Errors and/or Comments (Updated Printing) July 14, 1999

NOTE: Because of the prerequisites for our sequence from this book, we do not use Chapter 14.

Code: blank space added ( b ).


• There are several places where there are bad line breaks such as p. 42, #6d; p. 86, Ex 2.4,
T = {w, c, f}; p. 107, #34; p. 149, #20; p. 175, #27.

• Bad page breaks such as pp. 117-118, #19; pp. 383-384, #22.

Page/Chapter Error and/or Comment
p. 80 Apparently, there is no statement that elements should be listed only once in a set. (cf. p. 91, #7a)
p. 89 (B C) should be beneath figure to the top right.
p. 95, #30 If neither antigen is present, 
p. 96 Last two lines: A is NOT equivalent to C, and B is NOT equivalent to C.
p. 104, #17 Delete "it" from next to last line.
p. 110, Fig 2.15 Cuisenaire™ rods (or colored strips to match the rods) would be a better manipulative to demonstrate the associative property. The process is not clearly illustrated with the square tiles.

p. 113, ¶3, line 4 However, b
p. 114 Number-line Model: Arrow representing subtrahend should be pointing in the opposite direction for clarity. This is particularly true for connections to inverse operations. THE STUDENTS HAVE REALLY COMPLAINED ABOUT THIS!!
p. 127 4 ‡ 3 = 12 Think: 4 rows of 3 is 12. (I checked this in SF book. It is wrong there, too.)
p. 168 "Cloud" 2000 + 500 + 70 + 2; also 2572 = 2 • 1000 + 5 • 100 + 7 • 10 + 2
p. 174, 17c The spelling of represent on second line
p. 175, 27c Should be  and not A
p. 184 Devise a plan . . . 10 strips form a mat.
p. 186 ff "Leaving out the zeroes" does not help conceptual understanding in any operation. The common remark from students is why were we not taught "the correct way" so we would not make place value mistakes.

Instructional Algorithm II is being suppressed in my book with a magic marker, and I hope in all my students' books.

p. 188 ff "Carrying" should not be anywhere in the book. Trading, exchanging, and regrouping are preferred terms. Instructional Algorithm II loses all the benefits of the emphasis on place value.
p. 197, #15 Blanks look like minuses!! Format as in #14. 
p. 197, #15b Blank in front of 346.
p. 198, #25 The assumption is that Jennifer chooses one of each (4 • 3 • 2 = 24). If she chooses one sweater or blouse and one pair of slacks, that would give 
7 • 2 = 14.
p. 203 Second line above Example 3.17. ". . . 9, 24, 31 as noted above."
p. 206, #3 The "colored 2" is extremely hard to see.
p. 207, #7 The drawing is very confusing. Since I knew what was suggested, I worked backward. Maybe, that is not so bad. Yes, it is! I have three different markings to determine the information given.
p. 208, #13 Should be sequence and not sequences
p. 209, #18 Line 8: Place the products . . .
p. 210, #23 MASS not weight. Weight = mass • gravity.
p. 249 Rectangular array should be labeled 35 = 5 • 7 to be consistent with definition on p. 121.
pp. 253-254 The example indicates that the 600 is to be represented as the product of prime factors. At the end of the example, the prime power form appears. That line should be deleted, and the paragraph below should begin. In Example 4.3, suppose we write the representation of 600 as a product of powers of primes . . . 
p. 268 + signs should be inserted and vinculum extended for clarity and emphasis.
p. 281 LCM by intersection of sets. The inclusion of zero is confusing; but by the same token, students are uncomfortable with each non-zero integer being a multiple of zero by definition on p. 249.
p. 285, #14 Since I have used this activity for 20 years, I thought we were on the right track. However, the sentence "We say . . . given rod." needs some editing. After two semesters of "What does this mean?", I would like to see directions comparable to p. 78.
p. 285, #16 I know I missed the point on this one!! The problem did provoke a lot of discussion.
p. 287, #28-29 Even though #28a clearly states the three numbers, the "extra" commas created confusion.
p. 295 Under the clock, 5 -12 = 5 +12 3 = 8.
pp. 316-317 Actually, the use of the superscript for the additive inverse, opposite of, or negative integers has been one of the best innovations; and the exclusion of the use of the superscript is a weakness. Many middle school teachers have indicated that even if their textbooks do not use it, the teachers insist on it. Students want to read "negative 5" as "minus 5" otherwise. 
p. 320 The title of the theorem: The negative of the negative of an integer is at best careless and at worst a misunderstanding of the fact that negative numbers are numbers less than zero. 

x + 12 = 7 implies x = -7. Thus, x is negative. 

