Chapter III: Part III: Arithmetic

I. ARITHMETICAL OPERATIONS 205
Numbers 1-10 205
Tens, Hundreds and Thousands 208
Counting-frames 210

II. THE MULTIPLICATION TABLE 217

III. DIVISION 223

IV. OPERATIONS IN SEVERAL FIGURES 225
Addition 225
Subtraction 227
Multiplication 228
Multiplying on Ruled Paper 235
Long Division 237

V. EXERCISES WITH NUMBERS 241
Multiples, Prime Numbers and Factoring 241

VI. SQUARE AND CUBE OF NUMBERS 251

PART IV

GEOMETRY

I. PLANE GEOMETRY 259

II. DIDACTIC MATERIAL USED FOR GEOMETRY 265
Squares and Divided Figures 265
Fractions 267
Reduction of Common Fractions to Decimal Fractions 273
Equivalent Figures 277
Some Theorems Based on Equivalent Figures 282
Division of a Triangle 289
Inscribed and Concentric Figures 290

III. SOLID GEOMETRY 292
The Powers of Numbers 294
The Cube of a Binomial 295
Weights and Measures 295

PART V

DRAWING

I. LINEAR GEOMETRIC DESIGN DECORATION 301
Artistic Composition with the Insets 305

II. FREE-HAND DRAWING: STUDIES FROM LIFE 307

PART VI

MUSIC

I. THE SCALE 319

II. THE READING AND WRITING OF MUSIC 326
Treble and Bass Clefs 328

III. THE MAJOR SCALES 333

IV. EXERCISES IN RHYTHM 341
Singing 365
Musical Phrases for Rhythmic Exercises 367

V. MUSICAL AUDITIONS 376

PART VII

METRICS

I. THE STUDY OF METRICS IN ELEMENTARY SCHOOLS 383
Stanza and line 384
Rhyme 384
Tonic accents (stresses) 385
Parisyllabic lines 386
Imparisyllabic lines 388
The cæsura 391
Metrical analyses 392
Translator's note on English metrics 395
Material for nomenclature 404

APPENDIX I 409