Polygons Galore

by Dana Johnson, Marguerite M. Mason, Jill Adelson

Polygons Galore! is a mathematics unit for high-ability learners in grades 3-5 focusing on 2-D and 3-D components of geometry by exploring polygons and polyhedra and their properties. The van Hiele levels of geometric understanding provide conceptual underpinnings for unit activities. The unit consists of nine lessons that include student discovery of properties of polygons and polyhedra, investigations for finding areas of triangles and quadrilaterals, study of the Platonic solids, and real-world applications of polygons and polyhedra. It also includes activities related to identifying, comparing, and analyzing polygons by using properties of the polygons; constructing meanings for geometric terms; developing strategies to find areas of specific polygons; identifying and building regular and nonregular polyhedra; and recognizing geometric ideas and relationships as applied in daily life and in other disciplines, such as art.

Grades 3-5

122 pages, Paperback

First published February 28, 2013

Reviews

[Nicole Hale · Rating 4 out of 5]

As the title indicates, this book provides curriculum with a tight focus on polygons, a topic in geometry. The lessons are intended for upper elementary learners, particularly gifted students. The book opens with a brief introduction, a glossary of geometric terms, and then dives into the lessons and assessments. Nine lessons cover a range of polygon manipulations, from classification to properties to perimeter and area. Quite a few lessons deal with determining the area of different polygons, actually. The final two lessons branch out into polyhedra, with the last one being a discovery of how these geometric shapes are manifested in the world outside the classroom. A preassessment test is presented before the lessons, and following the lessons is a parallel postassessment test.

The activities in the lesson are primarily inquiry based, with lots of engagement, while the teacher provides some scaffolding but allocates more time for students to explore the concepts and derive their own conclusions and formulas. For example, in the sequence of three lessons on area, the teacher begins by discussing the area of a rectangle, what it is, and why the formula works. From then on, students are encouraged to use their knowledge of the area of a rectangle to figure out the area of triangles, parallelograms, kites, and rhombuses. For the trickier shapes, like a rhombus, the lesson even indicates that deriving a formula is not necessary; more to the point is just understanding how to find an area, using the foundation knowledge they already have. All of the lessons ask students to use critical and higher order thinking skills to learn the whys behind the formulas, to figure out what is happening with these shapes, and what all the mathematical terms really mean. A good textbook should also do this, but the reason these lessons are specified for high-ability learners is because they don't provide as much scaffolding as would be needed for an average grade-level text; the students are given some simple instructions, a little bit of guided practice, and then are asked to explore on their own. The lessons assume that they will pick up the basic knowledge quickly and easily, and then be able to apply it to deeper levels of understanding. They are all great examples of differentiating instruction for students more advanced in math.

As a former teacher at the elementary level, I have seen several math curriculum books, and they had improved greatly by the time I was teaching. The series I used in my last year was also inquiry based, focused on guiding students to learning the concepts beneath the routine math formulas, and had a lot of fun lessons. In particular, geometry always had great lessons because it is such a fun topic for young learners. So I do not agree with the authors of this book that classroom curriculums simply ask students to memorize formulas and definitions. Maybe in the high school level. However, I do agree that these polygon lessons would successfully draw in students who are gifted in mathematics. This group of students can easily be overlooked in the classroom, because teachers have to focus so much on helping students who don't understand, and boredom and frustration start to set in. I would definitely use this book as a resource for students who need an extra challenge, or as a supplement to the curriculum, because the lessons are great. They might cover topics that are not addressed in the standard curriculum (it really depends on what curriculum is being employed). If a teacher wanted to use them for a whole class, she could easily provide extra guidance for those students who needed it. Also, this book is a good resource for parents who home school their children. The lessons are well-written, the pre- and postassessments accurately gauge the ideas taught, and the subject is one of inherent fascination for elementary learners. I find this a worthwhile book to add to a teaching library.