The Curriculum of the Steiner School - Class 5

Notes and Lesson Plans

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 Waldorf-y than others. Please feel free to take what you like and leave the rest.

Fractions & Freehand Geometry
for Class 5

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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 free-hand 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

    from the circle to the ellipse
    points of a circle
    angle measurement
    acute, obtuse, right, straight, and full angles
    intersecting lines
    vertical, straight, and supplementary angles
    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 3-D 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:

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