1 Quality Teaching Strategies that Make Rigor, Relevance and Relationships a Reality Dallas Texas...

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Quality Teaching

Strategies that Make Rigor, Relevance and Relationships a Reality

Dallas TexasJanuary 18-20, 2007

Hilton Dallas Lincoln Centre

Bob Trammelrobertwtrammel@msn.com

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Workshop Parameters

• Silence Cell Phones Please• Restroom Breaks • Side Conversations• Listening to Others• Staying to the End of Each Day• Be an Engaged Workshop Participant• Stay True to the Workshop Objectives• Have Fun Too!!!!!!!!

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A Quick Glance Back to Yesterday

Think-Pair-Share ActivityThink-Pair-Share Activity

On a piece of paper, list 2- 4 items that On a piece of paper, list 2- 4 items that were of great interest to you from were of great interest to you from yesterday. yesterday.

Do this privately please. (1-2 Do this privately please. (1-2 minutes)minutes)

> On command, share your list with your > On command, share your list with your partner.partner.

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Workshop Objectives

As a result of this workshop, each participant will:

learn proven strategies that are engaging and rigorous, return to school and try the strategies in his or her own

classroom,develop plans for teaching the strategies to others,establish demonstration classrooms when possible to

model the strategies for colleagues,create sample lesson plans incorporating the strategies,

and evaluate the effectiveness of the strategies using

classroom and schoolwide data.

Today

Today

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In Each Strand……….

participant will :

learn how to make their subject area more rigorous by creating challenging assignments and assessments,

learn how to make their subject area more relevant by using real-world problems and applications, and

learn how to improve relationships with students by using engaging strategies and cooperative learning.

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In Addition, each team member will……………………………………….

MathL/Arts

Science

Soc. St.

Team Planning Time

Career Tech

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What was shared at your team meeting session last evening?

• Discuss at tables

• Let’s share with each other too!

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A Quick Glance at the Three Days

Day 2: Friday January 19th

> Continental Breakfast 7 - 8 am> Workshop Morning Session 8 - noon> Lunch noon -

1 pm> Workshop Afternoon Session 1 - 5 pm

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A Quick Glance at the Three Days

Day 3: Saturday January 20th

> Continental Breakfast 7 - 8 am

> Workshop Morning Session 8 – 11:30 am

> Team Planning Time 11:30 – 1 pm

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OK Let’s Get Started

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A Quick Glance Back to Yesterday

What is the Value of Algebra? by Cohen

What Should I Look for in a Math Classroom?

Annenberg Foundation

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Fort

Wayn

e Journ

al G

aze

tte

Au

gu

st 1

7,

20

05

13

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Handouts for Day 2

– Lesson Plan Design

– Growing…Growing…Growing (2 copies)

– Bobo the Forgetful Elf

– Pepsi…… The Choice of a New Generation

– Sierpinski Triangles (2 copies)

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Let’s Start Here Today!

learn how to make their subject area more rigorous by creating challenging assignments and assessments,

KWL Activity

What I Know What I Want to Know Learned

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BLOOM’S TAXONOMY

Knowledge & Comprehension

Analysis & Application

Synthesis & Evaluation

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BLOOM’S TAXONOMY

Evaluation

Synthesis

Analysis

Application

Comprehension

Knowledge

C

O

G

N

I

T

I

V

E

L

E

V

E

L

Judging

Creating

Breaking into parts

Solving

Understanding

Facts

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SREB PublicationAlgebra Readiness Guide

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Connecting Bloom’s Taxonomy to Basic, Proficient, Advanced Levels

Evaluation

Synthesis

Analysis

Application

Comprehension

Knowledge

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A Sliding Scale

Know Compre Appl Anal Synth Eval

Basic Proficient Advanced

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So What About Rigor??

• Rigor is directly related to Bloom’s Taxonomy. In order to achieve higher levels of rigor in the math classroom one must define basic, proficientbasic, proficient, and advancedadvanced Benchmark Proficiency Progressions across big ideas or a particular state standard or indicator.

Basic Proficient Advanced

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Academic RigorAcademic RigorNew Jersey (CCCS)New Jersey (CCCS)

Grade 8

Cluster I: Number Sense, Concepts, and Applications

Macro C: Use ratios, proportions, and percents in a

variety of situations.

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Basic-Proficient-AdvancedCognitive Levels

• In pairs, define what students should know and able to do for each cognitive level.

BasicBasic Proficient Proficient AdvancedAdvanced

Use ratios, proportions, and percents in avariety of situations.

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BasicBasic

• Find the percent of a given number.

• Find the percent of a part to a whole.

