Overview
Curator: Erica Skrip
Brief Description of Tech Tool:
This lesson is based on the Triangle Classification problem, in which students attempt to classify the triangles formed in a plane when a randomly selected point is connected to the endpoints of a given line segment. Offered by Illuminations, there is an online activity that allows students to grab and manipulate points in order to meet the criteria requested. The tool is accompanied by a triangle classification worksheet that asks students to complete the same type of exercise. This activtity allows students to think about many concepts related to triangles and to apply a diverse set of theorems. The ideas presented here can be used as the final lesson in a unit on triangles to summarize all that students have learned. Alternatively, the main problem from this lesson could be used as a final assessment activity for a unit on triangles.
Technical & Cost considerations: This learning activity can be found in the Illuminations collection offered by the National Council of Teachers of Mathematics. It is a free resource and available to the public, students, teachers, and parents. The activity tab of the lesson requires a flash player, a free download-able program for the device. The activity sheet is a pdf file, thus the device used must be capable of opening this type of file. This program should work on all devices in which a flash player is available. Further, it is great on the SmartBoard! (Assuming your SmartBoard is calibrated well). Students can work directly at the SmartBard and grab the points of the triangle.
Evaluation
Description of Learning Activity
According to the NCTM, the ideas presented in this acuity would best be used as a final lesson in a unit on triangles to summarize all that students have learned. Additionally, it could also be used as a final assessment activity for a unit on triangles. It is not suggested to be an introductory activity.
1. Learning Activity Types
- LA-Practice - Students could use this activity to increase their fluency in classifying and creating triangles. If the teacher uses the classification worksheet as an assessment tool, students could further use the activity tab of the learning tool to further practice prior to their assessment.
- LA-Present - N/A
- LA-Present-Demo - Students could use this tool as a learning activity that allows them to demonstrate their own learning, however it is not an activity to demonstrate new learning to the student.
- LA-Explore - This tool allows students to explore the effects of moving individual endpoints of a triangle. The tool does not allow students to explore new knowledge.
- LA-Apply - Students apply their knowledge of triangles and their classification properties in order to create the triangle(s) requested of the activity.
2. What mathematics is being learned?
Standards
CCSS:
- HSG.SRT.B.4 - Prove theorems about triangles.
- HSG.SRT.B.5 - Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
- HSG.CO.C.10 - Prove theorems about triangles.
- HSG.CO.D.12 - Make formal geometric constructions with a variety of tool and methods (... dynamic geometric software, etc.).
CCSS Mathematical Practices:
- Model with Mathematics
- Use appropriate tools strategically
- Attend to precision
- Look for and make use of structure
PSSM:
- Analyze properties and determine attributes of two- and three-dimensional objects.
- Establish the validity of geometric conjectures using deduction, prove theorems, and critique arguments made by others.
Proficiency Strands
- conceptual understanding - This tool allows students to demonstrate their conceptual understanding of the concepts.
- procedural fluency - This tool has an interactive activity component that students may use in order to increase their procedural fluency.
- adaptive reasoning - This tool would serve well as a tool of assessment. It allows students to create triangles and support their reasoning according to and use various triangular theorems. Students may be probed to explain and justify their work and conclusions.
Additional comments on what is being learned...
Students will:
- Identify points in the plane that, when connected to the endpoints of a given segment, form a specific type of triangle.
- Classify triangles according to sides (scalene, isosceles, equilateral).
- Classify triangles according to angles (right, acute, obtuse).
3. How is the mathematics represented?
The resource as a whole is a comprehensive interactive. The beginning of the tool provides an instructional plan designed for the teacher. The plan walks the teacher through what a lesson using this resource should look like. The NCTM suggests to the teacher to use this tool as a summative assessment for a triangular unit on classification.
As for the student, the lesson begins with an interactive activity where students are asked to create right and isosceles triangles. Students are to adjust the placement of endpoints A, B, and C by 'grabbing the point' and moving it around. While students move the endpoints, they can watch the various measurements of angles and legs change. Students are intended to move the endpoints in such a way to create the right or isosceles triangle while using the measurements tools to guide them. Using this activity, students can explore and practice the various correct solutions of the problem task. From there, the lesson offers an activity worksheet for students to complete. This activity sheet can be used as an assessment tool of students' overall understanding of the unit or an independent homework practice.
This activity appeals to the visual learner. It could also be argued that the lesson appeals to the kinesthetic learners as students are manipulating figures and creating geometric shapes using software, rather than in-hand manipulatives.
4. What role does technology play?
This tool allows students to instantly manipulate three endpoints, allowing for the creation of a limitless possibility of triangles. In doing so, students increase the amount of practice they receive as well as the options that they are able to analyze. The activity also offers tools that calculate the measurements necessary one would need in order to make decisions about the classifications of a triangle. The activity calculates the angle measures and leg lengths for students. Without the technology, these tasks are very time consuming and therefore reduces the number of problems in which a student could be exposed. This lesson is also beneficial because it gives students the opportunity to illustrate their understanding, something that appeals to the abundance of visual learners in many classrooms.
Affordances of Technology for Supporting Learning
- Computing & Automating - The activity offers tools that calculate various triangular measurements such as angle measures and leg lengths instantly in order to allow students to create their final product.
- Representing Ideas & Thinking - This tool allows student to visually represent their thinking and understanding of right and isosceles triangles.
- Capturing & Creating - This tool allows students to create various triangles by manipulating the three endpoints they are given A, B, and C.
5. How does the technology fit or interact with the social context of learning?
This tools can be used by an internet device that also supports the flash player required to use the activity. Although most activities can always be converted into partner work, this activity is best suited for individual work. It is not in a game or 'verse' format requiring more than one person and there is only one field of working while using the activity. Using this technological tool, teachers can monitor individual student understanding better than the collaborative work of more than one student. The activity itself doesn't promote the collaboration between individuals.
6. Additional Comments
This lesson also offers questions of reflection for students and for teachers and an extension application if so desired.