Geometric Drawing
updated March 29, 2020
This page has helpful links and LOADS of free resources to help you plan your sixth grade year. Enjoy!
Mission Statement  Consulting Services  Lending Library
Geometric Drawing
for Class 6
Pinterest  Renee Schwartz My curated collection of visuals! Browse sample main lesson book pages, watercolor paintings, chalkboard drawings, etc. for
Geometry.
FREE eBooks at the Online Waldorf Library Excellent resource! Published Waldorf curriculum books provided here in PDF format for you to download, keep, and read... for free!
Sample Lessons and Free Curriculum
Other Helpful Links
BLACKBOARD SKETCHING book
by
FREDERICK WHITNEY (1908) available online for free  with step by step directions and illustrations
Ernst Schuberth has written wonderful books on the teaching of geometry, but one should note that they are out of step with the progression
of math skills recommended by Jamie York. Jamie writes on page 83 of his Making Math Meaningful: A Source Book for Teaching Math in Grades One Through Five, "We recommend
freehand geometry in fifth grade, and geometric drawing (with compass and straightedge) for sixth grade, whereas Schuberth
lists both of these for a year earlier."
Thus, Schuberth's grade 4 & 5 book can be seen as a grade 5 & 6 book. Here are his grade 5 skills notes regarding lessons in Geometric Drawing,
which we may use for this block:
Ernst Schuberth  Freehand Geometry
circle
circle with color
distending, compacting, enveloping, dilating
Straight Lines and Points as Determinants of a Circle's Boundaries
tangents
pencil of lines
point row
circle area
Points and Straight Lines in Relation to the Circle
center point
center lines
diameter
radius
passant, tangent, secant
chord
avoidance point, boundary point, connection point, vanishing point
circle symmetry
symmetry axes
freehand geometry exercises
Drawing with compass and straight edge is then introduced and continues for the remainder of the book (pages 6284)
A Geometry Joke
My friend was cold so I told her to go stand in a corner. Corners are 90 degrees.
Books to Buy
I'm suggesting two books: Sheen's Geometry and the Imagination (which is available at the Online
Waldorf Library for free)
and
Barbara Dewey's Waldorf Geometry for Homeschoolers: Grade 6 (available in PDF format for $14.00). The link is to her online store at Waldorf without Walls.
In brief, his book is better for WHAT to do and her book is better for HOW to do it.
Waldorf Geometry for Homeschoolers: Grade 6 by Barbara Dewey
Recorded here is my own personal collection of articles, resources, favorite links, teaching ideas, and lesson plans. It encompasses many years, from the very beginning of my experience studying and learning about Waldorf to the present time. People from all around the world visit my site and recommend it to others. Welcome!
This site records my journey. I hope my honesty is encouraging and helps break down some barriers that may prevent people from trying Waldorf methods. Because this is an ongoing site documenting my curriculum planning and ideas, some materials are more Waldorfy than others. Please feel free to take what you like and leave the rest.
I am currently teaching this main lesson block, February 2017. When we are done I will create a blog
post with photographs of all of Becca's MLB pages.
List of Stories
I chose a twoblock treatment of Geometry this year, in order to cover all of the material. (The third 6th grade block is Business Mathematics.)
I believe some families do String, StraightEdge and Shadow: The Story of Geometry
as a main lesson block and then geometric drawing as a weekly followup special subject (akin to Form Drawing) throughout the year.
I decided that I didn't want
so much time to pass between geometric drawings, so that both the geometry discoveries and the fluency in drawing and using the tools build in a more immediate way, but there's NO time in the
introductory
Story of Geometry block to do much drawing at all! Thus, a followup block devoted completely to the drawing.
There isn't a story for each figure in Geometry but Barbara Dewey suggests "The lesson should begin with a poem
or poetic prose, which will be recited at the beginning of each lesson. It is important to have the artistic emphasis, even in science."
