Math Mammoth Geometry 1

117 pages
(includes answers)

Sample pages (PDF)
Contents
Review: Area of Rectangles Measuring Angles
Triangles
Classifying Quadrilaterals 2
Volume

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Este libro en español

Math Mammoth Geometry 1 covers all the typical geometry topics for grades 4-5: angles, triangles, quadrilaterals, other polygons, area, perimeter and volume.

The book starts out by reviewing the third grade concepts of area and the perimeter of rectangles. Students also apply these concepts in various problems, including problems where they write simple equations and a problem where they explore all possible perimeters for a given area.

The first part of the book covers 4th grade topics, with a focus on angles. Students learn about lines, rays, and angles; and about acute, right, obtuse, and straight angles. They learn how to measure and draw angles with a protractor. We also study angle problems where students write simple equations. The lesson Estimating Angles has an optional section on turning in an angle, which can be challenging, so feel free to omit it if you wish.

The lesson Parallel and Perpendicular Lines also ties in with the topic of angles, because two lines are perpendicular if they form a right angle. After that, we study parallelograms and other quadrilaterals in more detail, paying attention to their angles and lengths of sides.

We also study triangles and classify them according to their angles (acute, obtuse, or right triangles). The last (and easy) topic in the first part of the book is line symmetry.

The latter half of the book covers 5th grade topics, starting with the lesson Review: Angles. The focus of this portion is on two topics: classifying two-dimensional shapes, and volume.

The lesson Polygons covers the concept of a polygon and the names of several common ones. Students classify figures into polygons and non-polygons, and also into regular polygons versus non-regular polygons.

The next topic is classifying quadrilaterals. The focus is on understanding the classification, and understanding that attributes defining a certain quadrilateral also belong to all the “children” (subcategories) of that type of quadrilateral. For example, squares are also rhombi, because they have four congruent sides (the defining attribute of a rhombus).

A possible confusion point is the definition of a trapezoid. There exist two possible definitions:

• (Exclusive definition:) A trapezoid has exactly one pair of parallel sides.
• (Inclusive definition:) A trapezoid has at least one pair of parallel sides.

Both definitions are legitimate, but lead to different analysis when classifying quadrilaterals. Under the exclusive definition, a parallelogram is not a trapezoid, but under the inclusive definition, it is. Most college-bound textbooks favor the inclusive definition, and that is what is used in this text, also.

Then we study the classification of triangles. Students are now able to classify triangles both in terms of their sides and also in terms of their angles.

The second focus topic of this latter half is volume. Students learn that a cube with the side length of 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. They find the volume of right rectangular prisms by “packing” them with unit cubes and by using formulas. They recognize volume as additive and solve both geometric and real-word problems involving volume.

The book includes three optional lessons listed in the end: area and perimeter problems, star polygons, and circles. Use them as time allows. The lesson on area and perimeter can be important for those students who tend to forget these concepts. The lesson on star polygons is intended as a fun artistic topic. The lesson on circles involves the usage of a compass, which may be hard for some children at this age. Those who can master it will probably find the exercises involving multiple circles fascinating.

Geometry is a hands-on subject, and thus the lessons include quite a few drawing exercises which can be done on blank paper, in a notebook, or in the worktext (for most). I hope the students enjoy the hands-on experience. Besides, these drawing exercises are a good means of achieving a true conceptual understanding of geometry concepts.

Geometry is full of strange-sounding words. I suggest that student(s) keep a geometry notebook, where they draw picture(s) and text to explain every new concept or term. This will help them to remember those terms. They can also do the drawing exercises in the notebook. Encourage the students to be creative so that the notebook becomes their own special work. You can even give them credit for it.

Please see also the videos at https://www.mathmammoth.com/videos/geometry_1. Most of them match the topics in this book, and can be used to provide additional instruction.

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.

Feedback

See also the review by Sol Lederman.