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Geometry, Grade 6 is a complete unit with direct instruction to the student, ample practice problems and word problems. Common Core aligned. Great for independent practice/homework.
The main topics in this unit are
* the area of triangles
* the area of polygons
* nets and the surface area of prisms and pyramids
* conversions between units of area (both metric and customary)
* the volume of prisms with fractional side lengths
We start out by reviewing quadrilaterals and the basic drawing of shapes. Students need to use a ruler and a protractor, and measure the side lengths and angles to do the drawing problems.
Next, we get to the focus of the unit, which is the area of polygons. First, we study the area of a right triangle, which is very easy, as a right triangle is always half of a rectangle. Building on from there, the area of a parallelogram is the same as the area of a certain rectangle, thus we arrive at the usual formula for the area of a parallelogram as being the product of its height and its base.
Then, the area of any triangle is half of the area of a certain parallelogram. Lastly, the area of polygons can be determined by dividing them into triangles, finding the areas of those, and adding them. Students also practice their new skills in the context of a coordinate grid. They draw polygons in the coordinate plane and find their side lengths, perimeters, and areas.
Nets and surface area is the next major topic. Students draw nets and determine the surface area of prisms and pyramids using nets. They 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 fractional edge lengths. (Students have already studied this topic using whole-number edge lengths in the 5th grade.) 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
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