| 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 |
A  (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 product253
260.
(253.26) ÷ 103 means
the ones digit in 253 should be in the thousandths place
in the quotient0.253 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 . . ." |