#### Completing the 9 Lines Class Before the Fractions Class:

The Highest Advantage for Maximizing Your Learning

For those of you new to Making Math Real, The 9 Lines Multiplication Facts Acquisition and Applications Strategy is the best known and most widely practiced of all the Making Math Real Simultaneous Multisensory Structured Methodologies K-12 around the world. The 9 Lines is extremely effective, powerful, and develops the automatic retrieval and immediate application of the 100 multiplication and the 100 division facts. I consider the development of automaticity with the multiplication and division facts to be the most valuable development during the elementary grades.

Once students have learned the 9 Lines in early 3rd grade, the structured applications of the 9 Lines will directly support almost ** ALL** the math content areas that follow including all multiplication and division applications for whole numbers, fractions, and decimals, primes and composites, factoring: whole numbers and prime factorization, finding greatest common factors and least common multiples, exponents, and most significantly,

**, and this is only referring to grades 3, 4, and 5! 9 Lines applications also support the vast majority of math content from pre-algebra through calculus.**

*FRACTIONS***SUCCESS WITH FRACTIONS IS BASED ON 9 LINES APPLICATIONS, SO I CREATED THE 9 LINES STRUCTURE AND FORMAT SPECIFICALLY TO SUPPORT SUCCESSFUL FRACTIONS PROCESSING**

Almost all fraction applications require automatic retrieval of the multiplication and division facts: the four operations with fractions, especially addition and subtraction with proper and mixed fractions with unlike denominators, lowest terms and equivalent fractions, transforming mixed and improper fractions, and comparing and ordering fractions. Over the five decades I have been an educator, there has been an 80% failure rate nationwide (*Hard Lessons: Why Rational Number Arithmetic is So Hard for So Many People*, Siegler and Lortie-Forgues, 2017) for fractions and a major contributing factor has been students’ lack of automaticity with the multiplication and division facts. A key representative example of the significant need for automatic retrieval of the multiplication and division facts for processing fractions is the ability to find the greatest common factor (GCF) of two products. The ability to find the GCF of two products in which the GCF is ≤ 9 accounts for nearly all fractions applications in the elementary grades, and I created and designed the 9 Lines structure and format specifically to maximize students’ mental ability to find the GCF of two products in which the GCF is ≤ 9. The most prominent and powerful application of finding the GCF of two products is in simplifying equivalent fractions to lowest terms and generating equivalent fractions; and in using the 9 Lines, students can mentally simplify or generate equivalent fractions immediately.

**MAKING MATH REAL: FRACTIONS, DECIMALS, and ADVANCED PLACE VALUE IS SCHEDULED FOR THIS FALL…**

Baseline readiness for pre-algebra is the comprehensive integration of the four operations for whole numbers, fractions, and decimals and automatic retrieval of the 400 math facts. This crucial fundamental for algebra readiness is the basis for the two biggest Making Math Real courses: *The 4 Operations & the 400 Math Facts* and *Fractions, Decimals & Advanced Place Value*. Both of these courses are primarily based on the 9 Lines applications, and whereas I have not made the 9 Lines Intensive course a mandatory prerequisite course for *The 4 Operations & the 400 Math Facts* and *Fractions, Decimals & Advanced Place Value*, perhaps I should have… All MMR participants who have completed the 9 Lines Intensive prior to these courses have the highest advantage in maximizing their learning experience in these two seminal courses.

Rather than making the *9 Lines Intensive* a required prerequisite for *The 4 Operations & the 400 Math Facts* and *Fractions, Decimals & Advanced Place Value*, I have instead, encouraged all of you to complete the *9 Lines Intensive* prior to taking these courses by consistently scheduling *9 Lines Intensive* courses after the *Overview* course two times per year; and on the Recommended Course Sequence Guide, I have prominently placed the strongest recommendations for completing the *9 Lines Intensive* prior to enrolling in *The 4 Operations & the 400 Math Facts* and *Fractions, Decimals & Advanced Place Value*.

**…AND THE NEXT ***9 LINES INTENSIVE* IS SCHEDULED FOR THIS SUMMER,

**SO YOU CAN COMPLETE THE ***9 LINES* CLASS BEFORE THE *FRACTIONS* CLASS THIS FALL

**…AND THE NEXT**

*9 LINES INTENSIVE*IS SCHEDULED FOR THIS SUMMER,**SO YOU CAN COMPLETE THE**

*9 LINES*CLASS BEFORE THE*FRACTIONS*CLASS THIS FALLThe next Making Math Real: *The 9 Lines Intensive* is scheduled for June 20 – 28, 2022, and will not be offered again until February 2023; and the next *Fractions, Decimals & Advanced Place Value* class will not be offered again until Fall 2024. This summer’s Making Math Real: *The 9 Lines Intensive* is the best opportunity to take advantage of this optimal timing for maximizing your learning of MMR right now.

*Don’t miss out!*

Be well and stay healthy.

*David Berg, E.T.*

Founder & Director of the Making Math Real Institute

Creator of the Making Math Real Simultaneous Multisensory Structured Methods