MAVA Math: Number Sense Solutions

An Important Message To Teachers, Parents, and Students: (This Q&A is continued from the “Free Preview” for MAVA Math: Number Sense.) Should students complete a page before starting another page? Students do not need to complete a page before starting another page. In fact, spiraling among pages introduces a cumulative review effect. What is the meaning of the instruction “find”? Some problems have a specific operational instruction: add, subtract, multiply, or divide. However, many problems require the student to obtain a value–for example, a volume or a factor. While instructions of this general type such as “give,” “express,” “complete,” or “name” are often synonymous, this book consistently uses the instruction “find” to avoid confusion. Students should practice the skill and not ponder the wording of the instruction. 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. Can a child really operate from left to right and not get confused? By third grade, some children can notice quickly that a problem has no regrouping. Then writing its answer from left to right is faster and more natural. Reading and writing occur from left to right, as does division. Teaching rigid, absolute methods to talented children leads to lack of understanding and trust. Evaluate the child before sacrificing flexibility. What happens if students start doing problems mechanically, without thinking, by seeing a pattern in the answers? Always consider if a student can do the problem on a cumulative review sheet quickly and accurately. If yes, then the mechanical approach has a foundation. Otherwise, stop and return to the page later. Why are the answers to 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. The questions in this book either do not require labels or, in the case of unit conversions, provide labels. 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 removing the unit, a student may focus on the specific skill. Why do some pages have different font sizes? Often problems have a smaller font size to provide multiple answer columns or to fit within the framework of the book. Overall, a large font size is best for elementary school children. What do the words “increment” and “decrement” mean in MAVA Math: Number Sense Solutions? The comments use the computer programming meanings of these words–increment, to add one or increase by one and decrement, to subtract one or decrease by one. Why do some pages have multiple answer columns? Just as a music student will practice scales regularly, so may a math student practice certain problems multiple times. When space permits, this book provides several answer columns so that students may do a page more than once. First, use the outermost answer column. On the second use, cover that column with a clean sheet of paper, revealing the next answer column to the left. Continue in this manner until all answer columns are filled. Redoing a page after a period of time or the following year acts as a good review. Triple columns may be used in consecutive years for introduction, review, and mastery. Why do some skills have more than one technique discussed in the answer key? Math has inherent richness and beauty, yielding multiple approaches to many problems. Some students prefer way one of thinking and some another. What happens if a student has trouble with a page in this book? The fundamental guideline for this book is “break it down.” For any skill, do it with smaller numbers, or do it with whole instead of fractional answers. Break down the skill until it is as simple as possible. Then after a student is successful with the most basic task, build it back up gradually to the more advanced skill. All skills cannot be broken down totally in 298 pages. Also, a student does not need to attempt every problem or every page. What is the best way to memorize basic facts? Old fashioned flash cards are very helpful when used daily at bedtime for 5 minutes or less. Short, daily repetition over a long period of time is important. One operation each night is fine. Doing flash cards with a family member is supportive and nurturing. Over time with number sense work, other facts such as 85 + 15 or 12 x 5 become second nature. 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 or forty-one hundred in another problem. What happens if MAVA Math: Number Sense Solutions contains an error? MAVA Math: Number Sense Solutions was thoroughly proofed. However, any needed corrections will be posted on www.mavabooks.com. If a correction does not address your concern, then 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 develop number sense gain insight into the beauty of math, in turn leading to natural enjoyment. Competence is pleasurable.