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Math Mammoth Geometry 1 Workbook

134 pages
(of which 93 are lesson pages)
Price: $7.00 download

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Sample pages (PDF)
Contents
Measuring Angles
Triangles
Quadrilaterals
Circles
Area of Rectangles
Area of Triangles

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Math Mammoth Geometry 1 gives the student a thorough view of basic plane geometry. The topics suit best 4th-6th grade mathematics. The emphasis is on learning through drawing.

The problems in this book involve lots of drawing. Geometry is a “hands-on” subject, and many children like that. Moreover, drawing is an excellent means of achieving the conceptual understanding that geometry requires. Exercises marked with a notebook symbol are meant to be done in the student’s notebook or on blank paper.

The study of geometry is also full of strange-sounding words to learn. I encourage you to get the student (s) started with a geometry notebook, where they will write every new concept or term, and draw a picture or pictures and text to explain the term. This notebook will then be their own creation, and while working with it, the terms also will stick better in their memory. The students could also do the drawing exercises in this book, or just keep it as a terminology notebook, either way.

The lessons in the book

The first lessons concentrate on angles. Students are introduced to the concept of an angle, and learn about acute, right, obtuse, and straight angles. Students learn how to measure angles with a protractor, and estimate some common angles.

After angles, we study various shapes: triangles, quadrilaterals, polygons, and circles.

Students are now able to classify triangles both in terms of their sides and also in terms of their angles. The lesson has several drawing problems and one easy compass-and-ruler construction of an equilateral triangle.

Then we go on to study the seven different terms used for classifying quadrilaterals. Many textbooks concentrate only on learning the vocabulary, but I have also included several problems that require some thought and even one construction, that of a rhombus. I feel just learning the words—“rhombus,” “trapezoid,” “kite,” and so on—is nearly meaningless unless students can also do something with the figures, such as calculate their areas, find their angles, and reason about their properties.

In the lesson about circles, we learn the terms circle, radius, and diameter. Students draw circles and circle designs using a compass.

In the middle of the book, there is a brief section about congruent and similar figures. These lessons are introductory, as these topics will be studied more later.

Then follow several lessons that focus on calculating areas, beginning with the area of a right triangle, which is always half of the area of the corresponding rectangle. Once students learn to calculate the area of a parallelogram and realize that the principle applies not just to right triangles and rectangles, but that the area of any triangle is always half of the area of the corresponding parallelogram, then they can split any polygon into triangles and thus find its area.

In the last major section of the book, we study certain aspects of common solids: the volume of a rectangular prism, surface areas of some solids, and nets of common solids. (Printable pages of some of the nets are included also.)

The volumes of round-shaped solids, such as cylinders, cones, and spheres, are not studied until middle school, as students first need to study the concept of pi (3.1416...) and its relation to the area of a circle. Another limitation is that students cannot yet find the altitude of the triangle from only the lengths of its sides because that requires the Pythagorean Theorem. Because of these limitations, students cannot yet calculate the surface area or volume of most solids, and these calculations are therefore limited here to certain solids only.

Feedback/ reviews

I teach special education in the public school system, and just recently downloaded and have taught from Geometry 1. My middle school students love the hands-on approach and have really begun to explore the meaning of geometric terms and measurements through the use of this book. We have expanded it to include a project whereby they create designs using angles, arcs, and circles. We will be using these colorful designs to learn even more about measurements and geometric figures in conjunction with some of the lessons from the book. Thanks so much for opening up this opportunity to make math useful and fun for these students who often view math as a painful process they have to endure! Their attention to their drawings is truly amazing! We have all enjoyed the process!
Susan Medendorp
18 November, 2008

From a tutor who has used Geometry 1 with 3rd and 4th graders:

I used, and continue to use your Geometry 1 workbook as my main geometry curriculum. I use Math Advantage as a basis for my math lessons but skip around and supplement it greatly.

My son enjoys the Geometry workbook. I appreciate that you have included area, perimeter and volume in the book. Many books categorize those topics as measurement, but I've found that it is easier to teach them with geometry. The curriculum is more in depth than most for the recommended grade level.

