The Dance of Number: Solutions Manual – Steps 1 to 7

[Overview of the curriculum]
Here is a curriculum that:
* brings to light the multiplicities of the perichoretic nature of creation and mathematics,
* coordinates beauty, truth, and goodness with rigor and heuristics,
* teaches mastery of number sense and algebraic syntax,
* integrates math themes with history, science, and personalities,
* structures mathematics as an interconnected framework, and
* explores the dynamic interrelatedness of Arithmetic, Algebra, Geometry, Trigonometry, and Science, plus much, much more.
The Dance of Number is a sequenced and tightly integrated curriculum involving four textbooks totaling 1924 pages (Grades 6-10, ages 12-16) consisting of 14 chapters, called the steps of the Dance. The only prerequisite for the first textbook is above average reading comprehension. This curriculum starts from ground zero, teaches the basics of arithmetic from a fresh, vibrant perspective, and then takes the reader on a journey that leads to the borderlands of the mountain range called Calculus. There are plenty of side roads along the way where we stop to gaze at the scenic beauty (i.e., a unified look at principles of Algebra, Geometry, Trigonometry). It is a long trip; its completion is worth the effort.
The texts are not named Algebra I or Algebra II, etc., because the four-volume sequence tells an coordinated story engaging the student in the nature of the structure of number, the development of its history, and its interpenetration with science. As the student takes this journey, all the concepts of Arithmetic, high school Algebra, most of Geometry, and a complete study of Trigonometry are unfolded.
Because of this harmonized approach, these texts are different than most of what is on the market. The author wants the student to see how the ideas/branches of mathematics interpenetrate (e.g., you are doing algebraic operations and geometrical procedures as you are learning the elements of trigonometry). Our current textbook structure is not that successful at doing this.
This is the detailed solutions manual for Steps 1 to 7.