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 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) =

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) = Find P(green) =

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) =

Successful Curriculum Reform Why Do we need to change schools? What Needs to be done? How Do we do it?

Philosophy  Rigor  Relevance  Relationships  All Students

Philosophy  Relationships  Relevance  Rigor  All Students

Rigor Rigor Means Level of critical thinking skills Level of math application

Relevance My only skill is taking tests Relevance is more than passing the math FCAT

All Students

A B D C Rigor/Relevance Framework Knowledge Application

Assimilation of knowledge Acquisition Thinking Continuum

Knowledge Taxonomy 1. Recall Knowledge 2. Comprehension 3. Application 4. Analysis 5. Synthesis 6. Evaluation

Acquisition of knowledge Application Action Continuum

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  Curriculum  Instruction  Assessment  Activities

Quadrant D Lessons  6th Grade Math Big / Supporting Ideas  District Need / Big / Supporting Idea  6 th Grade Student Interest  70 Quadrant D 6 th Grade Lessons  Edited  Posted Online by FLDOE

C O R R C ollaborating O nline for R igor and R elevance

Develop ExploreApplyShareConnect 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 Map Reading Comprehension Strategy

DIRECT READING/ THINKING ACTIVITY Reading Comprehension Strategy

SQ3R Survey-Question-Read-Recite-Review Reading Comprehension Strategy

CLOZE Reading Comprehension Strategy

VENN DIAGRAM Reading 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: 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

A B D C Rigor/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

A B D C Rigor/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

A B D C Rigor/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

A B D C Rigor/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