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

*What are middle reviews?*

The word “middle” refers to middle school (grades 6ą8), although this book is adaptable to junior high. The word “review” suggests repetition, although certainly practice may include some extension of knowledge. The word “middle” parallels the word “grade” in *MAVA Math: Grade Reviews* which is a collection of reviews at the elementary school level.

*What is the importance of cumulative review?*

Children cannot learn without cumulative review. All children, regardless of math ability, have difficulty remembering skills and concepts unless practice occurs within a school year as well as from year to year.

*On which curriculum is this book based?*

A Curriculum Guide corresponding to the problems in this book appears after the two sample tests. Curricula vary somewhat from school to school and book to book. This book uses a blend of common approaches for basics as well as enriched material for insight.

*Does this book use a developmental approach?*

Yes, this book’s curriculum advances each topic from level to level. All 97 topics progress from Level 6 to Level 7 and from Level 7 to Level 8. Careful checking of the problems in this book has produced a logical plan of concepts and skills within each topic.

*Are these topics and problems all that exist in a typical curriculum?*

No, these topics and problems comprise a representative sample within the framework of the book–namely, 10 problems per page in a 2-column format. Some valuable exercises, such as statistical graphs, cannot fit in the allotted space. Creating a totally comprehensive math book is virtually impossible due to the richness of mathematics. Moreover, a curriculum that is too broad does not permit mastery.

*Why does this book have so many problems?*

People need practice to master any skill–not only in math but also, for example, in music and sports. The MAVA Math series of textbooks provides plentiful problems, so needed by students but often unavailable.

*How is this book best used?*

At one school students may study percents in the fall, whereas at another school students in the same grade may study percents in the spring. Thus, to make this book universally appropriate, the review problems cover the entire grade level rather than follow the sequence of one school or another. This book is best used by starting a grade level in January of that grade, completing about one third during the second semester, completing another third during the summer, and then completing the final third during the first semester of the next school year. Sixth graders would complete the last third of Level 5 of *MAVA Math: Grade Reviews* in the 1st semester of grade 6, the 1st third of Level 6 of this book in the 2nd semester of grade 6, the 2nd third of Level 6 of this book over the summer, and the final third of Level 6 of this book during the 1st semester of 7th grade. In the 2nd semester of 7th grade, students, having had a half year of 7th grade math, would begin Level 7. Then the cycle repeats. The supervising adult, whether teacher or parent, should spread the reviews over the available number of weeks.

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

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

*What is the grade level of this book?*

While this book aims at grades six through eight, some students may begin earlier. Also, students in high school lacking certain concepts and skills may find this book useful.

*What do the headers “Level” and “Number” mean?*

“Level,” a synonym for “grade,” is a more flexible word because children may work above or below grade level. “Number” simply counts the review pages. Within a level, a lower number does not imply that the review is easier than one with a higher number.

*If a problem type is listed in one level, does it also appear in later levels?*

The Curriculum Guide shows where a problem type first appears. While problem types are cumulative within this book, the significant increase in math from level to level prohibits thorough repetition. “None” in the list means no new problem types.

*Does this book have a corresponding Number Sense book?*

No. Mental math exercises are among the many problems in the reviews. Students should always be conscious of using number sense rather than using a calculator or doing a full operation algorithm.

*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.

*Should students complete a page before starting another page?*

Because curricula vary among publishers and schools, students may omit occasional problems from a page and then return to them later. Also, students need not do the pages in order within a grade level.

*Was this book field tested?*

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

*May parents help with the reviews?*

Students who receive continual help from their parents often show significantly less growth in math than students who learn to work independently. Moreover, most parents have forgotten middle school 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.

*Why are occasional problems quick or easy?*

An occasional quick or easy problem on a problem set is a welcome respite for a student and keeps both the pacing and progress moving forward.

*Does this book prepare for future math instruction?*

Yes. This book looks ahead to skills needed for classic algebra word problems. Moreover, this book provides a solid foundation for high school math, including the college admission SAT, for which a rich math education is important (fictitious operations as one example), and the ACT, for which broad retention of topics is essential.

*Should students use a calculator with this book?*

Students should not use a calculator. While starting calculator use in 6th grade is often appropriate, this book encourages practice of basic skills and number sense/mental math.

