Kids only get one chance at receiving a good education, we are working to ensure they get it! Too many grades of D or F in math? Today

Todays presentation focuses on what we can do to help struggling students, students living in poverty, become successful in their study of mathematics. Understanding What does do you understand really mean?

Understanding Divide Fractions Flip & Multiply Understanding ax + b = c

4x + 2 = 30 5x 4 = 3x + 16 2(3x 4) 2 = 4x + 10 x/3 x/4 = 6 (x 4)/2 + (x + 3)/5 = x 5

Axiom The more math you know, the easier math gets! Way of Thinking Math is more than just a body of knowledge, it is a way of thinking that affects the way we live.

Decisions Computation; 4 x 13 x 25 Algorithm (rule) Properties of Real Numbers Decisions Finding a common denominator

Multiply denominators Write multiples Factor Tree, LCM Reducing Method

Decisions Systems of Equations Graphing Substitution

Linear Combination Cramers Rule Decisions Quadratic Equations

Zero Product Property Completing the Square Quadratic Formula Rational Root Theorem The more math you know, the easier math gets!

Answering the Question What are you doing to help my child learn? The 5+1 Organizing Student Learning 5 +1

Instruction, Concept Development-Linkage Note Taking Homework Test Preparation Assessment

Student-Teacher Relationships My Kid Standard Expectation - Goals Being the best! What does it take to be the best? What are you willing to do? What are you doing

to improve instruction? What are you doing to help my child learn? Rules in Mathematics Dont make sense!

Math Rules! Division by Zero Dividing Fractions Rules for Exponentials

Rules for Integers Good News! Teachers are already employing many of the best practices needed to increase student achievement. Best practices Note taking

Homework Tests Components of an Effective Lesson Before presenting a lesson, refer to the assessment blueprint for the unit. Introduction Daily Reviews Daily Objective

Concept and Skill Development and Application Guided / Independent / Group Practice Homework Assignments Closure Long-Term Memory Review Actions follow beliefs 10 simple 2-letter words

If it is to be, it is up to me Whats needed? Refinement & Reinforcement of those practices. Its about you! Use the DATA

Increasing Student Achievement No simple answer- what works is work Success on Success Success on Success

First Test Important for confidence! Grade Distribution Success on Success Teach students how to learn effectively and efficiently. Concentration times Studying

Reading Thinking Reflecting

Organizing Writing

Analyzing Visualizing Reviewing Remembering Recalling Student-Teacher Relationships 1.

Treat your students the way you want your own children treated. 2. Build success on success. 3. Talk to your students. Be friendly.

4. Talk positively to your students about their opportunity to be successful. 5. Call home early with information and good news.

6. Make testing as much a reflection of your instruction as their studying. Student-Teacher Relationships 6.

Teach your students how to study effectively and efficiently (visual, audio, kinesthetic, concentration time). 7. Tell them you like them. 8.

Go over expectations explicitly and give examples. 9. Build trust, make sure they know you are there for them by telling them you are. 10. Tell them you want them to succeed.

11. Continually answer the question; What am I doing to help my students learn? Contradictory Rules Learning Students learn best when they are given feedback on their performance

and praised for doing things well Unsuccessful Students STAR System 3 Stars on the test unchanged, no computation, no manipulation 2 Stars on the test, changes in numbers 1 Star allows variability, so curriculum is

not narrowed The Phone Conversation Introduction Pleasure teaching your son/daughter, nice young man/lady Explanation, how I intend to help your child succeed Instruction Clear instruction, linkage, memory aids Notes, * system, very prescriptive Homework, comes from notes & instruction

Oral recitation, procedures & formulas Practice tests, * system Study/flash cards Reviews The Phone Conversation Permission to use those strategies/consequenes Parental help Know when tests are scheduled

Examine student notebooks Use flashcards to help study Administrative Expectations Observable Curriculum CEL/Teacher Expectancies 5 + 1

Grade Distributions Content & Pedagogy 1st Essential - Instruction Instruction Teach for understanding Its not a matter of if students will forget

information, its a matter of when they will forget Students should be able to reconstruct knowledge over time Instruction Preparation Creation of a practice test before instruction begins suggests that teachers prepared for

the unit; knowing where students traditionally experience difficulty and having resources and strategies ready to address those difficulties. Preparation Practice test

Cover curriculum appropriately (rigor) Grades - Fair & Portable Benchmarked Unit questions reflect questions on:

Curriculum Unit HSPE Semester exams College Entrance exams (ACT & SAT)

Balance Balance in mathematics has been defined as: Vocabulary & Notation Concept Development & Linkage Memorization of Important Facts & Procedure

Applications Appropriate Use of Technology should be reflected Balance in assessments and in the delivery of instruction.

