# Making Math Real: Fractions

## Making Math Real: Fractions

22 half-day Distance Learning Course  |  9:00 am to 1:30 pm daily  [Pacific Time]
Registration Fee:  \$2,849 for tuition & materials binder (shipped)
[see below]

MANDATORY PREREQUISITE: All students who enroll in this course must have completed the Making Math Real: Overview K-12, the 9 Lines Intensive, and it is STRONGLY RECOMMENDED to have completed the Making Math Real: The 4 Operations and the 400 Math Facts Part 1 and Part 2

PREREQUISITE FULFILLMENT NOTE: Successful completion of the Fractions course fulfills the prerequisite for the Making Math Real: Decimals course, and fulfills a partial prerequisite for taking the Pre-Algebra course. All three courses, Making Math Real: Fractions, Making Math Real: Decimals, and Making Math Real: Advanced Place Value are the combined prerequisites for enrolling in the Pre-Algebra course.

COURSE DESCRIPTION:

Making Math Real is a simultaneous multisensory structured methodology wherein each current mathematical development directly builds the foundation for the next.  Continuing the structure of concept-procedure integration and sensory-cognitive development, the 2 strands presented in the Making Math Real: Overview, this course provides the essential bridge linking the synthesis of the 4 operations and the 400 math facts to algebraic processing and development. Fractions and their related applications are required tools for successful mathematical processing through calculus.

Making Math Real: Fractions presents one of the largest and most intensive volumes of content of all the Making Math Real series of courses. In addition, Making Math Real: Fractions presents the mathematical content and development required for the successful transition from elementary grades mathematics to the algebra strand. For further reading on this subject, please see the following article (below): Fractions, Decimals & Advanced Place Value – The Three Essential Elements of Algebra Readiness

The baseline readiness from the elementary grades for pre-algebra is the four operations through fractions and decimals and the 400 math facts. Therefore, to be ready for algebra, students need all the content and development provided in Making Math Real: The 4 Operations and the 400 Math Facts Parts 1 and 2, and to complete the preparation for algebra readiness, the three courses Making Math Real: Fractions, Making Math Real: Decimals, and Making Math Real: Advanced Place Value.

FRACTIONS

In the fractions section of Making Math Real: Fractions, Decimals, and Advanced Place Value, all conceptual applications covering K-5 (6) will be presented. Since starting my career in education almost 50 years ago, fractions concepts and applications have been consistently an extremely high failure rate for students in the US.  From the research:

In 1978, more than 20,000 U.S. eighth graders (13- and 14-year-olds) were asked for the problem 12/13 + 7/8 whether 1, 2, 19, or 21 was closest to the sum. Only 24% answered correctly (Carpenter, Corbitt, Kepner, Lindquist, & Reys, 1980). The difficulty was not limited to fractions; on a similar NAEP (National Assessment of Educational Progress) problem with decimals (“Is 3.04 x 5.3 closest to 1.6, 16, 160, or 1,600”), only 21% of eighth graders answered correctly (Carpenter, Lindquist, Matthews, & Silver, 1983).

These data were collected a long time ago. In the ensuing years, numerous researchers, government commissions, organizations of mathematics teachers, and textbook writers have recommended ways of improving learning of rational numbers …Performance was essentially unchanged; 27% correct in 2014, versus 24% in 1978, again closely approximating a chance level of accuracy. (1)

(1)  Hard Lessons: Why Rational Number Arithmetic Is So Difficult for So Many People  Robert S. Siegler and Hugues Lortie-Forgues, Current Directions in Psychological Science, 2017, Vol. 26(4) 346–351

There is no educational justification for fractions to be “so difficult for so many people”.  The solution to this problem is the simultaneous multisensory structured curriculum delivery that directly supports students’ abilities to activate and sustain their comprehension-based working memory picture of all the interconnected concepts and applications of fractions.

Course emphasis will be on all fraction concept-applications presented in their correct scope and sequence across the grades including:

• Developing fraction number sense
• The four concepts of fractions
• The definitions of “numerator” and “denominator”
• Comparing and ordering fractions mentally
• Perceiving fraction magnitudes
• Rounding to the nearest whole number and to the nearest half
• Lowest terms and equivalent fractions: generating equivalent fractions and simplifying equivalent fractions to lowest terms
• Renaming to equivalent fractions with least common denominators
• Addition and subtraction of proper fractions with like and unlike denominators
• Mixed and improper fractions
• Addition and subtraction of mixed fractions with like and unlike denominators with and without renaming
• Concepts of fraction multiplication: multiplying by less than 1
• Cross simplifying fractions for proper, improper, and mixed fractions
• Concept of fraction division: why we transform division of fractions to multiplication
• Division of fractions for proper, improper, and mixed fractions
• Comparing and ordering fractions mathematically
• Fractions on the number line

NUMBER THEORY

The number theory unit covers 4th and 5th grades and will present the required fundamentals for all future applications of factoring in algebra through calculus. All of the number theory unit is based on the applications and extensions of the 9 Lines Multiplication Facts Acquisition and Application Strategy™.  Course emphasis will be on developing requisite factoring applications presented in their correct scope and sequence across the grades including:

• Definitions and derivations of factors, products and multiples
• Factoring whole numbers
• Definition and derivation of Greatest Common Factor (GCF)
• Mentally finding the GCF of two products for GCFs ≤ 9
• Definition and derivation of Least Common Multiple (LCM)
• Mentally finding the LCM of two products for GCFs ≤ 9
• Definition and derivation of Least Common Denominators
• Primes and composites
• Prime factorization
• GCF games and factoring puzzles

Extensive color-coding is a critical element of the structure. Please bring 4 colored pens or pencils in blue, green, red and black.

FROM THE DESK OF DAVID BERG, ET:
Published on: August 19th, 2017
The 4 Operations and The 400 Math Facts: The Essential Building Blocks for All Future Mathematics

Optional Academic Credit Costs & Registration: Optional units of credit are available for select courses at the low cost of \$134 per unit, paid directly to CSUEB Continuing Education, by the last day of every course.  CSUEB Online credit registration and payment instructions, along with the MMR grading policy, will be provided on the first day of every class. All credit registrations and payments must be submitted online through CSUEB’s website by the end of each course. No exceptions.

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