigued by technology, learners will construct and investigate geometric shapes and math ideas with GeoGebra. They will start enjoying math and even see connections to their environment! Teachers can use pre-made GeoGebra ggb files to teach math and they do not need to reinvent the wheel! Copyright 2016 Carol A. Marinas, Joseph M. Furner Having Fun with GeoGebra Santa Fe & Niagara Falls (Horseshoe Falls)

24. Now it is your turn to create or use a GGB! Consider creating GeoGebra files (ggb’s) to share on the GeoGebra Materials page for other math educators to use for teaching their students! As professionals, we create and share with each other for the sake of our students to help them learn math! GeoGebra is free, the resources are free, and it is now one of the best teaching tools to use to teach math to our young people, consider using it! Copyright 2016 Carol A. Marinas, Joseph M. Furner

25. Think about... One idea you gleaned that you can use in your classroom! \\ PowerPoint: http://matharoundus.comhttp://matharoundus.com Mathitudes: http://www.coe.fau.edu/centersandprograms/mathitudeshttp://www.coe.fau.edu/centersandprograms/mathitudes Contact Information: Dr. Carol A. Marinas drmarinas@yahoo.com Dr. Joseph M. Furner jfurner@fau.edu Questions and Answers Copyright 2016 Carol A. Marinas, Joseph M. Furner