Sophia Institute online Waldorf Certificate Studies Program

Waldorf Methods/Reading and Math 3
Introduction
Language is our most important means of mutual understanding and is therefore the primary medium of education. It is also a highly significant formative influence in the child’s psychological and spiritual development and its cultivation is central to the educational tasks of Steiner/Waldorf education. It is the aim of the curriculum to cultivate language skills and awareness in all subjects and teaching settings. Clearly the teaching of the mother tongue has a pivotal role within the whole education.
Mathematics in the Waldorf school is divided into stages. In the first stage, which covers the first five classes, mathematics is developed as an activity intimately connected to the life process of the child, and progresses from the internal towards the external. In the second stage, covering classes 6 to 8, the main emphasis is on the practical. Course Outlines
Waldorf Methods/Reading and Math 1
Lesson 1: Introduction Lesson 2: Reading/1st Grade Lesson 3: Reading/2nd Grade Lesson 4: Reading/3rd Grade Lesson 5: Math/1st Grade Waldorf Methods/Reading and Math 2 Lesson 1: Math/2nd Grade Lesson 2: Math/3rd Grade Lesson 3: Reading/4th Grade Lesson 4: Reading/5th Grade Lesson 5: Reading/6th Grade Waldorf Methods/Reading and Math 3 Lesson 1: Math/4th Grade Lesson 2: Math/5th Grade Lesson 3: Math/6th Grade Lesson 4: Reading/7th and 8th Grade Lesson 5: Math/7th and 8th Grade 

Tasks and Assignments for Waldorf Methods/Reading and Math 3.2.
Please study and work with the study material provided for this lesson. Then please turn to the following tasks and assignments listed below.
1. Study the material provided and look up other resources as needed and appropriate.
2. Create examples of curriculum that addresses the learning method and content appropriate for the age group in question as follows. Curriculum examples should include outlines and goals, activities, circle/games, stories, and illustrations/drawings:
Create 2 examples for this age group.
3. Additionally submit comments and questions, if any.
Please send your completed assignment via the online form or via email.
1. Study the material provided and look up other resources as needed and appropriate.
2. Create examples of curriculum that addresses the learning method and content appropriate for the age group in question as follows. Curriculum examples should include outlines and goals, activities, circle/games, stories, and illustrations/drawings:
Create 2 examples for this age group.
3. Additionally submit comments and questions, if any.
Please send your completed assignment via the online form or via email.
Study Material for Waldorf Methods/Reading and Math Lesson 3.2.
Arithmetic and Mathematics/Class 5
General Observations and Guidelines
Classes 4 and 5
Upon reaching their ninth year, children make a decisive change. Their close relationship to the world around them becomes different and more remote. The earlier harmony between outer and inner worlds is fundamentally broken.
This transformation in their soul is reflected in the mathematics curriculum when in Class 4 the children begin to work with broken numbers (fractions). By this means they meet something in the teaching content which they have also experienced in themselves.
It is not essential for the children to be able to manage fractions swiftly. It is much more important that they can experience these 'external' fractions very strongly. In connection with this, the historical development of fraction calculations in Egypt can give the teacher interesting and Significant teaching ideas. In order to do general justice to the subject of fractions it is recommended to use the following three methods as an introduction: To proceed from the whole to the parts, from the parts to the whole, and to establish the principle of equivalence. After this the four rules are practised with fractions, the same with simplifying, expansion and division of the denominator into prime factors.
After this, decimal fractions follow as a practical application. Once the divisibility border is crossed the children can discover the practicality of calculations in Class 5.
The aim according to Steiner is as follows: 'in Class 5 we want to continue with fractions and decimals and to give the children everything which will allow them to calculate freely with whole and fractional numbers,"
In Class 4 form drawing is led into elementary geometry. Here one can begin again with the basic linear polarity of circle and straight line. In order that the pupils get as intensive an image as possible of these forms, it is recommended that they do not initially use compasses and ruler, but draw free hand.
