middle school math initiative for florida rigor relevance reading florida and the islands...

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

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5

6

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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