Math Mammoth Geometry 2

75 pages
(includes answers)

Sample pages (PDF)
Contents
Area of Parallelograms
Area of Shapes not Drawn on Grid
Nets and Surface Area Volume problems

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Math Mammoth Geometry 2 continues the study of geometry after Math Mammoth Geometry 1, and is most suitable for grade 6. It concentrates on these topics:

• area of triangles;
• area of polygons;
• nets and surface area of prisms and pyramids;
• volume of rectangular prisms with sides of fractional length.

However, the book starts out with some review of topics from earlier grades, as we review the different types of quadrilaterals and triangles and students do some basic drawing exercises. In these drawing problems, students will need a ruler to measure lengths and a protractor to measure angles.

One focus of the book is the area of polygons. To reach this goal, we follow a step-by-step development. First, we study how to find the area of a right triangle, which is very easy, as a right triangle is always half of a rectangle. Next, we build on the idea that the area of a parallelogram is the same as the area of the related rectangle, and from that we develop the usual formula for the area of a parallelogram as the product of its base times its height. This formula then gives us a way to generalize finding the area of any triangle as half of the area of the corresponding parallelogram.

Finally, the area of a polygon can be determined by dividing it into triangles and rectangles, finding the areas of those and summing them. Students also practice their new skills in the context of a coordinate grid. They draw polygons in the coordinate plane and find the lengths of their sides, perimeters and areas.

Nets and surface area is another major topic. Students draw nets and determine the surface area of prisms and pyramids using nets. They also learn how to convert between different area units, not using conversion factors or formulas, but using logical reasoning where they learn to determine those conversion factors themselves.

Lastly, we study the volume of rectangular prisms, this time with edges of fractional length. (Students have already studied this topic in fifth grade with edges that are a whole number long.) The basic idea is to prove that the volume of a rectangular prism can be calculated by multiplying its edge lengths even when the edges have fractional lengths. To that end, students need to think how many little cubes with edges 1⁄2 or 1⁄3 unit go into a larger prism. Once we have established the formula for volume, students solve some problems concerning the volume of rectangular prisms.

You can find some videos that match the lessons in this book at this link (choose 6th grade).

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.

Note: The contents of this book were updated in February 2022, necessitated by the publishing of Math Mammoth Geometry 4 and the changes in Math Mammoth Geometry 3.