Fifth Grade Fractions & Freehand Geometry
updated October 18, 2022
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.
Fractions & Freehand Geometry
for Class 5
Mission Statement  Consulting Services  Lending Library
Pinterest  Renee Schwartz My curated collection of visuals! Browse sample main lesson book pages, watercolor paintings, chalkboard drawings, etc. for
Fractions.
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
Books to Buy
For mathematics I do like Jamie York's materials best. This topic, "Freehand Geometry and Fifth Grade
Fractions" is his recommended Main Lesson Block #1 of 3 for the fifth grade year.
You can also purchase Schuberth's book or download it (above).
Making Math Meaningful: A Source Book for Teaching Math in Grades One Through Five
Other Helpful Links
Mathematical progression of skills for this year in the following areas:
Jamie York  Fractions
The students should become fluent when working with common and unlike denominators.
Division of fractions is introduced.
All four processes with fractions and mixed numbers should be practiced regularly.
Ernst Schuberth  Freehand Geometry
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 4 skills notes regarding lessons in Geometric Drawing,
which we may use for this block:
"Every teacher can decide for himself where an appropriate place for geometric form drawing is in the lesson plan. For example, as a part of a form drawing block or tacked onto the end of an arithmetic block would certainly be suitable. Taking the seasons into consideration, I always found that the winter is the best time for geometry main lessons."
(page 13)
"Geometry in the fifth grade is similar to that in the fourth grade in as far as it is still freehand geometry and viewed as an extension of form drawing. The construction descriptions suggested here belong, in a narrower sense, to the mathematics lessons." (page 43)
NOTE: students are NOT given a straight edge or a compass until 6th grade
circle
from the circle to the ellipse
points of a circle
tangents
stargazing
lemniscate
clocks
angle measurement
degrees
acute, obtuse, right, straight, and full angles intersecting lines
vertical, straight, and supplementary angles
vertex
parallel lines
from the circle to the triangle
triangle exercises
from the circle to the square
square, rectangle, rhombus, parallelogram, trapezoid, deltoid
quadrangle exercises
light and shadow around a sphere
Geometry Nomenclature
If you're looking for a list of terminology to cover, I would suggest the following. This
is from the set of nomenclature in my NAMC Blackline Masters. This block could be a good time to do some origami!
If you can find Geofix, add that to this block as well, especially making nets for 3D figures.
Point, Line, Plane, Solid
Parallel Lines, Divergent Lines, Convergent Lines, Intersecting Lines
Perpendicular Lines, Oblique Lines, Curved Line, Straight Line
Ray, Line Segment, Origin, Endpoints
Sides of an Angle, Vertex of an Angle, Right Angle, Obtuse Angle
Acute Angle
Simple Closed Figure, Polygon, Triangle, Quadrilateral
Pentagon, Hexagon, Heptagon, Octagon
Nonagon, Decagon
Circle, Ellipse, Oval
Sides of a Triangle, Angles of a Triangle, Vertices of a Triangle, Base of a Triangle
Perimeter of a Triangle, Area of a Triangle
Equilateral Triangle, Isosceles Triangle, Scalene Triangle, Right Triangle
Obtuse Triangle, Acute Triangle
Legs of a Right Triangle, Hypotenuse
Square, Rectangle, Rhombus, Parallelogram
Trapezoid, Common Quadrilateral
Arc of a Circle, Chord of a Circle, Diameter of a Circle, Radius of a Circle
Circumference of a Circle
Fraction Finders from Mindware:
Puzzle #1 reducing fractions to whole numbers
Puzzles #2  3 equivalent fractions
Puzzles #4  5
reducing fractions to lowest terms
Puzzle #6 converting improper fractions to mixed numbers
Puzzle #7 converting mixed numbers to improper fractions
Puzzle #8 adding fractions with like denominators
Puzzles # 9  10
adding fractions with like denominators, reducing answers
Puzzles #11  13
adding fractions with unlike denominators
Puzzle #14
subtracting fractions with like denominators
Puzzles # 15  16
subtracting fractions with like denominators, reducing answers
Puzzles #17  19
subtracting fractions with unlike denominators
Puzzle #20
multiplying fractions by whole numbers, reducing answers
Puzzles #21  22
multiplying fractions by fractions
Puzzles #23  25
multiplying fractions by fractions, reducing answers
Puzzles #26  27
dividing fractions by fractions
Puzzles #28  30
(cross cancelling should wait until sixth grade)
Traditional Materials from TpT for practice / review / assessment:
I've moved this list to inside the blog post Skills Progression in Fractions
My blog posts from teaching this topic:
