Cabri Jr.: Exploring the Diameter and Circumference of a Circle

http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=6865

Students will be learning how pi is determined and its relationship to the circumference and diameter of a circle using a graphing calculator. Students will also be learning how to correctly graph circles, measure and draw a circle’s diameter, and measure a circle’s circumference using the Cabri Jr. program on the TI-84 calculator.

Geometry Hidden Picture

http://www.aplusmath.com/cgi-bin/games/geopicture

This technology is a geometry applet for students whose main goal is to identify geometric shapes based on their characteristics and properties in order to reveal pieces to a hidden picture. Students are successful when correctly identify the given geometric figures and they completely uncover the mystery picture that was hidden.

Pearson SuccessNet

http://www.pearsonsuccessnet.com

Pearson SuccessNet was created to assist both teacher in the classroom and for students at home. The site contains online videos that teachers can use in the classroom to introduce or explain a given concept (all secondary math concepts), while also providing students with online tutorials, videos, and practice problems that students can access from their home computer with a log-in identification. This program offers assistance to students who may need it outside the classroom, while providing technology to teachers inside the classroom. This is a pay site.

Online Resource Evaluations

Geometry Hidden Picture
http://www.aplusmath.com/cgi-bin/games/geopicture

Description
This technology is a geometry applet for students whose main goal is to identify geometric shapes based on their characteristics and properties in order to reveal pieces to a hidden picture. Students are successful when correctly identify the given geometric figures and they completely uncover the mystery picture that was hidden.

Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
- Geometry, 6-8: Students will be able to analyze characteristics and properties of two-dimensional shapes.

What is the nature of the mathematics?
The concepts being shown are analyzing the geometric characteristics and properties of two-dimensional shapes. Students are analyzing given shapes for specific characteristics and properties in order to successfully identify them by their geometric name.

How does learning take place?
Learning takes place as students try to identify the characteristics and properties of two-dimensional shapes. For example, if a student must find the shape of an obtuse triangle, students will have to analyze the given shapes for the properties and characteristics that are indicative of an obtuse triangle. Misconceptions can also be cleared up as students use the technology. If a student had the misconception that an equilateral triangle had only two congruent sides, by clicking an isosceles triangle students would be able to see that they were incorrect and had to fix their definition of what equilateral meant. Through analysis and reflection, significant learning can take place.

What role does technology play?
The technology affords students the chance to represent their geometric knowledge and thinking by identifying the correct properties and characteristics of two-dimensional shapes in order to reveal a hidden picture.

The technology will ask students to identify a particular geometric shape or characteristic (a right triangle, a radius, parallel lines, etc.). Students will then click on the shape they feel is best representative of what the applet is asking them to identify. If the student answers correctly, a piece of the missing picture is revealed. An incorrect answer by the student will result in another question and no piece revealed. The student “wins” when the hidden picture is revealed. Once completed, the technology offers many other hidden pictures for students to uncover in which they will have to identify even more geometric characteristics and properties.

How does it fit within existing school curriculum?
This applet is to be used as a supplement to a secondary geometry unit. This is not meant to teach students about the characteristics or properties of geometric shapes, but rather tests their knowledge. Thus this program can be used as an assessment piece for students to show their geometric knowledge. Older grades (late-secondary, high school) could use the program to review prior knowledge.

How does the technology fit or interact with the social context of learning?
This activity can be done individually or with a partner, depending on a teacher’s preference. As noted above, this applet can be of great use as an assessment piece for representing student knowledge, but it could also promote strong mathematical discussions about geometry if done in pairs. If a student misunderstood the meaning of an equilateral triangle, having a partner to work with would help clear up any misconceptions or confusions through social interaction. Also, pairing students who are struggling with the characteristics and properties of geometric shapes would be beneficial in allowing them to discuss answers together before making choices.

What do teachers and learners need to know?
Once the students discover the hidden picture, there is little replay value. While the technology offers students the opportunity to uncover a different picture, it does repeat a lot of the same geometric shapes. For instance, in the span of three games I had to identify a pentagon in all three games. For some students the reinforcement may be beneficial, but for most it will probably be repetitive and tiresome.