*Why are the decimal points bold?*

Some children 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 are answers distinguished from work in MAVA Math: Middle Reviews Solutions?*

Work is shown in the same font as the problem. Answers appear on the answer lines or in the charts. Otherwise, answers are circled to distinguish them from the text or from work. Students should be encouraged to circle answers not on answer lines or in charts.

*What happens if a student has trouble with a problem type in this book?*

Cumulative reviews help to find topics that children have not truly learned. Remediation, by backing up in grade level as much as necessary, should occur.

*Why do some answers abbreviate words?*

Math time should not be treated as an opportunity to teach language arts, whether spelling or handwriting. Too many students have difficulty with math or learn to dislike the subject. Attaching verbal skills to the study of math handicaps many students otherwise talented in math. Ideally, students will learn to correctly spell and neatly print math vocabulary words. However, requiring these skills while learning math is self-defeating. Most abbreviations used in this book are found on page vi.

*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 incorrect.

*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.

*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 plugged in directly to check its validity. However, measurements are best as mixed numbers. For example, one and three fourths cups flour is more helpful than seven fourths cups.

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

In Level 6, this book helps students organize their thinking by presenting an outline for some answers in the form of a blank chart or diagram. However, by Level 8, students should be able to create proper work in a blank space.

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.

*Why are some answers in bold font?*

In charts, number lines, and the like, some numbers come with the problem and some numbers are answers. To distinguish between the two situations, the bold numbers are answers. The numbers in regular font appear in the student book as part of the problem.

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

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? Students should understand both methods and decide based on the numbers in the problems. To find the slope of a line given 2 points, which point should be considered the 1st point and which the 2nd? Again, students should decide based on the coordinate numbers, always seeking fast and accurate calculation. The inherent richness and beauty of math yield multiple approaches to many problems. Moreover, some students prefer one way of thinking and some another.

*Why do some of the 97 topics have “see” following them?*

Due to the richness of math, placing a concept or skill into a category may be difficult. For example, GCFs may be included with fractions or with factors. Math topics should not be thought of as residing in closed cubbyholes but in porous receptacles. When problem types in this book are fully or partially covered in another category, the references appear in the topic heading.

*Why does this book contain 2 pre-algebra sample tests?*

The 2 sample tests, not comprehensive of the over 500 skills in this book, offer a means to test retention. No calculator and 90 minutes duration are suggested guidelines to evaluate highest performance. A student who scores low on the 1st test should study further before taking the 2nd test. The problems are straightforward to enable students to work quickly.

*How can one learn more about various problem types and solution methods such as GCF, LCM, prime factorization, cross-tabulation charts, and Multiplication Principle?*

Because MAVA Math books are more for practice than teaching, www.mavabooks.com offers public service chalkboard slide shows giving instruction on various topics. Visit the website often because new material appears continually.

*Does MAVA Math have another middle school level text?*

*MAVA Math: Middle Reviews* is designed for all middle school students, intended to supplement the daily textbook. *MAVA Math: Enhanced Skills*, with topics arranged alphabetically, is more advanced for 6th, 7th, and 8th grade students who wish to study math in depth or to enter math competitions.

*What are the words in chalkboard font in MAVA Math: Middle Reviews Solutions?*

Work is shown in the same font as the book. Chalkboard font is used for commentary such as an insightful method.

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

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

*What should a student do if MAVA Math: Middle Reviews is too difficult?*

If this book is too difficult for a student, then the message is clear: either the student has not been taught adequate math in elementary school and/or the student has not retained the math taught. Such a situation is common with students who have not done cumulative review regularly. Backing up to MAVA Math: Grade Reviews is recommended.

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

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

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

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

*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.”

*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 uses diagonal fraction lines only in paragraph form or in the hints due to limited space.

*What happens if MAVA Math: Middle Reviews Solutions contains an error?*

MAVA Math: Middle Reviews Solutions was thoroughly proofed. However, any needed corrections will be posted on www.mavabooks.com. If a correction does not address your concern, please send a concise and precise e-mail to info@mavabooks.com.

*Should math be fun?*

Of course, math should be fun. However, teaching math solely as a game does not lead to growth. Students who complete weekly cumulative reviews gain enough practice to truly learn math. Understanding in turn leads to natural enjoyment. Competence is pleasurable.

© 2013 Marla Weiss