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Middle School Math Initiative for Florida Rigor Relevance Reading. Florida and the Islands Comprehensive Center at ETS International Center for Leadership in Education Florida Council of Teachers of Mathematics Florida Department of Education. Understanding Probability. S = Sample Space - PowerPoint PPT Presentation
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Middle School Math Initiative for
Florida
RigorRelevance Reading
Florida and the Islands Comprehensive Center at ETS International Center for Leadership in Education
Florida Council of Teachers of Mathematics Florida Department of Education
Understanding Probability
S = Sample Space
The Sample Space is the set of all possible outcomes in a probability experiment.
Let S = { 1,2,3,4,5,6,7,8,9,10}
then n(S)=10
Find n(A) if A = {the whole numbers between 5 and 12}
n(A) = 6
since A = {6,7,8,9,10,11}
An Event consists of a set of outcomes of a probability experiment.
The probability, P, of Event (E) with sample space, S,
is defined as the ratio of n(E) to n(S)
i.e.,
P(E) = n E
n S
( )
( )
A bag of marbles has 3 red and 2 green marbles in it.
n(S) = 5
E= pull out a green marble
Find the probability of pulling out a red marble if you put your hand in the bag and pull out one marble. Find P(E).
Another way to say that:
P(Red) =n(successes)
n(total outcomes)=
3
5
Find P(green) 2
5=
What is the highest a probability
value can be?
What is the lowest a probability value can be?
In fact, 0 ≤ p ≤ 1
Or, if you prefer to use percents:
Every probability is between 0% and 100%.
In summary………
Sample Space
Event
P(E) = n E
n S
( )
( )
Successful Curriculum Reform
Why
Do we need
to change
schools?
What
Needs to
be done?
How
Do we do it?
Philosophy
RigorRelevanceRelationshipsAll Students
Philosophy
Relationships RelevanceRigorAll Students
RigorRigor
Rigor Means
• Level of critical thinking skills
• Level of math application
RelevanceRelevance
My only skill is
taking tests
Relevance is more than passing the
math FCAT
All StudentsAll Students
1
2
3
4
5
6
1 2 3 4 5
A B
DC
Rigor/Relevance Framework
KnowledgeKnowledge
ApplicationApplication
AssimilationAssimilationof knowledgeof knowledge
Acquisition Acquisition of knowledgeof knowledge
Thinking Thinking ContinuuContinuu
mm
Knowledge Taxonomy
1. Recall Knowledge1. Recall Knowledge2. Comprehension2. Comprehension 3. Application3. Application 4. Analysis4. Analysis 5. Synthesis5. Synthesis 6. Evaluation 6. Evaluation
AcquisitionAcquisitionof knowledgeof knowledge
ApplicationApplicationof knowledgeof knowledge
Action Action ContinuumContinuum
Application ModelApplication Model5 Application to real-world
unpredictable situations4 Application to real-world
predictable situations3 Application across
disciplines2 Application within discipline1 Knowledge of one discipline
R&R Framework ...A Useful Tool to evaluate
CurriculumInstructionAssessmentActivities
Quadrant D Lessons 6th Grade Math Big / Supporting Ideas
District Need / Big / Supporting Idea
6th Grade Student Interest 70 Quadrant D 6th Grade Lessons
EditedPosted Online by FLDOE
C O R RC O R RCollaborating
Online for
Rigor and
Relevance
Develop
Explore
Apply
Share
Connect
COMPONENTS
Strategies for Increasing Reading Comprehension in
Mathematics
Teaching key reading comprehension strategies for only 15 minutes a week can significantly increase student achievement.
Reading Comprehension Strategies
Affinity Anticipation Guide Cloze Concept Definition Map Cornell Graphic Organizer DR/TA Fishbone K-W-L-S Learning Logs Minute Paper
Pairs-Read Paraphrasing QAR RAFT Reciprocal Teaching Rock Around the Clock SQ3R Structured Note-taking Summarizing Venn Diagram Vocabulary in Context
Concept Definition MapReading Comprehension Strategy
DIRECT READING/ THINKING ACTIVITY Reading Comprehension Strategy
SQ3RSurvey-Question-Read-Recite-Review
Reading Comprehension Strategy
CLOZEReading Comprehension Strategy
VENN DIAGRAMReading Comprehension Strategy
It’s All About Math!
Middle School Mathematics Initiative!
“A Journey Towards Mathematics Excellence”
FASA Super Conference
July 20, 2007
It’s All About Math!
Sponsored by:
Florida Department of Education
Florida and the Islands Comprehensive Center at ETS (FLICC)
In Partnership with:
The International Center for Leadership in Education
ESCORT
Florida Council of Teachers of Mathematics
PAEC
It’s All About Math!
Participants:
2006 - 2008 First Cohort
30 Participating Districts
Lab Schools
Charter School
Florida School for the Deaf and Blind
It’s All About Math!
Goals:
•Increase the rigor and relevance of middle school mathematics instruction with a focus on sixth grade
•Increase the use of research-based literacy strategies for use in middle school mathematics classrooms
•Increase the use of data to inform instruction
•Build a statewide support network focused on the improvement of middle school mathematics curriculum and instruction
•Increase awareness of new Florida mathematics standards and legislation impacting middle school mathematics classrooms
It’s All About Math!
Regional Workshops:
Year 1
2 Regional Institutes
Increasing Rigor and Relevance in the Mathematics Classroom
Strategic Reading in the Content Areas
Summer Institute
Teaching to Mastery – Focus on Using the New Florida Standards for Mathematics to Achieve High Levels of Learning for
All Students
It’s All About Math!