Vocabulary & Notation There is no more single important factor that affects student achievement than vocabulary and notation Vocabulary Find the degree of the monomial

4x2y3z5 Vocabulary Best Bet? Bet A Probability of winning is 3/5 Bet B Odds of winning 3 to 5

Language Acquisition Double meanings area volume operation power mean feet product

MLL Solve Find the roots

Find the zeroes Find the value of the variable that makes the open sentence true MLL In a right triangle, the altitude from the right angle to the hypotenuse divides the hypotenuse into two segments in which the altitude is the geometric mean of the lengths

of the two segments. Geometric Mean Geometric Mean Proportion - Proportions equal fractions

Equivalent Fractions 4 6 = 6 9

MLL Math Language Learners Speaking Oral recitation Speaking Working in pairs (groups) Oral Recitation

Language Acquisition Teaches students how to learn Embeds in short tem memory Classroom Oral Recitation Procedure Adding/Subtracting Fractions 1.

2. 3. 4. 5. Find a common denominator Make equivalent fractions Add/Subtract numerators Bring down denominator

Reduce Classroom Oral Recitation Quadratic Formula 2 b b 4ac x

2a Time on Task Stake and local school districts usually determine the classroom time available to teachers and students. However, regardless of the quantity of time allocated to classroom instruction, it is the classroom teacher and school administrator who determine the effectiveness of the time allotted. According to a survey conducted by the American Association of School

Administrators, teachers identify student discipline as the single greatest factor that decreases time on task in the classroom. Generally, teachers with well-managed classrooms, have fewer disciplinary problems. These classrooms typically have teachers who have established rules and procedures are in the classroom when the students arrive, and begin class promptly. They reduce the wear and tear on themselves and students by establishing procedures for makeup work, they arrange their room to accommodate their teaching philosophy and style, and they develop routines that increase overall efficiency. The benefits of establishing these classroom procedures and

Time on Task When teachers begin class immediately, students view them as better prepared, more organized and systematic in instruction, and better able to explain the material. Students also see these teachers as better classroom managers, friendlier, less punitive, more consistent and predictable, and as one who values student learning. Routines like beginning class immediately, reviewing recently

taught material, orally reciting new material, having students take notes, and ending the class by reviewing important definitions, formulas, algorithms, and the daily objective keep students engaged and on task. Quality time on task is not a silver bullet that can cure all the problems facing education. However, it can play an important role in increasing student achievement. Content - Instruction What you teach affects student achievement

How you teach it affects student achievement Subtraction 51 15 6 88

14 6 13 5 92 15 9

71 14 5 16 9 44 10 4

6 2 12 4 10 3 63

When will I ever use this? Pythagorean Theorem Parabola Circumference Knowledge, Interest, & Enthusiasm Systems

Functions C = 10 + .05m y = 10 + .05x y = .05x + 10 y = (1/20)x + 10 Use simple straight forward examples that clarify what you are teaching.

Do not get bogged down in arithmetic. Multiplication by 11 by 25 Leading the department

Leaders make sure all department members know what and how material is assessed and what a good answer looks like. Leaders make sure all members teach and assess the standards on high-stakes tests. Different Ways to Measure the Same Standard

Finding Measures of Central Tendency 1. Find the mean of the following data: 78, 74, 81, 83, and 82. 2. In Teds class of thirty students, the average on the math exam was 80. Andrews class of twenty students had an average 90. What was the mean of the two classes combined?

3. Teds bowling scores last week were 85, 89, and 101. What score would he have to make on his next game to have a mean of 105? Finding Measures of Central Tendency 4. One of your students was absent on the day of the test. The class average for the 24 students present was 75%. After the other student took the test, the mean increased to 76%. What was

the last students score on the test? 5. Use the graph to find the mean. I cant teach __________ because my kids dont know _____________

Show them how - Linkage Introduce new concepts using familiar language Review and reinforce Compare and contrast Teach in a different context +

Polynomials 6 7 2 = 6(100) + 7(10) + 2(1) 2 6 10 + 7 10 + 2 6 n 6x

2 2 +7 n + 2 + 7x

+ 2 5 3 2 + 3 4 1=

(5 +3)(100) + (3 + 4)(10) +(2 + 1)(1) = (8)(100) + (7)(10) + (3)(1) = (800)

+ (70) + (3) = 8 7 3 Addition - Left to Right 362 412

+ + 213 = (4 +3+2)(100) + (1+6+1)(10) + (2+2+3)(1) = (9)(100) + (7)(1) = + (8)(10) (80) + (900)

+ (7) = 98 7 502 123 + + 271 = (1 +5+2)(100) + (2+0+7)(10) + (3+2+1)(1) = (8)(100) + (6)(1) =