Find 15% of 40. What percent of the marbles are red?

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ProficientProficient

• Solve discount problems involving percents.

• Find the percent increase or percent decrease for real-life consumer problems.

A coat that normally cost $85 is discounted 40%. What is the sale price of the coat?

A store owner buys a lawnmower for $90. She wants to sell the lawnmower at the store for $120. What was the percent of increase?

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AdvancedAdvanced• Compare and contrast real-life

percent problems as viewed by consumers. Justification of solution(s) is necessary.

> Jamie is shopping to purchase a new winter coat. Advertised are these two coats:

Original Price $125

Today only take 40% off.

Red Tag Special:

Take 20% off the marked price.

At the register another 25% off the reduced price.

Which coat is cheaper to buy? Explain how you know.

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Lesson Plan Design

Big Ideas

Instructional

StrategiesAssessment

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Content Indicator #4Ratios and Proportions

• Open the SREB guide to pages 18-19 please.

Ifn

then n2

25 500 ,

In the model town that a class is building, a car 15 feet long is represented by a scale model 3 inches long. If the same scale is used, a house 35 feet high would represented by a scale model how many inches high?

A B 3 C 5 D 7 E 45

3535

3

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Classify as B, P or A

1. Add: 238+462

a) 600 b) 690 c) 700 d) 790

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Classify as B, P or A

What is the length of the toothpick in the figure above?

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Classify as B, P or A

According to the graph above,how many times did the yearly increase of the price of a hamburger exceed 10 cents?

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Classify as B, P or A

Term 1 2 3 4

Fraction 1/2 2/3 3/4 4/5

If the list of fractions above continues in the same pattern, which term will be equal to 0.95?

a) The 100th b) The 95th c) The 20th d) The 19th

e) The 15th

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Classify as B, P or A

x y

0 -3

1 -1

2 1

Which of the following equations is true for the three pairs of x and y values in the table above?

a) 3x + 2 = y b) 3x – 2 = y c) 2x + 3 = y

d) 2x – 3 = y e) x – 3 = y

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Unit Design or Chapter Design

Algebra I

Solving Linear Inequalities

Big Ideas

Instructional

StrategiesAssessment

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Sequence of WorkDesigning a Unit in…..

• Start with the objectives linked to the unit. End in mind first, then go forward.

• The US math curriculum is way too full of meaningless junk. Try to eliminate the junk. Go for the “big ideas.” Remember less is more!!!

• Don’t ask a barber if you need a haircut. -------------------------

After unit objectives are defined, then design daily lesson plans.Assessments must be given often, but also summative too.

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Lesson Plan Design

Big Ideas

Instructional

StrategiesAssessment

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Identify the “Big Ideas” Solving Linear Inequalities

Algebra I • What Should Students Know and Be

Able to Do? Make a List Please!

Textbook Chapters:

Section 1: Solving Inequalities by Addition and SubtractionSection 2: Solving Inequalities by Multiplication and DivisionSection 3: Solving Multi-Step Inequalities

Section 4: Solving Compound Inequalities Section 5: Solving Open Sentences Involving Absolute ValueSection 6: Graphing Inequalities in Two Variables

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Chapter 6 “Big Ideas”My List!

• Use and Understand Inequality Properties• Translate Between Verbal-Symbolic-

Graphical Forms• Know the Word Description For Each

Inequality Symbol• Solve Real-Life Application Problems• Solve One-Variable Linear Inequalities• Compare and Contrast Solving Linear

One-Variable Equations to Inequalities• Understand the Effect of mult/div an

Inequality by a Negative Number• Solve Simple Compound Inequalities ( 3 <

2x + 1 < 9)

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Best Instructional Strategies• Compare Contrast• Think-Pair-Share• “Hook”• Multiple Representations (picture, table, lists, graph,

symbolic)• Note Taking• Bell Ringer Activities• Real-Life Applications• KWL • Teacher Directed Instruction• Exit Slips• Summarizing Objectives of the Day• Individual Guided Practice• Cooperative Learning Groups• Student Exhibitions• Socratic Method• Clear/Unclear Window• Setting objectives and providing feedback• Generating and testing hypotheses• Setting objectives and providing feedback• Nonlinguistic representations

Big Ideas

Instructional

StrategiesAssessment

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Categories of Instructional Categories of Instructional Strategies That Affect Student Strategies That Affect Student

Achievement (Achievement (in orderin order))• Identifying similarities and differences• Summarizing and note taking• Reinforcing effort and providing recognition• Homework and practice• Nonlinguistic representations• Cooperative Learning• Setting objectives and providing feedback• Generating and testing hypotheses• Questions, cues, and advanced organizers

Sources: Marzano(1998); Marzano, Gaddy& Dean (2000) Marzano, Pickering& Pollack (2001)

Big Ideas

Instructional

StrategiesAssessment

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Design A Lesson For 6.1Solving Inequalities by Add and

SubtObjectives:Students will learn inequality

relationships and properties.

