May parents help with the reviews?
During field testing, the students who received help from their parents showed significantly less growth in math than the students who learned to work independently. Parents should only monitor a child’s work, determining weak areas.
Does this book prepare for future math instruction?
Yes, this book looks ahead to skills needed in classic algebra word problems such as age problems needing charts. Moreover, it provides a solid foundation for middle school math.
Should children use a calculator with this book?
Children should not use a calculator with this book. They are still learning basic facts as well as developing number sense.
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. The 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.
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 4-digit numbers have commas and some do not?
The comma in a 4-digit number is optional. Its use best depends on whether the emphasis is thousands or hundreds. For example, 4100 may be more helpful as four thousand one hundred in one problem but as forty-one hundred in another problem.
Which are more valuable–fractions or decimals?
Decimals are useful in working with money. However, 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. Furthermore, fractions may yield an exact answer whereas decimals would yield an approximation if the numbers in the problem convert to repeating decimals.
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 (see above answer) or in the hints due to limited space.
Why do some problems or skills have more than one method shown in the solutions book?
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, always aiming for easier arithmetic. Similar questions may be asked of other techniques. The inherent richness and beauty of math yield multiple approaches to many problems. Some students prefer one way of thinking and some another.
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, backing up in grade level as much as necessary, should occur.
How can one learn more about various problem types and solution methods such as GCF, LCM, prime factorization, cross-tabulation charts, and multiplication principle?
While MAVA Math books do not have adequate space to fully teach concepts and skills, www.mavabooks.com does offer public service chalkboard slide shows giving instruction on various topics. Visit the website often because new material appears continually.
How rigid is the vocabulary list at the back of the book?
The vocabulary list, similar to the curriculum guide, is approximate. One must have guidelines to chart the progress of students and to have finite work for each school year. However, students learn at different paces across math in general and within specific topics. Moreover, as just one example, a two-year-old may be capable of identifying hexagons. By the end of seventh grade, students should know over five hundred math vocabulary words. This list appears in MAVA Math: Middle Reviews.
Why do some of the word problems have labels next to the work?
Many children have difficulty with word problems. While the labels are not necessary, if they help children focus on how their work matches the problem, then the labels are beneficial. Again, full words are not necessary as long as the students understand the abbreviations they select.
Should a student assume that lines are perpendicular and angles are right even if the symbol is not present?
Yes, at the elementary level, for example, one assumes that a picture of a square is a square, whereas at the high school level students may assume nothing. While some right angles in this book are detailed, marking all of them would introduce too much clutter for young children.