Regional Workshops:
Year 2
3 Regional Institutes
Using the New Mathematics Standards to develop Content Modules
Closing the Achievement Gap – Strategies to Help Struggling Students
Building Student/Teacher Relationships: Transitioning to Middle School
It’s All About Math!
Materials/Resources:
Rigor / Relevance Handbook
Instructional Strategies Handbook
Curriculum Matrix Kit
Strategic Reading in the Content Area Kit
1 Year Membership in the Successful Practices Network
Support of a Liaison
Opportunity for 25 teachers to participate in Collaborating Online for Rigor and Relevance (CORR)
I have come to a frightening conclusion. I am the decisive element in the classroom. It is my personal approach that creates the climate. It is my daily mood that makes the weather. As a teacher, I possess tremendous power to make a child's life miserable or joyous. I can be a tool of torture or an instrument of inspiration. I can humiliate or humor, hurt or heal. In all situations, it is my response that decides whether a crisis will be escalated or de-escalated, and a child humanized or de-humanized."
Haim Ginott
1
2
3
4
5
6
1 2 3 4 5
A B
DC
Rigor/Relevance FrameworkRigor/Relevance Framework• Analyze the graphs of the perimeters
and areas of squares having different-length sides.
• Determine the largest rectangular area for a fixed perimeter.
• Identify coordinates for ordered pairs that satisfy an algebraic relation or function.
• Determine and justify the similarity or congruence for two geometric shapes.
• Obtain historical data about local weather to predict the chance of snow, rain, or sun during year.
• Test consumer products and illustrate the data graphically.
• Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event.
• Make a scale drawing of the classroom on grid paper, each group using a different scale.
• Calculate percentages of advertising in a newspaper.
• Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles.
• Determine the median and mode of real data displayed in a histogram
• Organize and display collected data, using appropriate tables, charts, or graphs.
• Express probabilities as fractions, percents, or decimals.
• Classify triangles according to angle size and/or length of sides.
• Calculate volume of simple three- dimensional shapes.
• Given the coordinates of a quadrilateral, plot the quadrilateral on a grid.
A
1
2
3
4
5
6
1 2 3 4 5
A B
DC
Rigor/Relevance FrameworkRigor/Relevance Framework
• Express probabilities as fractions, percents, or decimals.
• Classify triangles according to angle size and/or length of sides.
• Calculate volume of simple three- dimensional shapes.
• Given the coordinates of a quadrilateral, plot the quadrilateral on a grid.
• Analyze the graphs of the perimeters and areas of squares having different-length sides.
• Determine the largest rectangular area for a fixed perimeter.
• Identify coordinates for ordered pairs that satisfy an algebraic relation or function.
• Determine and justify the similarity or congruence for two geometric shapes.
• Obtain historical data about local weather to predict the chance of snow, rain, or sun during year.
• Test consumer products and illustrate the data graphically.
• Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event.
• Make a scale drawing of the classroom on grid paper, each group using a different scale.
• Calculate percentages of advertising in a newspaper.
• Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles.
• Determine the median and mode of real data displayed in a histogram
• Organize and display collected data, using appropriate tables, charts, or graphs.
B
1
2
3
4
5
6
1 2 3 4 5
A B
DC
Rigor/Relevance FrameworkRigor/Relevance Framework
• Express probabilities as fractions, percents, or decimals.
• Classify triangles according to angle size and/or length of sides.
• Calculate volume of simple three- dimensional shapes.
• Given the coordinates of a quadrilateral, plot the quadrilateral on a grid.
• Obtain historical data about local weather to predict the chance of snow, rain, or sun during year.
• Test consumer products and illustrate the data graphically.
• Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event.
• Make a scale drawing of the classroom on grid paper, each group using a different scale.
• Calculate percentages of advertising in a newspaper.
• Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles.
• Determine the median and mode of real data displayed in a histogram
• Organize and display collected data, using appropriate tables, charts, or graphs.
• Analyze the graphs of the perimeters and areas of squares having different-length sides.
• Determine the largest rectangular area for a fixed perimeter.
• Identify coordinates for ordered pairs that satisfy an algebraic relation or function.
• Determine and justify the similarity or congruence for two geometric shapes.
C
1
2
3
4
5
6
1 2 3 4 5
A B
DC
Rigor/Relevance FrameworkRigor/Relevance Framework
• Express probabilities as fractions, percents, or decimals.
• Classify triangles according to angle size and/or length of sides.
• Calculate volume of simple three- dimensional shapes.
• Given the coordinates of a quadrilateral, plot the quadrilateral on a grid.
• Analyze the graphs of the perimeters and areas of squares having different-length sides.
• Determine the largest rectangular area for a fixed perimeter.
• Identify coordinates for ordered pairs that satisfy an algebraic relation or function.
• Determine and justify the similarity or congruence for two geometric shapes.
• Calculate percentages of advertising in a newspaper.
• Tour the school building and identify examples of parallel and perpendicular lines, planes, and angles.
• Determine the median and mode of real data displayed in a histogram
• Organize and display collected data, using appropriate tables, charts, or graphs.
• Obtain historical data about local weather to predict the chance of snow, rain, or sun during year.
• Test consumer products and illustrate the data graphically.
• Plan a large school event and calculate resources (food, decorations, etc.) you need to organize and hold this event.
• Make a scale drawing of the classroom on grid paper, each group using a different scale.
D