Although we deal with the most basic elements in the first geometry lessons, it is important to let the pupils feel something of that dimension which is connected with existential questions over and above the practical and utilitarian. This is made far easier if the beauty of form and strongly regulated connections of geometry are felt in addition to the working rules and methods.
In connection with stories from ancient Egypt in the history lessons, the Pythagorean rope can be introduced as a first introduction to Pythagoras' Theorem.
This transformation in their soul is reflected in the mathematics curriculum when in Class 4 the children begin to work with broken numbers (fractions). By this means they meet something in the teaching content which they have also experienced in themselves.
It is not essential for the children to be able to manage fractions swiftly. It is much more important that they can experience these 'external' fractions very strongly. In connection with this, the historical development of fraction calculations in Egypt can give the teacher interesting and Significant teaching ideas. In order to do general justice to the subject of fractions it is recommended to use the following three methods as an introduction: To proceed from the whole to the parts, from the parts to the whole, and to establish the principle of equivalence. After this the four rules are practised with fractions, the same with simplifying, expansion and division of the denominator into prime factors.
After this, decimal fractions follow as a practical application. Once the divisibility border is crossed the children can discover the practicality of calculations in Class 5.
The aim according to Steiner is as follows: 'in Class 5 we want to continue with fractions and decimals and to give the children everything which will allow them to calculate freely with whole and fractional numbers,"
In Class 4 form drawing is led into elementary geometry. Here one can begin again with the basic linear polarity of circle and straight line. In order that the pupils get as intensive an image as possible of these forms, it is recommended that they do not initially use compasses and ruler, but draw free hand.
Although we deal with the most basic elements in the first geometry lessons, it is important to let the pupils feel something of that dimension which is connected with existential questions over and above the practical and utilitarian. This is made far easier if the beauty of form and strongly regulated connections of geometry are felt in addition to the working rules and methods.
In connection with stories from ancient Egypt in the history lessons, the Pythagorean rope can be introduced as a first introduction to Pythagoras' Theorem.
Class 5
* Constant practice in mental arithmetic * Revision: the four rules with natural numbers
* Combinations of the four rules
* Calculations with fractions: expansion and reduction of equivalents (division into prime factors)
* Illustration and comparison of fractions,. Calculation with decimals. Consolidation of fractions methods
* Table of place values, rhythmically, through movement, and qualitatively introduced
* Introduction of the relationship of decimals to place values
* Measurements using decimals
* Recognition of connections between decimal numbers and decimal fractions
The main new task for Class 5 is learning to use a pair of compasses with accuracy, though some teachers prefer to wait until the beginning of Class 6. The forms previously drawn in Class 4 can now be accurately constructed. Children will naturally colour these flowerlike forms, and thus make an obvious link with the botany mainlesson in Class 5. A set square and ruler can also be used to draw accurate parallel lines.
* Starting with the construction of a circle, discovery of the main geometrical figures: triangle, hexagon, square, rhombus, parallelogram, octagon
* Division and joints on 24point circle
* Construction of perpendicular bisector, angle bisection, perpendicular bisector, angle bisection, perpendiculars
* Construction of different triangles; equilateral, isosceles, scalene, right angled
* The various angles; acute, obtuse, reflex.
* Circles touching a triangle; inside (incircle) and outside (circumcircle)
* Pythagoras' Theorem; visually using knotted string. (Egyptians used this to construct their pyramids). Grains covering an area, theorem drawn using Roman tiles (Isosceles triangle)
* Tessellation (tiling) involving accurate construction of parallel lines
* Exact construction of pentagon/pentagram
* Combinations of the four rules
* Calculations with fractions: expansion and reduction of equivalents (division into prime factors)
* Illustration and comparison of fractions,. Calculation with decimals. Consolidation of fractions methods
* Table of place values, rhythmically, through movement, and qualitatively introduced
* Introduction of the relationship of decimals to place values
* Measurements using decimals
* Recognition of connections between decimal numbers and decimal fractions
The main new task for Class 5 is learning to use a pair of compasses with accuracy, though some teachers prefer to wait until the beginning of Class 6. The forms previously drawn in Class 4 can now be accurately constructed. Children will naturally colour these flowerlike forms, and thus make an obvious link with the botany mainlesson in Class 5. A set square and ruler can also be used to draw accurate parallel lines.