+ (9)(10) (90) + (800) + (6) = 8 9 6 5 3 2 +

3 4 1= 8 7 3 (5x + 3x + 2) + (3x + 4x + 1) 2 2

(5x + 3x ) + (3x + 4x) + (2 + 1) 2 2 = 8x + 7x + 3 2 Add / Subtract

Rational Expressions 1 3 2 6 1

+ 2 3 + 6 5 6 1 1

+ 2 3 5 = 6 1

1 + 5 4 9 = 20

1 1 + 4 3 7 = 12

1 1 + 5 3 8 =

15 1 2 + 5 3 13

= 15 2 3 + 3 10

29 = 30 1 3 + 5 4

= 1 3 + 5 4

19 = 20 3 2 = + Y

XY X 3 2Y + 3X 2 = + Y XY

X C A = + D BD B

C AD + BC A = + D BD B

2 3 = + x+3 (x-1)(x+3) x-1 2 3(x+3) + 2(x-1)

3 = + (x-1)(x+3) x+3 x-1 Relations & Functions

Functions Special relation in which no 2 ordered pairs have the same 1st element. Menu Hamburger .4 00

00 Hotdog 3 00 Sandwich 5 00

Hd, 3 00 00 H, 4 H, 4

00 00 Hd,(3 00

00 S, 5 00 S), 5 00

(H, 4 ) (Hd, 3 ) (S, 5 ) Cold Drinks 1, .50 00

2, 1 50 3, 1 (1,

.50 ) 00 (2, 1 ) 50

(3, 1 ) (10, ? ) 1, .50 00 2, 1

50 3, 1 C = n x .50 = .50n or

y= 1 2 x (1,

.50 ) 00 (2, 1 ) 50

(3, 1 ) (10, ? ) (1, 50 00

) (2, 1 ) 00 (4, 2 ) 50

(3, 1 ) 75 (4, 1 ) Functions Special relation in which no 2 different ordered pairs have the same 1st element.

Multiplication 3 x 2 3 6 4 6 7

2 1 2 x x 3x x + 2x x + 5x

+ 2 + 3 + 6 2 2

2 + 6 (x + 3) (x + 2) = x + 5x + 6 (x + 4) (x + 5) =

x + 9x + 20 (x + 10) (x + 5) = 2 2

x + 15x + 50 2 (2x + 3) (3x + 5) 6x + 8x + 15 2 2x + 3 3x + 5

10x +15 6x + 9x 6x +19x +15 2 2 (2x + 3) (3x + 5) (2x + 3) (3x + 5)

6x + 19x + 15 2 FOIL 3 2 x 2 1 6

2 3 2 x 2 1 6 7 2 Equations of Lines

y - y1 = m x - x1 y - y1 = m (x - x1) Find the equation of a line passing through the point (2,3), with m = 4

y - y1 = m (x - x1) y - 3 = 4 (x - 2) point - slope Solve for y: y 3 = 4 (x - 2) y 3 = 4x - 8 y = 4x - 5

y = 4x - 5 slope - intercept y = mx + b 4x y = 5 general form

LINKING -Introduce using familiar language -Review & Reinforce -Compare & Contrast -Teach in different context Increased Student Achievement Linking Fractions

Decimals Percents Linking Pythagorean Theorem Distance Formula Equation of a Circle Trig Identity

Linking Special products in algebra Special products in arithmetic Linking Quadratic Formula Completing the Square Linking

Solving Linear Equations Order of Operations ax + b = c

Linear equations Equations containing absolute value Radical equations Systems of equations Quadratic equations Area-Volume

Rectangle Parallelogram Triangle Trapezoid

Composition of Functions Linked to evaluating functions f(g(x)) Make a purchase, pay a 7.5% sales tax and a $20 delivery fee. Why Linking? Its not a matter of if students are going to forget information, its a matter of when.

Linking concepts will allow students to reconstruct concepts and skills Basic Facts & Procedures Stopping to remember basic facts interrupts the flow of thought, which negatively impacts learning. Memorization

Memorizing can help students absorb and retain information on which understanding and critical thought are based. The more sophisticated mental operations of analysis, synthesis, and evaluation are impossible without rapid and accurate recall of bodies of specific knowledge. It is my job to teach:

Reading Writing Reading

Assign reading Explicitly introduce vocabulary & notation Preview reading Connect reading Check understanding of reading

Correct their understanding Use paper & pencil Organizing Student Thinking Whats the easiest way to help students to organize their thinking? Writing

Writing

Definitions Procedures Linkages Applications Compare & contrast Describe what they understand

Describe difficulty experienced Describe how to solve a problem Summarize Explain Problem Solving