-x + 7 = 2 implies -x = -5 implies x = 5. Thus, x is positive. 

-x + 7 = 12 implies -x = 5 implies x = -5. Thus, x is negative. 

p. 342, #8a,line 3 below 0,
p. 345, #34 By noon, ... by ,
p. 345, #38 Velocity not "speed"; e) Clarify t = 0 and 6, t = 1 and 5, and t = 2 and 4.
pp. 346-354 Strong doubts exist that the models for -4 • 5 = -20 and -4 • -5 = 20 will illuminate the situation. Problems 12-14 on pp. 357-358 are better. 
p. 370 ff I do not know what reaction there has been on fraction vs rational number. However, I do know that, for mathematicians, the definition on p. 372 is for rational numbers not fractions. The comment on p. 380 is better, but . . .
p. 376 Restriction to "reduced fraction" would have been better. The inclusion that the denominator be positive is a great feature!!
p. 377 Method 3. Prime power representation, not prime factorization, has been used.
p. 383, #22e-f Arrows need to be drawn from the cloud at the bottom of the page to each part for further clarification.
p. 389f There is no model for the concept of mixed fraction. The old rule is there!!
p. 404, #24 The definition of unit fraction should occur explicitly in Section 1. 
p. 436 "Slipping and sliding decimal points" is a method used when the person does not understand the concept of place value in decimals. On p. 434, there was a nice start with the chart, but the use of manipulatives would be even better. With place value, Example 7.2 could be solved by the following. (103)(253.26) means the ones digit in 253 should be in the thousands place in the product—253 260.

(253.26) ÷ 103 means the ones digit in 253 should be in the thousandths place in the quotient—0.253 26.

No guessing and no slipping-and-sliding are required!!

No wonder students and teachers do not know what to do with computations in decimals, computing percent, and writing numbers in scientific notation! 

p. 438, Last line . . . = -
p. 444 Example 7.6b has 23.4 as the problem, but the solution is for 23.
p. 447 Example 7.8, Understand the problem: . . . that is, is not rational, . . .
p. 449, #4 Determine the reduced rational number represented by these periodic decimals.
p. 449, #11, 
line 2
First Printing had "digits"; Updated Printing has "zeros." I think the intent of the problem was "digits" since reduced and 2 •  are used in the problem. However, the students have to think a little harder with "zeros"!
p. 454 ff Why include the traditional model? The mathematical error of 19 056 appearing in a product of two numbers that are approximately 32 and 5 is unbelievable! This violates everything a good mathematics teacher tries to do with estimation. Division is just as bad because the remainder is not 3 on 
p. 456. The remainder is 0.000 003.
p. 457, 460 The zero should be in the units place in appropriate places in the decimal expansion of  and 0.3333 . . . 
Same comment on decimal expansion of .
p. 459 In the line above Example 7.14, an additional statement should state that "Some calculators display 6.709 E 09. This display is equivalent to 
6.71 • ."
p. 465 "Expressing a ratio . . .fraction to simplest . . ." does not make sense.
p. 468 Devise a strategy: The second line should be "say that  . . ."
p. 474, Sect 7.4 Percentage change is a difficult concept to teach yet one of the most used concepts in everyday life, e.g., inflation, salary increases, production rates, etc. This is passed over until the problems. Unless the course instructor is really alert, the concept will be neglected.
p. 475 Slipping and sliding decimal points!! Place value is the key.
p. 475 Example 7.24c: The problem is 2.15, but the solution is for 1.255! 
p. 477 Solution to b: =.
p. 501  In Figure 8.11, the sum of the percentages is 105!!!
p. 495 Under Histograms, Third sentence: In a histogram, scores may be . . .
p. 515 The section begins saying that "average" has several meanings. Even though common usage equates arithmetic mean and average, for purposes of being accurate average ought to be deleted from the first sentence of the section on the mean and from the definition.
p. 516 Replace average with mean in definition of median.
p. 516 Delete comma: "Also, it follows from the definition that . . ."
p. 516 Read the definition of mode. There are several ways to approach the definition with clarity. For example, the mode is the value which occurs most frequently. Then, a note can explain how different books handle more than one such value.
p. 519 Upper and lower quartiles: Rank the data. The lower quartile is the value a fourth from the bottom; and the upper, fourth from the top. Repeat discussion on even versus odd as in definition of median. Also, this approach can be extended to percentiles. 

