Frayer Model Sample

The Frayer Model was developed by Dorothy Frayer and her colleagues at the University of Wisconsin. This graphic organizer will lead students to a thorough understanding of new words. The corners generally include definition, facts or characteristics, examples and non-examples.

This is the modified template used in my math classroom. Based on the content, the example corner may include non-examples as well.

In order for students to communicate mathematically, they need a deep understanding of the content. Summarizing critical vocabulary via the Frayer Model can jumpstart this process.

This vocabulary graphic organizer highlights the Common Core State Standard 8.G.A.3 that is included in MATH-8 and Accelerated MATH-7.


Thinking Transformations

In grade 4, Common Core standards include lines of symmetry based on folding two-dimensional figures...not reflections. In grade 7, Common Core standards include scale drawings based on proportional relationships...not dilations. So unless our 8th grade students remember slide, flip, and turn from their elementary days or they were in a 7th grade classroom that reviewed transformations for the Benchmark last Spring, the knowledge bank will likely appear significantly different than in the past years.

Let's begin with the end in mind. Our students must describe a sequence of transformations in a set of congruent two-dimensional figures. This implies that students need to
  • perform each type of transformation on a coordinate plane
  • recognize when conditions prove congruence vs. similarity
  • know the structure of coordinate notation to describe the sequence

Perhaps we can still draw from the elementary experiences with real-life images that display transformations and provide the backdrop for building vocabulary. Next we can transfer that knowledge to the coordinate plane; beginning with one point and then extending to polygons. In the past, students seem to struggle most with rotations. A set of question cards (with answers) can be used with the Kagan structures Inside-Outside Circle or Quiz-Quiz-Trade. Or perhaps 1-2 pages could be copied and used with the Kagan structure RallyCoach. This set is versatile to provide you with individual transformation practice or the freedom to create a mixed set of question cards. The set you create could be used strategically for small group meetings or Seminar study sessions.

When extending to polygons, let's work towards building the concept of congruence and similarity. The following lab activity uses color tiles and a work mat. Students build a figure and perform a variety of transformations to observe the properties. The record sheet is included and can be completed in pairs with the Kagan structure RallyCoach.

The key to every activity is the questioning that helps students gain conceptual understanding. The Properties of Transformations activity builds the conditions for congruence vs. similarity as summarized in the following mind map.

While building the mind map together, we can discuss rigid transformations...definitions of congruence and similarity...review proportional relationships within similarity...the possibilities are endless! And the understanding of these properties enable students to be successful in identifying a sequence of transformations from a pre-image to the subsequent image. A variety of approaches are included in the following set of questions and can be used with the Kagan structure Showdown.

These activities highlight the Common Core State Standards 8.G.A.1, 8.G.A.2, and 8.G.A.3 that are included in Accelerated MATH-7, MATH-8, and 7th Grade Accelerated Algebra 1.

Does that help? What else do you need? Chat with each other...some of our teachers tackled these standards last year...tap into their expertise. Remember to adjust your filter! And be sure to share your thoughts in the comments below. {All thoughts invited...the good, the bad, and the ugly!}