Tracy Thompson
7 June, 2008

From a parent who has used Geometry 1 with a 4th grader:

This book is quite good for building fundamental knowledge for children who are learning geometry. This is more than enough, comparing mine when in same grade 30 years ago.

Regards,
Slamet Suryanto

From a teacher who used Geometry 1 with 7th graders:

My students enjoyed the review!

Prudence Jencka

See also a review of Geometry 1 book by Sol Lederman.

Contents and Samples

The lesson Lines, Rays, and Angles concentrates on the concept of angle and how to tell which angle is 'bigger'. You can show the student with two pens how the angle opens and gets bigger. You can also use longer pens, etc., and demonstrate how the measure of the angle does not depend on the size of the sides but instead of "how much it has opened" or how much of the arc of the circle it has drawn.

Measuring Angles (sample) is a simple lesson teaching how to measure and draw angles with a protractor.

Parallel and Perpendicular Lines not only explains these terms, but also studies angles formed when a line intersects two parallel lines. We arrive at parallelograms and learn something about its angles.

The lesson on Triangles (sample) classifies them according to angles (acute, right, or obtuse triangles). This lesson has lots of drawing exercises. In particular, the problems about copying a triangle prepare the student for the (high school level) concepts of congruency tests.

Angles of a Triangle is a simple lesson about the angle sum in a triangle. The picture shown actually proves the sum to be what it is.

Triangles can also be classified according to their sides, and the next lesson on Equilateral and Isosceles Triangles does just that. Again there is a lot of drawing to do.

Quadrilaterals (sample) lets the student explore the seven different kinds of quadrilaterals first by drawing various kinds. Then, the angle sum of a quadrilateral is studied. The lesson also has a quadrilaterals puzzle that stretches the mind about their attributes.

Polygons 1 has easy problems geared more towards 3rd grade, and lesson Polygons 2 continues the topic. Polygon Tilings is a fun, simple lesson with possibility for creativity.

Circles lesson (sample) concentrates on the concept itself, not on any calculations, and contains many drawing exercises where the student needs to understand the relationship between the radius and the diameter. A few of the problems here are actual geometric constructions.

Congruent Figures briefly explores this concept. Then we go onto Similar Figures as a contrast. Again plenty of drawing problems are supplied.

Symmetry (sample) is a fairly simple lesson. After that, we study Congruent Transformations and the basics of translation, reflection, and rotation.

The last part of the book has lessons on perimeter, area, and volume. The problems in the lesson on Perimeter (sample) aren't simply about finding the perimeter, but also touch on the "inverse" problem.

The lessons on area have a definite train of thought building up to the area of triangles. That way the formula for the area of triangles is not just a dry memorized rule but a proven and justified fact.

First of all, Getting Started with Area is meant for 3rd-4th grade, teaching the concept itself as "little squares".

Area of Rectangle (see sample) practices this concept a lot, including problems with 'compound' figures.

Area Versus Perimeter has plenty of problems where students need to distinguish and compare between these two concepts.

In the lesson Area of Right Triangles, the emphasis is on realizing how a right triangle is half of a rectangle, and so its area is also half of the area of the rectangle.

Area of Parallelograms illustrates how parallelograms have the same area as a rectangle with the same altitude and base.

Area of Triangles (sample) shows how triangles are half of parallelograms, and proves the common area rule that way.

Volume is a basic lesson about the "little cubes". Lots of word problems are included.

Three-Dimensional Figures is an exploratory lesson concentrating on remembering the names of various basic figures, and finding out about their edges, vertices, and faces.

Better Yet - Package Deals!
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*BONUS* - SOFT-PAK MATH SOFTWARE

I bet you'd have to agree: this is a steal! You can get Soft-Pak math programs (list price $24.95) for just a small $3.50 s&h fee - just by ordering ANY of my books at Kagi or CurrClick!

* Math Maker, for printable math activities with answer keys
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By purchasing any of the books, permission IS granted for the teacher (or parent) to reproduce this material to be used with his/her students in a teaching situation; not for commercial resale. However, you are not permitted to share the material with another teacher.

In other words, you are permitted to make copies for the students/children you are teaching, but not for other teachers' usage.