Area of Mixed Polygons

In 7th grade math, we're working on area.  We've gone through all of the basic formulas with careful attention to how they are related to one another -- the triangle being half of a rectangle, the trapezoid being a combination of two triangles, and so forth. Now we're on to area of mixed polygons, such …

Units vs. Square Units (vs. Cubic Units)

When teaching basic geometry concepts, such as perimeter and area, you will save yourself quite a bit of grief if you start by making clear the difference between units and square units. Our common abbreviations for these, such as cm and cm², look deceivingly similar to each other and are easily confused by students who …

Pythagorean Theorem Follow-Up

Activity for the big kids today: Without using a ruler, determine whether this triangle is equilateral, isosceles, or scalene. Prove it.

Pythagorean Theorem

In over our heads with radicals in 8th grade Algebra this week, so we took some time to review the Pythagorean Theorem.  Geometry is so beautifully concrete.  In addition to demonstrations you can do with drawings and such, here's an example of a very cool model that my 8th graders found wonderfully entertaining.   As …

Geometry in the Real World

Whenever I'm working on geometry with my students, I try to keep the focus as real-world as possible.  So much of math operates in the abstract; geometry, by contrast, is thoroughly tangible.  This is a time when we can easily and naturally give ideas to the hand before we give them to the mind.  Take …

Geometry Across the Curriculum

I use geometric drawing across the curriculum in several projects.  Below is an in-progress shot of an 8th-grader's design for a stained glass window, an assignment from my medieval history unit that incorporates symbolism along with geometric design. In world history, we use geometric drawing when studying Roman and Islamic mosaics, and students have the …

Construct a Hexagon

The construction for a regular hexagon is a favorite of my students every year and the one most of them choose as a basis for their geometric design project.  We are simply going to begin with a line and use our compass to draw three congruent circles along it.  Start with the center circle. Mark …

Bisect an Angle

Today we'll be bisecting an angle, i.e. cutting an angle in half without using a protractor to measure.  Begin with any angle and draw an arc from the vertex (V) such that your arc crosses both rays of the angle.  Call the points where your arc crosses those rays points A and B. At this …

Bisect a Segment

Today we'll be doing a very simple construction -- bisecting a segment.  In other words, we will be cutting a line segment in half.  Begin by drawing matching circles from your two endpoints (A and B).  The radius of the circle is not important.  As long as it is more than half the length of …

Identify Geometric Shapes

Here's a little activity to wrap up our geometry study for the week.  Have your students consider the following drawing and try to identify as many polygons as they can.  If they need a little guidance, here are some possibilities... regular hexagons rectangles parallelograms rhombi other irregular quadrilaterals a multitude of triangles -- equilateral, isosceles, …