The class had no problem with our discussion, but a student who was absent said that the definition had to rank among the most confusing! 

p. 528, #10 The sentence " denotes . . . number." should be in part d).
p. 539 First line of theorem, distribution
p. 548 Add program RANDOMNUMBER to list, and change program to programs in line 2. 
p. 555 Last two lines: Since six . . . is  0.21.
p. 567 Line above dice display: ". . . + n(11)."
p. 572, line 2 and line 1 of ¶2 under Look back affect not effect
p. 580 Ex 9.21. The only reference in Section 1.6 is on p. 65. The discussion of bar codes is on pp. 298-302.
p. 583, line 2 below definition "If the outcomes in the sample space are not equally likely, this particular definition . . ."
p. 614, ¶3 The emphasis on using three points to name an angle in which a vertex is the vertex of more than one angle is good. There are places (see next line) where clarity is lacking in problems and drawings. Perhaps, in the next edition, more consistency about the use of three points or writing a number in the interior could be introduced.
pp. 614, 629 ¶2 An angle partitions BUT DOES NOT SEPARATE a plane. A part of the definition of separation requires convex sets. The exterior of an angle is NOT a convex set. One of the emphases of the NCTM STANDARDS is correct usage of mathematical terms.

Jordan Curve Theorem

p. 621 Theorem: delete commas "around" and only if.
p. 625, #9a-b "Carefully measure the angles with vertices . . . 
p. 631 Definition: delete commas "around" and only if.
p. 637 On the "definition" of isosceles triangle, the type of statement used with trapezoid would be better than the parenthetical phrase.
p. 640 Line 2. "make good advantage"???

Level 0, Line 4. "traingle" should be "triangle."

Level 3. Delete comma after system.

Last paragraph, next to last line. "creating" does not modify students!!

p. 646, #17 "partition" and not separate
p. 663, #6 I have the class tear a tangram as I'm introducing the polygons. Then, the class has to complete a chart showing how to make various regions with a certain number of pieces.

For my purposes, I move that problem to Section 10.2.

By the way, a nice reference to add to that problem is Grandfather Tang's Story written by Ann Tompert and published by Crown Publishers Inc.

p. 664 More problems using pentominoes would be helpful. For example, use V, P, W, T to make a 4 by 5 rectangle. Such problems improve spatial visualization skills. Some problems could be introduced here to reinforce tiling, but also could be very helpful in Chapter 12. I have introduced pentominoes very early in Chapter 10 material.
p. 702, ¶2 I hate to sound sexist, but have you men ever tried to make doll clothes by copying a paper pattern onto cloth? I don't think so! For those of us who sew, this phrase gives a good laugh!!!

There should be a comma after "As adults, . . ."

p. 717, #4 Comma after B in the first line
p. 717, #6 Replace "the length of CD is greater than AB" with AB > CD. If you want to leave the words, then insert "the length of" before AB. 
p. 721, #35 Replace construct with draw in the first line.
p. 735, #8b Should read "a Mira (if available) and compass"
Chapter 12 In the book, I think too much emphasis has been placed on the US System of measurement. The metric system is so much easier to use. I introduce the metric system from day one. I require the students to use centimeter graph paper and a metric only ruler. By the time we officially study measurement, the students have experienced the connection between our decimal system and the metric system.

When I first made the comments above, I had not taught the book. My opinion has been reinforced after teaching the chapter. An instructor auditing the course suggested that I use the material in Section 12.1 as appropriate to other sections of the chapter. She further suggested that the problems that may be important be integrated into later sections.

Section 12.2 was easy to teach with perimeter and area in the same section. This is the first book for this sequence that has attempted to use the units. In most instances, units were appropriately handled. However, I have a "little" complaint. On p. 784, Example 12.9, no units were given. The way to handle lattice area is to say that the distance between two vertical or horizontal pegs is one unit. Then, the area can be expressed in square units.

Section 12.3 refers to units; but in general, no unit is used. 

Section 12.4 can be described as a hellish experience. The students are so weak in surface area and volume. The problems lumped surface area and volume together. That would be fine if there were problems in which the individual concepts could be reinforced. 

The students suggested in their last journal entry that I dump the book (Section 12.4) for the next class and treat the topics individually and then use the problems that combine the concepts as "review."

p. 791, #13c The measurements given do not form a triangle. We decided 5.4 cm should be 15.4 cm.
p. 807  Last line of solution: Parentheses should be inserted around 384 + 960.
p. 808 Above and to the right of "Surface Area of a Right Cylinder": cm and not
p. 808 Last line of solution: Parentheses should be inserted around 20 + 100.
p. 809 Example 12.20. Last sentence of statement of problem: What is the surface area of the cone? 

Last sentence on page: This is also the surface area of the cone. 

p. 810, ¶2, line 3 Capitalize v.
p. 812 Formula: . . . base of area
p. 826, #38 Start new ¶ "For each of the following solutions (or responses) write . . ."