**Making Math Real: Mental Math Intensive**

** **Online 6 half-day mini-course via Zoom

**Spring 2023 Offering: May 6-7, 20-21, June 3-4, 2023 | 9:00 am-1:00 pm PT****Registration Fee: **$749***Mandatory Prerequisite: ***All students who enroll in this mini-course must have completed the Making Math Real: Overview K-12 and the The 4 Operations & 400 Math Facts courses.*

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*participants will create their own materials in class*.

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**Zoom Instructions & Online Class Etiquette Guidelines**

**The focus of the Mental Math Intensive will be on:**

- Brand new material, never before presented in any MMR class
- Extensions for all students as well as accelerated learners
- For all 4 operations math facts
- Expansions of the addition and subtraction facts with specific mental applications within two and three-digit addition, subtraction, and multiplication problem solving
- Expansions of Balancing 0s to introduce “Simplifying 0s”
- Expansions of the division facts in combination with increasing and decreasing decimals by powers of 10 to mentally solve multi-digit decimal and whole number division problems
- Mental solving for missing addends, minuends, and subtrahends in 1, 2, and 3-digit problem solving
- Deepen integration of symbol imaging
- Increasing and decreasing by powers and multiples of 10 using multiplication and division
- Opens the door to the unlimited expansions for accelerated learning

As presented in the Making Math Real: *Overview K-12*, the development of numeracy is based on two separate domains of mathematical processing and development:

**Exact Math:**the paper-pencil-based algorithmic structures of problem solving.**Approximate Math:**the integration of mathematically-based organizational structures supporting mental math applications including estimation and numerous forms of mental problem solving.

Each of these domains is completely distinct in terms of the way the brain activates and applies their respective structures, and therefore, the way in which we structure their respective instruction to students is also completely distinct. **Exact Math** is a parietal-temporal integration and its instructional structure is both “concrete to abstract” and the “integrity of incrementation”; and **Approximate Math** is a frontoparietal integration that relies heavily on the development of a significant array of regulatory executive processes that support front-to-back connections in the brain as well as the integration of a strong number sense-based mental organizing system. The way the brain processes each of these is entirely different, so all instruction must account for these differences, therefore, we do not use paper-pencil structures to teach and apply mental math structures, and we do not use mental math structures to teach and apply paper-pencil structures.

The successful and comprehensive development of numeracy requires balanced distribution of paper-pencil and mental math instruction and development across the grades K-12, and it is incumbent upon all math educators to account for this distribution within lesson planning and scopes and sequences within and across the grades.

Although there are ample inclusions of mental math structures and development throughout all the Making Math Real courses, this *Mental Math* Intensive Mini-Course will provide an unprecedented focus on purely mental math applications that have never been presented in any Making Math Real course to date. These unique mental math incremental structures are also part of, and open the door to another domain of Making Math Real that has never been presented publicly: Making Math Real for the accelerated learner.

*IMPORTANT NOTE: THE MENTAL MATH STRUCTURES INCLUDED IN THIS MINI-COURSE ARE INTENDED FOR ALL STUDENTS, NOT JUST FOR THE ACCELERATED MATH STUDENT*

The mental math incremental structures presented in this Intensive Mini-Course will introduce the earliest levels of expansions to the basic MMR structures, and will provide the basis for possible ongoing expansions outside the parameters of this introductory course. Therefore, all the mental math methods presented in this course are appropriate for all students, not just for accelerated students.

Since the development of automaticity is far more challenging for the addition and subtractions facts, the focus of this mini-intensive course will be on the expansions of the addition and subtraction facts with specific mental applications within two and three-digit addition, subtraction, and multiplication problem solving as well as deepening the developmental integration of symbol imaging. In addition, mental applications for solving for missing addends, minuends, and subtrahends will be included, which provide the specific organizational structures for solving the more challenging addition and subtraction-related word problems. Lastly, mental applications of multiplication and division for increasing and decreasing by powers and multiples of 10 will be included to support mentally solving multi-digit whole number and decimal division problems.

Since all the content in the *Mental Math Intensive Mini-Course* is based on the content from Making Math Real: *The 4 Operations & 400 Math Facts*, all participants must have successfully completed Making Math Real: *The 4 Operations & 400 Math Facts* course to enroll in the *Mental Math* Intensive Mini-Course.