Go back to definition Look for a pattern Make a table or list Draw a picture Guess & Check

Examine a simpler case Examine a related problem Identify a sub-goal Write an equation Work backward Definitions

Instruction Instruction check Practice test demonstrating preplanning Test reflect other high stakes tests Understanding of instruction 2nd Essential - Note taking

Note Taking Researchers - #1 Memory Aid - Writing it Down Complete homework assignment Prepare for unit test Prepare for high-stakes tests Rules and examples

Title Date Objective Vocabulary & Notation Pattern Development Rule Examples Variation

Use simple straight forward examples to clarify initial teaching! Increase difficulty later. Note check Student notes reflect instruction Contain title, date, objective, definitions,

how to say it, pattern development, linkage, rules and exercises with developed rules White space Star * System Explanations ~ Cautions 3rd Essential - Homework Homework

Homework should reflect what you say you value. Vocabulary & Notation Conceptual Understanding & Linkage Basic Facts & Procedures Make sure students understand the concept or skill before sending home to

practice Practice Guided Group Independent Homework

Page 270, 132 odd Homework-Studying

Reading Thinking Reflecting Organizing Writing

Analyzing Visualizing Reviewing Remembering Recalling

Homework Read Sec. 9.4 - Expressions involving logarithms Define logarithm Write a procedure for converting logarithms to exponentials Explain why when multiplying logs with the same base, you add the logs log (AB) = logA + logB

Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21,23, 31 Homework Read Sec 9.4 - Adding Fractions Define Fraction Draw a model for adding fractions Write a procedure for adding fractions Explain the link between adding fractions and decimals

Page 270 1, 3, 6, 7, 9, 12, 13, 14, 21, 23, 31 Homework Assignment Sheet demonstrates thoughtful preparation Homework check A quick look at the homework assignments suggest the care teachers take to reinforce

the daily instruction to help students prepare for unit, semester and other high stakes tests. Star * System Reviews Recently taught material

Long term review Assessing Student Work What do your students know? How do you know they know it? 1 1

+ 3 4 7 = 12 7

5 = + 18 24 Reducing Method 18 = 3 24

4 18 3 = 24 4 18 x 4 = 72 24 x 3 = 72

CD = 72 5 15 = 24 72 7 28

+ = 18 72 43 72 18 3

= 24 4 4th Essential Test Preparation 4th Essential- Test Preparation Test what you say you value: Instruction Assessment Balance

Questions reflecting other high-stakes tests Cumulative questions Practice tests - Parallel construction Setting a date Testing Testing drives instruction

Differentiation 1355 41 1355 47 Differentiation x2 + 7x + 12 x2 + 7x + 2 Leads to decisions!

Tests Test Design Design tests that encourage study. Test what you say you value Test Preparation Do you know what you are going to test your students on BEFORE you begin to

teach a unit? Use the * System on notes, homework, and practice tests to to prepare for test Practice Tests Parallel constructed; especially for students who have not experienced success in math. Tests

Monitor student learning Memory Aids Help your students remember ABBA SOHCAHTOA

Quadratic Formula 5th Essential - Tests Form A ~ Form B Test Check

Balanced assessment Cover the assigned curriculum/benchmarks Questions reflect other high stakes tests Grades are fair Grades are portable

Parallel constructed Tests Are test results a reflection of instruction? Organizing Student Learning Making the connection Instruction to Note taking to

Homework to Test preparation to Tests Organizing Student Learning Helps students focus and study more effectively and efficiently resulting in increased student achievement

This organization strategy leads to Transparency Credibility Trust 5 + 1 Summary 1) 2)

3) 4) 5) Student-teacher relationships ~parent communication~ Understanding instruction Notes that reflect & reinforce instruction Homework that supports and reflects

instruction Test preparation Parallel constructed tests Today What ideas would you consider using? What are you willing to do?

Next steps What are you willing to do to increase student achievement? Explicitly go over expectations with staff in August; 5+1 Parental communication Observe instruction in September/October with emphasis on 5+1 and understanding Collect grade distributions for 1st unit test

Conduct pre- and post- observation conferences within a week and provide meaningful suggestions, recommendations, or directions that improve instruction Continue observations, conferences & monitor grade distributions Next steps What are you willing to do to increase student achievement? Create pre tests that reflect unit and other high stakes tests

Parental communication Introduce new concepts and skills using concept development or linkage Be more prescriptive & directive with notes that reflect instruction Create homework assignments that encourage study Use star * system in notes, homework & practice tests Create parallel constructed tests Recommended Next Steps

Contact Information Bill Hanlon [email protected] 800.218.5482 www.hanlonmath.com www.rpdp.net