Students will solve simple one-variable linear equalities by using pictures (diagrams), tables, and symbols.

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• Note: This Will Be a Two-Day Lesson(75

min) Day 1 of 2: Focus on Inequal. Algorithms Day 2 of 2: Word Problems ----------------------------------------• Build a Lesson Plan for Day 1 of 2• Make This a Detailed Lesson Plan• Write Lesson Objectives (short form)B,P,A• Incorporate Best Practices Marzano etc.• Short Assessment Items to Measure Mastery

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Putting Cognitive Levels on A “Big Idea” or State Standard

Solve One-Variable Linear Inequalities (Using Properties of Addition and Subtraction)

Can we identify specific criteria for each of these cognitive levels?

Basic Proficient Advanced• Solve simple linear

ineq. with coefficient 1. One or two steps. x – 1 > 11

• Show above ineq table, picture, graph

• Graph the solution to simple linear ineq with coefficient of 1.

• Solve real life inequality word problems.

• Compare and contrast solving equations and inequ.

x – 1 > 11

x – 1 = 11

• Given the graphed solution of an linear inequality in one variable, give three inequalities symbolically.

• Give a real life example involving a linear inequality.

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• Lesson Objectives• Bell Ringer Activity• Yesterday’s Homework• Think Pair-Share Activity• “HOOK”• Direct Teaching• Guided Practice• Summarize Objectives• Guide Practice (Homework)• Exit Slip

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• Bell Ringer Activity---------------------------------------- Evaluate - 7 + 5 = ____ - 8 + -3 = ___ -3 – 6 = ____ -8 – 3 = ___What is the math symbol for less than?Solve for “x” 2x – 1 = 20Show that 4 > -2 by using a number line.

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• Yesterday’s Homework

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• Think Pair - Share (2-4 minutes)----------------------------------------What do you know about inequalities?

Pencil Paper Individual Work (Make a List of Things)

Share with Partner

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• HOOK (15-20 minutes)----------------------------------------Real-Life Application to Motivate theInterpersonal Learner---------------------------------------

At the amusement park the admission cost is $5 per person and rides are $3 each. Jim plans to spend no more than $25 in all at the park. What is the most rides Jim can buy with his limit of $25?

> Solve by creating a table >Solve by using an inequality

relationship

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Design A Lesson For 6.1Solving Inequalities by Addition

and Subtraction Properties• HOOK (Table)

No. No. RidesRides

Total Total CostsCosts

0 $5

1 5 + 3 = $8

2 5 + 6 = $11

3 5 + 9 = $14

4 5 + 12 = $17

5 5 + 15 = $20

6 5 + 18 = $23

7 5 + 21 = $26

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• HOOK (Symbolic)

Symbolic Form From Words……………..

3r + 5 < 253r + 5 -5 < 25 – 5 3r < 20 3r < 20

3 3 r < 6⅔ or 6 rides

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• Direct Instruction (15-20 minutes)

Use inequality properties to solve a variety of one-variable linear inequalities. Make reference to strategies used to solve linear one-variable equations. (Compare/Contrast)

---------------------------------------- t + 3 > -2 Solve and Graph

Solution 4w – 6 < 12 Solve and Graph

Solution ⅞x - 8 > ⅜x + 15 Solve and Graph

Solution

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t + 3 > -2 Solve and Graph Solution

t

t

t t > - 5

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• Guided Practice (10 minutes)

Write an inequality for the model.

x 11

- 1- 1- 1

x + 2 > - 3

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Design A Lesson For 6.1Solving Inequalities by Add and

Subt• Guided Practice (10 minutes)

Solve: x + 2 > - 3

Show Solution Graphically:

In your own words, describe the solution.

__________________________________________________________________________

0- 5- 10

105

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Design A Lesson For 6.1Solving Inequalities by Add and Subt

• Summarize Objectives of Lesson Note: Could be Teacher Directed Instruction or

Class Driven• Solving inequalities (linear one-variable) can be

done by using a model or by using properties.• It appears that the solution to an inequality is

more than one answer in most cases.• Solving equations and inequalities follow similar

steps and similar properties. (an exception is coming later)

• Graphing the solution to an inequality on a number line is a great visual.

