Math Mammoth Geometry 1

134 pages
(includes answers)

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

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Este libro en español

Math Mammoth Geometry 1 gives the student a thorough view of basic plane geometry. The topics suit best 4th-5th grade mathematics. The emphasis is on learning through drawing.

The PDF version of this book is enabled for annotation. This means that if you prefer, your student can fill it in on the computer, using the typewriter and drawing tools in Adobe Reader version 9 or greater.

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.

This book is also suitable for a geometry notebook or journal project. This simply means that for each new TERM in the book, the student explains that term and draws the corresponding figure, using 1-2 blank pages. In the end, the student will have his/her very own geometry book to keep and show around!

As an example how this book teaches area, please see this video of mine. It is based on the area lesson in the book, and can be used in conjunction with the book.

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.

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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* Math User, for answering the 900 multi-level word problems
* True/False Math Challenger for mastering facts 1-12

NOTE: if you purchase any one of the Math Mammoth bundles at Kagi store, you will get Soft-Pak in the download or included on the CD for FREE.

Soft-Pak may also be purchased at great 75% discount without a Math Mammoth purchase - click here for details.

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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.

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Math Mammoth books are PDF files. You will need Adobe Reader to view them, including if you use a Mac or Linux. You can try other PDF viewers, but they seem to either omit or mess up some of the images.