3.G 2: Divide Shapes Into Equal Parts, But Without Fractions (#210)


A Year in the Life: Ambient Math Wins the Race to the Top!
Day 210

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math. Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”

And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times. Why ambient? A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful. CCSS math standards are listed here in blue, followed by ambient math suggestions.

Geometry 3.G
Reason with shapes and their attributes.
2. Partition shapes into parts with equal areas.  Express the idea of each part as a unit fraction of the whole.  For example, partition into 4 parts with equal area, describe the area of each part as 1/4 the area of the shape.

Again, form drawing more than adequately addresses this standard with forms that are divided into symmetrical parts, horizontally, vertically, or both.  Though fractional terms are not directly used, the foundations for fractional thinking are built.  Here are several examples taken from the Math By Hand / Form Drawing/Stories book (the small letters indicate colors).


Here, the form is begun by finding 4 equally spaced points on a circle and marking them.  The contrasting straight line and curved forms are then built off the 4 corners.  Note how the differences resonate: the top left is crystal-like and the bottom right, flower-like.



Here, the square is tilted on end to form a diamond, then the space is divided equally in 4 parts with the cross.  Each quarter part is then further divided with the triangles.  This form could also be transformed into a curved form, similar to the one above.



Here, the space is again divided equally into 4 parts, but without the square border.  The curved half-circles contrast with the straight line form, and can also be drawn without the cross guidelines.

As always, form drawing is an excellent exercise in flexibility, creativity, and self control.  And the foundations are wonderfully built for approaching geometry with instruments later on, but not until Grade 6.

Knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal. Now the fun begins!  We have come to the end of the Common Core Grade 3 math standards, and so will devote some time and posts to exploring the joys of “homesteading” in the third grade.


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