1.
Cynthia, Peter, Nancy, and Kevin arre all carpenters.
Last week each built the following number of chairs.
Cynthia—36 Peter—45 Nancy—74 Kevin—13
What is the average number of chairs they built?
A.
39
B.
C.
D.
E.
42
55
59
63
How could number sense help you
solve this problem?
2.
There are 600 school children in the
Lakeville district. If 54 of them are high
school seniors, what is the percentage
of high school seniors in the Lakeville
district?
A.
B.
C.
D.
E.
2.32%
0.9%
9%
11%
90%
What are the three types of
percentage problems your
students will see?
Susan’s take-home pay is $300 per
week, of which she spends $80 on food and
$150 on rent. What fraction of her take-home
pay does she spend on food?
3.
A.
B.
C.
D.
E.
2
75
4
15
1
2
23
30
29
30
What part of this problem will
cause students to give a wrong
answer?
4. Which of the following expresses
the prime factorization of 54?
A. 9 x 6
B. 3 x 3 x 6
C. 3 x 3 x 2
D. 3 x 3 x 3 x 2
E. 5.4 x 10
What are the only two
possibilities and why?
5. The number 1134 is divisible by
all of the following except
A. 3
B. 6
C. 9
D. 12
E. 14
What are some divisibility rules
that help you here?
6. When is
A.
B.
C.
D.
E.
11  a
2
an integer?
Only when a is negative
Only when a is positive
Only when a is odd
Only when a equals 0
Only when a is even
A calculator would help students
working the last problem.
True
False
7.
On Friday, Jane does one-third of her
homework. On Saturday, she does one-sixth
of the remainder. What fraction of her
homework is still left to be done?
A.
B.
4
9
1
2
C.
5
9
D.
5
6
7
12
E.
What is it about this problem that
assures lots of incorrect answers?
8. If the ratio of 2x to 5y
is 1:20, what is the ratio
of x to y?
A.
B.
C.
D.
E.
1:40
1:20
1:10
1:8
1:4
Work this problem three
different ways.
9.
If the area of circle A is 16π, then
what is the circumference of
circle B if its radius is one-half that
of circle A?
A. 2π
B. 4π
C. 6π
D. 8π
E. 16π
What percentage of your
students will correctly answer
that geometry problem?
Vocabulary
Introduction: Why Study Vocabulary in
Math Class?
The thesis of this book is that vocabulary
acquisition impacts the learning of
mathematics.
Confident math students understand and
use the specialized vocabulary associated
with the math they are doing, where every
word. . .clarifies a given situation
Descriptions of mathematically
powerful students

Understand the power of mathematics as
a tool for making sense of situations,
information, and events in their world

Are persistent in their search for solutions
to complex, messy, or ill-defined tasks
Descriptions of mathematically
powerful students (con’t)

Enjoy doing mathematics and find the
pursuit of solutions to complex problems
both challenging and engaging

Understand that mathematics is not just
arithmetic
Descriptions of mathematically
powerful students (con’t)

Make connections within and among
mathematical ideas and domains

Have a disposition to search for patterns
and relationships

Make conjectures and investigate them
Descriptions of mathematically
powerful students (con’t)

Have “number sense” and are able to
make sense of numerical information

Use algorithmic thinking, and are able to
estimate and mentally compute
Descriptions of mathematically
powerful students (con’t)

Work both independently and
collaboratively as problem posers and
problem solvers

Communicate and justify their thinking and
ideas both orally and in writing
Descriptions of mathematically
powerful students (con’t)

Use available tools to solve problems and
to examine mathematical ideas
Pick a goal or two (or three)
These descriptions are
on pages 3 and 4.
Discuss them in your
group
Identify several that you
will target this year
Write them down!!!!!!!
BIG IDEAS
All Students need to be mathematically
literate
 Mathematics vocabulary, studied in
context, has a profound effect on
performance
 Vocabulary instruction. . .supports learning
new concepts, deeper conceptual
understanding, and more effective
communication

Mathematical communication
requires more than mastery of
numbers and symbols. It requires
the development of a common
language using vocabulary that is
understood by all.
From NCTM’s Curriculum and
Evaluation Standards for School
Mathematics (1989)
Writing and talking about their
thinking clarifies students’ ideas
and gives the teacher valuable
information from which to make
instructional decisions.
Emphasizing communication in a
mathematics class helps shift the
classroom from and environment
in which students are totally
dependent on the teacher to one
in which students are assume
more responsibility for validating
their own thinking.
Miki Murray lays the groundwork
Letter to the parents
Day 1: ”Expectations for Mathematics,”
Binder Organization and Problem
Exploration
Day 2: Student Guidelines for Mathematics
Journal and Binder, Problem-Solving
Write-Up, and Resources Scavenger Hunt
Day 3: Math Survey
With a talking
partner, discuss
the efficacy of
the letter and the
three days.
Blachowicz and Fisher’s summary on the
research on essential elements for robust
vocabulary development
1.
2.
3.
4.
Immerse students in words
Encourage students to be active in
making connections between words and
experiences
Encourage students to personalize word
learning
Build on multiple sources of information
5.
6.
7.
Help students control their learning
Aid students in developing independent
strategies
Assist students in using words in
meaningful ways; meaningful use leads
to long-lasing learning
…the vocabulary focus. . .is not an
add-on to the curriculum, or more
to teach; it is a way to teach
mathematics
from Principles and Standards
for School Mathematics
Beginning in the middle grades,
students should understand the
role of mathematical definitions
and should use them in
mathematics work. Doing so
should become pervasive in high
school.
from Principles and Standards
for School Mathematics
However, it is important to avoid a
premature rush to impose formal
mathematical language; students
need to develop an appreciation
for the need for precise definitions
Some guidelines and hints
Begin each unit with an informal assessment
of where students are in terms of their
math language
Vocabulary student is always undertaken in
the context of developing mathematical
understanding
Some guidelines and hints (con’t)
Vocabulary is a tool for communicating and
demonstrating understanding
Students need to hear, see, and use
terminology in mathematical contexts first
One strategy
Miki Murray uses a combination of a
personal vocabulary list (add five words—
not necessarily new ones—each week)
Keep a personal word wall to keep track of
words
Multiplication & Division
Games
Take a Break
Format of the
Educational Planning
Assessment System
(EPAS)…
45
The
EXPLORE
Purpose: Help 8
th
graders plan
for their high school coursework as
well as career choices.
Score
Range: 1 – 25
Testing
46
Window:
September
The
PLAN
Purpose: Helps students measure
their academic development and make
plans for remaining high school years
and beyond.
Score
Range: 1 – 32
Testing
47
Window:
September
The
ACT
Purpose:
Assess general
educational development and their ability to
successfully complete freshmen level
college courses
Score
Range: 1 - 36
Testing Window:
Administration - March 9
ACT Make-up Day - March 23
ACT Accommodations Window - March 9-23
48
Kentucky and the ACT
 Why
is Kentucky administering?
 What is the law surrounding this
mandate?
Senate Bill 130
http://www.lrc.ky.gov/record/06rs/sb130.htm
Related to the bill is KRS 158.6453
49
The Math Test
ACT