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Design A Lesson For 6.1Solving Inequalities by Add and Subt

• Guide Practice (Homework)• Selected Problems from textbook

and/or other resources.

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Design A Lesson For 6.1Solving Inequalities by Add and Subt

• Exit Slip (5 minutes at end of period)• Student completes one problem on a

half-sheet of paper. This problem is collected by the teacher.

• i.e., Solve and graph the solution on the provided number for x – 3 < - 2

0- 5- 10

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A Final Look at Lesson Features

• Lesson Objectives• Bell Ringer Activity• Yesterday’s Homework• Think Pair-Share Activity• “HOOK”• Direct Teaching• Guided Practice• Summarize Objectives• Guide Practice (Homework)• Exit Slip

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Graphic Organizer

Big Ideas

Instructional

StrategiesAssessment

Prof.Basic Adv

Best Practices

Basic

Adv

Prof.

Go Back to Check Cog.

Levels

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Short Cycle Assessment

• Solve x + 15 > 22

• The solution to an inequality is shown:

Write an inequality that has this solution.

• Pan Balance Problem

t

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Now It’s Your TurnLesson Plan Design

In your group do only one of the enclosed big ideas.

Big Idea 1: Solve linear equations in one variable.Big Idea 2: Graph two-variable linear equations in the coordinate plane.Big Idea 3: Solve Pythagorean Theorem problems.Big Idea 4: Find the surface area of a variety of three dimensional standard shapes.Big Idea 5: Solve quadratic equations (one variable) by an appropriate method.

Use Flip Chart Paper (may take two sheets) and Markers:• > Write the Big idea at the top of the paper.• > Write an abbreviated lesson plan showing:• - Objectives• - Define Basic, Proficient, and Advanced cognitive levels• - Best Instructional Practices (Look at the Marzano List Carefully) • > Show just one or two assessment items that could be used to

measure the criteria under the cognitive levels.

• Let’s have this ready to share in about 30 minutes.

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Growing $10

Jamie invested $10 in a Certificate of Deposit Account at a local bank that earns enough interest to double in value every 14 years. Jamie invested $10 on January 1, 2007. Jamie has decided to leave the $10 investment untouched until the year 2200 and at that time the monies in the account will be donated to a charity of her heir’s choice. (note; this will be an inheritance) About how much money will be in the account on January 1, 2200?------------------------------------------------------------------------------------Show all work!

Amount of dollars in the account on January 1, 2200: _________________

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Happy Integers

robertwtrammel@msn.com

Source: Mathematics Teacher Dec-Jan. 2006 Issue

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Cheery Sequence

Definition:

Start with any positive integer. Calculate the sum of the squares of the digits to produce the next term. If the sequence eventually has a period of “8”, then the sequence is called “cheery.”

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Example 1: 5

5, 25 , 29 , 85 , 89 , 145 , 42 , 20 , 4 , 16 , 37 , 58 , 89

Cheery Sequence Examples

Period……… 8

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Example 1: 543

543, 50 , 25 , 29 , 85 , 89 , 145 , 42 , 20 , 4 , 16 , 37 , 58 , 89

Cheery Sequence Examples

Period……… 8

52 + 42 + 32 = 50

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Happy Integers

Definition:

A happy integer is an integer whose cheery sequence has a period of 1.

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Example 1: 1

1, 1, 1 , 1 , 1 , ………

Happy Integer Examples

Period………1

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Example 1: 13

13, 10 , 1, 1 , 1 , 1 , ………

Happy Integer Examples

Period……… 1

12 + 32 = 10

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Questions to Ponder

• Question #1

Do all integers generate cheery sequences that have periods of either 8 or 1, or do other periods exist? (i.e., find an integer with a period of 5)

• Question #2

Is there an infinite number of happy integers, or is there a largest one?

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Questions to Ponder

• Question #3

Are there any consecutive integers both of which are happy? Happy Twins

• Question #4

Are there strings of more than two consecutive happy integers?

Like Happy Triplets

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Let’s Explore Cheery Sequences

• Question #1Do all integers generate cheery sequences that have periods of either 8 or 1, or do other periods exist? (i.e., find an integer with a period of 5)

• Question #2

Is there an infinite number of happy integers, or is there a largest one?

• Question #3Are there any consecutive integers both of which are happy? Happy Twins??

• Question #4Are there strings of more than two consecutive happy integers?

Like Happy Triplets???

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Happy WordsExtended Concept

• Assign Numerical Values to Letters

A…..1B…..2C…..3

z…..26

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Is EASTER a happy word?E ………. 5A……….. 1S………… 19T ……….. 20E……….. 5R……….. 18

5 + 1 + 19 + 20 + 5 + 18 = 6868 100, 1, 1, 1, 1, ….

