**An Important Message To Teachers, Parents, and Students**

*What are Enhanced Skills?*

All *MAVA Math* workbooks have two-word titles: *Number Sense*, *Grade Reviews*, and *Middle Reviews*. *Enhanced Skills* keeps that format while indicating that the combined lessons are of a more advanced nature, suitable for students who wish to study math in depth or to enter math competitions.

*What is this book’s curriculum?*

The detailed specificity of the Contents acts as a curriculum guide. This book includes a blend of basic skills as well as enriched material.

*What is the grade level of this book?*

While this book aims at grades six through eight, some students may begin earlier or later.

*How many years should students take to complete this book?*

Mathematically gifted students may complete the book in grades 6 and 7, finishing any remaining pages concurrently with Honors Algebra I in 8th grade. Other students could complete the book in 3 years.

*Why do topics appear in alphabetical order?*

Presenting the topics in alphabetical order offers maximum flexibility for teachers and students who may construct their own desired progression of lessons. Alphabetical order also permits students to easily supplement classroom work or contest preparation.

*Does this book use a developmental approach?*

Yes. Within each of the 79 topics, lesson 1 precedes lesson 2 developmentally. With AGE PROBLEMS for example, students should learn how to solve problems linearly prior to constructing charts. However, for the topics with many lessons, slight reordering may make sense for some teachers and students.

*Are these topics and problems all that exist in advanced middle school math?*

No. While this book is very comprehensive, another 426 pages still would not exhaust the rich variety of possible exercises.

*Does this book’s curriculum vary dramatically in any way from those typically seen?*

Yes. This book’s breadth, depth, and quantity of problems are not commonly found in one comprehensive volume.

*Was this book field-tested?*

Yes. Many problems in this book were used as part of comprehensive worksheets written by Marla Weiss for classroom settings. This material, unified for the first time in this book, yielded students who loved math, performed high on standardized tests, and earned countless awards at math competitions.

*Does MAVA Math offer another middle school level workbook?*

Yes. *MAVA Math: Middle Reviews*, intended to supplement the daily textbook, is designed for all middle school students. The accompanying answer book is *MAVA Math: Middle Reviews Solutions.*

*May this book be used as the sole textbook?*

Yes. This book in draft form was used as the sole textbook, supplemented with contest materials, for grades 6 and 7. Those students excelled in math.

*Should certain pages of certain topics be done before others?*

Yes. For example, students should know DIVISIBILITY 1 (rules) before FRACTIONS 1 (simplifying) or FRACTIONS 2 (multiplying). This book trusts teachers to order math.

*Does this book prepare for future math instruction?*

Yes. This book provides a solid foundation for high school math, including algebra skills, algebra word problems, plane geometry, and space geometry.

*Should students use a calculator with this book?*

Students should use a calculator only when absolutely essential. This book encourages practice of number sense throughout, not only on the pages titled MENTAL MATH.

*What are the different types of MENTAL MATH?*

Mental math may mean: 1. responding to an oral question; 2. doing all work in one’s head for a written problem; and 3. doing minimal written work for a written problem.

*Does this book cover a complete course in Algebra I?*

No. This book covers most topics in pre-algebra and some topics in algebra but is not in any way intended to cover a full Algebra I course.

*Why do some answers abbreviate words?*

Math class is not an opportunity to teach language arts, whether spelling, handwriting, or composition. Attaching verbal skills to the study of math slows students both in daily work and annual progress. Ideally, students will learn to express themselves mathematically. However, mathematicians write in a specific style, totally different from English essays. Most abbreviations used in this book are found on pages 427ą428.

*Why do some geometry problems use upper case as well as lower case abbreviations?*

When a problem involves two circles, use capital R for the radius of the larger one and lowercase r for the radius of the smaller one. Moreover, use B for the larger base of a trapezoid and b for the smaller one. Clarity of notation leads to improved focus and accurate answers.

*Why are the answers to some measurement problems a number without a label following?*

Consider the question: How far do you live from school? The answer could be 2 miles or 2 turtle steps. A label is needed for accuracy. Now consider the question: How many miles do you live from school? The answer may be 2 without ambiguity because a label, namely miles, is built into the question. Requiring a label at all times is unnecessary.

*Should all improper fractions be converted to mixed numbers?*

No. The term “improper fraction” is a misnomer. Converting from a fraction greater than one to a mixed number is a valuable skill, but it need not always be done. For example, as a solution to an equation, the fraction is better because it may be substituted directly to check its validity. However, measurements are best as mixed numbers. For example, one and three fourths cups flour is usually more helpful than seven fourths cups.

