# Seeing Numbers: Introducing subQuan

Seeing Numbers Intro Rev3B.pdf

### Chapter 1: Place Shapes

The concept of place and its value proved to be a leap in man’s ability to understand and manipulate numbers. However, the concept of Place Shapes provides the foundation for number sense that opens the eyes to see! Discover for yourself how place value and place came about.

### Chapter 2: subQuan

When unit cubes are organized into shapes, and then the groups of shapes are ordered by size, and then coded symbolically, taking notice of any shapes that are missing, the result is extremely eye-opening. But referring to this as ordered-organized-shapes-converted-into-symbols-to-represent-a-number is awkward. Call them subQuans. SubQuans gives us a far-reaching perspective on the patterns in numbers that surpasses what we see from only looking at numbers in the traditional way. SubQuans are a superset of traditional numbers.

### Chapter 3: Missing Negatives

Often real-life organizes ‘things’ into rectangular patterns. You will decompose rectangular patterns into place shapes to obtain subQuans. This opens your eyes to seeing subQuan patterns in tiles, bricks, fabric, and other everyday objects. Turning our eyes to not quite perfect rectangles opens our minds to negatives!

### Chapter 4: Measurement

The ruler is the first number tool and helps you in two ways. First to build the place shapes and second to determine a fully composed subQuan.

### Chapter 5: subQuan Metapatterns

A metapattern is a pattern of patterns. These patterns can be discovered from place shapes, measurements, or rectangular patterns. The metapattern of subQuans unlocks one of the powers of numbers: the power to predict! Algebra teaches this power symbolically, but with subQuan we discover the power visually which lays a solid foundation for understanding algebra. This is big.

### Chapter 6: Change

Simply taken the change between each pair of numbers in a sequence of data can help determine the metapattern. This powerful analytic tool becomes understandable with a foundation of subQuan.

### Appendix 1: Digit-Speak

This appendix introduces the reader to digit-speak: A straight-forward solution to the conflict between how our brains understand simple number patterns and how some of our languages contradict those patterns. The magnitude of the conflict is very dependent on the reader’s language. Digit-speak is used throughout the book.

### Appendix 2: Subitizing

Subitizing is an ability recently discovered as instinctual, even in other mammals, birds, and possibly fish and amphibians. Infants one day old can distinguish between zero, one, two, and three objects, movements, and sounds. Learning to subitize removes the crutch of counting and allows you see the number of shapes in each place more quickly. Subitizing usage is preferred, but not required in this book.