Cabri Jr.: Exploring the Diameter and Circumference of a Circle
http://education.ti.com/educationportal/activityexchange/Activity.do?cid=US&aId=6865

Description
Students will be learning how pi is determined and its relationship to the circumference and diameter of a circle using a graphing calculator. Students will also be learning how to correctly graph circles, measure and draw a circle’s diameter, and measure a circle’s circumference using the Cabri Jr. program on the TI-84 calculator.

Evaluation
What mathematics is (potentially) being learned?
NCTM Standard(s) addressed?
-Geometry, Grades 6-8: Students will use visualization (drawing geometric objects with specified properties) and analyze characteristics to understand relationships.

What is the nature of the mathematics?
This program allows students to discover the origination of the number, pi, through discovery-based learning. Using Cabri Jr., students must create a circle and manipulate the length of its circumference and diameter in order to examine the ratios that exist that show the originations of pi.

How does learning take place?
The learning takes place as students examine different measures of different circles and begin to explore the relationship between the diameters and circumferences of each. Students are also learning how to construct circles using a graphing calculator. In higher level math classes in high school and beyond many students will use graphing calculators regularly in their classrooms. It’s important that students not only know how to use the basic functions on a graphing calculator, but to also be able to explore some of the more advanced functions available.

What role does technology play?
The Cabri Jr. program offers two types of affordances of technology that support student learning. One is that it automates, simplifies, and transforms tasks. This is evident in the construction of circles, as well as the measuring of the diameter and circumference. Students do not have to spend time creating circles using compasses and measuring lengths with tape measures, as the task is done by the command of the student in the program. This also ensures accurate measurements and “perfectly” constructed circles by all students in the classroom. A second affordance is that Cabri Jr. represents knowledge and thinking. The Cabri Jr. program is on a graphing calculator, which allows students to display constructed circles, diameters, and measurements. Cabri Jr. provides the opportunity for students to show their abilities to create and measure circles, thus showing their knowledge of the properties of a circle, as well as their abilities to use Cabri Jr. and the graphing calculator effectively.

How does it fit within existing school curriculum?
This technology is not intended to replace any current technologies or curriculum designs. It is to be used by teachers and students as a resource for uncovering the derivation of pi, and therefore should be used by teachers and students as a supplement to an existing curriculum unit on geometry. It offers a new and different avenue for learning that is engaging and exciting for students, and could be useful for any secondary and high school classroom.

How does the technology fit or interact with the social context of learning?
This is an activity done individually, but does allow for some group collaboration in the sharing of data, results, and ideas. The technology is a tool used to promote learning, and it is the responsibility of the teacher to use the technology in the manner most beneficial to their particular classroom.

What do teachers and learners need to know?
There is an assumption that students are already familiar with the basic uses and functions of the graphing calculator (they know where the buttons are) and have worked in Cabri Jr. in previous classroom activities (This is not an activity intended for a class that has not used graphing calculators before). Students must also know relevant terms, like circle, diameter, circumference, pi, and measure. These are all terms that students have used in prior elementary grade levels, but may need refreshing before starting this activity.

What is also missing from the technology, however, is any sort of table or place to record results, make and write conjectures, and explore conclusions. This is something neither the website nor the technology provides, and is imperative to include with the lesson, as it is difficult for student learning to occur without careful examination of the relationships between multiple circles. The technology can only allow students to construct one circle at a time in its viewing window, and while it allows for the manipulation of that circle (the changing of its size), it does not allow multiple circles to be represented simultaneously. Because of which, a resource to record observations and data is needed. As stated in the PSSM, “With well-designed activities, appropriate tools, and teachers' support, students can make and explore conjectures about geometry and can learn to reason carefully about geometric ideas.” The Cabri Jr. technology offers an appropriate tool, but the teacher still needs to offer the support so students learning can occur and for the activity to be well-designed.