*How does a student best learn problem solving?*

While the ultimate goal is to solve a variety of problems in random order, students need to learn one problem type at a time. After mastery, then problems may be jumbled.

*Can cumulative review be built into this book?*

Yes. Students do not have to complete a page once starting it. Returning to a page at a later time builds in cumulative review.

*Why do some problems have charts and diagrams pre-drawn while others do not?*

At the advanced level of this book, students need to be able to draw their own diagrams and construct their own charts. However, in some problems, a diagram shows information that is not in the text.

*Which are more valuable–fractions or decimals?*

Decimal math may be easily done on a calculator. Fractions are more important in higher math. For example, a student who does not understand how to add 1/2 + 1/3 cannot possibly add 1/x + 1/y (diagonal fraction lines for ease of typing only). Furthermore, fractions yield an exact answer when decimals sometimes yield an approximation.

*Do some problems or skills have more than one method of solution?*

Yes. To find the perimeter of a rectangle, should one add the length and width and then double, or should one double each measurement and then add? To find the slope of a line given 2 points, which point should be considered the 1st point and which the 2nd? Students should understand both methods and decide based on the numbers in the problems, always seeking fast and accurate calculation. The inherent richness and beauty of math yield multiple approaches to many problems. PERCENTS 5 (x is y% of z) is just one of many pages that show multiple methods. The WLOG method is another example.

*Why do some of the 79 topics have “see” following them?*

Due to the richness of math, placing a concept or skill into a category may be difficult. For example, integers may be even or odd, and equations may contain exponents. Similarly, a problem about the percent change in the area of a rectangle covers three topics. The placement is often arbitrary. Thus, the ”see” references guide the user.

*Why does this book use two different fonts?*

All problems appear in the Arial font. All work, answers, and comments appear in the Chalkboard font. Final answers are in Chalkboard Bold.

*Why are negative, opposite, and subtraction signs all represented by the same symbol?*

Some math texts use both a smaller, higher line and a longer, mid-level line. Because all three signs operate equivalently, this book uses just the longer, mid-level line for simplicity.

*Why are the decimal points bold?*

Some students do not see decimal points in normal font. Similarly, some students do not write decimal points darkly enough. A happy medium exists between a light dot and a wart.

*How can one learn more about various problem types and solution methods?*

The website www.mavabooks.com offers short videos giving instruction on various topics. More will be added as time permits.

*Why are equilateral triangles also labeled isosceles?*

The definition of isosceles triangle is a three-sided polygon with at least 2 congruent sides. Therefore, an equilateral triangle is isosceles, but the converse is not true.

*Why is functional notation used in situations that do not involve functions?*

Functional notation is precise and concise. For example, P(even) is neater than writing “probability of tossing an even.” Similarly, GCF(35, 49) is neater than writing the “greatest common factor of 35 and 49.”

*What does the word “unit” mean?*

Unit is a general term. Regarding distance, “unit” may mean many different measurements such as inches, feet, miles, or centimeters. Understanding that the label must be square units for area and cubic units for volume is more important than what the actual unit is. By using the generic “unit,” students may focus on specific skills.

Why does this book list over 500 vocabulary words?

Students cannot do math problems without understanding the words contained therein. Unfortunately, many math words have multiple meanings. Consider base–e.g., base of a triangle, base two arithmetic, and a number (base) raised to a power (exponent).

Students learn math vocabulary when they continually hear the words used correctly.

*May parents help with the pages?*

Students who receive continual math help from their parents often show less growth than students who learn to work independently. Moreover, most parents have forgotten math or don’t know the best ways to approach many problems. Parents should only monitor a child’s work, determining weak areas needing further help.

*May students and teachers write diagonal fraction lines?*

Never! For correct fraction work, students must clearly see numerators and denominators, only accomplished by writing horizontal fraction lines. This book occasionally uses diagonal fraction lines for ease of typing only.

*Should students memorize all of the Pythagorean triples and prime numbers at the end of this book?*

No. The lists are for reference. However, math memorization should not stop with the four whole number operation facts. Further memorization, which will speed work, may include primes, Pythagorean triples, formulae, perfect squares and cubes, and square roots of non-squares (root 48 is 4 root 3).

*What happens if MAVA Math: Enhanced Skills or MAVA Math: Enhanced Skills Solutions contains an error?*

Both books were thoroughly proofed. However, any needed corrections will be posted on www.mavabooks.com. Please send a concise and precise e-mail to info@mavabooks.com if a correction does not address your concern.

*Should math be fun?*

Of course, math should be fun. However, teaching math solely as a game does not lead to growth. Students who study rigorous math truly learn math. Understanding in turn leads to natural enjoyment. Competence is pleasurable.

Copyright ® 2015 Marla Weiss