She suggests choose one of
the following quotes from the prose of Joannes Kepler (15711630):
The whole of creation forms a marvellous symphony in the order of ideas and of spirit as in that of material beings. All is held
and linked together by mutual, indissoluble affinities; all forms a harmonious whole.
from Harmonies of the World
... all nature and the graceful sky are symbolized in the art of Geometria...
from Tertius Interveniens
If you haven't already done Astronomy, here is a chapter from a free book offered online at the Baldwin Project (www.mainlesson.com) called Stories of the Great Scientists by Charles R. Gibson:
Johann Kepler (15711630): From PotBoy in a Tavern to Imperial
Mathematician and Astronomer
I chose the first quote for us to put in the main lesson book and the second one for us to recite each morning. Dewey also suggests "The child should be able to write (with help)
a description of how each construction was done to go with each drawing in the main lesson book." We are using extralarge 12 x 18 inch spiral bound MLBs
which will open and lay flat more easily.
Here was our structure:
Day One
background on Kepler
present and explain two quotes  learn shorter one for daily recitation  present new blue MLB  add longer quote in lieu of table of contents page
figure 2, 3 from Sheen
(same as figure 2, 3 from Dewey; Sheen shows better how figure 3 is constructed)
provide compass and nice new lead
Steps:
draw figure on practice paper  may have to make several trials to figure it out
draft words of explanation  how it was created
draw figure in MLB  put clipboard under page (to protect other MLB pages from the compass point and to hold the paper still)
finetune words of explanation and add to MLB
(we wrote it that day and not on the next day  she kept figuring out better how to describe the process as she did it)
here is a chalkboard drawing with an alternative quote to introduce Geometry  William Blake
and a chalkboard drawing of William Blake
and a third choice for a Plato quote to introduce Geometry and a chalkboard drawing
Day Two
figure 4, 5 from Dewey
(figure 4 is same as figure 4 from Sheen; Dewey provides extra logical extensions from this)
Day Three
Day Four
figure 6 from Sheen
(she put the intermediate step of figure 6  with the full compass circles  and the completed figure 6 in her MLB)
Day Five
perfect equilateral triangle then figure 8, 9 from
Sheen
provide a protractor and a straight edge
The children should become quite conversant with these names and their meanings:
equilateral (Latin), equal sides
isosceles (Greek), equal legs
scalene (Greek), limping, uneven
limp around the classroom with one leg shorter than the other, being scalene triangles
Day Six
inspired by figure 10 from Sheen, cover image  create your own imaginative design!
Becca used a page from a 17 x 20 inch pad of paper; this page is attached into the MLB and folds out to open
on the facing page, fig 10a from Sheen
acute, obtuse, and right angles
discuss acuteangle triangles, obtuseangle triangles, rightangle triangles
here is a sample chalkboard drawing for classifying triangles
sample "find the missing angle" problems chalkboard drawing
Day Seven
figure 7, 8, 9 from Dewey
Day Eight
figure 10 from Dewey
using the colored pencils as she shows in her example (red, green, yellow, orange, blue)
showing how to calculate how many lines connect the points of a hexagon (15)
Day Nine
Day Ten
cover image from Dewey (same as figure 19 from Sheen)
a 24 sided regular polygon in a circle with all of its diagonals
each of the 24 angular points is joined to every other one
there are altogether 276 straight lines in the figure
(calculate this, using one of the formulas from Dewey  given for figure 10)
another version of the division of 24  chalkboard drawing
Day Eleven
Day Twelve
Day Thirteen
Day Fourteen
THE END!
There's so much more you can do for this topic, but Sheen
specifically states that his book will carry the class through several years of the Geometry
curriculum. So don't panic or rush.
A NOTE:
I would never use these books for teaching any mathematical concepts because I think they are too confusing, but kids who are older and already familiar
with the concepts do enjoy reading them and catching all the puns. I introduced them after the Circle Terminology MLB page on Day Twelve.
The series of 9 books by Cindy Neuschwander includes:
My blog posts from teaching this topic:
