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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

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slide1

Middle School Math Initiative for Florida

RigorRelevance Reading

Florida and the Islands Comprehensive Center at ETSInternational Center for Leadership in EducationFlorida Council of Teachers of Mathematics Florida Department of Education

slide3

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

sinceA = {6,7,8,9,10,11}

slide4

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) =

slide5

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).

slide6

Another way to say that:

P(Red) =

n(successes)

=

n(total outcomes)

Find P(green)

=

slide7

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%.

slide8

In summary………

Sample Space

Event

P(E) =

philosophy
Philosophy
  • Rigor
  • Relevance
  • Relationships
  • All Students
philosophy1
Philosophy
  • Relationships
  • Relevance
  • Rigor
  • All Students
rigor
Rigor
  • Rigor Means
  • Level of critical thinking skills
  • Level of math application
relevance
Relevance

Relevance is more than passing the math FCAT

My only

skill is

taking

tests

slide15

Rigor/Relevance Framework

6

Knowledge

D

C

5

4

3

A

B

2

1

Application

1

2

3

4

5

slide16

Assimilation

of knowledge

Thinking Continuum

Acquisition

of knowledge

knowledge taxonomy
Knowledge Taxonomy

6. Evaluation

5. Synthesis

4. Analysis

3. Application

2. Comprehension

1. Recall Knowledge

slide18

Action Continuum

Acquisition

of knowledge

Application

of knowledge

application model
Application Model

5 Application to real-world unpredictable situations

4 Application to real-world predictable situations

3 Application across disciplines

2 Application within discipline

1 Knowledge of one discipline

r r framework a useful tool to evaluate
R&R Framework ...A Useful Tool to evaluate
  • Curriculum
  • Instruction
  • Assessment
  • Activities
quadrant d lessons
Quadrant D Lessons
  • 6th Grade Math Big / Supporting Ideas
    • District Need / Big / Supporting Idea
  • 6th Grade Student Interest
  • 70 Quadrant D 6th Grade Lessons
    • Edited
    • Posted Online by FLDOE
c o r r

C O R R

Collaborating

Online for

Rigor and

Relevance

slide25

Develop

Connect

Apply

Explore

Share

COMPONENTS

slide27

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

Reading Comprehension Strategies
slide29

Concept Definition Map

Reading Comprehension Strategy

slide30

DIRECT READING/ THINKING ACTIVITY

Reading Comprehension Strategy

slide31

SQ3R

Survey-Question-Read-Recite-Review

Reading Comprehension Strategy

slide32

CLOZE

Reading Comprehension Strategy

slide33

VENN DIAGRAM

Reading Comprehension Strategy

slide35
Middle School Mathematics Initiative!

“A Journey Towards Mathematics Excellence”

It’s All About Math!

FASA Super Conference

July 20, 2007

slide36

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

slide37

It’s All About Math!

Participants:

2006 - 2008 First Cohort

30 Participating Districts

Lab Schools

Charter School

Florida School for the Deaf and Blind

slide38

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
slide39

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

slide40

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

slide41

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)

slide42

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
slide43

Rigor/Relevance Framework

6

  • 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.
  • 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.

D

C

  • 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.

5

4

A

3

  • 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.

2

B

A

1

1

2

3

4

5

slide44

Rigor/Relevance Framework

6

  • 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.
  • 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.

D

C

5

4

B

3

  • 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.

2

B

A

1

1

2

3

4

5

slide45

Rigor/Relevance Framework

6

  • 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.
  • 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.

D

C

5

C

4

3

  • 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.

2

B

A

1

1

2

3

4

5

slide46

Rigor/Relevance Framework

6

  • 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.

D

C

5

D

4

3

  • 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.

2

B

A

1

1

2

3

4

5