Illuminations - Congruence Theorems
Curator: Sophia Borden
The applet has students pick three different components out of 3 sides and 3 angles and is asked to create two congruent triangles. It then asks students to create a triangle that is not congruent. The goal is to evaluate which sets of components work at always creating congruent triangles.
Grade Level: 7
PSSM Content Standard: Analyze characteristics and properties of two- and three- dimensional geometric shapes and develop mathematical arguments about geometric relationships.
CCSSM Content Standard: Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
Math Content: angles, triangles, triangle congruence theorems, congruence
Evaluation
What is being learned? What mathematics is the focus of the activity/technology? Is relational or instrumental understanding emphasized?
The user of the applet evaluates which sets of 3 components always create congruent triangles. Relational understanding is emphasized because of the applet’s exploratory nature instead of just telling the user which ones work and which sets do not work.
How does learning take place? What are the underlying assumptions (explicit or implicit) about the nature of learning?
The learning takes place mostly through exploration.
What role does technology play? What advantages or disadvantages does the technology hold for this role? What unique contribution does the technology make in facilitating learning?
The technology allows students to explore and evaluate which sets of three components make congruent triangles every time quickly.
How does it fit within existing school curriculum? (e.g., is it intended to supplement or supplant existing curriculum? Is it intended to enhance the learning of something already central to the curriculum or some new set of understandings or competencies?)
It can be used to supplement existing curriculum or supplant it depending on how it is used in the classroom.
How does the technology fit or interact with the social context of learning? (e.g., Are computers used by individuals or groups? Does the technology/activity support collaboration or individual work? What sorts of interaction does the technology facilitate or hinder?)
The technology may be used better if used by a group because the exploration and evaluation would may be better suited for group discussions.
How are important differences among learners taken into account?
The technology would help visual learners and learners that do better by actively engaging in activities as opposed to just reading or listening.
What do teachers and learners need to know? What demands are placed on teachers and other "users"? What knowledge is needed? What knowledge supports does the innovation provide (e.g., skills in using particular kinds of technology)?
Students need to know what makes two shapes congruent to each other.
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