a.39 b.42 c.55 d.59 e.63
DESCRIPTION
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.42 C.55 D.59 E.63. - PowerPoint PPT PresentationTRANSCRIPT
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. 42
C. 55
D. 59
E. 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. 2.32%
B. 0.9%
C. 9%
D. 11%
E. 90%
What are the three types of percentage problems your students will see?
3. 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?
A.
B.
C.
D.
E.
75
2
15
4
2
1
30
23
30
29
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. 3B. 6 C. 9D. 12E. 14
What are some divisibility rules that help you here?
6. When is an integer?
A. Only when a is negative
B. Only when a is positive
C. Only when a is odd
D. Only when a equals 0
E. Only when a is even
2
11 a
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.
C.
D.
E.
2
19
4
9
5
6
5
12
7
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. 1:40
B. 1:20
C. 1:10
D. 1:8
E. 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 groundworkLetter 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. Immerse students in words
2. Encourage students to be active in making connections between words and experiences
3. Encourage students to personalize word learning
4. Build on multiple sources of information
5. Help students control their learning
6. Aid students in developing independent strategies
7. 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 Standardsfor 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 Standardsfor 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 & DivisionGames
Take a Break
45
Format of the Educational Planning Assessment System (EPAS)…
The EXPLOREPurpose: Help 8th graders plan for their high school coursework as well as career choices.
Score Range: 1 – 25
Testing Window: September
46
The PLANPurpose: Helps students measure their academic development and make plans for remaining high school years and beyond.
Score Range: 1 – 32
Testing Window: September
47
The ACTPurpose: Assess general educational development and their ability to successfully complete freshmen level college courses
Score Range: 1 - 36Testing Window:
Administration - March 9ACT Make-up Day - March 23ACT Accommodations Window - March 9-23
48
Kentucky and the ACT
Why is Kentucky administering?
What is the law surrounding this mandate?
Senate Bill 130http://www.lrc.ky.gov/record/06rs/sb130.htm
Related to the bill is KRS 158.6453
49
The Math TestACT
There are sixty multiple choice questions in sixty minutes
It’s the mathematics needed for college mathematics courses
50
Math Content
51
Math Content
52
53
SubjectNumber of Questions
How Long It Takes
English 40 30 minutes
Math 30 30 minutes
Reading 30 30 minutes
Science 28 30 minutes
ACT’s College Readiness Benchmarks
College Course or
Course Area
TestEXPLORE
ScorePLAN Score
ACT Score
English Comp.
English 13 15 18
Social Sciences
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, a benchmark of 22 on the mathematicssection 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.
www.act.org
56
57
58
59
Look at 2008 state results…
60
EXPLORE
2006-07 (N=49,518)
2007-08 (N=48,194)
2008-09 (N=48,653)
National*
Composite 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 2006-07
(N=49,631)2007-08 (N=50,097)
2008-09 (N= 50,531)
National*
Composite 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 Rational-Number 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
HelpGeogebra WikiEnglishMiddle School
Geometry Formulas
Take a Break
TI-73 APPS
•Area Forms•Number Line