RightStart Geometry (or RightStartTM Mathematics: A Hands-On Geometric Approach) course is a full year of geometry, meant primarily for middle school level. It is very hands-on, including drawing in nearly every lesson. This drawing is done with proper tools (a T-square and triangular rulers) for greater accuracy. In my opinion, that is the best way to study geometry: learning by DRAWING.
The course starts with some basics in drawing, and the goes on to explore the equilateral triangle and how to divide it into halves, sixths, thirds, fourths, eights, ninths, etc. (lessons 4-9) During these initial lessons, the student is often asked to compare how many times greater one figure is to another. This is, of course, paving the way to the concept of area.
Dividing equilateral triangle
Lessons 10-17 introcude centimeters, inches, perimeter, drawing parellograms, rectangles, rhombuses, and squares. I cannot but admire the beauty of this approach: after drawing all those special rectangles in various situations, the student is then (lesson 17) well ready to analyze and categorize the different types of quadrilaterals.
Fractions are the topic of lessons 18-19 with the help of fraction chart that the student has to complete. They pave the way to studying 16th parts and the inch ruler in lesson 20. Lessons 21-22 reviews fractions as parts of geometrical shapes and teaches crosshatching.
Ratios of areas is the concept studied in lesson 23, with the worksheet of nested squares. The next few lessons have the students complete a grid patterns to fill a rectangle, first with square centimeters, then with square inches. Obviously this leading to the formula of Area of rectangle and some calculations.
I found the two following lessons (28-29) very clever. The first one has an investigation where the student moves part of the rectangle to form a square, and in the second one the student makes a square larger, both connecting the geometry with multiplication patterns and even algebra.
In fact, RightStart Geometry has these kind of tidbits here and there. (For example, later on we find Rectangles Inscribed in a Triangle.) I felt these kind of lessons were like GEMS - little fascinating topics going beyond the basics but still within the student's grasp. You could perhaps omit them if in a hurry, but they are especially good if the child is really interested in geometry or is gifted.
There is a short lesson on Perimeter, and then lessons on Area of parallelogram and triangle, on into area of trapezoids, hexagons, octagons, and ratios of area (31-41).
Usually math texbooks concentrate on problems of calculating the area of figures with their dimensions given. RightStart Geometry worksheets (most of the time) only give the student the figures - he has do the measuring himself, plus decide WHAT to measure, or if any helping lines are needed. This 'hands-on' approach is sure to make those area formulas to stick better in the child's memory.
And I'm not meaning those were the only kinds of problems on the worksheets - no by far. The problems are very variable. For example, on area of octagons, the student is to SHOW many different ways to FIND the area of the octagon, without any calculations. Or, on ratios of areas, the student is to draw figures with some same dimensions as the given figure, but half or twice the area (or vice versa).
Then come sections on angles (lessons 42-47), congruent triangles (48-50), and medians in triangles (51-53). The discussion here is on explorative basis, discovering the properties and theorems.
Congruent triangles, or medians in triangles, are not usually found in your typical middle school math. Here RightStart Geometry does a big favor to students, because when they have already encountered and explored the triangle congruency theorems during middle school, it will be much easier for them in high school geometry. In fact, high school students who have difficulty with geometry, probably would greatly benefit from studying RightStart Geometry first.
Next come lessons centered around Pythagorean theorem (56-61). Again, I found the discussion to be more thorough and in-depth than typical school books. The student gets to explore and draw squares on the sides of the triangle for two lessons, construct geometrical proofs of the theorem, learn square root concept, apply Pythagorean theorem in word problems - and draw the square root spiral!
On to cirles. Similarly, Pi is not just thrown out there in one lesson, but the concept is prepared well: in one lesson the student measures diameters and circumferences of round objects, in two others he draws inscribed or circumscribed regular polygons, before encountering Pi and the formula for the circumference.
Then there are circle designs, yin-yang symbol, trefoil, circle spiral etc. to draw while studying tangents and tangent circles.
The next come bisecting angles and perpendicular bisectors. After those, something special again: The Amazing Nine-Point Circle. How to Draw Arcs is sure to delight all budding artists. The course goes on to study angles in arcs and arc lenght - again topics not normally found in middle school geometry.
Area of circle (lessons 77-80) and applications is the next major topic. Again, there is one preliminary lesson with a geometric way to estimate the area and another way (the sectors into parallelogram) to find the area.
Rotations lesson from RightStart Geometry
Geometric transformations (lessons 83-96) are not an easy topic to comprehend well. Most math books show a few examples and have a few problems on the various transformations, but RightStart Geometry lets students encounter many many drawing situations in several lessons for each of the transformations (reflection, rotation, and translation), which can then build a solid understanding of this area of geometry.
For example, the student uses the goniometer and a tangram design to understand rotating of a design. Making wheel designs allows for some creativivity while deepening the understanding of rotational geometry.
After the basics, the lessons also include the 'inverse' operations: finding the line of reflection or the center of rotation. The topic of transformations is closed by exploring deeper the subject of symmetry (topics such as as lines of symmetry, rotational symmetry, order of rotational symmetry) and how it connects with geometrical transformations.
Then the course goes on to several fascinating and interesting topics such as tessellations, fractals, golden ratio, platonic solids, and more.
This course covers middle school geometry, yes, but it also has a lot of the topics from a high school geometry course (but not all). Also, it doesn't involve proof. However, some homeschoolers might be able to substitute this course for a high school geometry course (ask in your local homeschool group).
Pricing (in 2012): Basic Starter Kit $120, Deluxe Starter Kit $200.
Visit the website here: RightStart Geometry.
Review by Maria Miller, MSc, author of HomeschoolMath.net