There are sixty multiple choice
questions in sixty minutes

It’s the mathematics needed for
college mathematics courses
50
Math Content
Algebra
Geometry
Trigonometry
51
• 55%
• 40% of which is pre and
elementary algebra
• 38%
• 7%
• These questions won’t make or
break a score!
Math Content
Pre-Algebra
• 23%
• 14 Questions
Elementary Algebra
• 17%
• 10 Questions
Intermediate
Algebra
• 15%
• 9 Questions
Coordinate
Geometry
• 15%
• 9 Questions
Plane Geometry
• 23%
• 14 Questions
Trigonometry
• 7%
• 4 Questions
52
Subject
English
Math
Reading
Science
53
Number of
Questions
40
30
30
28
How Long
It Takes
30 minutes
30 minutes
30 minutes
30 minutes
ACT’s College Readiness
Benchmarks
College
Course or
Course
Area
English
Comp.
Social
Sciences
Test
EXPLORE
Score
PLAN
Score
ACT
Score
English
13
15
18
Reading
15
17
21
Algebra
Mathematics
17
19
22
Biology
Science
20
21
24
54
What does College
Readiness mean, and
what does it have to
do with me?
55
What do the benchmarks mean?
According to the ACT site, www.act.org
a benchmark of 22 on the mathematics
section means a student has approximately a 50%
chance of earning a B or better and 75% chance
of earning a C or better in an equivalent college
course.
56
57
58
59
Look at 2008
state results…
60
EXPLORE
Kentucky - State Summary
National*
14.2
13.8
13.7
13.6
English
2008-09
(N=48,653)
15.1
14.6
14.4
14.2
Mathema
tics
2007-08
(N=48,194)
13.8
13.9
13.7
13.8
Reading
2006-07
(N=49,518)
15.9
16.0
15.8
15.8
Science
*National
normative data
based a national
study conducted
in Fall 2005
14.9
14.7
14.5
14.5
Composit
e
0.0
5.0
10.0
15.0
20.0
25.0
EXPLORE
Composite
2006-07
2007-08
2008-09
National*
(N=49,518) (N=48,194) (N=48,653)
14.5
14.5
14.7
14.9
Science
15.8
15.8
16.0
15.9
Reading
13.8
13.7
13.9
13.8
Mathematics
14.2
14.4
14.6
15.1
English
13.6
13.7
13.8
14.2
PLAN
Kentucky - State Summary
16.9
15.9
15.3
15.6
English
17.4
16.4
16.2
16.3
Mathematics
16.9
16.0
16.1
16.0
Reading
18.2
17.4
17.2
17.3
Science
17.5
16.6
16.3
16.4
Composite
0.0
8.0
16.0
National*
2008-09 (N=
50,531)
2007-08
(N=50,097)
2006-07
(N=49,631)
*National
normative data
based a
national study
conducted in
Fall 2005
24.0
32.0
PLAN
Composite
2006-07
2007-08
2008-09
National*
(N=49,631) (N=50,097)
(N= 50,531)
16.4
16.3
16.6
17.5
Science
17.3
17.2
17.4
18.2
Reading
16.0
16.1
16.0
16.9
Mathematics
16.3
16.2
16.4
17.4
English
15.6
15.3
15.9
16.9
Chapter 7
Pipes, Tubes, and Beakers:
New Approaches to Teaching the RationalNumber System
Additive vs. Multiplicative Reasoning
Relative vs. Absolute Reasoning



Take a look at the box on pg. 311.
Discuss with a talking partner the difference between the reasoning
above.
Which of the types of reasoning results in the correct answer to who
grew the most, String Bean, or Slim.
As stated in the book, “Students cannot
succeed in algebra if they do not
understand rational numbers.”
What factors inhibit student understanding of
rational numbers?

Rational numbers can take on may forms.
 0.8
= 1/8 (Really??!!)
 Part over whole…3 parts out of 4
Quotient Interpretation…3 divided by 4
 A ratio…3 boys to 4 girls


What is the unit?
Let’s Eat
Geogebra
Share experiences
 Geometry

 Help
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Wiki
 English
 Middle

School
Geometry Formulas
Take a Break
TI-73 APPS
•Area Forms
•Number Line