* Starting with the construction of a circle, discovery of the main geometrical figures: triangle, hexagon, square, rhombus, parallelogram, octagon
* Division and joints on 24point circle
* Construction of perpendicular bisector, angle bisection, perpendicular bisector, angle bisection, perpendiculars
* Construction of different triangles; equilateral, isosceles, scalene, right angled
* The various angles; acute, obtuse, reflex.
* Circles touching a triangle; inside (incircle) and outside (circumcircle)
* Pythagoras' Theorem; visually using knotted string. (Egyptians used this to construct their pyramids). Grains covering an area, theorem drawn using Roman tiles (Isosceles triangle)
* Tessellation (tiling) involving accurate construction of parallel lines
* Exact construction of pentagon/pentagram
Numeracy Checklist for Class 4 to 5
Most children within the normal range of ability will be able to:
Number
4 carry out all four processes of number confidently
4 read and understand numbers up to six figures
4 know the multiplication tables up to 12 out of sequence
4 do long multiplication with numbers up to 122 as multiplier
4 find factors of a given number
4 identify prime numbers less than 100
4/5 answer more complex mental arithmetic questions involving a mix of processes (e.g. The 12.38 train to Reading takes 18 minutes. but left 14 minutes late, when did it arrive? or I doubled a number and added 8 and got 32, what was the number?)
4/5 do long division including making use of remainder and estimating approximate answers.
4/5 find Lowest Common Multiple or Highest Common Factors
5 use all four processes with fractions including mixed numbers and improper fractions
5 understand how to use decimal notation, decimal fractions and interchange of decimal with common fractions
5 carry out four processes with decimals
5 use long division and multiplication using the decimal point
5 apply the Rule of Three (if, then, therefore) to practical problems
Measurement
4 record information such as height, weight, volume, etc.
5 work with metric measurement including estimation
5 work with aspects of time including 24 hour clock
5/6 calculate average speeds
Geometry
5 draw freehand archetypal geometric shapes: different kinds of triangle, rectangle, quadrilaterals, polygons and circles
5 divide circles into 17, 16 or 20 parts, deriving regular figures like pentagon and hexagon from them
Number
4 carry out all four processes of number confidently
4 read and understand numbers up to six figures
4 know the multiplication tables up to 12 out of sequence
4 do long multiplication with numbers up to 122 as multiplier
4 find factors of a given number
4 identify prime numbers less than 100
4/5 answer more complex mental arithmetic questions involving a mix of processes (e.g. The 12.38 train to Reading takes 18 minutes. but left 14 minutes late, when did it arrive? or I doubled a number and added 8 and got 32, what was the number?)
4/5 do long division including making use of remainder and estimating approximate answers.
4/5 find Lowest Common Multiple or Highest Common Factors
5 use all four processes with fractions including mixed numbers and improper fractions
5 understand how to use decimal notation, decimal fractions and interchange of decimal with common fractions
5 carry out four processes with decimals
5 use long division and multiplication using the decimal point
5 apply the Rule of Three (if, then, therefore) to practical problems
Measurement
4 record information such as height, weight, volume, etc.
5 work with metric measurement including estimation
5 work with aspects of time including 24 hour clock
5/6 calculate average speeds
Geometry
5 draw freehand archetypal geometric shapes: different kinds of triangle, rectangle, quadrilaterals, polygons and circles
5 divide circles into 17, 16 or 20 parts, deriving regular figures like pentagon and hexagon from them