Therefore Easter is Happy!!!!

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Elves and Linear Equations

Bobo the Forgetful ElfPart 1

Bobo the forgetful elf works at the North Pole. Yesterday he worked putting wheels on toy motorcycles and cars. All North Pole workers keep track of their own inventory in an honor system arrangement. Unfortunately, Bobo cannot remember what happened yesterday, and all his work has already been shipped. He does remember that he used 140 wheels for 50 vehicles, and there were no partial vehicles (i.e., all vehicles had the correct number of wheels).You have been given the assignment of reconstructing Bobo’s inventory. Submit a short report that indicates all possibilities, explaining why you believe you have found them all. Your report must include all of your thinking and must carefully detail and demonstrate the procedures that were used.

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PEPSI Challenge

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Sierpenski Triangles

Step #0 (original triangle)Step #1 (3 triangles)Step #2 (? triangles)Step #3 (? triangles)

Step #10 (? triangles)

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So How Are We Doing??

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Workshop Objectives

As a result of this workshop, each participant will:

learn proven strategies that are engaging and rigorous, return to school and try the strategies in his or her own

classroom,develop plans for teaching the strategies to others,establish demonstration classrooms when possible to

model the strategies for colleagues,create sample lesson plans incorporating the strategies,

and evaluate the effectiveness of the strategies using

classroom and schoolwide data.

X

X

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In Each Strand……….

participant will :

learn how to make their subject area more rigorous by creating challenging assignments and assessments,

learn how to make their subject area more relevant by using real-world problems and applications, and

learn how to improve relationships with students by using engaging strategies and cooperative learning.

X

X

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Points to Ponder Tonight

Cooperative Learning Strategies> How do you set-up a cooperative

learning classroom environment?> How do get all students engaged?> What is your role as a teacher?> How often do you use cooperative

learning groups?> Do you evaluate cooperative

learning groups? If so, how?

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Testing PositiveYou are at the doctor’s office to take a blood test to detect a virus called “Alpha.” Before taking this test, you read the scientific research about the virus and the screening procedure provided in a brochure. Brochure

Virus Alpha

> The infection rate is very low about ½ of a percent of the population.

> The blood test is 98% accurate detecting Alpha.

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You left the doctor’s office with a sense of confidence since only half-of-one percent of the general population has virus Alpha.

Three days after your blood test the nurse from the doctor’s office calls and informs you that you have tested positive for virus Alpha. How concerned should you be about this news???

Testing Positive

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Testing PositiveHow Serious???

Let’s say 20,000 were tested for Alpha.

20,000(.005) =

100 tested +

20,000(.995) =

19,900 tested

Start

INF NON

V NV V NV

98% (accurate)

100(.98)

2% (inaccurate)

100(.02)

98% (accurate)

19,990(.98)

2% (inaccurate)

19,990(.02)

98 True +

2 398 False +

19,502

People Notified And Have Alpha: 98496

or 19.8%

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Cross Curricular ConnectionConnection

Social Studies

Voting Methods

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• Voting Methods Make A Difference!!!

• In an election 55 voters were asked to list 5 candidates (A, B, C , D, and E) in order of preference.

i.e., 1st – 2nd – 3rd - 4th – 5th

• Six preference orders are shown below

(next slide) with the number of voters out of the 55 total.

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P1 P2 P3 P4 P5 P6

A B C D E E

D E B C B C

E D E E D D

C C D B C B

B A A A A A

18 12 10 9 4 2

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• Which candidate should win the election?? _________

• Describe your voting method in detail.

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PLURALITY Voting System

Winner?

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Assigning Values(5- 4- 3- 2- 1)

Voting System

Winner?

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Run Off Top 2

Voting SystemWinner?

Top two candidates with 1st place votes are candidate A(18) and candidate B(12).

“B” wins 3 times out of 6

“A” wins 1 time out of 6

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Drop Low ScoreVoting System

Winner?

1st Round

Drop EDrop E

A 18 votes

B 12+4=16

C 10+2=12

D 9

2nd Round

Drop DDrop D

A 18 votes

B 16

C 12+9=21

3rd Round

Drop BDrop B

A 18 votes

C 21+16=37

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Pair-WiseVoting System

Winner?A vs B … B winsA vs. C …C winsA vs. D… D winsA vs. E… EE winsB vs. C… C winsB vs. D… TieB vs. E… EE winsC vs. D… D winsC vs. E… E E winsD vs. E… EE wins